BESA® Wiki - User contributions [en]

Pipeline for simultaneous EEG-fMRI recording

2019-04-08T10:29:44Z

Jamie: /* fMRI gradient removal */

{{BESAInfobox
|title = Module information
|module = BESA Research Basic or higher
|version = 7.0 or higher
}}

=Pipeline for simultaneous EEG-fMRI recording=
== Before you start ==

* Check if you have a clock synchronization between EEG and MRI systems
* Be sure that you have jitter between trials in ERP experiment (i.e. random value of ±200ms). Some further guidelines about paradigm creation can be found here: (Rusiniak et al., 2013a).
* Try to limit subject movement to minimum.
* Make sure electrode to skin impedance is as low as possible.
* Design EEG-fMRI recording session to be long enough for proper artifact creation. Usually the experiment should last at least 6 minutes.
* Especially for the first few registrations repeat the experiment outside of the bore to compare results.

==Pipeline overview==
The recommended pipeline of processing EEG data registered during fMRI session looks as follows:

[[File:EEG-fMRI pipeline.png]]

'''Please note that some steps are grouped with colors:'''
* orange color indicates steps that are part of typical processing of ERP data.
* blue color indicates optional, yet strongly recommended EEG-MRI data co-registration.
* yellow color marks the steps related to fMRI gradient artifact removal
* green steps are reserved for BCG (and blink) artifact correction
* violet color indicates steps for time-frequency analysis. Here also information about rejected epochs is provided for averaging purpose.

==fMRI gradient removal==
Please note that you need hardware clock synchronization between EEG equipment and MRI scanner before removing fMRI gradient artifact. Do not perform any sampling rate change (especially do not downsample data!) before performing this preprocessing step. Clock synchronization assures alignment between triggers present in EEG data and start of fMRI volume acquisition as well as consistent span between samples containing artifact. That means that every epoch containing fMRI induced artifact is identical.
To remove fMRI gradient select the menu entry '''Artifact\fMRI artifact...'''. The following dialog box will appear:

[[File:FMRI_dialogbox.PNG]]

Some of the parameters are strongly dependent on fMRI acquisition:
* Length of fMRI volume - it should be exactly the time of volume acquisition (time when MR gradients are ON for one volume acquisition). For continuous fMRI sessions this value is automatically detected. If you use sparse acquisition (between fMRI volumes there is a short period of silence), use time of volume acquisition parameter.
* fMRI trigger code - code in the EEG recording provided by MR scanner.
* Delay between marker and start of volume acquisition - a delay between marker in EEG provided by MR scanner and real start of fMRI volume acquisition. This value can be also used if sparse acquistion is used and scanning starts with some delays
* Number of scans to skip - if dummy scans (MR volumes acquired to stabilize magnetization) have corresponding markers in EEG data adjust this value to match number of real volumes used for fMRI analysis.
* Realignment file - direct output file from first step of fMRI analysis (realignment). We support native realignment file as generated by SPM, FSL, AFNI and Brainvoyager.

Other parameters should be carefully selected depending on the data:
* Number of artifact occurrence averages - The default value is 16. That means that 8 preceding and 8 proceeding artifact occurrences are used to create averaged template. Note that if odd number is used (ie. 17) the signal from volume that is being currently corrected is also used for averaging. If a larger number is selected then the artifact is more stable and more differentiated from EEG data. However if there is a lot of movement during the recording session the artifact template will be incorrect. A smaller number of artifact occurrences for averaging or more advanced methods of artifact removal should be selected in such situation.
* Movement threshold - this parameter is only used for two advanced methods: ''Allen et al. 2000 Modified'' and ''Mossmann et al. 2009''. When changing this value check how the template creation matrix looks. If you note that matrix is very segmented (as below) you might consider increasing the threshold value.

[[File:FMRI_distorted_matrix.PNG]]

If you wish you can downsample data and export file with fMRI artifact gradient removed after using aforementioned tool by pressing '''WrS''' button:

[[file:FMRI export.PNG]]

==BCG artifact correction==
First scroll through data and mark bad electrodes and bad blocks of data. Note that especially at the beginning of the recording there might be fragments of data still contaminated with fMRI gradient artifact, as shown below. It is correct behavior since MRI machine use so-called dummy scans that are not for data collection but magnetization stabilization. These volumes are also not usually bound with triggers in the data. If you use paradigm it should start after these scans. The most typical approach is to start stimuli presentation after fMRI session starts (experiment should be triggered by MRI scanner)

[[File:FMRI dummy.PNG|800px]]

===Recommendation for artifact template creation===
For BCG artifact removal we recommend using PCA based template creation. ICA approach is a bit difficult for this matter since BCG artifact is a complex signal distortion (constituted usually from more than three components). Also the main assumption of ICA is violated - components are dependent. Keep in mind that BCG artifact is induced by, Hall effect, pulsating skin and head movement. All of described phenomena are related to the heart beat. On top of it the part related to the movement can consist of up to six components in the worst scenario (head movement and head rotation, both possible in three dimensions).
===How to create template===

Before attempting artifact creation, it is wise to set filtration to match artifact frequency. For BCG following filter settings should be sufficient:
{| class="wikitable"
! style="font-weight: bold;" | Filter
! style="font-weight: bold;" | Cutoff frequency
! style="font-weight: bold;" | Filter slope
! style="font-weight: bold;" | Filter type
|-
| Low Cutoff
| 1
| zero phase
| 12 dB/oct
|-
| High Cutoff
| 20
| zero phase
| 24 dB/oct
|}

Mark a block of data where BCG is clearly noticeable. you can either use EKG channel or just all channels as the BCG is very prominent (check example below). If you decide to use EKG channel rembmer that BCG artifact starts around 200-300 ms after QRS complex visible in EKG.

[[File:Fmri BCG.PNG|800px]]

Go to menu '''Search''' and verify if '''Search, Average, View''' option is checked. If not, please enable it.

Press '''SaV''' button in toolbar to start creation of artifact template. In the displayed dialog use settings as below to perform searching for artifact occurrences similar to the selected block, using all channels with criterion for similarity of 65% correlation, after applying predefined filters. When you press OK search will start.

[[File:FMRI SaV.PNG]]

When search is finished you will see averaged artifact in buffor on left side of the data window, as shown below. If you start scrolling through data the averaged block disappear. You can switch it on at anytime by menu '''View/Averaged Buffers'''. Note that you have blue vertical lines (if you selected to assign BCG artifacts to pattern 1) in trigger line at the bottom of screen. For good artifact correction they should cover almost whole file. Also at the bottom of averaged buffer you can see the number of averages (277 for example). Make sure that this number is relatively big to be sure the artifact template is correctly created.

[[File:FMRI BCG averaged.PNG|800px]]

===How to select proper number of components for artifact correction===
Finally click right mouse button over the averaged buffer and select '''Whole Segment'''. Click with right mouse button over yellow tinted area and select '''Define Artifact Topography'''. A new window will popup. Check EKG box and select number of components used for artifact correction. The component number is followed by the number how much signal variability is explained by the component, expressed in percentage. A question without answer is how many components should be reduced, since it really depends on the data. As a good starting point you may select all components that explain more than 1% of BCG variance (so basically select number with variance lower than 1% - as in example below 5(0.68)). Note that data will be automatically updated to the current settings. You can adjust this number at any further stage of data processing.

[[File:FMRI components.PNG]]

==Final data processing==

If you need you can perform also blink artifact correction using similar approach to the EKG reduction (but select only one component at the final stage, since it is very well established artifact).

Now you can proceed with further data processing. There are some minor differences in comparison with general BESA pipeline:
* if you want to perform averaging you will be similarly asked if you want to turn off artifact correction. Please do so, by pressing '''Yes''' button. The artifact correction should be turned on again just after averaging. When averaged file is open go to menu '''Artifact/Load...''' and select file with exact name of your data file but with extension .atf. When artifact coefficient file is loaded go to menu '''Artifact\Options''' and change method of brain activity modeling to Surrogate. Please verify if selected number of artifact components used for reduction can be lowered.
* As you might noticed we recommend performing source localization while artifact correction is off, and load artifact coefficients directly to the source analysis module. For EEG-fMRI data however it is acceptable to use artifact corrected data as input to the source analysis module.
* if you want to perform '''Time-domain beamformer''' accessed from ERP module (average tab) you will be prompted if artifact correction should be turned off. We recommend to perform beamformer with artifact correction off, but for EEG-fMRI data set please keep it on (press '''No''' button), since big BCG artifact will affect results.

*

==Good practice==
Please keep in mind that simultaneous EEG-fMRI recording is a difficult yet powerful technique. The following rules could help one to perform a successful experiment:
* Remember that proper '''EEG and MRI hardware clock syncrhonization''' is esential for fMRI gradient artifact removal. BESA Research internaly perform checks if the synchronizaiton is sufficient however it is user responsibility to maintain hardware configuraiton. Under any circumstances '''do not change EEG data sampling rate''' prior fMRI gradient removal procedure.
* For an ERP experiment remember to introduce temporal '''jitter between trials''' (e.g. a random value in the range of ±200 ms). Also, applying a pure EEG or a pure fMRI paradigm will probably have the effect that one of the modalities will not show satisfying results. Proper paradigm preparation is essential for success. Some further guidelines can be found here: (Rusiniak et al., 2013a).
* Inform your subject how important it is '''not to move'''.
* Keep electrode to skin '''impedance as low as possible'''.
* The EEG-fMRI recording session should be long enough to allow for proper artifact creation. Usually the experiment should '''last at least 6 minutes'''.
* At the same time try to '''limit the time of experiment to a minimum''' and preferably perform EEG-fMRI registration before other sequences to limit movement due to an inconvenient supine position.
* From the standard position, move the '''subject about 4 cm towards caudal direction''' to reduce artifacts: The MRI laser crosshair should be not in the Nasion position but in the middle of forehead (Mullinger et al., 2011).
* Especially for the first few registrations '''repeat the experiment outside of the MR bore''' to compare results.
==References==
* Abreu, R., Leal, A., Figueiredo, P., 2018. EEG-Informed fMRI: A Review of Data Analysis Methods. Front. Hum. Neurosci. 12, 29. https://doi.org/10.3389/fnhum.2018.00029
* Allen, P.J., Josephs, O., Turner, R., 2000. A Method for Removing Imaging Artifact from Continuous EEG Recorded during Functional MRI. NeuroImage 12, 230–239. https://doi.org/10.1006/nimg.2000.0599
* Moosmann, M., Schönfelder, V.H., Specht, K., Scheeringa, R., Nordby, H., Hugdahl, K., 2009. Realignment parameter-informed artefact correction for simultaneous EEG–fMRI recordings. NeuroImage 45, 1144–1150. https://doi.org/10.1016/j.neuroimage.2009.01.024BESA® Research 7.0
* Mullinger, K.J., Yan, W.X., Bowtell, R., 2011. Reducing the gradient artefact in simultaneous EEG-fMRI by adjusting the subject’s axial position. NeuroImage 54, 1942–1950.
* Rusiniak, M., Lewandowska, M., Wolak, T., Pluta, A., Milner, R., Ganc, M., Włodarczyk, A., Senderski, A., Śliwa, L., Skarżyński, H., 2013a. A modified oddball paradigm for investigation of neural correlates of attention: a simultaneous ERP–fMRI study. Magn. Reson. Mater. Phys. Biol. Med. 26, 511–526. https://doi.org/10.1007/s10334-013-0374-7
* Rusiniak, M., Wolak, T., Lewandowska, M., Cieśla, K., Skarzynski, H., 2013b. The relation between EPI sequence parameters and electroencephalographic data during simultaneus EEG-fMRI registration: an initial report., in: ESMRMB 2013 Congress, Book of Abstracts, Saturday. Presented at the ESMRMB, Springer, Toulouse, p. 661. https://doi.org/10.1007/s10334-013-0384-5

Source Analysis 3D Imaging

2019-04-08T09:38:13Z

Jamie: /* Brain Atlases */

{{BESAInfobox
|title = Module information
|module = BESA Research Standard or higher
|version = 6.1 or higher
}}


== Overview ==

BESA Research features a set of new functions that provide 3D images that are displayed superimposed to the individual subject's anatomy. This chapter introduces these different images and describe their properties and applications.

The 3D images can be divided into three categories:

'''Volume images:'''

* '''The Multiple Source Beamformer (MSBF)''' is a tool for imaging brain activity. It is applied in the time-domain or time-frequency domain. The beamformer technique in time-frequency domain can image not only evoked, but also induced activity, which is not visible in time-domain averages of the data.
* '''Dynamic Imaging of Coherent Sources (DICS)''' can find coherence between any two pairs of voxels in the brain or between an external source and brain voxels. DICS requires time-frequency-transformed data and can find coherence for evoked and induced activity.

The following imaging methods provide an image of brain activity based on a distributed multiple source model:
* '''CLARA''' is an iterative application of LORETA images, focusing the obtained 3D image in each iteration step.
* '''LAURA '''uses a spatial weighting function that has the form of a local autoregressive function.
* '''LORETA''' has the 3D Laplacian operator implemented as spatial weighting prior.
* '''sLORETA''' is an unweighted minimum norm that is standardized by the resolution matrix.
* '''swLORETA '''is equivalent to sLORETA, except for an additional depth weighting.
* '''SSLOFO '''is an iterative application of standardized minimum norm images with consecutive shrinkage of the source space.
* A '''User-defined volume image''' allows to experiment with the different imaging techniques. It is possible to specify user-defined parameters for the family of distributed source images to create a new imaging technique.
* Bayesian source imaging: '''SESAME''' uses a semi-automated Bayesian approach to estimate the number of dipoles along with their parameters.

'''Surface image:'''

* The '''Surface Minimum Norm Image'''. If no individual MRI is available, the minimum norm image is displayed on a standard brain surface and computed for standard source locations. If available, an individual brain surface is used to construct the distributed source model and to image the brain activity.
* '''Cortical LORETA'''. Unlike classical LORETA, cortical LORETA is not computed in a 3D volume, but on the cortical surface.
* '''Cortical CLARA'''. Unlike classical CLARA, cortical CLARA is not computed in a 3D volume, but on the cortical surface.

'''Discrete model probing:'''

These images do not visualize source activity. Rather, they visualize properties of the currently applied discrete source model:
* The '''Multiple Source Probe Scan (MSPS)''' is a tool for the validation of a discrete multiple source model.
* The '''Source Sensitivity image''' displays the sensitivity of a selected source in the current discrete source model and is therefore data independent.

== Multiple Source Beamformer (MSBF) in the Time-frequency Domain ==

 
'''Short mathematical introduction'''

The BESA beamformer is a modified version of the linearly constrained minimum variance vector beamformer in the time-frequency domain as described in [https://dx.doi.org/10.1073/pnas.98.2.694 Gross et al., "Dynamic imaging of coherent sources: Studying neural interactions in the human brain", PNAS 98, 694-699, 2001]. It allows to image evoked and induced oscillatory activity in a user-defined time-frequency range, where time is taken relative to a triggered event.

The computation is based on a transformation of each channel's single trial data from the time domain into the time-frequency domain. This transformation is performed by the BESA Research Source Coherence module and leads to the complex spectral density Si (f,t), where i is the channel index and f and t denote frequency and time, respectively. Complex cross spectral density matrices C are computed for each trial:

<math>\mathrm{C}_{ij}\left( f,t \right) = \mathrm{S}_{i}\left( f,t \right) \cdot \mathrm{S}_{j}^{*}\left( f,t \right)</math>


The output power P of the beamformer for a specific brain region at location r is then computed by the following equation:

<math>\mathrm{P}\left( r \right) = \operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{-1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{-1}</math>


Here, Cr-1 is the inverse of the SVD-regularized average of Cij(f,t) over trials and the time-frequency range of interest; L is the leadfield matrix of the model containing a regional source at target location r and, optionally, additional sources whose interference with the target source is to be minimized; tr'[] is the trace of the [3×3] (MEG:[2×2]) submatrix of the bracketed expression that corresponds to the source at target location r.

In BESA Research, the output power P(r) is normalized with the output power in a reference time-frequency interval Pref(r). A value q ist defined as follows:

<math> \mathrm{q}\left( r \right) =
\begin{cases}
\sqrt{\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}(r)}} - 1 = \sqrt{\frac{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{\text{ref},r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}} - 1, & \text{for }\mathrm{P}(r) \geq \mathrm{P}_{\text{ref}}(r) \\

1 - \sqrt{\frac{\mathrm{P}_{\text{ref}}\left( r \right)}{\mathrm{P}\left( r \right)}} = 1 - \sqrt{\frac{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{\text{ref},r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}}, & \text{for }\mathrm{P}(r) < \mathrm{P}_{\text{ref}}(r)
\end{cases} </math>


Pref can be computed either from the corresponding frequency range in the baseline of the same condition (i.e. the beamformer images event-related power increase or decrease) or from the corresponding time-frequency range in a control condition (i.e. the beamformer images differences between two conditions). The beamformer image is constructed from values q(r) computed for all locations on a grid specified in the '''General Settings tab'''. For MEG data, the innermost grid points within a sphere of approx. 12% of the head diameter are assigned interpolated rather than calculated values).
q-values are shown in %, where where q[%] = q*100. Alternatively to the definition above, q can also be displayed in units of dB:

<math>\mathrm{q}\left\lbrack \text{dB} \right\rbrack = 10 \cdot \log_{10}\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}</math>


A beamformer operator is designed to pass signals from the brain region of interest r without attenuation, while minimizing interference from activity in all other brain regions. Traditional single-source beamformers are known to mislocalize sources if several brain regions have highly correlated activity. Therefore, the BESA beamformer extends the traditional single-source beamformer in order to implicitly suppress activity from possibly correlated brain regions. This is achieved by using a multiple source beamformer calculation that contains not only the leadfields of the source at the location of interest r, but also those of possibly interfering sources. As a default, BESA Research uses a bilateral beamformer, where specifically contributions from the homologue source in the opposite hemisphere are taken into account (the matrix L thus being of dimension N×6 for EEG and N×4 for MEG, respectively, where N is the number of sensors). This allows for imaging of highly correlated bilateral activity in the two hemispheres that commonly occurs during processing of external stimuli.

In addition, the beamformer computation can take into account possibly correlated sources at arbitrary locations that are specified in the current solution. This is achieved by adding their leadfield vectors to the matrix L in the equation above.

'''Applying the Beamformer'''

This chapter illustrates the usage of the BESA beamformer. The displayed figures are generated using the file ''''Examples/Learn-by-Simulations/AC-Coherence/AC-Osc20.foc'''' (see BESA Tutorial 6: "''Time-frequency analysis and Source coherence''").

'''Starting the beamformer from the time-frequency window'''

The BESA beamformer is applied in the time-frequency domain and therefore requires the Source Coherence module to be enabled. The time-frequency beamformer is especially useful to image in- or decrease of induced oscillatory activity. Induced activity cannot be observed in the averaged data, but shows up as enhanced averaged power in the TSE (Temporal-Spectral Evolution) plot. For instructions on how to initiate a beamformer computation in the time-frequency window, please refer to Chapter '''[[Source_Coherence_How_to...#How_to_Start_the_Beamformer_from_the_Time-Frequency_Window|How to Create Beamformer Images]]'''.

After the beamformer computation has been initiated in the time-frequency window, the source analysis window opens with an enlarged 3D image of the q-value computed with a '''bilateral beamformer'''. The result is superimposed onto the MR image assigned to the data set (individual or standard).

[[Image:SA 3Dimaging (5).gif]]

''Beamformer image after starting the computation in the Time-Frequency window. A bilateral pair of sources in the auditory cortex accounts for the highly correlated oscillatory induced activity. Only the bilateral beamformer manages to separate these activities; a traditional single-source beamformer would merge the two sources into one image maximum in the head center instead.''

'''Multiple source beamformer in the Source Analysis window'''

The 3D imaging display is part of the source analysis window. If you press the '''Restore''' button at the right end of the title bar of the 3D window, the window appears at the bottom right of the source analysis window. In the channel box, the averaged (evoked) data of the selected condition is shown. When a control condition was selected, its average is appended to the average of the target condition.

[[Image:SA 3Dimaging (6).gif]]

''Source Analysis window with beamformer image. The two sources have been added using the '''''Switch to''''' '''''Maximum''''' and '''''Add Source '''''toolbar buttons (see below). Source waveforms are computed from the displayed averaged data. Therefore, they do not represent the activity displayed in the beamformer image, which in this simulation example is induced (i.e. not phase-locked to the trigger)!''

When starting the beamformer from the time-frequency window, a bilateral beamformer scan is performed. In the source analysis window, the beamformer computation can be repeated taking into account possibly correlated sources that are specified in the current solution. Interfering activities generated by all sources in the current solution that are in the 'On' state are specifically suppressed ('''they enter the matrix L in the beamformer calculation''', see Chapter ''Short mathematical description'' above). The computation can be started from the '''Image''' menu or from the '''Image selector button''' dropdown menu. The '''Image''' menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window.

[[Image:SA 3Dimaging (7).gif]]

''Multiple source beamformer image calculated in the presence of a source in the left hemisphere. A '''single''' source scan has been performed. The source set in the current solution accounts for the left-hemispheric q-maximum in the data. Accordingly, the beamformer scan reveals only the as yet unmodeled additional activity in the right hemisphere (note the radiological convention in the 3D image display).''

The beamformer scan can be performed with a '''single''' or a '''bilateral''' source scan. The default scan type depends on the current solution:
* When the beamformer is started from the Time-Frequency window, the Source Analysis window opens with a new solution and a '''bilateral''' beamformer scan is performed.
* When the beamformer is started within the Source Analysis window, the default is
** a scan with a '''single''' source in addition to the sources in the current solution, if at least one source is active.
** a '''bilateral''' scan if no source in the current solution is active.

The default scan type is the multiple source beamformer. The non-default scan type can be enforced using the corresponding ''Volume Image / Beamformer'' entry in the '''Image''' menu.

'''Inserting Sources out of the Beamformer Image'''

The beamformer image can be used to add sources to the current solution. A simple double-click anywhere in the 2D- or 3D-view will generate a non-oriented regional source at the corresponding location. However, a better and easier way to create sources at image maxima and minima is to use the toolbar buttons '''Switch to Maximum''' [[Image:SA 3Dimaging (8).gif]] and '''Add Source''' [[Image:SA 3Dimaging (9).gif]].

Use the '''Switch to Maximum''' button to place the red crosshair of the 3D window onto a local image maximum or minimum. Hitting the '''Add Source''' button creates a regional source at the location of the crosshair and therefore ensures the exact placement of the source at the image extremum. Moreover, the '''Add Source''' button generates an oriented regional source. BESA Research automatically estimates the source orientation that contributes most to the power in the target time-frequency interval (or the reference time-frequency interval, if its power is larger than that in the target interval). The accuracy of this orientation estimate depends largely on the noise content of the data. The smaller the signal-to-noise ratio of the data, the lower is the accuracy of the orientation estimate. '''This feature allows to use the beamformer as a tool to create a source montage for source coherence analysis, where it is of advantage to work with oriented sources'''.

'''Notes:'''

* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image '''menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the''' Image''' menu.
* For scaling options, use the [[Image:SA 3Dimaging (10).gif]] and [[Image:SA 3Dimaging (11).gif]] '''Image Scale toolbar''' buttons.
* Parameters used for the beamformer calculations can be set in the '''Standard Volumes''' of the ''Image Settings dialog box.''

== Dynamic Imaging of Coherent Sources (DICS) ==

 
'''Short mathematical introduction'''

Dynamic Imaging of Coherent Sources (DICS) is a sophisticated method for imaging cortico-cortical coherence in the brain, or coherence between an external reference (e.g. EMG channel) and cortical structures. DICS can be applied to localize evoked as well as induced coherent cortical activity in a user-defined time-frequency range.

DICS was implemented in BESA closely following [https://dx.doi.org/10.1073/pnas.98.2.694 Gross et al., "Dynamic imaging of coherent sources: Studying neural interactions in the human brain", PNAS 98, 694-699, 2001].

The computation is based on a transformation of each channel's single trial data from the time domain into the frequency domain. This transformation is performed by the BESA Research Coherence module and results in the complex spectral density matrix that is used for constructing the spatial filter similar to beamforming.

DICS computation yields a 3-D image, each voxel being assigned a coherence value. Coherence values can be described as a neural activity index and do not have a unit. The neural activity index contrasts coherence in a target time-frequency bin with coherence of the same time-frequency bin in a baseline.

'''DICS for cortico-cortical coherence is computed as follows:'''

Let L(r) be the leadfield in voxel r in the brain and C the complex cross-spectral density matrix. The spatial filter W(r) for the voxel r in the head is defined as follows:

<math>W\left( r \right) = \left\lbrack L^{T}\left( r \right) \cdot C^{- 1} \cdot L\left( r \right) \right\rbrack^{- 1} \cdot L^{T}(r) \cdot C^{- 1}</math>


The cross-spectrum between two locations (voxels) r1 and r2 in the head are calculated with the following equation:

<math>C_{s}\left( r_{1},r_{2} \right) = W\left( r_{1} \right) \cdot C \cdot W^{*T}\left( r_{2} \right),</math>


where <nowiki>*T</nowiki> means the transposed complex conjugate of a matrix. The cross-spectral density can then be calculated from the cross spectrum as follows:

<math>c_{s}\left( r_{1},r_{2} \right) = \lambda_{1}\left\{ C_{s}\left( r_{1},r_{2} \right) \right\},</math>


where λ1{} indicates the largest singular value of the cross spectrum. Once the cross spectral density is estimated, the connectivity¹(CON) between the two brain regions r1 and r2 are calculated as follows:

<math>\text{CON}\left( r_{1},r_{2} \right) = \frac{c_{s}^{\text{sig}}\left( r_{1},r_{2} \right) - c_{s}^{\text{bl}}(r_{1},r_{2})}{c_{s}^{\text{sig}}\left( r_{1},r_{2} \right) + c_{s}^{\text{bl}}(r_{1},r_{2})},</math>


where cssig is the cross-spectral density for the signal of interest between the two brain regions r1 and r2, and csbl is the corresponding cross spectral density for the baseline or the control condition, respectively. In the case DICS is computed with a cortical reference, r1 is the reference region (voxel) and remains constant while r2 scans all the grid points within the brain sequentially. In that way, the connectivity between the reference brain region and all other brain regions is estimated. The value of CON(r1, r2) falls in the interval [-1 1]. If the cross-spectral density for the baseline is 0 the connectivity value will be 1. If the cross-spectral density for the signal is 0 the connectivity value will be -1.

¹ Here, the term connectivity is used rather than coherence, as strictly speaking the coherence equation is defined slightly differently. For simplicity reasons the rest of the tutorial uses the term coherence.

'''DICS for cortico-muscular coherence is computed as follows:'''

When using an external reference, the equation for coherence calculation is slightly different compared to the equation for cortico-cortical coherence. First of all, the cross-spectral density matrix is not only computed for the MEG/EEG channels, but the external reference channel is added. This resulting matrix is Call. In this case, the cross-spectral density between the reference signal and all other MEG/EEG

channels is called cref. It is only one column of Call. Hence, the cross-spectrum in voxel r is calculated with the following equation:

<math>C_{s}\left( r \right) = W\left( r \right) \cdot c_{\text{ref}}</math>


and the corresponding cross-spectral density is calculated as the sum of squares of Cs:

<math>c_{s}\left( r \right) = \sum_{i = 1}^{n}{C_{s}\left( r \right)_{i}^{2}},</math>


where n is 2 for MEG and 3 for EEG. This equation can also be described as the squared Euclidean norm of the cross-spectrum:

<math>c_{s}\left( r \right) = \left\| C_{s} \right\|^{2},</math>


The power in voxel r is calculated as in the cortico-cortical case:

<math>p\left( r \right) = \lambda_{1}\left\{ C_{s}(r,r) \right\}.</math>


At last, coherence between the external reference and cortical activity is calculated with the equation:

<math>\text{CON}\left( r \right) = \frac{c_{s}(r)}{p\left( r \right) \cdot C_{\text{all}}(k,k)},</math>


where Call(k, k) is the (k,k)-th diagonal element of the matrix Call.

DICS is particularly useful, if coherence is to be calculated without an a-priory source model (in contrast to source coherence based on pre-defined source montages). However, the recommended analysis strategy for DICS is to use a brain source as a starting point for coherence calculation that is known to contribute to the EEG/MEG signal of interest. For example, one might first run a beamformer on the time-frequency range of interest and use the voxel with the strongest oscillatory activity as a starting point for DICS. The resulting coherence image will again lead to several maxima (ordered by magnitude), which in turn can serve as starting points for DICS calculation. This way, it is possible to detect even weak sources that show coherent activity in the given time-frequency range.

The other significant application for DICS is estimating coherence between an external source and voxels in the brain. For example, an external source can be muscle activity recoded by an electrode placed over the according peripheral region. This way, the direct relationship between muscle activity and brain activation can be measured.

'''Starting DICS computation from the Time-Frequency Window'''

DICS is particularly useful, if coherence in a user-defined time-frequency bin (evoked or induced) is to be calculated between any two brain regions or between an external reference and the brain. DICS runs only on time-frequency decomposed data, so time-frequency analysis needs to be run before starting DICS computation.

To start the DICS computation, left-drag a window over a selected time-frequency bin in the Time-Frequency Window. Right-click and select “Image”. A dialogue will open (see fig. 1) prompting you to specify time and frequency settings as well as the baseline period. It is recommended to use a baseline period of equal length as the data period of interest. Make sure to select “DICS” in the top row and press “'''Go'''”.

[[Image:SA 3Dimaging (21).gif|450px|thumb|c|none|Fig. 1: Time and frequency settings for DICS and MSBF]]

Next, a window will appear allowing you to specify the reference source for coherence calculation (see fig. 2). It is possible to select a channel (e.g. EMG) or a brain source. If a brain source is chosen and no source analysis was computed beforehand, the option “Use current cross-hair position” must be chosen. In case discrete source analysis was computed previously, the selected source can be chosen as the reference for DICS. Please note that DICS can be re-computed with any cross-hair or source position at a later stage.

[[Image:SA 3Dimaging (1).jpg|400px|thumb|c|none|Fig. 2: Possible options for choosing the reference]]

Confirming with “'''OK'''” will start computation of coherence between the selected channel/voxel and all other brain voxels. In case DICS is computed for a reference source in the brain, it can be advantageous to run a beamforming analysis in the selected time-frequency window first and use one of the beamforming maxima as reference for DICS. Fig. 3 shows an example for DICS calculation.

[[Image:SA 3Dimaging (22).gif|500px|thumb|c|none|Fig. 3: Coherence between left-hemispheric auditory areas and the selected voxel in the right auditory cortex.]]

Coherence values range between -1 and 1. If coherence in the signal is much larger than coherence in the baseline (control condition) then the DICS value is going to approach 1. Contrary, if coherence in the baseline is much larger than coherence in the signal, then the DICS value is going to approach -1. At last, if coherence in the signal is equal to coherence in the baseline, then the DICS value is 0.

In case DICS is to be re-computed with a different reference, simply mark the desired reference position by placing the cross-hair in the anatomical view and select “DICS” in the middle panel of the source analysis window (see Fig. 4). In case an external reference is to be selected, click on “DICS” in the middle panel to bring up the DICS dialogue (see. Fig. 2) and select the desired channel. Please note that DICS computation will only be available after running time-frequency analysis.

[[Image:SA 3Dimaging (23).gif|700px|thumb|c|none|Fig. 4: Integration of DICS in the Source Analysis window]]

== Multiple Source Beamformer (MSBF) in the Time Domain ==
''(requires Besa Research 7.0 or higher)''

===Short mathematical introduction===

Beamforming approach can be also applied in the time domain data. This approach was introduced as linearly constrained minimum variance (LCMV) beamformer (Van Veen et al., 1997). It allows to image evoked activity in a user-defined time range, where time is taken relative to a triggered event, and to estimate source waveforms using the calculated spatial weight at locations of interest. For an implementation of the beamformer in the time domain, data covariance matrices are required, while complex cross spectral density matrices are used for the beamformer approaches in the time-frequency domain as described in the ''[[Source_Analysis_3D_Imaging#Multiple_Source_Beamformer_.28MSBF.29_in_the_Time-frequency_Domain|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section.

The bilateral beamformer introduced in the ''[[Source_Analysis_3D_Imaging#Multiple_Source_Beamformer_.28MSBF.29_in_the_Time-frequency_Domain|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section is also implemented for the time-domain beamformer to take into account contributions from the homologue source in the opposite. This allows for imaging of highly correlated bilateral activity in the two hemispheres that commonly occurs during processing of external stimuli. In addition, the beamformer computation can take into account possibly correlated sources at arbitrary locations.
The beamformer spatial weight W(r) for the voxel r in the brain is defined as follows (Van Veen et al., 1997):

[[File:MSBF1.png]]

where '''C-1''' is the inversed regularized average of covariance matrix over trials, '''L''' is the leadfield matrix of the model containing a regional source at target location r and optionally
additional sources whose interference with the target source is to be minimized. The beamformer spatial weight '''W'''(r) can be applied to the measured data to estimate source
waveform at a location r (beamformer virtual sensor):

[[File:MSBF2.png]]

where '''S'''(r,t) represents the estimated source waveform and '''M'''(t) represents measured EEG or MEG signals.
The output power P of the beamformer for a specific brain region at location r is computed by the following equation:

[[File:MSBF3.png]]

where tr’[ ] is the trace of the [3×3] (MEG: [2×2]) submatrix of the bracketed expression that corresponds to the source at target location r.
Beamformer can suppress noise sources that are correlated across sensors. However, uncorrelated noise will be amplified in a spatially non-uniform manner, with increasing
distortion with increasing distance from the sensors (Van Veen et al., 1997; Sekihara et al., 2001). For this reason, estimated source power should be normalized by a noise power.
In BESA Research, the output power P(r) is normalized with the output power in a baseline interval or with the output power of a uncorrelated noise: P(r) / Pref (r).
The time-domain beamformer image is constructed from values q(r) computed for all locations on a grid specified in the '''General Settings''' tab. A value q(r) is defined as described in
the ''[[Source_Analysis_3D_Imaging#Multiple_Source_Beamformer_.28MSBF.29_in_the_Time-frequency_Domain|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section with data covariance matrices instead of cross-spectral density matrices.

===Applying the Beamformer===

This chapter illustrates the usage of the BESA beamformer in the time domain. The displayed figures are generated using the file ‘Examples/ERP-Auditory-Intensity/S1.cnt’.

'''Starting the time-domain beamformer from the Average tab of the Paradigm dialog box'''

The time-domain beamformer is needed data covariance matrices and therefore requires the ERP module to be enabled. After the beamformer computation has been initiated in the
'''Average tab of the Paradigm dialog box''', the source analysis window opens with an enlarged 3D image of the q-value computed with a bilateral beamformer. The result is
superimposed onto the MR image assigned to the data set (individual or standard).

[[File:MSBF44.png|500px|thumb|c|none|Beamformer image for auditory evoked data after starting the computation in the '''Average tab of the Paradigm dialog box'''. The bilateral beamformer manages to separate the activities in auditory areas, while a traditional single-source beamformer would merge the two sources into one image maximum in the head center instead.]]

'''Multiple-source beamformer in the Source Analysis window'''

The 3D imaging display is part of the source analysis window. In the Channel box, the averaged (evoked) data of the selected condition is shown. Selected covariance intervals in
the ERP module can be checked in the Channel box. The red, gray, and blue rectangles indicate signal, baseline, and common interval, respectively.

[[File:MSBF55.png|700px|thumb|c|none|Source Analysis window with beamformer image. The two beamformer virtual sensors have been added using the Switch to Maximum and Add Source toolbar buttons (see below).
Source waveforms are computed using the beamformer spatial weights and the displayed averaged data (the noise normalized weights (5% noise) option was used to compute the
beamformer image).]]

When starting the beamformer from the '''Average tab of the Paradigm dialog box''', the bilateral beamformer scan is performed. In the source analysis window, the beamformer computation can be repeated taking into account possibly correlated sources that are specified in the current solution. Interfering activities generated by all sources in the current solution that are in the 'On' state are specifically suppressed (they enter the leadfield matrix L in the beamformer calculation). The computation can be started from the '''Image''' menu or from the Image selector button [[File:MSBF_Button.png|22px|Image: 22 pixels]] dropdown menu. The Image menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window.

[[File:MSBF66.png|700px|thumb|c|none|Multiple-source beamformer image calculated in the presence of a source in the left hemisphere. A single-source scan has been performed instead of a bilateral beamforemr. The source set in the current solution accounts for the left-hemispheric q-maximum in the data. Accordingly, the beamformer scan reveals only the as yet unmodeled additional activity in the right hemisphere (note the radiological convention in the 3D image display). The source waveform of the beamformer virtual sensor in the left hemisphere is not shown since the location (blue square in the figure) is not considered for the multiple-source beamformer.]]

The beamformer scan can be performed with a single or a bilateral source scan. The default scan type depends on the current solution:
When the beamformer is started from the '''Average tab of the Paradigm dialog box''' the Source Analysis window opens with a new solution and a bilateral beamformer scan is
performed.
When the beamformer is started within the Source Analysis window, the default is:

* a scan with a single source in addition to the sources in the current solution, if at least one source is active.
* a bilateral scan if no source in the current solution is active.
* a scan with a single source when scalar-type beamformer is selected in the '''beamformer option dialog box'''.

The default scan type is the multiple source beamformer. The non-default scan type can be enforced using the corresponding Volume Image / Beamformer entry in the Image main
menu or in the beamformer option dialog box (only for the time-domain beamformer).

===Inserting Sources as Beamformer Virtual Sensor out of the Beamformer Image===

This is similar to the inserting sources out of the beamformer image in Multiple Source Beamformer (MSBF) in the Time-frequency Domain section.
The beamformer image can be used to add beamformer virtual sensors to the current solution. A simple double-click anywhere in the 3D view (not in the 2D view) will generate a
source at the corresponding location. A better and easier way to create sources at image maxima and minima is to use the toolbar buttons '''Switch to Maximum''' [[Image:SA 3Dimaging (8).gif]] and '''Add Source''' [[Image:SA 3Dimaging (9).gif]].

This feature allows to use the beamformer as a tool to create a source montage for '''source coherence''' analysis. A source montage file (*.mtg) for beamformer virtual sensors can
be saved using File \ Save Source Montage As… entry.

The time-domain beamformer image can be also used to add regional or dipole sources to the current solution. Press '''N''' key when there is no source in the current source array or
there is more than one beamformer virtual sensor. To create a new source array for beamformer virtual sensor, press '''N''' key when there is more than one regional or dipole source in
the current source array.

===Notes===

* You can hide or re-display the last computed image by selecting ''Hide Image'' entry in the '''Image''' menu.
* The current image can be exported to ASCII, ANALYZE, or BrainVoyager (vmp) format from the '''Image''' menu.
* For scaling options, use [[Image:SA 3Dimaging (10).gif]] and [[Image:SA 3Dimaging (11).gif]] '''Image Scale toolbar''' buttons.
* Parameters used for the beamformer calculations can be set in the '''Standard Volume tab of the Image Settings dialog box'''.
* Note that Model, Residual, Order, and Residual variance are not shown for the beamformer virtual sensor type sources.

===References===

* Sekihara, K., Nagarajan, S. S., Poeppel, D., Marantz, A., & Miyashita, Y. (2001). Reconstructing spatio-temporal activities of neural sources using an MEG vector beamformer technique. IEEE Transactions on Biomedical Engineering, 48(7), 760–771.

* Van Veen, B. D., Van Drongelen, W., Yuchtman, M., & Suzuki, A. (1997). Localization of brain electrical activity via linearly constrained minimum variance spatial filtering. IEEE Transactions on Biomedical Engineering, 44(9), 867–880

== CLARA ==

CLARA ('Classical LORETA Analysis Recursively Applied') is an iterative application of weighted LORETA images with a reduced source space in each iteration.

In an initialization step, a LORETA image is calculated. Then in each iteration the following steps are performed:

# The obtained image is spatially smoothed (this step is left out in the first iteration).
# All grid points with amplitudes below a threshold of 1% of the maximum activity are set to zero, thus being effectively eliminated from the source space in the following step.
# The resulting image defines a spatial weighting term (for each voxel the corresponding image amplitude).
# A LORETA image is computed with an additional spatial weighting term for each voxel as computed in step 3. By the default settings in BESA Research, the regularization values used in the iteration steps are slightly higher than that of the initialization LORETA image.

The procedure stops after 2 iterations, and the image computed in the last iteration is displayed. Please note that you can change all parameters by creating a user-defined volume image.

The advantage of CLARA over non-focusing distributed imaging methods is visualized by the figure below. Both images are computed from the N100 response in an auditory oddball experiment (file '''Oddball.fsg''' in subfolder ''fMRI+EEG-RT-Experiment'' of the ''Examples'' folder). The CLARA image is much more focal than the sLORETA image, making it easier to determine the location of the image maxima.

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (24).gif|thumb|350px|sLORETA image]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (25).gif|thumb|350px|CLARA image]] </li>
</ul></div>

'''Notes:'''

* Starting CLARA: CLARA can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter ''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]'' for important information on regularization of distributed inverses.

== LAURA ==

LAURA (Local Auto Regressive Average) belongs to the distributed inverse method of the family of weighted minimum norm methods ([https://doi.org/10.1023/A:1012944913650 Grave de Peralta Menendeza et al., "Noninvasive Localization of Electromagnetic Epileptic Activity. I. Method Descriptions and Simulations", BrainTopography 14(2), 131-137, 2001]). LAURA uses a spatial weighting function that includes depth weighting and that term has the form of a local autoregressive function.

The source activity is estimated by applying the general formula for a weighted minimum norm:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T}\left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings.''

In LAURA, V contains both a depth weighting term W and a representation of a local autoregressive function A. V is computed as:

<math>\mathrm{V} = \left( \mathrm{U}^{T} \cdot \mathrm{U} \right)^{-1}</math>


Where

<math>\mathrm{U} = \left( \mathrm{W} \cdot \mathrm{A} \right) \otimes \mathrm{I}_{3}</math>


Here, <math>\otimes</math> denotes the Kronecker product. I3 is the [3×3] identity matrix. W is an [s×s] diagonal matrix (with s the number of source locations on the grid), where each diagonal element is the inverse of the maximum singular value of the corresponding regional source's leadfields. The formula for the diagonal components Aii and the off-diagonal components Aik are as follows:

<math>\mathrm{A}_{ii} = \frac{26}{\mathrm{N}_{i}}\sum_{k \subset V_{i}}^{}\frac{1}{\mathrm{d}_{ik}^{2}}</math>


<math>
\mathrm{A}_{ik} =
\begin{cases}
- 1/\operatorname{dist}\left( i,k \right)^{2}, & \text{if } k \subset V_{i} \\
0, & \text{otherwise}
\end{cases}
</math>


Here, Vi is the vicinity around grid point i that includes the 26 direct neighbors.

The LAURA image in BESA Research displays the norm of the 3 components of S at each location r. Using the menu function ''Image / Export Image As... ''you have the option to save this norm of S or alternatively all components separately to disk.

'''Notes:'''

* '''Grid spacing:''' Due to memory limitations, LAURA images require a grid spacing of 7 mm or more.
* '''Computation time:''' Computation speed during the first LAURA image calculation depends on the grid spacing (computation is faster with larger grid spacing). After the first computation of a LAURA image, a '''*.laura''' file is stored in the data folder, containing intermediate results of the LAURA inverse. This file is used during all subsequent LAURA image computations. Thereby, the time needed to obtain the image is substantially reduced.
* '''MEG:''' In the case of MEG data, an additional constraint is implemented in the LAURA algorithm that prevents solutions from containing radial source currents (compare Pascual-Marqui, ISBET Newsletter 1995, 22-29). In MEG, an additional source space regularization is necessary in the inverse matrix operation required compute V
* '''Starting LAURA:''' LAURA can be started from the''' Image''' menu or from the '''Image Selection''' button.
* '''Regularization:''' Please refer to Chapter'' “Regularization of distributed volume images” ''for important information on regularization of distributed inverses.

== LORETA ==

LORETA ("Low Resolution Electromagnetic Tomography") is a distributed inverse method of the family of ''weighted minimum norm'' methods. LORETA was suggested by R.D. Pascual-Marqui (International Journal of Psychophysiology. 1994, 18:49-65). LORETA is characterized by a smoothness constraint, represented by a discrete 3D Laplacian.

The source activity is estimated by applying the general formula for a weighted minimum norm:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T}\left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings.''

In LORETA, V contains both a depth weighting term and a representation of the 3D Laplacian matrix. V is computed as:

<math>\mathrm{V} = \left( \mathrm{U}^{T} \cdot \mathrm{U} \right)^{- 1}</math>


where

<math>\mathrm{U} = \left( \mathrm{W} \cdot \mathrm{A} \right) \otimes \mathrm{I}_{3}</math>


Here, <math>\otimes</math> denotes the Kronecker product. I3 is the [3x3] identity matrix. W is an [sxs] diagonal matrix (with s the number of source locations on the grid), where each diagonal element is the inverse of the maximum singular value of the corresponding regional source's leadfields. A contains the 3D Laplacian and is computed as

<math>\mathrm{A} = \mathrm{Y} - \mathrm{I}_{s}</math>


with Is the [sxs] identity matrix, where s is the number of sources (= three times the number of grid points) and

<math>\mathrm{Y} = \frac{1}{2}\left\{ \mathrm{I}_{s} + \left\lbrack \operatorname{diag}\left( \mathrm{Z} \cdot \left\lbrack 111 \ldots 1 \right\rbrack^{T} \right) \right\rbrack^{- 1} \right\} \cdot \mathrm{Z}</math>


where

<math>
\mathrm{Z}_{ik} =
\begin{cases}
1/6, & \text{if } \operatorname{dist}\left( i,k \right) = 1 \text{ grid point} \\
0, & \text{otherwise}
\end{cases}
</math>


The LORETA image in BESA Research displays the norm of the 3 components of S at each location r. Using the menu function ''Image / Export Image As... ''you have the option to save this norm of S or alternatively all components separately to disk.

'''Notes:'''
* '''Grid spacing:''' Due to memory limitations, LORETA images require a grid spacing of 5 mm or more.
* '''Computation time:''' Computation speed during the first LORETA image calculation depends on the grid spacing (computation is faster with larger grid spacing). After the first computation of a LORETA image, a '''<nowiki>*.loreta</nowiki>''' file is stored in the data folder, containing intermediate results of the LORETA inverse. This file is used during all subsequent LORETA image computations. Thereby, the time needed to obtain the image is substantially reduced.
* '''MEG''': In the case of MEG data, an additional constraint is implemented in the LORETA algorithm that prevents solutions from containing radial source currents (Pascual-Marqui, ISBET Newsletter 1995, 22-29). In MEG, an additional source space regularization is necessary in the inverse matrix operation required compute V.
* '''Starting LORETA:''' LORETA can be started from the''' Image''' menu or from the '''Image Selection '''button.
* '''Regularization:''' Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed source models.

== sLORETA ==

This distributed inverse method consists of a ''standardized, unweighted minimum norm''. The method was originally suggested by R.D. Pascual-Marqui (Methods & Findings in Experimental & Clinical Pharmacology 2002, 24D:5-12) Starting point is an unweighted minimum norm computation:

<math>\mathrm{S}_{\text{MN}}\left( t \right) = \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings''.

This minimum norm estimate is now standardized to produce the sLORETA activity at a certain brain location r:

<math>\mathrm{S}_{\text{sLORETA}, r} = \mathrm{R}_{rr}^{-1/2} \cdot \mathrm{S}_{\text{MN},r}</math>


SsMN,r is the [3x1] (MEG: [2x1]) minimum norm estimate of the 3 (MEG: 2) dipoles at location r. Rrr is the [3x3] (MEG: [2x2]) diagonal block of the resolution matrix R that corresponds to the source components at the target location r. The resolution matrix is defined as:

<math>\mathrm{R} = \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{L}^{T} + \lambda \cdot \mathrm{I} \right)^{-1} \cdot \mathrm{L}</math>


The sLORETA image in BESA Research displays the norm of SsLORETA, r at each location r. Using the menu function ''Image / Export Image As...'' you have the option to save this norm of SsLORETA, r or alternatively all components separately to disk.

'''Notes:'''

* sLORETA can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter [[#Regularization_of_distributed_volume_images|''Regularization of distributed volume images'']] for important information on regularization of distributed inverses.

== swLORETA ==

This distributed inverse method is a ''standardized, depth-weighted minimum norm'' (E. Palmero-Soler et al 2007 Phys. Med. Biol. 52 1783-1800). It differs from sLORETA only by an additional depth weighting.

Starting point is a depth-weighted minimum norm computation:

<math>\mathrm{S}_{\text{MN}}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings''.

V is the diagonal depth weighting matrix. For s grid locations, V is of dimension [3s x 3s] (MEG: [2s x 2s]). Each diagonal element of V is the inverse of the first singular value of the leadfield of the corresponding regional source. Hence, the first 3 (MEG: 2) diagonal elements equal the inverse of the largest eigenvalue of the leadfield matrix of regional source 1, and so on.

This minimum norm estimate is now standardized to produce the swLORETA activity at a certain brain location r:

<math>\mathrm{S}_{\text{swLORETA},r} = \mathrm{R}_{rr}^{-1/2} \cdot \mathrm{S}_{\text{MN},r}</math>


SsMN,r is the [3x1] (MEG: [2x1]) depth-weighted minimum norm estimate of the regional source at location r. Rrr is the [3x3] (MEG: [2x2]) diagonal block of the resolution matrix R that corresponds to the source components at the target location r. The resolution matrix is defined as:

<math>\mathrm{R} = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} + \lambda \cdot \mathrm{I} \right)^{-1} \cdot \mathrm{L}</math>


The swLORETA image in BESA Research displays the norm of SswLORETA, r at each location r. Using the menu function ''Image / Export Image As...'' you have the option to save this norm of SswLORETA, r or alternatively all components separately to disk.

'''Notes:'''

* sLORETA can be started from the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== sSLOFO ==

SSLOFO (standardized shrinking LORETA-FOCUSS) is an iterative application of weighted distributed source images with a reduced source space in each iteration ([https://dx.doi.org/10.1109/TBME.2005.855720 Liu et al., "Standardized shrinking LORETA-FOCUSS (SSLOFO): a new algorithm for spatio-temporal EEG source reconstruction", IEEE Transactions on Biomedical Engineering 52(10), 1681-1691, 2005]).

In an initialization step, an [[#sLORETA | sLORETA]] image is calculated. Then in each iteration the following steps are performed:

# A weighted minimum norm solution is computed according to the formula <math display="inline">\mathrm{S} = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}</math> . Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D is the data at the time point under consideration. V is a diagonal spatial weighting matrix that is computed in the previous iteration step. In the first iteration, the elements of V contain the magnitudes of the initially computed LORETA image.
# Standardization of this weighted minimum norm image is performed with the resolution matrix as in [[#sLORETA | sLORETA]].
# The obtained standardized weighted minimum norm image is being smoothed to get Ssmooth.
# All voxels with amplitudes below a threshold of 1% of the maximum activity get a weight of zero in the next iteration step, thus being effectively eliminated from the source space in the next iteration step.
# For all other voxels, compute the elements of the spatial weighting matrix V to be used in the next iteration as follows: <math display="inline">\mathrm{V}_{ii,\text{next iteration}} = \frac{1}{\left\| \mathrm{L}_{i} \right\|} \cdot \mathrm{S}_{ii,\text{smooth}} \cdot \mathrm{V}_{ii,\text{current iteration}}</math>



The procedure stops after 3 iterations. Please note that you can change all parameters by creating a [[#User-Defined Volume Image | user-defined volume image]].

'''Notes:'''
* '''Starting sSLOFO''': sSLOFO can be started from the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter ''[[#Regularization of distributed volume images | Regularization of distributed volume images]]'' for important information on regularization of distributed inverses.

== User-Defined Volume Image ==

In addition to the predefined 3D imaging methods in BESA Research, it is possible to create user-defined imaging methods based on the general formula for distributed inverses:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. Custom-defined parameters are:* The spatial weighting matrix V: This may include depth weighting, image weighting, or cross-voxel weighting with a 3D Laplacian (as in LORETA) or an autoregressive function (as in LAURA).

* Regularization: The term in parentheses is generally regularized. Note that regularization has a strong effect on the obtained results. Please refer to chapter “''Regularization of Distributed Volume Images” ''for more information.
* Standardization: Optionally, the result of the distributed inverse can be standardized with the resolution matrix (as in sLORETA).
* Iterations: Inverse computations can be applied iteratively. Each iteration is weighted with the image obtained in the previous iteration.

All parameters for the user-defined volume image are specified in the User-Defined Volume Tab of the Image Settings dialog box. Please refer to chapter “''User-Defined Volume Tab”'' for details.

'''Notes:'''
* Starting the user-defined volume image: the image calculation can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== Regularization of distributed volume images ==

Distributed source images require the inversion of a term of the form L V LT. This term is generally regularized before its inversion. In BESA Research, selection can be made between two different regularization approaches (parameters are defined in the ''Image Settings dialog box''):

* '''Tikhonov regularization''': In Tikhonov regularization, the term L V LT is inverted as (L V LT +λ I)-1. Here, l is the regularization constant, and I is the identity matrix.
* One way of determining the optimum regularization constant is by minimizing the ''generalized cross'' ''validation error'' (CVE).
* Alternatively, the regularization constant can be specified manually as a percentage of the trace of the matrix L V LT.
* '''TSVD''': In the truncated singular value decomposition (TSVD) approach, an SVD decomposition of L V LT is computed as  L V LT = U S UT, where the diagonal matrix S contains the singular values. All singular values smaller than the specified percentage of the maximum singular values are set to zero. The inverse is computed as U S-1 UT, where the diagonal elements of S-1 are the inverse of the corresponding non-zero diagonal elements of S.

Regularization has a critical effect on the obtained distributed source images. The results may differ completely with different choices of the regularization parameter (see examples below). Therefore, it is important to evaluate the generated image critically with respect to the regularization constant, and to keep in mind the uncertainties resulting from this fact when interpreting the results. The default setting in BESA Research is a TSVD regularization with a 0.03% threshold. However, this value might need to be adjusted to the specific data set at hand.

The following example illustrates the influence of the regularization parameter on the obtained images. The data used here is condition '''St-Cor of dataset Examples \ TFC-Error-Related-Negativity \ Correct+Error.fsg''' at 176 ms following the visual stimulus. Discrete dipole analysis reveals the main activity in the left and right lateral visual cortex at this latency.

[[Image:SA 3Dimaging (42).gif]]

''Discrete source model at 176 ms: Main activity in the left and right lateral visual cortex, no visual midline activity.''

LORETA images computed at this latency depend critically on the choice of the regularization constant. The following 3D images are created with TSVD regularization with SVD cutoffs of 0.1%, 0.005%, and 0.0001%, respectively. The volume grid size was 9 mm. The example demonstrates the dramatic effect of regularization and demonstrates the typical tradeoff between too strong regularization (leading to too smeared 3D images that tend to show blurred maxima) and too small regularization (resulting in too superficial 3D images with multiple maxima).

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (43).gif|thumb|350px|'''SVD cutoff 0.1%''': Regularization too strong. No separation between sources, mislocalization towards the middle of the brain.]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (44).gif|thumb|350px|'''SVD cutoff 0.005%''': Appropriate regularization. Separation of the bilateral activities. Location in agreement with the discrete multiple source model.]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (45).gif|thumb|350px|'''SVD cutoff 0.0001%''': Too small regularization. Mislocalization, too superficial 3D image. ]] </li>
</ul></div>

The automatic determination of the regularization constant using the CVE approach does not necessarily result in the optimum regularization parameter either. In this example, the unscaled CVE approach rather resembles the TSVD image with a cutoff of 0.0001%, i.e. regularization is too small. Therefore, it is advisable to compare different settings of the regularization parameter and make the final choice based on the above-mentioned considerations.

== Cortical LORETA ==

Cortical LORETA is principally the same technique as LORETA, however, Cortical LORETA is not computed in a 3D volume, but on the cortical surface.

The cortical reconstruction in BESA Research fed from BESA MRI is a closed 2D surface with no boundaries and a very close approximation of the actual cortical form. It consists of an irregular triangulated grid.

The Laplace operator that is used for identifying a smooth solution in a three-dimensional space is exchanged with a Laplace operator that runs on the two-dimensional cortical surface.

There is a wide variety of 2D Laplace operators with different characteristics. The general form of the discrete Laplace operator is

<math>\Delta f\left( p_{i} \right) = \frac{1}{d_{i}}\sum_{j \in N(i)}^{}{w_{ij}\left\lbrack f\left( p_{i} \right) - f\left( p_{j} \right) \right\rbrack},</math>


where '''pi''' is the '''i-th''' node of the triangular mesh, '''f(pi) '''is the value of a function f defined on the cortical mesh at the node '''pi''', '''wij''' is the weight for the connection between the nodes '''pi''' and '''pj''' and '''di''' is a normalization factor for the '''i-th''' row of the operator. Furthermore, '''N(i)''' is the set of indices corresponding to the direct (also called "1-ring") neighbors of '''pi'''.

BESA offers the choice of three Laplace operators with slightly different characteristics.

* '''Unweighted Graph Laplacian''': This is the simplest operator. It takes into account only the adjacency of the nodes and not the geometry of the mesh:

<math>
w_{ij} =
\begin{cases}
1, & \text{if } p_{i} \text{ and } p_{j} \text{ are connected by an edge} \\
0, & \text{otherwise}
\end{cases}
</math>

<math>d_{i} = 1</math>


[[Image:SA 3Dimaging (4).jpg |450px]]

* '''Weighted Graph Laplacian:''' This operator is similar to the unweighted graph Laplacian but with different weights for the different connections. The connections between nearby nodes get larger weights than the connections between farther nodes:

<math>w_{ij} = \frac{1}{\operatorname{dist}\left( p_{i},p_{j} \right)}</math>

<math>d_{i} = \sum_{j \in N(i)}^{} {\operatorname{dist}\left(p_{i}, p_{j} \right)}</math>


where '''dist''' ('''pi''' , '''pj''') is the distance between the nodes '''pi '''and '''pj'''.

[[Image:SA 3Dimaging (6).jpg|450px]]

* '''Geometric Laplacian with mixed area weights''': This operator takes into account the angles in the corresponding triangles into account as well as the area around the nodes in order to determine the connection weights:

<math>w_{ij} = \frac{\cot\left( \alpha_{ij} \right) + \cot\left( \beta_{ij} \right)}{2}</math>

<math>d_{i} = A_{\text{mixed}}</math>


where '''αij''' and '''βij''' denote the two angles opposite to the edge ('''i , j''') and '''Amixed '''is either the Voronoi area, or 1/2 of the triangle area or 1/4 of the triangle area depending on the type of the triangle.

[[Image:SA 3Dimaging (8).jpg|450px]]

'''Regularization and other parameters:'''

[[Image:CorticalLOR.png‎]]

* '''SVD cutoff''': The regularization for the inverse operator as a percent of the largest singular value.
* '''Depth weighting''': Turn depth weighting on or off.
* '''Laplacian type''': Selection of Laplacian operators (see above).

'''Notes:'''
* '''Starting Cortical LORETA''': Cortical LORETA can be started from the sub-menu '''Surface Image''' of the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]''” for important information on regularization of distributed inverses.

== Cortical CLARA ==

Cortical CLARA is principally the same technique as CLARA, but Cortical CLARA is not computed in a 3D volume, but on the cortical surface. Instead of using a LORETA image as the basis for the iterative application, cortical CLARA uses cortical LORETA.

'''Regularization and other parameters:'''

[[Image:SA 3Dimaging (47).gif]]

* '''SVD cutoff''': The regularization for the inverse operator as a percent of the largest singular value.
* '''Depth weighting''': Turn depth weighting on or off.
* '''Laplacian type''': Selection of Laplacian operators (see Cortical LORETA).
* '''No of iterations''': Number of iterations for CLARA. The more iterations are used, the sparser becomes the solution.
* '''Automatic''': The algorithm tries to determine the number of iterations automatically. The goodness of fit (GOF) is calculated after every iteration and if there is a big jump in the GOF then the algorithm will stop. If no jumps appear during the calculations then CLARA iterates until the specified number of iterations is reached.
* '''Regularize iterations''': If one wants to use different regularization for the CLARA iterations than the value specified as "SVD cutoff", this option should be selected.
* '''Amount to clip from img (%)''': Cortical CLARA uses the solution from the previous iteration as an additional weighting matrix for the current iteration. That weighting matrix is constructed by cutting the "low" activity from the solution. This number specifies how much of the activity should be cut from the previous solution in order to construct the weighting matrix. This value is given as a percentage of the maximal activity. Default value is 10%.

'''Notes:'''

* '''Starting Cortical CLARA:''' Cortical CLARA can be started from the sub-menu '''Surface Image''' of the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]''” for important information on regularization of distributed inverses.

== Cortex Inflation ==

The inflated cortex is a smoothened version of the individual cortical surface with minimal metric distortions (Fischl, B. et al. (1999). Cortical Surface-Based Analysis: II: Inflation, Flattening, and a Surface-Based Coordinate System. ''NeuroImage'', 9(2), 195–207). Gyri and sulci are smoothened out. The original distances between each point on the cortex and its neighbors are, however, mostly preserved.

[[Image:SA 3Dimaging (48).gif]]

''Cortical LORETA map overlaid on top of the inflated cortical surface.''

A lighter gray color overlaid on top of the surface image indicates the location of a gyrus of the individual cortex surface, while a darker gray color indicates the location of a sulcus. The inflated cortical surface can be computed in '''BESA MRI 2.0'''. For more details please refer to the BESA MRI 2.0 help.

== Surface Minimum Norm Image ==

'''Introduction'''

The minimum norm approach is a common method to estimate a distributed electrical current image in the brain at each time sample (Hämäläinen & Ilmoniemi 1984). The source activities of a large number of regional sources are computed. The sources are evenly distributed using 1500 standard locations 10% and 30% below the smoothed standard brain surface (when using the standard MRI) or using between 3000-4000 locations on the individual brain surface defined by the gray-white-matter boundary.

Since the number of sources is much larger than the number of sensors in a minimum norm solution, the inverse problem is highly underdetermined and must be stabilized by a mathematical constraint, the minimum norm. Out of the many current distributions that can account for the recorded sensor data, the solution with the minimum L2 norm, i.e. the minimum total power of the current distribution is displayed in BESA Research.

First, the forward solution (leadfield matrix L) of all sources is calculated in the current head model. Then, the source activities S(t) of all source components are computed from the data matrix D(t) using an inverse regularized by the estimated noise covariance matrix:

<math>\mathrm{S}\left( t \right) = \mathrm{R} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{R} \cdot \mathrm{L}^{T} + \mathrm{C}_N \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed regional source model, CN denotes the noise correlation matrix in sensor space, and R is a weighting matrix in source space. R and CN can be designed in different ways in order to optimize the minimum norm result. The total activity of each regional source is computed as the root mean square of the source activities S(t) of its 3 (MEG:2) components. This total source activity is transformed to a color-coded image of the brain surface. (When the standard brain is used, two sources are assigned to each surface location, located 10% and 30% below the surface, respectively. The color that is displayed on the standard brain surface is the larger of the two corresponding source activities.)

'''Weighting options'''

The minimum norm current imaging techniques of BESA Research provide different weighting strategies. Two weighting approaches are available: Depth weighting and spatio-temporal approaches.
* '''Depth weighting:''' Without depth weighting, deep sources appear very smeared in a minimum-norm reconstruction. With depth weighting, both deep and superficial sources produce a similar, more focal result. If this weighting method is selected, the leadfield of each regional source is scaled with the largest singular value of the SVD (singular value decomposition) of the source's leadfield.
* '''Spatio-temporal weighting''': Spatio-temporal weighting tries to assign large weight to sources that are assumed to be more likely to contribute to the recorded data.
** '''Subspace correlation after single source scan''': This method divides the signal into a signal and a noise subspace. The correlation of the leadfield of a regional source i with the signal subspace (pi) is computed to find out if the source location contributes to the measured data. The weighting matrix R becomes a diagonal matrix. Each of the three (MEG: 2) components of a regional source get the same weighting value pi2. This approach is based on the signal subspace correlation measure introduced by J.C. Mosher, R. M. Leahy (Recursive MUSIC: A Framework for EEG and MEG Source Localization, IEEE Trans. On Biomed. Eng. Vol. 45, No. 11, November 1998)
** '''Dale & Sereno 1993:''' In the approach of Dale and Sereno (J Cogn Neurosci, 1993, 5: 162-176) a signal subspace needs not be defined. The correlation pi of the leadfield of regional source i with the inverse of the data covariance matrix is computed along with the largest singular value λmax of the data covariance matrix. The weighting matrix R is a diagonal matrix with weights: [[Image:SA 3Dimaging (50).gif]]. Each of the three (MEG: 2) components of a regional source receives the same weighting value.

'''Noise regularization'''

Two methods to estimate the channel noise correlation matrix CN are provided by the program:
* '''Use baseline:''' Select this option to estimate the noise from the user-definable baseline. The signal is computed from the data at non-baseline latencies.
* '''Use 15% lowest values:''' The baseline activity is computed from the data at those 15% of all displayed latencies that have the lowest global field power. The signal is computed from all displayed latencies.

In each case, the activity (noise or signal, respectively) is defined as root-mean-square across all respective latencies for each channel.

The noise covariance matrix CN is constructed as a diagonal matrix. The entries in the main diagonal are proportional to the noise activity of the individual channels (if selected) or are all equally proportional to the average noise activity over all channels. The noise covariance matrix CN is then scaled such that the ratio of the Frobenius norms of the weighted leadfield projector matrix (LRLT) and the noise covariance matrix CN equals the Signal-to-Noise ratio. This scaling can be multiplied by an additional factor (default=1) to sharpen (<1) or smoothen (>1) the minimum norm image.

'''Applying the Minimum Norm Image'''

The minimum-norm algorithm is started via the ''Surface minimum norm image dialog box'', which is opened from the''' Image''' menu, or by typing the shortcut '''Ctrl-M''': Please refer to Chapter ''“Surface'' ''Minimum Norm Tab”'' for more details.

As opposed to the other 3D images available from the '''Image '''menu, the surface minimum norm image is not computed on a volumetric grid, but rather for locations on the brain surface. Accordingly, the results of the minimum norm image are displayed superimposed to the brain surface mesh rather than to the volumetric MR image.

The figure below shows a minimum norm image computed from the file '''Examples\Epilepsy\Spikes\Spikes-Child4_EEG+MEG_averaged.fsg'''. The EEG spike peak was imaged using the individual brain surface of the subject. A baseline from -300 to -70 ms was used. Minimum norm was computed with depth weighting, Spatio-temporal weighting according to Dale & Sereno 1993 and individual noise weighting with a noise scale factor of 0.01. The minimum norm image reveals the location of the spike generator in the close vicinity of the frontal left-hemispheric lesion in this subject.

[[Image:SA 3Dimaging (51).gif]]

== Multiple Source Probe Scan (MSPS) ==

 
'''Introduction'''

The MSPS function provides a tool for the validation of a given solution. It is based on the following theoretical consideration: If the recorded EEG/MEG data has been modeled adequately, i.e. all active brain regions are represented by a source in the current solution, then any additional probe source added to the solution will not show any activity apart from noise. The only exception occurs if this probe source is placed in close vicinity to one of the sources in the current solution. In that case, the solution's source and the probe source will share the activity of the corresponding brain area. The MSPS applies these considerations by scanning the brain on a pre-defined grid with a regional probe added to the current solution. Grid extent and density can be specified in the Image settings. The power P of the probe source at location r in the signal interval is compared with the power of the probe source in a reference interval, defining a value q:

<math>\mathrm{q}\left( r \right) = \sqrt{\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}} - 1</math>


MSPS can be computed on time domain or time-frequency domain data:
* In the time domain, q(r) is computed from the source waveform of the probe source. Here, P(r) is the mean power of the probe source at location r in the marked latency range, and Pref(r) is the mean probe source power in the user-definable baseline interval.
* In the time-frequency domain, an MSPS image can be computed from the complex cross spectral density matrices. By applying the inverse operator for a source configuration consisting of the current solution and the probe source, the power of the probe source can be computed for the target interval [P(r)] and the reference time-frequency interval [Pref(r)]. In the resulting MSPS image, q-values are shown in %, where q[%] = q*100.

The inverse operator used to determine the probe source power uses different regularization constants for the probe source and the sources in the current solution. The regularization constant of the sources in the current solution can be specified in the Image settings (default 4%). The regularization constant of the probe source is internally set to 0%.

Alternatively to the definition above, q can also be displayed in units of dB:

<math>\mathrm{q}\left\lbrack \text{dB} \right\rbrack = 10 \cdot \log_{10}\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}</math>


Values of q smaller than zero are not shown in the MSPS image.

According to the considerations above, an MSPS of a correct source model should optimally yield image maxima around the sources in the current solution only. If the MSPS image is blurred or shows maxima at locations different from the modeled sources, this indicates a non-sufficient or incorrect solution.

'''Applying the MSPS'''

This chapter illustrates the application of the Multiple Source Probe Scan. The figures are generated with data from file '''Examples/Epilepsy/Spikes/Rolandic-Spike-Child.fsg''' (-300 : +200 ms, filtered from 3 Hz [forward] to 40 Hz [zero-phase]).

'''Time domain versus time-frequency domain MSPS'''

The multiple source probe scan can be computed in the time domain or the time-frequency domain. The latter is possible only when time-frequency domain data is available for the current condition, i.e. if the condition has been created by starting a multiple source beamformer (MSBF) computation from the source coherence window. In this case, evoking the MSPS calculation from the '''Imaging '''button or from the '''Image''' menu will bring up the following dialog window that allows to choose between time- or time-frequency MSPS. If only time domain data is available, this dialog window will not appear and MSPS will be computed in the time domain.

[[Image:SA 3Dimaging (53).gif]]

For a time-frequency domain MSPS, the target and the reference time-frequency interval have been specified already in the Time-Frequency window (see Chapter "''How To Create Beamformer Images''"). For a time-domain MSPS, the target and the reference epoch have to be specified in the Source Analysis window as described below.

'''Time domain MSPS'''

The time-domain MSPS image displays the ratio of the power of a regional probe source in the signal and the baseline interval. The currently set baseline is indicated by a horizontal line in the upper left corner of the channel box.

[[Image:SA 3Dimaging (54).gif|thumb|c|none|330px|The black horizontal bar in the upper part of the channel box (here circled in red) indicates the baseline interval.]]

By default, BESA Research defines the pre-stimulus interval of the current data segment as baseline. The baseline should represent a latency range in which no event-related activity is present in the data. There are several possibilities to modify the baseline interval: by clicking on the horizontal line with the left mouse button or by using the corresponding entry in the '''Condition '''menu or '''Fit Interval''' popup menu.

Mark an interval to define the target epoch, i.e. the time-interval for which the current solution is to be tested. Start the MSPS by selecting it from the '''Image selection '''button or from the '''Image''' menu to start the probe source scan. The''' Image '''menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window. The 3D window opens and displays the scan result.

<div><ul>
<li style="display: inline-block;"> [[Image:SA 3Dimaging (55).gif|thumb|c|none|650px|This figure shows the MSPS image applied on the three left-hemispheric sources in the solution ''''Rolandic-Spike-Child-RS2.bsa''''. The baseline is set from -300ms to -50 ms. The right-hemispheric sources have been switched off. The fit interval is set to the latency range of large overall activity in the data (-43 ms : 117 ms). A realistic FEM model appropriate for the subject's age (12 years, conductivity ratios (cr) 50) is applied. The MSPS image does not show maxima at the modeled source locations and rather shows a spread q-value distribution.]] </li>

<li style="display: inline-block;"> [[Image:SA 3Dimaging (56).gif|thumb|c|none|650px|The MSPS image for the same latency range when the right-hemispheric sources have been included. The MSPS image appears more focal and shows maxima around the modeled brain regions. This indicates the substantial improvement of the solution by adding the right-hemispheric sources that model the propagation of the epileptic spike from the left to the right hemisphere (note the radiological side convention in the 3D window).]] </li>
</ul></div>

'''Time-Resolved MSPS'''

If the MSPS has been computed on time domain data, the image can be shown separately for each latency in the selected interval. After the MSPS has been computed for the marked epoch, double-click anywhere within this epoch to display the ratio of the probe source magnitude at the selected latency and the mean probe source magnitude in the baseline. Scanning the latency range by moving the cursor (e.g. with the left and right arrow cursor keys) provides a time-resolved MSPS image.

Time-resolved MSPS images are not available if the MSPS has been computed on data in the time-frequency domain.

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (57).gif|thumb|450px|MSPS image of the spike peak activity at 0ms. The activity mainly occurs in the left hemisphere. This fact is illustrated by the source waveforms and confirmed in the MSPS image, which shows a focal maximum around the location of the red sources.]] </li>

<li style="display: inline-block;"> [[File:SA 3Dimaging (58).gif|thumb|450px|Around +27 ms, the spike has propagated to the right hemisphere. This becomes evident from the waveforms of the blue sources, which show a significant latency lag with respect to the first three sources, and from the MSPS image, which shows the maximum around blue sources at this latency.]] </li>
</ul></div>



'''Notes:'''

* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image''' menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the''' Image''' menu.
* For scaling options, please refer to the '''scaling buttons''' popup menu .
* Parameters used for the MSPS calculations can be set in the ''General Settings tab'' of the ''Image Settings dialog box.''

== Source Sensitivity ==

'''Introduction'''

The 'Source sensitivity' function displays the sensitivity of the selected source in the current source model to activity in other brain regions. Sensitivity is defined as the fraction of power at the scanned brain location that is mapped onto the selected source.

To compute the source sensitivity, unit brain activity is modeled at different locations (probe source) throughout the brain. To this data, the current source model is applied to compute the source waveforms SCM of all modeled sources:

<math>\mathrm{S}_{\text{CM}} = \mathrm{L}_{\text{CM}}^{-1} \cdot \mathrm{L}_{\text{PS}}</math>


Here LCM-1 is the regularized inverse operator for the current model, and LPS is the leadfield of the regional probe source (dimension [Nx3] for EEG and [Nx2] for MEG, respectively, where N is the number of sensors). The source amplitude SSS of the selected source in the model is a 3x3 (MEG: 2x2) sub-matrix of SCM (if the selected source is a regional source) or a 1x3-matrix (MEG: 1x2) (if the selected source is a dipole). The root mean square of the singular values of SCM is defined as the source sensitivity.

The 3D source sensitivity image displays this value for all locations on a grid specified under '''Image/Settings'''. Grid density can be specified in the Image Settings.

'''Applying the Source Sensitivity Image'''

The Source Sensitivity image is evoked from the '''Image''' menu or by pressing the corresponding hot key (default: '''V''').

This function is enabled only when a solution with an active selected source is present in the Source Analysis window. The source sensitivity image then displays the sensitivity of the selected source to activity in other brain regions.

[[Image:SA 3Dimaging (59).gif]]

''Source Sensitivity image for the selected frontal source (green) in model ''''''High_Intensity_3RS.bsa'''''' in folder 'Examples/ERP_Auditory_Intensity'. The data displayed is the '100dB' condition in file ''''''All_Subjects_cc.fsg''''''. The selected source is sensitive to activity in the frontal brain region (yellow/white), while it is not influenced by activity in the vicinity of the left and right auditory cortex areas, which are modeled by the red and blue source in the model (transparent/gray).''

'''Notes:'''

* The sensitivity image is independent of the recorded sensor signals. It only depends on the current source model, the sensor configuration, the head model, and the regularization constant.
* If the regularization constant is set to zero, each source has a sensitivity of 100% to activity around its own location. With increasing regularization, the spatial filter becomes less focused, and the sensitivity of a source to activity at its location decreases.
* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image''' menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the '''Image''' menu.

==SESAME==

SESAME (Sequential Semi-Analytic Monte-Carlo Estimation) is a Bayesian approach for estimating sources that uses Markov-Chain Monte-Carlo method for efficient computation of the probability distribution as described in Sommariva, S., & Sorrentino, A. "Sequential Monte Carlo samplers for semi-linear inverse problems and application to magnetoencephalography." Inverse Problems 30.11 (2014): 114020. It allows to automatically estimate simultaneously the number of dipoles, their locations and time courses requiring virtually no user input.
The algorithm is divided in two blocks:

* The first block consists of a Monte Carlo sampling algorithm that produces, with an adaptive number of iterations, a set of samples representing the posterior distribution for the number of dipoles and the dipole locations.
* The second block estimates the source time courses, given the number of dipoles and the dipole locations.

The Monte Carlo algorithm in the first block works by letting a set of weighted samples evolve with each iteration. At each iteration, the samples (a multi-dipole state) approximates the n-th element of a sequence of distributions p1, …, pN, that reaches the desired posterior distribution (pN = p(x|y)). The sequence is built as pN = p(x) p(y|x) α(n), such that α(1) = 0, α(N) = 1. The actual sequence of values of alpha is determined online. Dipole moments are estimated after the number of dipoles and the dipole locations have been estimated with the Monte Carlo procedure. This continues until a steady state is reached.
The SESAME image in BESA Research displays the final probability of source location along with an estimate for number of sources. Using the menu function '''Image / Export Image As...''' you have the option to save this SESAME image.

'''Notes:'''
*'''Grid spacing:''' Due to memory and computational limitations, it is recommended to use SESAME with a grid spacing of 5 mm or more.
*'''Fit Interval:''' SESAME requires a fit interval of more than 2 samples to start the computation.
*'''Computation time:''' Computation speed during SESAME calculation depends on the grid spacing (computation is faster with larger grid spacing) and number of channels.

==Brain Atlas==

===Introduction===

Brain atlas is a priori data that can be applied over any discrete or distributed source image displayed in the 3D window. It is a reference value that strongly depends on the selected brain atlas and should not be used as medical reference since individual brains may differ from the brain atlas.

[[Image:BrainAtlas1.png]]

===Brain Atlases===

In BESA Research the atlases listed below are provided. BESA is not the author of the atlases; please cite the appropriate publications if you use any of the atlases in your publication.

'''Brainnetome''' This is one of the most modern brain probabilistic atlas where structural, functional, and connectivity information was used to perform cortical parcellation. It was introduce by Fan and colleagues ('''2016'''), and is still work in progress. The atlas was created using data from 40 healthy adults taking part in the Human Connectome Project. In March 2018, the atlas consists of 246 structures labeled independently for each hemisphere. In BESA we provide the max probability map with labeling. Please visit the Brainnetome webpage to see more details related to the indicated brain regions (i.e. behavioral domains, paradigm classes and regions connectivity).

'''AAL''' Automated Anatomical Labeling atlas was created in 2002 by Tzourio-Mazoyer and collegues ('''2002'''). It is the mostly used atlas nowadays. The atlas is based on the averaged brain of one subject (young male) who was scanned 27 times. The atlas resolution is 1mm isometric. The brain sulci were drawn manually on every 2mm slice and then brain regions were automatically assigned. The atlas consists of 116 regions which are asymmetrical between hemispheres. The atlas is implemented as in the '''SPM12''' toolbox.

'''Brodmann''' The Brodmann map was created by Brodmann ('''1909'''). The brain regions were differentiated by cytoarchitecture of each cortical area using the Nissi method of cell staining. The digitalization of the original Brodmann map was performed by Damasio and Damasio ('''1989'''). The digitalized atlas consists of 44 fields that are symmetric between hemispheres. BESA used the atlas implementation as in Chris Roden’s '''MRICro''' software.

'''AAL2015''' Automated Anatomical Labeling revision 2015. This is the updated AAL atlas. In comparison to the previous version (AAL) mainly the frontal lobe shows a higher degree of parcellation (Rolls, Joliot, and Tzourio-Mazoyer 2015). The atlas is implemented as in the '''SPM12''' toolbox.

'''Talairach''' Atlas was created in 1988 by Talairach and Tournoux ('''1988''') and it is based on the post mortem brain slices of a 60 year old right handed European female. It was created by drawing and matching regions with the Brodmann map. The atlas is available at 5 tissue levels, however we used only the volumetric gyrus level as it is the most known in neuroscience and is the most appropriate for EEG. The atlas consists of 55 regions that are symmetric between hemispheres. The native resolution of the atlas was 0.43x0.43x2- 5mm. Please note that the poor resolution in Z direction is a direct consequence atlas definition, and since it is a post-mortem atlas it will not correctly match the brain template
(noticeable mainly on brain edges). The atlas digitalization was performed by Lancaster and colleagues ('''2000''') resulting in a “golden standard” for neuroscience. The atlas was first implemented in a software called '''talairach daemon'''.

===Visualization modes===

'''Just Labels.''' Displayed are only Talairach Coordinates, the currently used brain atlas and the region name where the crosshair is placed. No atlas overlay will be visible on the 3D image.

'''brainCOLOR.''' All information is displayed as in “Just Labels” mode but also the atlas is visible as an overlay over the MRI. The coloring is performed using the algorithm introduced by Klein and colleagues (Klein et al. 2010). With this method of coloring the regions which are part of the same lobe are colored in a similar color but with different color shade. The shade is computed by the algorithm to make these regions visually differentiable from each other as much as possible.

'''Individual Color.''' In this mode the native brain atlas color is used if provided by the authors of the brain atlas (i.e. Yeo7). Where this was not available BESA autogenerated colors for the atlas using an approach similar to political map coloring. This approach aims to differentiate most regions that are adjacent to each other and no presumptions on lobes is applied.

'''Contour.''' Only region contours (borders between atlas regions) are drawn with blue color. This is the default mode in BESA Research.

===References===

* Brodmann, Korbinian. 1909. Vergleichende Lokalisationslehre Der Großhirnrinde. Leipzig: Barth. https://www.livivo.de/doc/437605.
* Damasio, Hanna, and Antonio R. Damasio. 1989. Lesion Analysis in Neuropsychology. Oxford University Press, USA.
* Fan, Lingzhong, Hai Li, Junjie Zhuo, Yu Zhang, Jiaojian Wang, Liangfu Chen, Zhengyi Yang, et al. 2016. “The Human Brainnetome Atlas: A New Brain Atlas Based on Connectional Architecture.” Cerebral Cortex 26 (8): 3508–26. https://doi.org/10.1093/cercor/bhw157.
* Klein, Arno, Andrew Worth, Jason Tourville, Bennett Landman, Tito Dal Canton, Satrajit S. Ghosh, and David Shattuck. 2010. “An Interactive Tool for Constructing Optimal Brain Colormaps.” http://braincolor.mindboggle.info/docs/SFN2010_BrainCOLORmap_poster_ArnoKlein.pdf.
* Lancaster, Jack L., Marty G. Woldorff, Lawrence M. Parsons, Mario Liotti, Catarina S. Freitas, Lacy Rainey, Peter V. Kochunov, Dan Nickerson, Shawn A. Mikiten, and Peter T. Fox. 2000. “Automated Talairach Atlas Labels for Functional Brain Mapping.” Human Brain Mapping 10 (3): 120–131.
*Rolls, Edmund T., Marc Joliot, and Nathalie Tzourio-Mazoyer. 2015. “Implementation of a New Parcellation of the Orbitofrontal Cortex in the Automated Anatomical Labeling Atlas.” NeuroImage 122 (November): 1–5. https://doi.org/10.1016/j.neuroimage.2015.07.075.
* Talairach, J, and P Tournoux. 1988. Co-Planar Stereotaxic Atlas of the Human Brain. 3-Dimensional Proportional System: An Approach to Cerebral Imaging. Thieme.
*Thomas Yeo, B. T., F. M. Krienen, J. Sepulcre, M. R. Sabuncu, D. Lashkari, M. Hollinshead, J. L. Roffman, et al. 2011. “The Organization of the Human Cerebral Cortex Estimated by Intrinsic Functional Connectivity.” Journal of Neurophysiology 106 (3): 1125–65. https://doi.org/10.1152/jn.00338.2011.
* Tzourio-Mazoyer, N., B. Landeau, D. Papathanassiou, F. Crivello, O. Etard, N. Delcroix, B. Mazoyer, and M. Joliot. 2002. “Automated Anatomical Labeling of Activations in SPM Using a Macroscopic Anatomical Parcellation of the MNI MRI Single-Subject Brain.” NeuroImage 15 (1): 273–89. https://doi.org/10.1006/nimg.2001.0978.

{{BESAManualNav}}

Source Analysis 3D Imaging

2019-04-08T09:25:59Z

Jamie: /* Brain Atlas */

{{BESAInfobox
|title = Module information
|module = BESA Research Standard or higher
|version = 6.1 or higher
}}


== Overview ==

BESA Research features a set of new functions that provide 3D images that are displayed superimposed to the individual subject's anatomy. This chapter introduces these different images and describe their properties and applications.

The 3D images can be divided into three categories:

'''Volume images:'''

* '''The Multiple Source Beamformer (MSBF)''' is a tool for imaging brain activity. It is applied in the time-domain or time-frequency domain. The beamformer technique in time-frequency domain can image not only evoked, but also induced activity, which is not visible in time-domain averages of the data.
* '''Dynamic Imaging of Coherent Sources (DICS)''' can find coherence between any two pairs of voxels in the brain or between an external source and brain voxels. DICS requires time-frequency-transformed data and can find coherence for evoked and induced activity.

The following imaging methods provide an image of brain activity based on a distributed multiple source model:
* '''CLARA''' is an iterative application of LORETA images, focusing the obtained 3D image in each iteration step.
* '''LAURA '''uses a spatial weighting function that has the form of a local autoregressive function.
* '''LORETA''' has the 3D Laplacian operator implemented as spatial weighting prior.
* '''sLORETA''' is an unweighted minimum norm that is standardized by the resolution matrix.
* '''swLORETA '''is equivalent to sLORETA, except for an additional depth weighting.
* '''SSLOFO '''is an iterative application of standardized minimum norm images with consecutive shrinkage of the source space.
* A '''User-defined volume image''' allows to experiment with the different imaging techniques. It is possible to specify user-defined parameters for the family of distributed source images to create a new imaging technique.
* Bayesian source imaging: '''SESAME''' uses a semi-automated Bayesian approach to estimate the number of dipoles along with their parameters.

'''Surface image:'''

* The '''Surface Minimum Norm Image'''. If no individual MRI is available, the minimum norm image is displayed on a standard brain surface and computed for standard source locations. If available, an individual brain surface is used to construct the distributed source model and to image the brain activity.
* '''Cortical LORETA'''. Unlike classical LORETA, cortical LORETA is not computed in a 3D volume, but on the cortical surface.
* '''Cortical CLARA'''. Unlike classical CLARA, cortical CLARA is not computed in a 3D volume, but on the cortical surface.

'''Discrete model probing:'''

These images do not visualize source activity. Rather, they visualize properties of the currently applied discrete source model:
* The '''Multiple Source Probe Scan (MSPS)''' is a tool for the validation of a discrete multiple source model.
* The '''Source Sensitivity image''' displays the sensitivity of a selected source in the current discrete source model and is therefore data independent.

== Multiple Source Beamformer (MSBF) in the Time-frequency Domain ==

 
'''Short mathematical introduction'''

The BESA beamformer is a modified version of the linearly constrained minimum variance vector beamformer in the time-frequency domain as described in [https://dx.doi.org/10.1073/pnas.98.2.694 Gross et al., "Dynamic imaging of coherent sources: Studying neural interactions in the human brain", PNAS 98, 694-699, 2001]. It allows to image evoked and induced oscillatory activity in a user-defined time-frequency range, where time is taken relative to a triggered event.

The computation is based on a transformation of each channel's single trial data from the time domain into the time-frequency domain. This transformation is performed by the BESA Research Source Coherence module and leads to the complex spectral density Si (f,t), where i is the channel index and f and t denote frequency and time, respectively. Complex cross spectral density matrices C are computed for each trial:

<math>\mathrm{C}_{ij}\left( f,t \right) = \mathrm{S}_{i}\left( f,t \right) \cdot \mathrm{S}_{j}^{*}\left( f,t \right)</math>


The output power P of the beamformer for a specific brain region at location r is then computed by the following equation:

<math>\mathrm{P}\left( r \right) = \operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{-1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{-1}</math>


Here, Cr-1 is the inverse of the SVD-regularized average of Cij(f,t) over trials and the time-frequency range of interest; L is the leadfield matrix of the model containing a regional source at target location r and, optionally, additional sources whose interference with the target source is to be minimized; tr'[] is the trace of the [3×3] (MEG:[2×2]) submatrix of the bracketed expression that corresponds to the source at target location r.

In BESA Research, the output power P(r) is normalized with the output power in a reference time-frequency interval Pref(r). A value q ist defined as follows:

<math> \mathrm{q}\left( r \right) =
\begin{cases}
\sqrt{\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}(r)}} - 1 = \sqrt{\frac{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{\text{ref},r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}} - 1, & \text{for }\mathrm{P}(r) \geq \mathrm{P}_{\text{ref}}(r) \\

1 - \sqrt{\frac{\mathrm{P}_{\text{ref}}\left( r \right)}{\mathrm{P}\left( r \right)}} = 1 - \sqrt{\frac{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{\text{ref},r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}}, & \text{for }\mathrm{P}(r) < \mathrm{P}_{\text{ref}}(r)
\end{cases} </math>


Pref can be computed either from the corresponding frequency range in the baseline of the same condition (i.e. the beamformer images event-related power increase or decrease) or from the corresponding time-frequency range in a control condition (i.e. the beamformer images differences between two conditions). The beamformer image is constructed from values q(r) computed for all locations on a grid specified in the '''General Settings tab'''. For MEG data, the innermost grid points within a sphere of approx. 12% of the head diameter are assigned interpolated rather than calculated values).
q-values are shown in %, where where q[%] = q*100. Alternatively to the definition above, q can also be displayed in units of dB:

<math>\mathrm{q}\left\lbrack \text{dB} \right\rbrack = 10 \cdot \log_{10}\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}</math>


A beamformer operator is designed to pass signals from the brain region of interest r without attenuation, while minimizing interference from activity in all other brain regions. Traditional single-source beamformers are known to mislocalize sources if several brain regions have highly correlated activity. Therefore, the BESA beamformer extends the traditional single-source beamformer in order to implicitly suppress activity from possibly correlated brain regions. This is achieved by using a multiple source beamformer calculation that contains not only the leadfields of the source at the location of interest r, but also those of possibly interfering sources. As a default, BESA Research uses a bilateral beamformer, where specifically contributions from the homologue source in the opposite hemisphere are taken into account (the matrix L thus being of dimension N×6 for EEG and N×4 for MEG, respectively, where N is the number of sensors). This allows for imaging of highly correlated bilateral activity in the two hemispheres that commonly occurs during processing of external stimuli.

In addition, the beamformer computation can take into account possibly correlated sources at arbitrary locations that are specified in the current solution. This is achieved by adding their leadfield vectors to the matrix L in the equation above.

'''Applying the Beamformer'''

This chapter illustrates the usage of the BESA beamformer. The displayed figures are generated using the file ''''Examples/Learn-by-Simulations/AC-Coherence/AC-Osc20.foc'''' (see BESA Tutorial 6: "''Time-frequency analysis and Source coherence''").

'''Starting the beamformer from the time-frequency window'''

The BESA beamformer is applied in the time-frequency domain and therefore requires the Source Coherence module to be enabled. The time-frequency beamformer is especially useful to image in- or decrease of induced oscillatory activity. Induced activity cannot be observed in the averaged data, but shows up as enhanced averaged power in the TSE (Temporal-Spectral Evolution) plot. For instructions on how to initiate a beamformer computation in the time-frequency window, please refer to Chapter '''[[Source_Coherence_How_to...#How_to_Start_the_Beamformer_from_the_Time-Frequency_Window|How to Create Beamformer Images]]'''.

After the beamformer computation has been initiated in the time-frequency window, the source analysis window opens with an enlarged 3D image of the q-value computed with a '''bilateral beamformer'''. The result is superimposed onto the MR image assigned to the data set (individual or standard).

[[Image:SA 3Dimaging (5).gif]]

''Beamformer image after starting the computation in the Time-Frequency window. A bilateral pair of sources in the auditory cortex accounts for the highly correlated oscillatory induced activity. Only the bilateral beamformer manages to separate these activities; a traditional single-source beamformer would merge the two sources into one image maximum in the head center instead.''

'''Multiple source beamformer in the Source Analysis window'''

The 3D imaging display is part of the source analysis window. If you press the '''Restore''' button at the right end of the title bar of the 3D window, the window appears at the bottom right of the source analysis window. In the channel box, the averaged (evoked) data of the selected condition is shown. When a control condition was selected, its average is appended to the average of the target condition.

[[Image:SA 3Dimaging (6).gif]]

''Source Analysis window with beamformer image. The two sources have been added using the '''''Switch to''''' '''''Maximum''''' and '''''Add Source '''''toolbar buttons (see below). Source waveforms are computed from the displayed averaged data. Therefore, they do not represent the activity displayed in the beamformer image, which in this simulation example is induced (i.e. not phase-locked to the trigger)!''

When starting the beamformer from the time-frequency window, a bilateral beamformer scan is performed. In the source analysis window, the beamformer computation can be repeated taking into account possibly correlated sources that are specified in the current solution. Interfering activities generated by all sources in the current solution that are in the 'On' state are specifically suppressed ('''they enter the matrix L in the beamformer calculation''', see Chapter ''Short mathematical description'' above). The computation can be started from the '''Image''' menu or from the '''Image selector button''' dropdown menu. The '''Image''' menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window.

[[Image:SA 3Dimaging (7).gif]]

''Multiple source beamformer image calculated in the presence of a source in the left hemisphere. A '''single''' source scan has been performed. The source set in the current solution accounts for the left-hemispheric q-maximum in the data. Accordingly, the beamformer scan reveals only the as yet unmodeled additional activity in the right hemisphere (note the radiological convention in the 3D image display).''

The beamformer scan can be performed with a '''single''' or a '''bilateral''' source scan. The default scan type depends on the current solution:
* When the beamformer is started from the Time-Frequency window, the Source Analysis window opens with a new solution and a '''bilateral''' beamformer scan is performed.
* When the beamformer is started within the Source Analysis window, the default is
** a scan with a '''single''' source in addition to the sources in the current solution, if at least one source is active.
** a '''bilateral''' scan if no source in the current solution is active.

The default scan type is the multiple source beamformer. The non-default scan type can be enforced using the corresponding ''Volume Image / Beamformer'' entry in the '''Image''' menu.

'''Inserting Sources out of the Beamformer Image'''

The beamformer image can be used to add sources to the current solution. A simple double-click anywhere in the 2D- or 3D-view will generate a non-oriented regional source at the corresponding location. However, a better and easier way to create sources at image maxima and minima is to use the toolbar buttons '''Switch to Maximum''' [[Image:SA 3Dimaging (8).gif]] and '''Add Source''' [[Image:SA 3Dimaging (9).gif]].

Use the '''Switch to Maximum''' button to place the red crosshair of the 3D window onto a local image maximum or minimum. Hitting the '''Add Source''' button creates a regional source at the location of the crosshair and therefore ensures the exact placement of the source at the image extremum. Moreover, the '''Add Source''' button generates an oriented regional source. BESA Research automatically estimates the source orientation that contributes most to the power in the target time-frequency interval (or the reference time-frequency interval, if its power is larger than that in the target interval). The accuracy of this orientation estimate depends largely on the noise content of the data. The smaller the signal-to-noise ratio of the data, the lower is the accuracy of the orientation estimate. '''This feature allows to use the beamformer as a tool to create a source montage for source coherence analysis, where it is of advantage to work with oriented sources'''.

'''Notes:'''

* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image '''menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the''' Image''' menu.
* For scaling options, use the [[Image:SA 3Dimaging (10).gif]] and [[Image:SA 3Dimaging (11).gif]] '''Image Scale toolbar''' buttons.
* Parameters used for the beamformer calculations can be set in the '''Standard Volumes''' of the ''Image Settings dialog box.''

== Dynamic Imaging of Coherent Sources (DICS) ==

 
'''Short mathematical introduction'''

Dynamic Imaging of Coherent Sources (DICS) is a sophisticated method for imaging cortico-cortical coherence in the brain, or coherence between an external reference (e.g. EMG channel) and cortical structures. DICS can be applied to localize evoked as well as induced coherent cortical activity in a user-defined time-frequency range.

DICS was implemented in BESA closely following [https://dx.doi.org/10.1073/pnas.98.2.694 Gross et al., "Dynamic imaging of coherent sources: Studying neural interactions in the human brain", PNAS 98, 694-699, 2001].

The computation is based on a transformation of each channel's single trial data from the time domain into the frequency domain. This transformation is performed by the BESA Research Coherence module and results in the complex spectral density matrix that is used for constructing the spatial filter similar to beamforming.

DICS computation yields a 3-D image, each voxel being assigned a coherence value. Coherence values can be described as a neural activity index and do not have a unit. The neural activity index contrasts coherence in a target time-frequency bin with coherence of the same time-frequency bin in a baseline.

'''DICS for cortico-cortical coherence is computed as follows:'''

Let L(r) be the leadfield in voxel r in the brain and C the complex cross-spectral density matrix. The spatial filter W(r) for the voxel r in the head is defined as follows:

<math>W\left( r \right) = \left\lbrack L^{T}\left( r \right) \cdot C^{- 1} \cdot L\left( r \right) \right\rbrack^{- 1} \cdot L^{T}(r) \cdot C^{- 1}</math>


The cross-spectrum between two locations (voxels) r1 and r2 in the head are calculated with the following equation:

<math>C_{s}\left( r_{1},r_{2} \right) = W\left( r_{1} \right) \cdot C \cdot W^{*T}\left( r_{2} \right),</math>


where <nowiki>*T</nowiki> means the transposed complex conjugate of a matrix. The cross-spectral density can then be calculated from the cross spectrum as follows:

<math>c_{s}\left( r_{1},r_{2} \right) = \lambda_{1}\left\{ C_{s}\left( r_{1},r_{2} \right) \right\},</math>


where λ1{} indicates the largest singular value of the cross spectrum. Once the cross spectral density is estimated, the connectivity¹(CON) between the two brain regions r1 and r2 are calculated as follows:

<math>\text{CON}\left( r_{1},r_{2} \right) = \frac{c_{s}^{\text{sig}}\left( r_{1},r_{2} \right) - c_{s}^{\text{bl}}(r_{1},r_{2})}{c_{s}^{\text{sig}}\left( r_{1},r_{2} \right) + c_{s}^{\text{bl}}(r_{1},r_{2})},</math>


where cssig is the cross-spectral density for the signal of interest between the two brain regions r1 and r2, and csbl is the corresponding cross spectral density for the baseline or the control condition, respectively. In the case DICS is computed with a cortical reference, r1 is the reference region (voxel) and remains constant while r2 scans all the grid points within the brain sequentially. In that way, the connectivity between the reference brain region and all other brain regions is estimated. The value of CON(r1, r2) falls in the interval [-1 1]. If the cross-spectral density for the baseline is 0 the connectivity value will be 1. If the cross-spectral density for the signal is 0 the connectivity value will be -1.

¹ Here, the term connectivity is used rather than coherence, as strictly speaking the coherence equation is defined slightly differently. For simplicity reasons the rest of the tutorial uses the term coherence.

'''DICS for cortico-muscular coherence is computed as follows:'''

When using an external reference, the equation for coherence calculation is slightly different compared to the equation for cortico-cortical coherence. First of all, the cross-spectral density matrix is not only computed for the MEG/EEG channels, but the external reference channel is added. This resulting matrix is Call. In this case, the cross-spectral density between the reference signal and all other MEG/EEG

channels is called cref. It is only one column of Call. Hence, the cross-spectrum in voxel r is calculated with the following equation:

<math>C_{s}\left( r \right) = W\left( r \right) \cdot c_{\text{ref}}</math>


and the corresponding cross-spectral density is calculated as the sum of squares of Cs:

<math>c_{s}\left( r \right) = \sum_{i = 1}^{n}{C_{s}\left( r \right)_{i}^{2}},</math>


where n is 2 for MEG and 3 for EEG. This equation can also be described as the squared Euclidean norm of the cross-spectrum:

<math>c_{s}\left( r \right) = \left\| C_{s} \right\|^{2},</math>


The power in voxel r is calculated as in the cortico-cortical case:

<math>p\left( r \right) = \lambda_{1}\left\{ C_{s}(r,r) \right\}.</math>


At last, coherence between the external reference and cortical activity is calculated with the equation:

<math>\text{CON}\left( r \right) = \frac{c_{s}(r)}{p\left( r \right) \cdot C_{\text{all}}(k,k)},</math>


where Call(k, k) is the (k,k)-th diagonal element of the matrix Call.

DICS is particularly useful, if coherence is to be calculated without an a-priory source model (in contrast to source coherence based on pre-defined source montages). However, the recommended analysis strategy for DICS is to use a brain source as a starting point for coherence calculation that is known to contribute to the EEG/MEG signal of interest. For example, one might first run a beamformer on the time-frequency range of interest and use the voxel with the strongest oscillatory activity as a starting point for DICS. The resulting coherence image will again lead to several maxima (ordered by magnitude), which in turn can serve as starting points for DICS calculation. This way, it is possible to detect even weak sources that show coherent activity in the given time-frequency range.

The other significant application for DICS is estimating coherence between an external source and voxels in the brain. For example, an external source can be muscle activity recoded by an electrode placed over the according peripheral region. This way, the direct relationship between muscle activity and brain activation can be measured.

'''Starting DICS computation from the Time-Frequency Window'''

DICS is particularly useful, if coherence in a user-defined time-frequency bin (evoked or induced) is to be calculated between any two brain regions or between an external reference and the brain. DICS runs only on time-frequency decomposed data, so time-frequency analysis needs to be run before starting DICS computation.

To start the DICS computation, left-drag a window over a selected time-frequency bin in the Time-Frequency Window. Right-click and select “Image”. A dialogue will open (see fig. 1) prompting you to specify time and frequency settings as well as the baseline period. It is recommended to use a baseline period of equal length as the data period of interest. Make sure to select “DICS” in the top row and press “'''Go'''”.

[[Image:SA 3Dimaging (21).gif|450px|thumb|c|none|Fig. 1: Time and frequency settings for DICS and MSBF]]

Next, a window will appear allowing you to specify the reference source for coherence calculation (see fig. 2). It is possible to select a channel (e.g. EMG) or a brain source. If a brain source is chosen and no source analysis was computed beforehand, the option “Use current cross-hair position” must be chosen. In case discrete source analysis was computed previously, the selected source can be chosen as the reference for DICS. Please note that DICS can be re-computed with any cross-hair or source position at a later stage.

[[Image:SA 3Dimaging (1).jpg|400px|thumb|c|none|Fig. 2: Possible options for choosing the reference]]

Confirming with “'''OK'''” will start computation of coherence between the selected channel/voxel and all other brain voxels. In case DICS is computed for a reference source in the brain, it can be advantageous to run a beamforming analysis in the selected time-frequency window first and use one of the beamforming maxima as reference for DICS. Fig. 3 shows an example for DICS calculation.

[[Image:SA 3Dimaging (22).gif|500px|thumb|c|none|Fig. 3: Coherence between left-hemispheric auditory areas and the selected voxel in the right auditory cortex.]]

Coherence values range between -1 and 1. If coherence in the signal is much larger than coherence in the baseline (control condition) then the DICS value is going to approach 1. Contrary, if coherence in the baseline is much larger than coherence in the signal, then the DICS value is going to approach -1. At last, if coherence in the signal is equal to coherence in the baseline, then the DICS value is 0.

In case DICS is to be re-computed with a different reference, simply mark the desired reference position by placing the cross-hair in the anatomical view and select “DICS” in the middle panel of the source analysis window (see Fig. 4). In case an external reference is to be selected, click on “DICS” in the middle panel to bring up the DICS dialogue (see. Fig. 2) and select the desired channel. Please note that DICS computation will only be available after running time-frequency analysis.

[[Image:SA 3Dimaging (23).gif|700px|thumb|c|none|Fig. 4: Integration of DICS in the Source Analysis window]]

== Multiple Source Beamformer (MSBF) in the Time Domain ==
''(requires Besa Research 7.0 or higher)''

===Short mathematical introduction===

Beamforming approach can be also applied in the time domain data. This approach was introduced as linearly constrained minimum variance (LCMV) beamformer (Van Veen et al., 1997). It allows to image evoked activity in a user-defined time range, where time is taken relative to a triggered event, and to estimate source waveforms using the calculated spatial weight at locations of interest. For an implementation of the beamformer in the time domain, data covariance matrices are required, while complex cross spectral density matrices are used for the beamformer approaches in the time-frequency domain as described in the ''[[Source_Analysis_3D_Imaging#Multiple_Source_Beamformer_.28MSBF.29_in_the_Time-frequency_Domain|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section.

The bilateral beamformer introduced in the ''[[Source_Analysis_3D_Imaging#Multiple_Source_Beamformer_.28MSBF.29_in_the_Time-frequency_Domain|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section is also implemented for the time-domain beamformer to take into account contributions from the homologue source in the opposite. This allows for imaging of highly correlated bilateral activity in the two hemispheres that commonly occurs during processing of external stimuli. In addition, the beamformer computation can take into account possibly correlated sources at arbitrary locations.
The beamformer spatial weight W(r) for the voxel r in the brain is defined as follows (Van Veen et al., 1997):

[[File:MSBF1.png]]

where '''C-1''' is the inversed regularized average of covariance matrix over trials, '''L''' is the leadfield matrix of the model containing a regional source at target location r and optionally
additional sources whose interference with the target source is to be minimized. The beamformer spatial weight '''W'''(r) can be applied to the measured data to estimate source
waveform at a location r (beamformer virtual sensor):

[[File:MSBF2.png]]

where '''S'''(r,t) represents the estimated source waveform and '''M'''(t) represents measured EEG or MEG signals.
The output power P of the beamformer for a specific brain region at location r is computed by the following equation:

[[File:MSBF3.png]]

where tr’[ ] is the trace of the [3×3] (MEG: [2×2]) submatrix of the bracketed expression that corresponds to the source at target location r.
Beamformer can suppress noise sources that are correlated across sensors. However, uncorrelated noise will be amplified in a spatially non-uniform manner, with increasing
distortion with increasing distance from the sensors (Van Veen et al., 1997; Sekihara et al., 2001). For this reason, estimated source power should be normalized by a noise power.
In BESA Research, the output power P(r) is normalized with the output power in a baseline interval or with the output power of a uncorrelated noise: P(r) / Pref (r).
The time-domain beamformer image is constructed from values q(r) computed for all locations on a grid specified in the '''General Settings''' tab. A value q(r) is defined as described in
the ''[[Source_Analysis_3D_Imaging#Multiple_Source_Beamformer_.28MSBF.29_in_the_Time-frequency_Domain|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section with data covariance matrices instead of cross-spectral density matrices.

===Applying the Beamformer===

This chapter illustrates the usage of the BESA beamformer in the time domain. The displayed figures are generated using the file ‘Examples/ERP-Auditory-Intensity/S1.cnt’.

'''Starting the time-domain beamformer from the Average tab of the Paradigm dialog box'''

The time-domain beamformer is needed data covariance matrices and therefore requires the ERP module to be enabled. After the beamformer computation has been initiated in the
'''Average tab of the Paradigm dialog box''', the source analysis window opens with an enlarged 3D image of the q-value computed with a bilateral beamformer. The result is
superimposed onto the MR image assigned to the data set (individual or standard).

[[File:MSBF44.png|500px|thumb|c|none|Beamformer image for auditory evoked data after starting the computation in the '''Average tab of the Paradigm dialog box'''. The bilateral beamformer manages to separate the activities in auditory areas, while a traditional single-source beamformer would merge the two sources into one image maximum in the head center instead.]]

'''Multiple-source beamformer in the Source Analysis window'''

The 3D imaging display is part of the source analysis window. In the Channel box, the averaged (evoked) data of the selected condition is shown. Selected covariance intervals in
the ERP module can be checked in the Channel box. The red, gray, and blue rectangles indicate signal, baseline, and common interval, respectively.

[[File:MSBF55.png|700px|thumb|c|none|Source Analysis window with beamformer image. The two beamformer virtual sensors have been added using the Switch to Maximum and Add Source toolbar buttons (see below).
Source waveforms are computed using the beamformer spatial weights and the displayed averaged data (the noise normalized weights (5% noise) option was used to compute the
beamformer image).]]

When starting the beamformer from the '''Average tab of the Paradigm dialog box''', the bilateral beamformer scan is performed. In the source analysis window, the beamformer computation can be repeated taking into account possibly correlated sources that are specified in the current solution. Interfering activities generated by all sources in the current solution that are in the 'On' state are specifically suppressed (they enter the leadfield matrix L in the beamformer calculation). The computation can be started from the '''Image''' menu or from the Image selector button [[File:MSBF_Button.png|22px|Image: 22 pixels]] dropdown menu. The Image menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window.

[[File:MSBF66.png|700px|thumb|c|none|Multiple-source beamformer image calculated in the presence of a source in the left hemisphere. A single-source scan has been performed instead of a bilateral beamforemr. The source set in the current solution accounts for the left-hemispheric q-maximum in the data. Accordingly, the beamformer scan reveals only the as yet unmodeled additional activity in the right hemisphere (note the radiological convention in the 3D image display). The source waveform of the beamformer virtual sensor in the left hemisphere is not shown since the location (blue square in the figure) is not considered for the multiple-source beamformer.]]

The beamformer scan can be performed with a single or a bilateral source scan. The default scan type depends on the current solution:
When the beamformer is started from the '''Average tab of the Paradigm dialog box''' the Source Analysis window opens with a new solution and a bilateral beamformer scan is
performed.
When the beamformer is started within the Source Analysis window, the default is:

* a scan with a single source in addition to the sources in the current solution, if at least one source is active.
* a bilateral scan if no source in the current solution is active.
* a scan with a single source when scalar-type beamformer is selected in the '''beamformer option dialog box'''.

The default scan type is the multiple source beamformer. The non-default scan type can be enforced using the corresponding Volume Image / Beamformer entry in the Image main
menu or in the beamformer option dialog box (only for the time-domain beamformer).

===Inserting Sources as Beamformer Virtual Sensor out of the Beamformer Image===

This is similar to the inserting sources out of the beamformer image in Multiple Source Beamformer (MSBF) in the Time-frequency Domain section.
The beamformer image can be used to add beamformer virtual sensors to the current solution. A simple double-click anywhere in the 3D view (not in the 2D view) will generate a
source at the corresponding location. A better and easier way to create sources at image maxima and minima is to use the toolbar buttons '''Switch to Maximum''' [[Image:SA 3Dimaging (8).gif]] and '''Add Source''' [[Image:SA 3Dimaging (9).gif]].

This feature allows to use the beamformer as a tool to create a source montage for '''source coherence''' analysis. A source montage file (*.mtg) for beamformer virtual sensors can
be saved using File \ Save Source Montage As… entry.

The time-domain beamformer image can be also used to add regional or dipole sources to the current solution. Press '''N''' key when there is no source in the current source array or
there is more than one beamformer virtual sensor. To create a new source array for beamformer virtual sensor, press '''N''' key when there is more than one regional or dipole source in
the current source array.

===Notes===

* You can hide or re-display the last computed image by selecting ''Hide Image'' entry in the '''Image''' menu.
* The current image can be exported to ASCII, ANALYZE, or BrainVoyager (vmp) format from the '''Image''' menu.
* For scaling options, use [[Image:SA 3Dimaging (10).gif]] and [[Image:SA 3Dimaging (11).gif]] '''Image Scale toolbar''' buttons.
* Parameters used for the beamformer calculations can be set in the '''Standard Volume tab of the Image Settings dialog box'''.
* Note that Model, Residual, Order, and Residual variance are not shown for the beamformer virtual sensor type sources.

===References===

* Sekihara, K., Nagarajan, S. S., Poeppel, D., Marantz, A., & Miyashita, Y. (2001). Reconstructing spatio-temporal activities of neural sources using an MEG vector beamformer technique. IEEE Transactions on Biomedical Engineering, 48(7), 760–771.

* Van Veen, B. D., Van Drongelen, W., Yuchtman, M., & Suzuki, A. (1997). Localization of brain electrical activity via linearly constrained minimum variance spatial filtering. IEEE Transactions on Biomedical Engineering, 44(9), 867–880

== CLARA ==

CLARA ('Classical LORETA Analysis Recursively Applied') is an iterative application of weighted LORETA images with a reduced source space in each iteration.

In an initialization step, a LORETA image is calculated. Then in each iteration the following steps are performed:

# The obtained image is spatially smoothed (this step is left out in the first iteration).
# All grid points with amplitudes below a threshold of 1% of the maximum activity are set to zero, thus being effectively eliminated from the source space in the following step.
# The resulting image defines a spatial weighting term (for each voxel the corresponding image amplitude).
# A LORETA image is computed with an additional spatial weighting term for each voxel as computed in step 3. By the default settings in BESA Research, the regularization values used in the iteration steps are slightly higher than that of the initialization LORETA image.

The procedure stops after 2 iterations, and the image computed in the last iteration is displayed. Please note that you can change all parameters by creating a user-defined volume image.

The advantage of CLARA over non-focusing distributed imaging methods is visualized by the figure below. Both images are computed from the N100 response in an auditory oddball experiment (file '''Oddball.fsg''' in subfolder ''fMRI+EEG-RT-Experiment'' of the ''Examples'' folder). The CLARA image is much more focal than the sLORETA image, making it easier to determine the location of the image maxima.

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (24).gif|thumb|350px|sLORETA image]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (25).gif|thumb|350px|CLARA image]] </li>
</ul></div>

'''Notes:'''

* Starting CLARA: CLARA can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter ''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]'' for important information on regularization of distributed inverses.

== LAURA ==

LAURA (Local Auto Regressive Average) belongs to the distributed inverse method of the family of weighted minimum norm methods ([https://doi.org/10.1023/A:1012944913650 Grave de Peralta Menendeza et al., "Noninvasive Localization of Electromagnetic Epileptic Activity. I. Method Descriptions and Simulations", BrainTopography 14(2), 131-137, 2001]). LAURA uses a spatial weighting function that includes depth weighting and that term has the form of a local autoregressive function.

The source activity is estimated by applying the general formula for a weighted minimum norm:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T}\left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings.''

In LAURA, V contains both a depth weighting term W and a representation of a local autoregressive function A. V is computed as:

<math>\mathrm{V} = \left( \mathrm{U}^{T} \cdot \mathrm{U} \right)^{-1}</math>


Where

<math>\mathrm{U} = \left( \mathrm{W} \cdot \mathrm{A} \right) \otimes \mathrm{I}_{3}</math>


Here, <math>\otimes</math> denotes the Kronecker product. I3 is the [3×3] identity matrix. W is an [s×s] diagonal matrix (with s the number of source locations on the grid), where each diagonal element is the inverse of the maximum singular value of the corresponding regional source's leadfields. The formula for the diagonal components Aii and the off-diagonal components Aik are as follows:

<math>\mathrm{A}_{ii} = \frac{26}{\mathrm{N}_{i}}\sum_{k \subset V_{i}}^{}\frac{1}{\mathrm{d}_{ik}^{2}}</math>


<math>
\mathrm{A}_{ik} =
\begin{cases}
- 1/\operatorname{dist}\left( i,k \right)^{2}, & \text{if } k \subset V_{i} \\
0, & \text{otherwise}
\end{cases}
</math>


Here, Vi is the vicinity around grid point i that includes the 26 direct neighbors.

The LAURA image in BESA Research displays the norm of the 3 components of S at each location r. Using the menu function ''Image / Export Image As... ''you have the option to save this norm of S or alternatively all components separately to disk.

'''Notes:'''

* '''Grid spacing:''' Due to memory limitations, LAURA images require a grid spacing of 7 mm or more.
* '''Computation time:''' Computation speed during the first LAURA image calculation depends on the grid spacing (computation is faster with larger grid spacing). After the first computation of a LAURA image, a '''*.laura''' file is stored in the data folder, containing intermediate results of the LAURA inverse. This file is used during all subsequent LAURA image computations. Thereby, the time needed to obtain the image is substantially reduced.
* '''MEG:''' In the case of MEG data, an additional constraint is implemented in the LAURA algorithm that prevents solutions from containing radial source currents (compare Pascual-Marqui, ISBET Newsletter 1995, 22-29). In MEG, an additional source space regularization is necessary in the inverse matrix operation required compute V
* '''Starting LAURA:''' LAURA can be started from the''' Image''' menu or from the '''Image Selection''' button.
* '''Regularization:''' Please refer to Chapter'' “Regularization of distributed volume images” ''for important information on regularization of distributed inverses.

== LORETA ==

LORETA ("Low Resolution Electromagnetic Tomography") is a distributed inverse method of the family of ''weighted minimum norm'' methods. LORETA was suggested by R.D. Pascual-Marqui (International Journal of Psychophysiology. 1994, 18:49-65). LORETA is characterized by a smoothness constraint, represented by a discrete 3D Laplacian.

The source activity is estimated by applying the general formula for a weighted minimum norm:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T}\left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings.''

In LORETA, V contains both a depth weighting term and a representation of the 3D Laplacian matrix. V is computed as:

<math>\mathrm{V} = \left( \mathrm{U}^{T} \cdot \mathrm{U} \right)^{- 1}</math>


where

<math>\mathrm{U} = \left( \mathrm{W} \cdot \mathrm{A} \right) \otimes \mathrm{I}_{3}</math>


Here, <math>\otimes</math> denotes the Kronecker product. I3 is the [3x3] identity matrix. W is an [sxs] diagonal matrix (with s the number of source locations on the grid), where each diagonal element is the inverse of the maximum singular value of the corresponding regional source's leadfields. A contains the 3D Laplacian and is computed as

<math>\mathrm{A} = \mathrm{Y} - \mathrm{I}_{s}</math>


with Is the [sxs] identity matrix, where s is the number of sources (= three times the number of grid points) and

<math>\mathrm{Y} = \frac{1}{2}\left\{ \mathrm{I}_{s} + \left\lbrack \operatorname{diag}\left( \mathrm{Z} \cdot \left\lbrack 111 \ldots 1 \right\rbrack^{T} \right) \right\rbrack^{- 1} \right\} \cdot \mathrm{Z}</math>


where

<math>
\mathrm{Z}_{ik} =
\begin{cases}
1/6, & \text{if } \operatorname{dist}\left( i,k \right) = 1 \text{ grid point} \\
0, & \text{otherwise}
\end{cases}
</math>


The LORETA image in BESA Research displays the norm of the 3 components of S at each location r. Using the menu function ''Image / Export Image As... ''you have the option to save this norm of S or alternatively all components separately to disk.

'''Notes:'''
* '''Grid spacing:''' Due to memory limitations, LORETA images require a grid spacing of 5 mm or more.
* '''Computation time:''' Computation speed during the first LORETA image calculation depends on the grid spacing (computation is faster with larger grid spacing). After the first computation of a LORETA image, a '''<nowiki>*.loreta</nowiki>''' file is stored in the data folder, containing intermediate results of the LORETA inverse. This file is used during all subsequent LORETA image computations. Thereby, the time needed to obtain the image is substantially reduced.
* '''MEG''': In the case of MEG data, an additional constraint is implemented in the LORETA algorithm that prevents solutions from containing radial source currents (Pascual-Marqui, ISBET Newsletter 1995, 22-29). In MEG, an additional source space regularization is necessary in the inverse matrix operation required compute V.
* '''Starting LORETA:''' LORETA can be started from the''' Image''' menu or from the '''Image Selection '''button.
* '''Regularization:''' Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed source models.

== sLORETA ==

This distributed inverse method consists of a ''standardized, unweighted minimum norm''. The method was originally suggested by R.D. Pascual-Marqui (Methods & Findings in Experimental & Clinical Pharmacology 2002, 24D:5-12) Starting point is an unweighted minimum norm computation:

<math>\mathrm{S}_{\text{MN}}\left( t \right) = \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings''.

This minimum norm estimate is now standardized to produce the sLORETA activity at a certain brain location r:

<math>\mathrm{S}_{\text{sLORETA}, r} = \mathrm{R}_{rr}^{-1/2} \cdot \mathrm{S}_{\text{MN},r}</math>


SsMN,r is the [3x1] (MEG: [2x1]) minimum norm estimate of the 3 (MEG: 2) dipoles at location r. Rrr is the [3x3] (MEG: [2x2]) diagonal block of the resolution matrix R that corresponds to the source components at the target location r. The resolution matrix is defined as:

<math>\mathrm{R} = \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{L}^{T} + \lambda \cdot \mathrm{I} \right)^{-1} \cdot \mathrm{L}</math>


The sLORETA image in BESA Research displays the norm of SsLORETA, r at each location r. Using the menu function ''Image / Export Image As...'' you have the option to save this norm of SsLORETA, r or alternatively all components separately to disk.

'''Notes:'''

* sLORETA can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter [[#Regularization_of_distributed_volume_images|''Regularization of distributed volume images'']] for important information on regularization of distributed inverses.

== swLORETA ==

This distributed inverse method is a ''standardized, depth-weighted minimum norm'' (E. Palmero-Soler et al 2007 Phys. Med. Biol. 52 1783-1800). It differs from sLORETA only by an additional depth weighting.

Starting point is a depth-weighted minimum norm computation:

<math>\mathrm{S}_{\text{MN}}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings''.

V is the diagonal depth weighting matrix. For s grid locations, V is of dimension [3s x 3s] (MEG: [2s x 2s]). Each diagonal element of V is the inverse of the first singular value of the leadfield of the corresponding regional source. Hence, the first 3 (MEG: 2) diagonal elements equal the inverse of the largest eigenvalue of the leadfield matrix of regional source 1, and so on.

This minimum norm estimate is now standardized to produce the swLORETA activity at a certain brain location r:

<math>\mathrm{S}_{\text{swLORETA},r} = \mathrm{R}_{rr}^{-1/2} \cdot \mathrm{S}_{\text{MN},r}</math>


SsMN,r is the [3x1] (MEG: [2x1]) depth-weighted minimum norm estimate of the regional source at location r. Rrr is the [3x3] (MEG: [2x2]) diagonal block of the resolution matrix R that corresponds to the source components at the target location r. The resolution matrix is defined as:

<math>\mathrm{R} = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} + \lambda \cdot \mathrm{I} \right)^{-1} \cdot \mathrm{L}</math>


The swLORETA image in BESA Research displays the norm of SswLORETA, r at each location r. Using the menu function ''Image / Export Image As...'' you have the option to save this norm of SswLORETA, r or alternatively all components separately to disk.

'''Notes:'''

* sLORETA can be started from the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== sSLOFO ==

SSLOFO (standardized shrinking LORETA-FOCUSS) is an iterative application of weighted distributed source images with a reduced source space in each iteration ([https://dx.doi.org/10.1109/TBME.2005.855720 Liu et al., "Standardized shrinking LORETA-FOCUSS (SSLOFO): a new algorithm for spatio-temporal EEG source reconstruction", IEEE Transactions on Biomedical Engineering 52(10), 1681-1691, 2005]).

In an initialization step, an [[#sLORETA | sLORETA]] image is calculated. Then in each iteration the following steps are performed:

# A weighted minimum norm solution is computed according to the formula <math display="inline">\mathrm{S} = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}</math> . Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D is the data at the time point under consideration. V is a diagonal spatial weighting matrix that is computed in the previous iteration step. In the first iteration, the elements of V contain the magnitudes of the initially computed LORETA image.
# Standardization of this weighted minimum norm image is performed with the resolution matrix as in [[#sLORETA | sLORETA]].
# The obtained standardized weighted minimum norm image is being smoothed to get Ssmooth.
# All voxels with amplitudes below a threshold of 1% of the maximum activity get a weight of zero in the next iteration step, thus being effectively eliminated from the source space in the next iteration step.
# For all other voxels, compute the elements of the spatial weighting matrix V to be used in the next iteration as follows: <math display="inline">\mathrm{V}_{ii,\text{next iteration}} = \frac{1}{\left\| \mathrm{L}_{i} \right\|} \cdot \mathrm{S}_{ii,\text{smooth}} \cdot \mathrm{V}_{ii,\text{current iteration}}</math>



The procedure stops after 3 iterations. Please note that you can change all parameters by creating a [[#User-Defined Volume Image | user-defined volume image]].

'''Notes:'''
* '''Starting sSLOFO''': sSLOFO can be started from the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter ''[[#Regularization of distributed volume images | Regularization of distributed volume images]]'' for important information on regularization of distributed inverses.

== User-Defined Volume Image ==

In addition to the predefined 3D imaging methods in BESA Research, it is possible to create user-defined imaging methods based on the general formula for distributed inverses:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. Custom-defined parameters are:* The spatial weighting matrix V: This may include depth weighting, image weighting, or cross-voxel weighting with a 3D Laplacian (as in LORETA) or an autoregressive function (as in LAURA).

* Regularization: The term in parentheses is generally regularized. Note that regularization has a strong effect on the obtained results. Please refer to chapter “''Regularization of Distributed Volume Images” ''for more information.
* Standardization: Optionally, the result of the distributed inverse can be standardized with the resolution matrix (as in sLORETA).
* Iterations: Inverse computations can be applied iteratively. Each iteration is weighted with the image obtained in the previous iteration.

All parameters for the user-defined volume image are specified in the User-Defined Volume Tab of the Image Settings dialog box. Please refer to chapter “''User-Defined Volume Tab”'' for details.

'''Notes:'''
* Starting the user-defined volume image: the image calculation can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== Regularization of distributed volume images ==

Distributed source images require the inversion of a term of the form L V LT. This term is generally regularized before its inversion. In BESA Research, selection can be made between two different regularization approaches (parameters are defined in the ''Image Settings dialog box''):

* '''Tikhonov regularization''': In Tikhonov regularization, the term L V LT is inverted as (L V LT +λ I)-1. Here, l is the regularization constant, and I is the identity matrix.
* One way of determining the optimum regularization constant is by minimizing the ''generalized cross'' ''validation error'' (CVE).
* Alternatively, the regularization constant can be specified manually as a percentage of the trace of the matrix L V LT.
* '''TSVD''': In the truncated singular value decomposition (TSVD) approach, an SVD decomposition of L V LT is computed as  L V LT = U S UT, where the diagonal matrix S contains the singular values. All singular values smaller than the specified percentage of the maximum singular values are set to zero. The inverse is computed as U S-1 UT, where the diagonal elements of S-1 are the inverse of the corresponding non-zero diagonal elements of S.

Regularization has a critical effect on the obtained distributed source images. The results may differ completely with different choices of the regularization parameter (see examples below). Therefore, it is important to evaluate the generated image critically with respect to the regularization constant, and to keep in mind the uncertainties resulting from this fact when interpreting the results. The default setting in BESA Research is a TSVD regularization with a 0.03% threshold. However, this value might need to be adjusted to the specific data set at hand.

The following example illustrates the influence of the regularization parameter on the obtained images. The data used here is condition '''St-Cor of dataset Examples \ TFC-Error-Related-Negativity \ Correct+Error.fsg''' at 176 ms following the visual stimulus. Discrete dipole analysis reveals the main activity in the left and right lateral visual cortex at this latency.

[[Image:SA 3Dimaging (42).gif]]

''Discrete source model at 176 ms: Main activity in the left and right lateral visual cortex, no visual midline activity.''

LORETA images computed at this latency depend critically on the choice of the regularization constant. The following 3D images are created with TSVD regularization with SVD cutoffs of 0.1%, 0.005%, and 0.0001%, respectively. The volume grid size was 9 mm. The example demonstrates the dramatic effect of regularization and demonstrates the typical tradeoff between too strong regularization (leading to too smeared 3D images that tend to show blurred maxima) and too small regularization (resulting in too superficial 3D images with multiple maxima).

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (43).gif|thumb|350px|'''SVD cutoff 0.1%''': Regularization too strong. No separation between sources, mislocalization towards the middle of the brain.]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (44).gif|thumb|350px|'''SVD cutoff 0.005%''': Appropriate regularization. Separation of the bilateral activities. Location in agreement with the discrete multiple source model.]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (45).gif|thumb|350px|'''SVD cutoff 0.0001%''': Too small regularization. Mislocalization, too superficial 3D image. ]] </li>
</ul></div>

The automatic determination of the regularization constant using the CVE approach does not necessarily result in the optimum regularization parameter either. In this example, the unscaled CVE approach rather resembles the TSVD image with a cutoff of 0.0001%, i.e. regularization is too small. Therefore, it is advisable to compare different settings of the regularization parameter and make the final choice based on the above-mentioned considerations.

== Cortical LORETA ==

Cortical LORETA is principally the same technique as LORETA, however, Cortical LORETA is not computed in a 3D volume, but on the cortical surface.

The cortical reconstruction in BESA Research fed from BESA MRI is a closed 2D surface with no boundaries and a very close approximation of the actual cortical form. It consists of an irregular triangulated grid.

The Laplace operator that is used for identifying a smooth solution in a three-dimensional space is exchanged with a Laplace operator that runs on the two-dimensional cortical surface.

There is a wide variety of 2D Laplace operators with different characteristics. The general form of the discrete Laplace operator is

<math>\Delta f\left( p_{i} \right) = \frac{1}{d_{i}}\sum_{j \in N(i)}^{}{w_{ij}\left\lbrack f\left( p_{i} \right) - f\left( p_{j} \right) \right\rbrack},</math>


where '''pi''' is the '''i-th''' node of the triangular mesh, '''f(pi) '''is the value of a function f defined on the cortical mesh at the node '''pi''', '''wij''' is the weight for the connection between the nodes '''pi''' and '''pj''' and '''di''' is a normalization factor for the '''i-th''' row of the operator. Furthermore, '''N(i)''' is the set of indices corresponding to the direct (also called "1-ring") neighbors of '''pi'''.

BESA offers the choice of three Laplace operators with slightly different characteristics.

* '''Unweighted Graph Laplacian''': This is the simplest operator. It takes into account only the adjacency of the nodes and not the geometry of the mesh:

<math>
w_{ij} =
\begin{cases}
1, & \text{if } p_{i} \text{ and } p_{j} \text{ are connected by an edge} \\
0, & \text{otherwise}
\end{cases}
</math>

<math>d_{i} = 1</math>


[[Image:SA 3Dimaging (4).jpg |450px]]

* '''Weighted Graph Laplacian:''' This operator is similar to the unweighted graph Laplacian but with different weights for the different connections. The connections between nearby nodes get larger weights than the connections between farther nodes:

<math>w_{ij} = \frac{1}{\operatorname{dist}\left( p_{i},p_{j} \right)}</math>

<math>d_{i} = \sum_{j \in N(i)}^{} {\operatorname{dist}\left(p_{i}, p_{j} \right)}</math>


where '''dist''' ('''pi''' , '''pj''') is the distance between the nodes '''pi '''and '''pj'''.

[[Image:SA 3Dimaging (6).jpg|450px]]

* '''Geometric Laplacian with mixed area weights''': This operator takes into account the angles in the corresponding triangles into account as well as the area around the nodes in order to determine the connection weights:

<math>w_{ij} = \frac{\cot\left( \alpha_{ij} \right) + \cot\left( \beta_{ij} \right)}{2}</math>

<math>d_{i} = A_{\text{mixed}}</math>


where '''αij''' and '''βij''' denote the two angles opposite to the edge ('''i , j''') and '''Amixed '''is either the Voronoi area, or 1/2 of the triangle area or 1/4 of the triangle area depending on the type of the triangle.

[[Image:SA 3Dimaging (8).jpg|450px]]

'''Regularization and other parameters:'''

[[Image:CorticalLOR.png‎]]

* '''SVD cutoff''': The regularization for the inverse operator as a percent of the largest singular value.
* '''Depth weighting''': Turn depth weighting on or off.
* '''Laplacian type''': Selection of Laplacian operators (see above).

'''Notes:'''
* '''Starting Cortical LORETA''': Cortical LORETA can be started from the sub-menu '''Surface Image''' of the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]''” for important information on regularization of distributed inverses.

== Cortical CLARA ==

Cortical CLARA is principally the same technique as CLARA, but Cortical CLARA is not computed in a 3D volume, but on the cortical surface. Instead of using a LORETA image as the basis for the iterative application, cortical CLARA uses cortical LORETA.

'''Regularization and other parameters:'''

[[Image:SA 3Dimaging (47).gif]]

* '''SVD cutoff''': The regularization for the inverse operator as a percent of the largest singular value.
* '''Depth weighting''': Turn depth weighting on or off.
* '''Laplacian type''': Selection of Laplacian operators (see Cortical LORETA).
* '''No of iterations''': Number of iterations for CLARA. The more iterations are used, the sparser becomes the solution.
* '''Automatic''': The algorithm tries to determine the number of iterations automatically. The goodness of fit (GOF) is calculated after every iteration and if there is a big jump in the GOF then the algorithm will stop. If no jumps appear during the calculations then CLARA iterates until the specified number of iterations is reached.
* '''Regularize iterations''': If one wants to use different regularization for the CLARA iterations than the value specified as "SVD cutoff", this option should be selected.
* '''Amount to clip from img (%)''': Cortical CLARA uses the solution from the previous iteration as an additional weighting matrix for the current iteration. That weighting matrix is constructed by cutting the "low" activity from the solution. This number specifies how much of the activity should be cut from the previous solution in order to construct the weighting matrix. This value is given as a percentage of the maximal activity. Default value is 10%.

'''Notes:'''

* '''Starting Cortical CLARA:''' Cortical CLARA can be started from the sub-menu '''Surface Image''' of the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]''” for important information on regularization of distributed inverses.

== Cortex Inflation ==

The inflated cortex is a smoothened version of the individual cortical surface with minimal metric distortions (Fischl, B. et al. (1999). Cortical Surface-Based Analysis: II: Inflation, Flattening, and a Surface-Based Coordinate System. ''NeuroImage'', 9(2), 195–207). Gyri and sulci are smoothened out. The original distances between each point on the cortex and its neighbors are, however, mostly preserved.

[[Image:SA 3Dimaging (48).gif]]

''Cortical LORETA map overlaid on top of the inflated cortical surface.''

A lighter gray color overlaid on top of the surface image indicates the location of a gyrus of the individual cortex surface, while a darker gray color indicates the location of a sulcus. The inflated cortical surface can be computed in '''BESA MRI 2.0'''. For more details please refer to the BESA MRI 2.0 help.

== Surface Minimum Norm Image ==

'''Introduction'''

The minimum norm approach is a common method to estimate a distributed electrical current image in the brain at each time sample (Hämäläinen & Ilmoniemi 1984). The source activities of a large number of regional sources are computed. The sources are evenly distributed using 1500 standard locations 10% and 30% below the smoothed standard brain surface (when using the standard MRI) or using between 3000-4000 locations on the individual brain surface defined by the gray-white-matter boundary.

Since the number of sources is much larger than the number of sensors in a minimum norm solution, the inverse problem is highly underdetermined and must be stabilized by a mathematical constraint, the minimum norm. Out of the many current distributions that can account for the recorded sensor data, the solution with the minimum L2 norm, i.e. the minimum total power of the current distribution is displayed in BESA Research.

First, the forward solution (leadfield matrix L) of all sources is calculated in the current head model. Then, the source activities S(t) of all source components are computed from the data matrix D(t) using an inverse regularized by the estimated noise covariance matrix:

<math>\mathrm{S}\left( t \right) = \mathrm{R} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{R} \cdot \mathrm{L}^{T} + \mathrm{C}_N \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed regional source model, CN denotes the noise correlation matrix in sensor space, and R is a weighting matrix in source space. R and CN can be designed in different ways in order to optimize the minimum norm result. The total activity of each regional source is computed as the root mean square of the source activities S(t) of its 3 (MEG:2) components. This total source activity is transformed to a color-coded image of the brain surface. (When the standard brain is used, two sources are assigned to each surface location, located 10% and 30% below the surface, respectively. The color that is displayed on the standard brain surface is the larger of the two corresponding source activities.)

'''Weighting options'''

The minimum norm current imaging techniques of BESA Research provide different weighting strategies. Two weighting approaches are available: Depth weighting and spatio-temporal approaches.
* '''Depth weighting:''' Without depth weighting, deep sources appear very smeared in a minimum-norm reconstruction. With depth weighting, both deep and superficial sources produce a similar, more focal result. If this weighting method is selected, the leadfield of each regional source is scaled with the largest singular value of the SVD (singular value decomposition) of the source's leadfield.
* '''Spatio-temporal weighting''': Spatio-temporal weighting tries to assign large weight to sources that are assumed to be more likely to contribute to the recorded data.
** '''Subspace correlation after single source scan''': This method divides the signal into a signal and a noise subspace. The correlation of the leadfield of a regional source i with the signal subspace (pi) is computed to find out if the source location contributes to the measured data. The weighting matrix R becomes a diagonal matrix. Each of the three (MEG: 2) components of a regional source get the same weighting value pi2. This approach is based on the signal subspace correlation measure introduced by J.C. Mosher, R. M. Leahy (Recursive MUSIC: A Framework for EEG and MEG Source Localization, IEEE Trans. On Biomed. Eng. Vol. 45, No. 11, November 1998)
** '''Dale & Sereno 1993:''' In the approach of Dale and Sereno (J Cogn Neurosci, 1993, 5: 162-176) a signal subspace needs not be defined. The correlation pi of the leadfield of regional source i with the inverse of the data covariance matrix is computed along with the largest singular value λmax of the data covariance matrix. The weighting matrix R is a diagonal matrix with weights: [[Image:SA 3Dimaging (50).gif]]. Each of the three (MEG: 2) components of a regional source receives the same weighting value.

'''Noise regularization'''

Two methods to estimate the channel noise correlation matrix CN are provided by the program:
* '''Use baseline:''' Select this option to estimate the noise from the user-definable baseline. The signal is computed from the data at non-baseline latencies.
* '''Use 15% lowest values:''' The baseline activity is computed from the data at those 15% of all displayed latencies that have the lowest global field power. The signal is computed from all displayed latencies.

In each case, the activity (noise or signal, respectively) is defined as root-mean-square across all respective latencies for each channel.

The noise covariance matrix CN is constructed as a diagonal matrix. The entries in the main diagonal are proportional to the noise activity of the individual channels (if selected) or are all equally proportional to the average noise activity over all channels. The noise covariance matrix CN is then scaled such that the ratio of the Frobenius norms of the weighted leadfield projector matrix (LRLT) and the noise covariance matrix CN equals the Signal-to-Noise ratio. This scaling can be multiplied by an additional factor (default=1) to sharpen (<1) or smoothen (>1) the minimum norm image.

'''Applying the Minimum Norm Image'''

The minimum-norm algorithm is started via the ''Surface minimum norm image dialog box'', which is opened from the''' Image''' menu, or by typing the shortcut '''Ctrl-M''': Please refer to Chapter ''“Surface'' ''Minimum Norm Tab”'' for more details.

As opposed to the other 3D images available from the '''Image '''menu, the surface minimum norm image is not computed on a volumetric grid, but rather for locations on the brain surface. Accordingly, the results of the minimum norm image are displayed superimposed to the brain surface mesh rather than to the volumetric MR image.

The figure below shows a minimum norm image computed from the file '''Examples\Epilepsy\Spikes\Spikes-Child4_EEG+MEG_averaged.fsg'''. The EEG spike peak was imaged using the individual brain surface of the subject. A baseline from -300 to -70 ms was used. Minimum norm was computed with depth weighting, Spatio-temporal weighting according to Dale & Sereno 1993 and individual noise weighting with a noise scale factor of 0.01. The minimum norm image reveals the location of the spike generator in the close vicinity of the frontal left-hemispheric lesion in this subject.

[[Image:SA 3Dimaging (51).gif]]

== Multiple Source Probe Scan (MSPS) ==

 
'''Introduction'''

The MSPS function provides a tool for the validation of a given solution. It is based on the following theoretical consideration: If the recorded EEG/MEG data has been modeled adequately, i.e. all active brain regions are represented by a source in the current solution, then any additional probe source added to the solution will not show any activity apart from noise. The only exception occurs if this probe source is placed in close vicinity to one of the sources in the current solution. In that case, the solution's source and the probe source will share the activity of the corresponding brain area. The MSPS applies these considerations by scanning the brain on a pre-defined grid with a regional probe added to the current solution. Grid extent and density can be specified in the Image settings. The power P of the probe source at location r in the signal interval is compared with the power of the probe source in a reference interval, defining a value q:

<math>\mathrm{q}\left( r \right) = \sqrt{\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}} - 1</math>


MSPS can be computed on time domain or time-frequency domain data:
* In the time domain, q(r) is computed from the source waveform of the probe source. Here, P(r) is the mean power of the probe source at location r in the marked latency range, and Pref(r) is the mean probe source power in the user-definable baseline interval.
* In the time-frequency domain, an MSPS image can be computed from the complex cross spectral density matrices. By applying the inverse operator for a source configuration consisting of the current solution and the probe source, the power of the probe source can be computed for the target interval [P(r)] and the reference time-frequency interval [Pref(r)]. In the resulting MSPS image, q-values are shown in %, where q[%] = q*100.

The inverse operator used to determine the probe source power uses different regularization constants for the probe source and the sources in the current solution. The regularization constant of the sources in the current solution can be specified in the Image settings (default 4%). The regularization constant of the probe source is internally set to 0%.

Alternatively to the definition above, q can also be displayed in units of dB:

<math>\mathrm{q}\left\lbrack \text{dB} \right\rbrack = 10 \cdot \log_{10}\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}</math>


Values of q smaller than zero are not shown in the MSPS image.

According to the considerations above, an MSPS of a correct source model should optimally yield image maxima around the sources in the current solution only. If the MSPS image is blurred or shows maxima at locations different from the modeled sources, this indicates a non-sufficient or incorrect solution.

'''Applying the MSPS'''

This chapter illustrates the application of the Multiple Source Probe Scan. The figures are generated with data from file '''Examples/Epilepsy/Spikes/Rolandic-Spike-Child.fsg''' (-300 : +200 ms, filtered from 3 Hz [forward] to 40 Hz [zero-phase]).

'''Time domain versus time-frequency domain MSPS'''

The multiple source probe scan can be computed in the time domain or the time-frequency domain. The latter is possible only when time-frequency domain data is available for the current condition, i.e. if the condition has been created by starting a multiple source beamformer (MSBF) computation from the source coherence window. In this case, evoking the MSPS calculation from the '''Imaging '''button or from the '''Image''' menu will bring up the following dialog window that allows to choose between time- or time-frequency MSPS. If only time domain data is available, this dialog window will not appear and MSPS will be computed in the time domain.

[[Image:SA 3Dimaging (53).gif]]

For a time-frequency domain MSPS, the target and the reference time-frequency interval have been specified already in the Time-Frequency window (see Chapter "''How To Create Beamformer Images''"). For a time-domain MSPS, the target and the reference epoch have to be specified in the Source Analysis window as described below.

'''Time domain MSPS'''

The time-domain MSPS image displays the ratio of the power of a regional probe source in the signal and the baseline interval. The currently set baseline is indicated by a horizontal line in the upper left corner of the channel box.

[[Image:SA 3Dimaging (54).gif|thumb|c|none|330px|The black horizontal bar in the upper part of the channel box (here circled in red) indicates the baseline interval.]]

By default, BESA Research defines the pre-stimulus interval of the current data segment as baseline. The baseline should represent a latency range in which no event-related activity is present in the data. There are several possibilities to modify the baseline interval: by clicking on the horizontal line with the left mouse button or by using the corresponding entry in the '''Condition '''menu or '''Fit Interval''' popup menu.

Mark an interval to define the target epoch, i.e. the time-interval for which the current solution is to be tested. Start the MSPS by selecting it from the '''Image selection '''button or from the '''Image''' menu to start the probe source scan. The''' Image '''menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window. The 3D window opens and displays the scan result.

<div><ul>
<li style="display: inline-block;"> [[Image:SA 3Dimaging (55).gif|thumb|c|none|650px|This figure shows the MSPS image applied on the three left-hemispheric sources in the solution ''''Rolandic-Spike-Child-RS2.bsa''''. The baseline is set from -300ms to -50 ms. The right-hemispheric sources have been switched off. The fit interval is set to the latency range of large overall activity in the data (-43 ms : 117 ms). A realistic FEM model appropriate for the subject's age (12 years, conductivity ratios (cr) 50) is applied. The MSPS image does not show maxima at the modeled source locations and rather shows a spread q-value distribution.]] </li>

<li style="display: inline-block;"> [[Image:SA 3Dimaging (56).gif|thumb|c|none|650px|The MSPS image for the same latency range when the right-hemispheric sources have been included. The MSPS image appears more focal and shows maxima around the modeled brain regions. This indicates the substantial improvement of the solution by adding the right-hemispheric sources that model the propagation of the epileptic spike from the left to the right hemisphere (note the radiological side convention in the 3D window).]] </li>
</ul></div>

'''Time-Resolved MSPS'''

If the MSPS has been computed on time domain data, the image can be shown separately for each latency in the selected interval. After the MSPS has been computed for the marked epoch, double-click anywhere within this epoch to display the ratio of the probe source magnitude at the selected latency and the mean probe source magnitude in the baseline. Scanning the latency range by moving the cursor (e.g. with the left and right arrow cursor keys) provides a time-resolved MSPS image.

Time-resolved MSPS images are not available if the MSPS has been computed on data in the time-frequency domain.

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (57).gif|thumb|450px|MSPS image of the spike peak activity at 0ms. The activity mainly occurs in the left hemisphere. This fact is illustrated by the source waveforms and confirmed in the MSPS image, which shows a focal maximum around the location of the red sources.]] </li>

<li style="display: inline-block;"> [[File:SA 3Dimaging (58).gif|thumb|450px|Around +27 ms, the spike has propagated to the right hemisphere. This becomes evident from the waveforms of the blue sources, which show a significant latency lag with respect to the first three sources, and from the MSPS image, which shows the maximum around blue sources at this latency.]] </li>
</ul></div>



'''Notes:'''

* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image''' menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the''' Image''' menu.
* For scaling options, please refer to the '''scaling buttons''' popup menu .
* Parameters used for the MSPS calculations can be set in the ''General Settings tab'' of the ''Image Settings dialog box.''

== Source Sensitivity ==

'''Introduction'''

The 'Source sensitivity' function displays the sensitivity of the selected source in the current source model to activity in other brain regions. Sensitivity is defined as the fraction of power at the scanned brain location that is mapped onto the selected source.

To compute the source sensitivity, unit brain activity is modeled at different locations (probe source) throughout the brain. To this data, the current source model is applied to compute the source waveforms SCM of all modeled sources:

<math>\mathrm{S}_{\text{CM}} = \mathrm{L}_{\text{CM}}^{-1} \cdot \mathrm{L}_{\text{PS}}</math>


Here LCM-1 is the regularized inverse operator for the current model, and LPS is the leadfield of the regional probe source (dimension [Nx3] for EEG and [Nx2] for MEG, respectively, where N is the number of sensors). The source amplitude SSS of the selected source in the model is a 3x3 (MEG: 2x2) sub-matrix of SCM (if the selected source is a regional source) or a 1x3-matrix (MEG: 1x2) (if the selected source is a dipole). The root mean square of the singular values of SCM is defined as the source sensitivity.

The 3D source sensitivity image displays this value for all locations on a grid specified under '''Image/Settings'''. Grid density can be specified in the Image Settings.

'''Applying the Source Sensitivity Image'''

The Source Sensitivity image is evoked from the '''Image''' menu or by pressing the corresponding hot key (default: '''V''').

This function is enabled only when a solution with an active selected source is present in the Source Analysis window. The source sensitivity image then displays the sensitivity of the selected source to activity in other brain regions.

[[Image:SA 3Dimaging (59).gif]]

''Source Sensitivity image for the selected frontal source (green) in model ''''''High_Intensity_3RS.bsa'''''' in folder 'Examples/ERP_Auditory_Intensity'. The data displayed is the '100dB' condition in file ''''''All_Subjects_cc.fsg''''''. The selected source is sensitive to activity in the frontal brain region (yellow/white), while it is not influenced by activity in the vicinity of the left and right auditory cortex areas, which are modeled by the red and blue source in the model (transparent/gray).''

'''Notes:'''

* The sensitivity image is independent of the recorded sensor signals. It only depends on the current source model, the sensor configuration, the head model, and the regularization constant.
* If the regularization constant is set to zero, each source has a sensitivity of 100% to activity around its own location. With increasing regularization, the spatial filter becomes less focused, and the sensitivity of a source to activity at its location decreases.
* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image''' menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the '''Image''' menu.

==SESAME==

SESAME (Sequential Semi-Analytic Monte-Carlo Estimation) is a Bayesian approach for estimating sources that uses Markov-Chain Monte-Carlo method for efficient computation of the probability distribution as described in Sommariva, S., & Sorrentino, A. "Sequential Monte Carlo samplers for semi-linear inverse problems and application to magnetoencephalography." Inverse Problems 30.11 (2014): 114020. It allows to automatically estimate simultaneously the number of dipoles, their locations and time courses requiring virtually no user input.
The algorithm is divided in two blocks:

* The first block consists of a Monte Carlo sampling algorithm that produces, with an adaptive number of iterations, a set of samples representing the posterior distribution for the number of dipoles and the dipole locations.
* The second block estimates the source time courses, given the number of dipoles and the dipole locations.

The Monte Carlo algorithm in the first block works by letting a set of weighted samples evolve with each iteration. At each iteration, the samples (a multi-dipole state) approximates the n-th element of a sequence of distributions p1, …, pN, that reaches the desired posterior distribution (pN = p(x|y)). The sequence is built as pN = p(x) p(y|x) α(n), such that α(1) = 0, α(N) = 1. The actual sequence of values of alpha is determined online. Dipole moments are estimated after the number of dipoles and the dipole locations have been estimated with the Monte Carlo procedure. This continues until a steady state is reached.
The SESAME image in BESA Research displays the final probability of source location along with an estimate for number of sources. Using the menu function '''Image / Export Image As...''' you have the option to save this SESAME image.

'''Notes:'''
*'''Grid spacing:''' Due to memory and computational limitations, it is recommended to use SESAME with a grid spacing of 5 mm or more.
*'''Fit Interval:''' SESAME requires a fit interval of more than 2 samples to start the computation.
*'''Computation time:''' Computation speed during SESAME calculation depends on the grid spacing (computation is faster with larger grid spacing) and number of channels.

==Brain Atlas==

===Introduction===

Brain atlas is a priori data that can be applied over any discrete or distributed source image displayed in the 3D window. It is a reference value that strongly depends on the selected brain atlas and should not be used as medical reference since individual brains may differ from the brain atlas.

[[Image:BrainAtlas1.png]]

===Brain Atlases===

In BESA Research the atlases listed below are provided. BESA is not the author of the atlases; please cite the appropriate publications if you use any of the atlases in your publication.

'''Brainnetome''' This is one of the most modern brain probabilistic atlas where structural, functional, and connectivity information was used to perform cortical parcellation. It was introduce by Fan and colleagues (2016), and is still work in progress. The atlas was created using data from 40 healthy adults taking part in the Human Connectome Project. In March 2018, the atlas consists of 246 structures labeled independently for each hemisphere. In BESA we provide the max probability map with labeling. Please visit the Brainnetome webpage to see more details related to the indicated brain regions (i.e. behavioral domains, paradigm classes and regions connectivity).

'''AAL''' Automated Anatomical Labeling atlas was created in 2002 by Tzourio-Mazoyer and collegues (2002). It is the mostly used atlas nowadays. The atlas is based on the averaged brain of one subject (young male) who was scanned 27 times. The atlas resolution is 1mm isometric. The brain sulci were drawn manually on every 2mm slice and then brain regions were automatically assigned. The atlas consists of 116 regions which are asymmetrical between hemispheres. The atlas is implemented as in the SPM12 toolbox.

'''Brodmann''' The Brodmann map was created by Brodmann (1909). The brain regions were differentiated by cytoarchitecture of each cortical area using the Nissi method of cell staining. The digitalization of the original Brodmann map was performed by Damasio and Damasio (1989). The digitalized atlas consists of 44 fields that are symmetric between hemispheres. BESA used the atlas implementation as in Chris Roden’s MRICro software.

'''AAL2015''' Automated Anatomical Labeling revision 2015. This is the updated AAL atlas. In comparison to the previous version (AAL) mainly the frontal lobe shows a higher degree of parcellation (Rolls, Joliot, and Tzourio-Mazoyer 2015). The atlas is implemented as in the SPM12 toolbox.

'''Talairach''' Atlas was created in 1988 by Talairach and Tournoux (1988) and it is based on the post mortem brain slices of a 60 year old right handed European female. It was created by drawing and matching regions with the Brodmann map. The atlas is available at 5 tissue levels, however we used only the volumetric gyrus level as it is the most known in neuroscience and is the most appropriate for EEG. The atlas consists of 55 regions that are symmetric between hemispheres. The native resolution of the atlas was 0.43x0.43x2- 5mm. Please note that the poor resolution in Z direction is a direct consequence atlas definition, and since it is a post-mortem atlas it will not correctly match the brain template
(noticeable mainly on brain edges). The atlas digitalization was performed by Lancaster and colleagues (2000) resulting in a “golden standard” for neuroscience. The atlas was first implemented in a software called talairach daemon.

===Visualization modes===

'''Just Labels.''' Displayed are only Talairach Coordinates, the currently used brain atlas and the region name where the crosshair is placed. No atlas overlay will be visible on the 3D image.

'''brainCOLOR.''' All information is displayed as in “Just Labels” mode but also the atlas is visible as an overlay over the MRI. The coloring is performed using the algorithm introduced by Klein and colleagues (Klein et al. 2010). With this method of coloring the regions which are part of the same lobe are colored in a similar color but with different color shade. The shade is computed by the algorithm to make these regions visually differentiable from each other as much as possible.

'''Individual Color.''' In this mode the native brain atlas color is used if provided by the authors of the brain atlas (i.e. Yeo7). Where this was not available BESA autogenerated colors for the atlas using an approach similar to political map coloring. This approach aims to differentiate most regions that are adjacent to each other and no presumptions on lobes is applied.

'''Contour.''' Only region contours (borders between atlas regions) are drawn with blue color. This is the default mode in BESA Research.

===References===

* Brodmann, Korbinian. 1909. Vergleichende Lokalisationslehre Der Großhirnrinde. Leipzig: Barth. https://www.livivo.de/doc/437605.
* Damasio, Hanna, and Antonio R. Damasio. 1989. Lesion Analysis in Neuropsychology. Oxford University Press, USA.
* Fan, Lingzhong, Hai Li, Junjie Zhuo, Yu Zhang, Jiaojian Wang, Liangfu Chen, Zhengyi Yang, et al. 2016. “The Human Brainnetome Atlas: A New Brain Atlas Based on Connectional Architecture.” Cerebral Cortex 26 (8): 3508–26. https://doi.org/10.1093/cercor/bhw157.
* Klein, Arno, Andrew Worth, Jason Tourville, Bennett Landman, Tito Dal Canton, Satrajit S. Ghosh, and David Shattuck. 2010. “An Interactive Tool for Constructing Optimal Brain Colormaps.” http://braincolor.mindboggle.info/docs/SFN2010_BrainCOLORmap_poster_ArnoKlein.pdf.
* Lancaster, Jack L., Marty G. Woldorff, Lawrence M. Parsons, Mario Liotti, Catarina S. Freitas, Lacy Rainey, Peter V. Kochunov, Dan Nickerson, Shawn A. Mikiten, and Peter T. Fox. 2000. “Automated Talairach Atlas Labels for Functional Brain Mapping.” Human Brain Mapping 10 (3): 120–131.
*Rolls, Edmund T., Marc Joliot, and Nathalie Tzourio-Mazoyer. 2015. “Implementation of a New Parcellation of the Orbitofrontal Cortex in the Automated Anatomical Labeling Atlas.” NeuroImage 122 (November): 1–5. https://doi.org/10.1016/j.neuroimage.2015.07.075.
* Talairach, J, and P Tournoux. 1988. Co-Planar Stereotaxic Atlas of the Human Brain. 3-Dimensional Proportional System: An Approach to Cerebral Imaging. Thieme.
*Thomas Yeo, B. T., F. M. Krienen, J. Sepulcre, M. R. Sabuncu, D. Lashkari, M. Hollinshead, J. L. Roffman, et al. 2011. “The Organization of the Human Cerebral Cortex Estimated by Intrinsic Functional Connectivity.” Journal of Neurophysiology 106 (3): 1125–65. https://doi.org/10.1152/jn.00338.2011.
* Tzourio-Mazoyer, N., B. Landeau, D. Papathanassiou, F. Crivello, O. Etard, N. Delcroix, B. Mazoyer, and M. Joliot. 2002. “Automated Anatomical Labeling of Activations in SPM Using a Macroscopic Anatomical Parcellation of the MNI MRI Single-Subject Brain.” NeuroImage 15 (1): 273–89. https://doi.org/10.1006/nimg.2001.0978.

{{BESAManualNav}}

File:BrainAtlas1.png

2019-04-08T09:10:40Z

Jamie:

Source Analysis 3D Imaging

2019-04-08T09:10:25Z

Jamie:

Source Analysis 3D Imaging

2019-03-28T14:23:37Z

Jamie: /* Short mathematical introduction */

{{BESAInfobox
|title = Module information
|module = BESA Research Standard or higher
|version = 6.1 or higher
}}


== Overview ==

BESA Research features a set of new functions that provide 3D images that are displayed superimposed to the individual subject's anatomy. This chapter introduces these different images and describe their properties and applications.

The 3D images can be divided into three categories:

'''Volume images:'''

* '''The Multiple Source Beamformer (MSBF)''' is a tool for imaging brain activity. It is applied in the time-domain or time-frequency domain. The beamformer technique in time-frequency domain can image not only evoked, but also induced activity, which is not visible in time-domain averages of the data.
* '''Dynamic Imaging of Coherent Sources (DICS)''' can find coherence between any two pairs of voxels in the brain or between an external source and brain voxels. DICS requires time-frequency-transformed data and can find coherence for evoked and induced activity.

The following imaging methods provide an image of brain activity based on a distributed multiple source model:
* '''CLARA''' is an iterative application of LORETA images, focusing the obtained 3D image in each iteration step.
* '''LAURA '''uses a spatial weighting function that has the form of a local autoregressive function.
* '''LORETA''' has the 3D Laplacian operator implemented as spatial weighting prior.
* '''sLORETA''' is an unweighted minimum norm that is standardized by the resolution matrix.
* '''swLORETA '''is equivalent to sLORETA, except for an additional depth weighting.
* '''SSLOFO '''is an iterative application of standardized minimum norm images with consecutive shrinkage of the source space.
* A '''User-defined volume image''' allows to experiment with the different imaging techniques. It is possible to specify user-defined parameters for the family of distributed source images to create a new imaging technique.
* Bayesian source imaging: '''SESAME''' uses a semi-automated Bayesian approach to estimate the number of dipoles along with their parameters.

'''Surface image:'''

* The '''Surface Minimum Norm Image'''. If no individual MRI is available, the minimum norm image is displayed on a standard brain surface and computed for standard source locations. If available, an individual brain surface is used to construct the distributed source model and to image the brain activity.
* '''Cortical LORETA'''. Unlike classical LORETA, cortical LORETA is not computed in a 3D volume, but on the cortical surface.
* '''Cortical CLARA'''. Unlike classical CLARA, cortical CLARA is not computed in a 3D volume, but on the cortical surface.

'''Discrete model probing:'''

These images do not visualize source activity. Rather, they visualize properties of the currently applied discrete source model:
* The '''Multiple Source Probe Scan (MSPS)''' is a tool for the validation of a discrete multiple source model.
* The '''Source Sensitivity image''' displays the sensitivity of a selected source in the current discrete source model and is therefore data independent.

== Multiple Source Beamformer (MSBF) in the Time-frequency Domain ==

 
'''Short mathematical introduction'''

The BESA beamformer is a modified version of the linearly constrained minimum variance vector beamformer in the time-frequency domain as described in [https://dx.doi.org/10.1073/pnas.98.2.694 Gross et al., "Dynamic imaging of coherent sources: Studying neural interactions in the human brain", PNAS 98, 694-699, 2001]. It allows to image evoked and induced oscillatory activity in a user-defined time-frequency range, where time is taken relative to a triggered event.

The computation is based on a transformation of each channel's single trial data from the time domain into the time-frequency domain. This transformation is performed by the BESA Research Source Coherence module and leads to the complex spectral density Si (f,t), where i is the channel index and f and t denote frequency and time, respectively. Complex cross spectral density matrices C are computed for each trial:

<math>\mathrm{C}_{ij}\left( f,t \right) = \mathrm{S}_{i}\left( f,t \right) \cdot \mathrm{S}_{j}^{*}\left( f,t \right)</math>


The output power P of the beamformer for a specific brain region at location r is then computed by the following equation:

<math>\mathrm{P}\left( r \right) = \operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{-1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{-1}</math>


Here, Cr-1 is the inverse of the SVD-regularized average of Cij(f,t) over trials and the time-frequency range of interest; L is the leadfield matrix of the model containing a regional source at target location r and, optionally, additional sources whose interference with the target source is to be minimized; tr'[] is the trace of the [3×3] (MEG:[2×2]) submatrix of the bracketed expression that corresponds to the source at target location r.

In BESA Research, the output power P(r) is normalized with the output power in a reference time-frequency interval Pref(r). A value q ist defined as follows:

<math> \mathrm{q}\left( r \right) =
\begin{cases}
\sqrt{\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}(r)}} - 1 = \sqrt{\frac{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{\text{ref},r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}} - 1, & \text{for }\mathrm{P}(r) \geq \mathrm{P}_{\text{ref}}(r) \\

1 - \sqrt{\frac{\mathrm{P}_{\text{ref}}\left( r \right)}{\mathrm{P}\left( r \right)}} = 1 - \sqrt{\frac{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{\text{ref},r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}}, & \text{for }\mathrm{P}(r) < \mathrm{P}_{\text{ref}}(r)
\end{cases} </math>


Pref can be computed either from the corresponding frequency range in the baseline of the same condition (i.e. the beamformer images event-related power increase or decrease) or from the corresponding time-frequency range in a control condition (i.e. the beamformer images differences between two conditions). The beamformer image is constructed from values q(r) computed for all locations on a grid specified in the '''General Settings tab'''. For MEG data, the innermost grid points within a sphere of approx. 12% of the head diameter are assigned interpolated rather than calculated values).
q-values are shown in %, where where q[%] = q*100. Alternatively to the definition above, q can also be displayed in units of dB:

<math>\mathrm{q}\left\lbrack \text{dB} \right\rbrack = 10 \cdot \log_{10}\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}</math>


A beamformer operator is designed to pass signals from the brain region of interest r without attenuation, while minimizing interference from activity in all other brain regions. Traditional single-source beamformers are known to mislocalize sources if several brain regions have highly correlated activity. Therefore, the BESA beamformer extends the traditional single-source beamformer in order to implicitly suppress activity from possibly correlated brain regions. This is achieved by using a multiple source beamformer calculation that contains not only the leadfields of the source at the location of interest r, but also those of possibly interfering sources. As a default, BESA Research uses a bilateral beamformer, where specifically contributions from the homologue source in the opposite hemisphere are taken into account (the matrix L thus being of dimension N×6 for EEG and N×4 for MEG, respectively, where N is the number of sensors). This allows for imaging of highly correlated bilateral activity in the two hemispheres that commonly occurs during processing of external stimuli.

In addition, the beamformer computation can take into account possibly correlated sources at arbitrary locations that are specified in the current solution. This is achieved by adding their leadfield vectors to the matrix L in the equation above.

'''Applying the Beamformer'''

This chapter illustrates the usage of the BESA beamformer. The displayed figures are generated using the file ''''Examples/Learn-by-Simulations/AC-Coherence/AC-Osc20.foc'''' (see BESA Tutorial 6: "''Time-frequency analysis and Source coherence''").

'''Starting the beamformer from the time-frequency window'''

The BESA beamformer is applied in the time-frequency domain and therefore requires the Source Coherence module to be enabled. The time-frequency beamformer is especially useful to image in- or decrease of induced oscillatory activity. Induced activity cannot be observed in the averaged data, but shows up as enhanced averaged power in the TSE (Temporal-Spectral Evolution) plot. For instructions on how to initiate a beamformer computation in the time-frequency window, please refer to Chapter '''[[Source_Coherence_How_to...#How_to_Start_the_Beamformer_from_the_Time-Frequency_Window|How to Create Beamformer Images]]'''.

After the beamformer computation has been initiated in the time-frequency window, the source analysis window opens with an enlarged 3D image of the q-value computed with a '''bilateral beamformer'''. The result is superimposed onto the MR image assigned to the data set (individual or standard).

[[Image:SA 3Dimaging (5).gif]]

''Beamformer image after starting the computation in the Time-Frequency window. A bilateral pair of sources in the auditory cortex accounts for the highly correlated oscillatory induced activity. Only the bilateral beamformer manages to separate these activities; a traditional single-source beamformer would merge the two sources into one image maximum in the head center instead.''

'''Multiple source beamformer in the Source Analysis window'''

The 3D imaging display is part of the source analysis window. If you press the '''Restore''' button at the right end of the title bar of the 3D window, the window appears at the bottom right of the source analysis window. In the channel box, the averaged (evoked) data of the selected condition is shown. When a control condition was selected, its average is appended to the average of the target condition.

[[Image:SA 3Dimaging (6).gif]]

''Source Analysis window with beamformer image. The two sources have been added using the '''''Switch to''''' '''''Maximum''''' and '''''Add Source '''''toolbar buttons (see below). Source waveforms are computed from the displayed averaged data. Therefore, they do not represent the activity displayed in the beamformer image, which in this simulation example is induced (i.e. not phase-locked to the trigger)!''

When starting the beamformer from the time-frequency window, a bilateral beamformer scan is performed. In the source analysis window, the beamformer computation can be repeated taking into account possibly correlated sources that are specified in the current solution. Interfering activities generated by all sources in the current solution that are in the 'On' state are specifically suppressed ('''they enter the matrix L in the beamformer calculation''', see Chapter ''Short mathematical description'' above). The computation can be started from the '''Image''' menu or from the '''Image selector button''' dropdown menu. The '''Image''' menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window.

[[Image:SA 3Dimaging (7).gif]]

''Multiple source beamformer image calculated in the presence of a source in the left hemisphere. A '''single''' source scan has been performed. The source set in the current solution accounts for the left-hemispheric q-maximum in the data. Accordingly, the beamformer scan reveals only the as yet unmodeled additional activity in the right hemisphere (note the radiological convention in the 3D image display).''

The beamformer scan can be performed with a '''single''' or a '''bilateral''' source scan. The default scan type depends on the current solution:
* When the beamformer is started from the Time-Frequency window, the Source Analysis window opens with a new solution and a '''bilateral''' beamformer scan is performed.
* When the beamformer is started within the Source Analysis window, the default is
** a scan with a '''single''' source in addition to the sources in the current solution, if at least one source is active.
** a '''bilateral''' scan if no source in the current solution is active.

The default scan type is the multiple source beamformer. The non-default scan type can be enforced using the corresponding ''Volume Image / Beamformer'' entry in the '''Image''' menu.

'''Inserting Sources out of the Beamformer Image'''

The beamformer image can be used to add sources to the current solution. A simple double-click anywhere in the 2D- or 3D-view will generate a non-oriented regional source at the corresponding location. However, a better and easier way to create sources at image maxima and minima is to use the toolbar buttons '''Switch to Maximum''' [[Image:SA 3Dimaging (8).gif]] and '''Add Source''' [[Image:SA 3Dimaging (9).gif]].

Use the '''Switch to Maximum''' button to place the red crosshair of the 3D window onto a local image maximum or minimum. Hitting the '''Add Source''' button creates a regional source at the location of the crosshair and therefore ensures the exact placement of the source at the image extremum. Moreover, the '''Add Source''' button generates an oriented regional source. BESA Research automatically estimates the source orientation that contributes most to the power in the target time-frequency interval (or the reference time-frequency interval, if its power is larger than that in the target interval). The accuracy of this orientation estimate depends largely on the noise content of the data. The smaller the signal-to-noise ratio of the data, the lower is the accuracy of the orientation estimate. '''This feature allows to use the beamformer as a tool to create a source montage for source coherence analysis, where it is of advantage to work with oriented sources'''.

'''Notes:'''

* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image '''menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the''' Image''' menu.
* For scaling options, use the [[Image:SA 3Dimaging (10).gif]] and [[Image:SA 3Dimaging (11).gif]] '''Image Scale toolbar''' buttons.
* Parameters used for the beamformer calculations can be set in the '''Standard Volumes''' of the ''Image Settings dialog box.''

== Dynamic Imaging of Coherent Sources (DICS) ==

 
'''Short mathematical introduction'''

Dynamic Imaging of Coherent Sources (DICS) is a sophisticated method for imaging cortico-cortical coherence in the brain, or coherence between an external reference (e.g. EMG channel) and cortical structures. DICS can be applied to localize evoked as well as induced coherent cortical activity in a user-defined time-frequency range.

DICS was implemented in BESA closely following [https://dx.doi.org/10.1073/pnas.98.2.694 Gross et al., "Dynamic imaging of coherent sources: Studying neural interactions in the human brain", PNAS 98, 694-699, 2001].

The computation is based on a transformation of each channel's single trial data from the time domain into the frequency domain. This transformation is performed by the BESA Research Coherence module and results in the complex spectral density matrix that is used for constructing the spatial filter similar to beamforming.

DICS computation yields a 3-D image, each voxel being assigned a coherence value. Coherence values can be described as a neural activity index and do not have a unit. The neural activity index contrasts coherence in a target time-frequency bin with coherence of the same time-frequency bin in a baseline.

'''DICS for cortico-cortical coherence is computed as follows:'''

Let L(r) be the leadfield in voxel r in the brain and C the complex cross-spectral density matrix. The spatial filter W(r) for the voxel r in the head is defined as follows:

<math>W\left( r \right) = \left\lbrack L^{T}\left( r \right) \cdot C^{- 1} \cdot L\left( r \right) \right\rbrack^{- 1} \cdot L^{T}(r) \cdot C^{- 1}</math>


The cross-spectrum between two locations (voxels) r1 and r2 in the head are calculated with the following equation:

<math>C_{s}\left( r_{1},r_{2} \right) = W\left( r_{1} \right) \cdot C \cdot W^{*T}\left( r_{2} \right),</math>


where <nowiki>*T</nowiki> means the transposed complex conjugate of a matrix. The cross-spectral density can then be calculated from the cross spectrum as follows:

<math>c_{s}\left( r_{1},r_{2} \right) = \lambda_{1}\left\{ C_{s}\left( r_{1},r_{2} \right) \right\},</math>


where λ1{} indicates the largest singular value of the cross spectrum. Once the cross spectral density is estimated, the connectivity¹(CON) between the two brain regions r1 and r2 are calculated as follows:

<math>\text{CON}\left( r_{1},r_{2} \right) = \frac{c_{s}^{\text{sig}}\left( r_{1},r_{2} \right) - c_{s}^{\text{bl}}(r_{1},r_{2})}{c_{s}^{\text{sig}}\left( r_{1},r_{2} \right) + c_{s}^{\text{bl}}(r_{1},r_{2})},</math>


where cssig is the cross-spectral density for the signal of interest between the two brain regions r1 and r2, and csbl is the corresponding cross spectral density for the baseline or the control condition, respectively. In the case DICS is computed with a cortical reference, r1 is the reference region (voxel) and remains constant while r2 scans all the grid points within the brain sequentially. In that way, the connectivity between the reference brain region and all other brain regions is estimated. The value of CON(r1, r2) falls in the interval [-1 1]. If the cross-spectral density for the baseline is 0 the connectivity value will be 1. If the cross-spectral density for the signal is 0 the connectivity value will be -1.

¹ Here, the term connectivity is used rather than coherence, as strictly speaking the coherence equation is defined slightly differently. For simplicity reasons the rest of the tutorial uses the term coherence.

'''DICS for cortico-muscular coherence is computed as follows:'''

When using an external reference, the equation for coherence calculation is slightly different compared to the equation for cortico-cortical coherence. First of all, the cross-spectral density matrix is not only computed for the MEG/EEG channels, but the external reference channel is added. This resulting matrix is Call. In this case, the cross-spectral density between the reference signal and all other MEG/EEG

channels is called cref. It is only one column of Call. Hence, the cross-spectrum in voxel r is calculated with the following equation:

<math>C_{s}\left( r \right) = W\left( r \right) \cdot c_{\text{ref}}</math>


and the corresponding cross-spectral density is calculated as the sum of squares of Cs:

<math>c_{s}\left( r \right) = \sum_{i = 1}^{n}{C_{s}\left( r \right)_{i}^{2}},</math>


where n is 2 for MEG and 3 for EEG. This equation can also be described as the squared Euclidean norm of the cross-spectrum:

<math>c_{s}\left( r \right) = \left\| C_{s} \right\|^{2},</math>


The power in voxel r is calculated as in the cortico-cortical case:

<math>p\left( r \right) = \lambda_{1}\left\{ C_{s}(r,r) \right\}.</math>


At last, coherence between the external reference and cortical activity is calculated with the equation:

<math>\text{CON}\left( r \right) = \frac{c_{s}(r)}{p\left( r \right) \cdot C_{\text{all}}(k,k)},</math>


where Call(k, k) is the (k,k)-th diagonal element of the matrix Call.

DICS is particularly useful, if coherence is to be calculated without an a-priory source model (in contrast to source coherence based on pre-defined source montages). However, the recommended analysis strategy for DICS is to use a brain source as a starting point for coherence calculation that is known to contribute to the EEG/MEG signal of interest. For example, one might first run a beamformer on the time-frequency range of interest and use the voxel with the strongest oscillatory activity as a starting point for DICS. The resulting coherence image will again lead to several maxima (ordered by magnitude), which in turn can serve as starting points for DICS calculation. This way, it is possible to detect even weak sources that show coherent activity in the given time-frequency range.

The other significant application for DICS is estimating coherence between an external source and voxels in the brain. For example, an external source can be muscle activity recoded by an electrode placed over the according peripheral region. This way, the direct relationship between muscle activity and brain activation can be measured.

'''Starting DICS computation from the Time-Frequency Window'''

DICS is particularly useful, if coherence in a user-defined time-frequency bin (evoked or induced) is to be calculated between any two brain regions or between an external reference and the brain. DICS runs only on time-frequency decomposed data, so time-frequency analysis needs to be run before starting DICS computation.

To start the DICS computation, left-drag a window over a selected time-frequency bin in the Time-Frequency Window. Right-click and select “Image”. A dialogue will open (see fig. 1) prompting you to specify time and frequency settings as well as the baseline period. It is recommended to use a baseline period of equal length as the data period of interest. Make sure to select “DICS” in the top row and press “'''Go'''”.

[[Image:SA 3Dimaging (21).gif|450px|thumb|c|none|Fig. 1: Time and frequency settings for DICS and MSBF]]

Next, a window will appear allowing you to specify the reference source for coherence calculation (see fig. 2). It is possible to select a channel (e.g. EMG) or a brain source. If a brain source is chosen and no source analysis was computed beforehand, the option “Use current cross-hair position” must be chosen. In case discrete source analysis was computed previously, the selected source can be chosen as the reference for DICS. Please note that DICS can be re-computed with any cross-hair or source position at a later stage.

[[Image:SA 3Dimaging (1).jpg|400px|thumb|c|none|Fig. 2: Possible options for choosing the reference]]

Confirming with “'''OK'''” will start computation of coherence between the selected channel/voxel and all other brain voxels. In case DICS is computed for a reference source in the brain, it can be advantageous to run a beamforming analysis in the selected time-frequency window first and use one of the beamforming maxima as reference for DICS. Fig. 3 shows an example for DICS calculation.

[[Image:SA 3Dimaging (22).gif|500px|thumb|c|none|Fig. 3: Coherence between left-hemispheric auditory areas and the selected voxel in the right auditory cortex.]]

Coherence values range between -1 and 1. If coherence in the signal is much larger than coherence in the baseline (control condition) then the DICS value is going to approach 1. Contrary, if coherence in the baseline is much larger than coherence in the signal, then the DICS value is going to approach -1. At last, if coherence in the signal is equal to coherence in the baseline, then the DICS value is 0.

In case DICS is to be re-computed with a different reference, simply mark the desired reference position by placing the cross-hair in the anatomical view and select “DICS” in the middle panel of the source analysis window (see Fig. 4). In case an external reference is to be selected, click on “DICS” in the middle panel to bring up the DICS dialogue (see. Fig. 2) and select the desired channel. Please note that DICS computation will only be available after running time-frequency analysis.

[[Image:SA 3Dimaging (23).gif|700px|thumb|c|none|Fig. 4: Integration of DICS in the Source Analysis window]]

== Multiple Source Beamformer (MSBF) in the Time Domain ==
''(requires Besa Research 7.0 or higher)''

===Short mathematical introduction===

Beamforming approach can be also applied in the time domain data. This approach was introduced as linearly constrained minimum variance (LCMV) beamformer (Van Veen et al., 1997). It allows to image evoked activity in a user-defined time range, where time is taken relative to a triggered event, and to estimate source waveforms using the calculated spatial weight at locations of interest. For an implementation of the beamformer in the time domain, data covariance matrices are required, while complex cross spectral density matrices are used for the beamformer approaches in the time-frequency domain as described in the ''[[Source_Analysis_3D_Imaging#Multiple_Source_Beamformer_.28MSBF.29_in_the_Time-frequency_Domain|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section.

The bilateral beamformer introduced in the ''[[Source_Analysis_3D_Imaging#Multiple_Source_Beamformer_.28MSBF.29_in_the_Time-frequency_Domain|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section is also implemented for the time-domain beamformer to take into account contributions from the homologue source in the opposite. This allows for imaging of highly correlated bilateral activity in the two hemispheres that commonly occurs during processing of external stimuli. In addition, the beamformer computation can take into account possibly correlated sources at arbitrary locations.
The beamformer spatial weight W(r) for the voxel r in the brain is defined as follows (Van Veen et al., 1997):

[[File:MSBF1.png]]

where '''C-1''' is the inversed regularized average of covariance matrix over trials, '''L''' is the leadfield matrix of the model containing a regional source at target location r and optionally
additional sources whose interference with the target source is to be minimized. The beamformer spatial weight '''W'''(r) can be applied to the measured data to estimate source
waveform at a location r (beamformer virtual sensor):

[[File:MSBF2.png]]

where '''S'''(r,t) represents the estimated source waveform and '''M'''(t) represents measured EEG or MEG signals.
The output power P of the beamformer for a specific brain region at location r is computed by the following equation:

[[File:MSBF3.png]]

where tr’[ ] is the trace of the [3×3] (MEG: [2×2]) submatrix of the bracketed expression that corresponds to the source at target location r.
Beamformer can suppress noise sources that are correlated across sensors. However, uncorrelated noise will be amplified in a spatially non-uniform manner, with increasing
distortion with increasing distance from the sensors (Van Veen et al., 1997; Sekihara et al., 2001). For this reason, estimated source power should be normalized by a noise power.
In BESA Research, the output power P(r) is normalized with the output power in a baseline interval or with the output power of a uncorrelated noise: P(r) / Pref (r).
The time-domain beamformer image is constructed from values q(r) computed for all locations on a grid specified in the '''General Settings''' tab. A value q(r) is defined as described in
the ''[[Source_Analysis_3D_Imaging#Multiple_Source_Beamformer_.28MSBF.29_in_the_Time-frequency_Domain|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section with data covariance matrices instead of cross-spectral density matrices.

===Applying the Beamformer===

This chapter illustrates the usage of the BESA beamformer in the time domain. The displayed figures are generated using the file ‘Examples/ERP-Auditory-Intensity/S1.cnt’.

'''Starting the time-domain beamformer from the Average tab of the Paradigm dialog box'''

The time-domain beamformer is needed data covariance matrices and therefore requires the ERP module to be enabled. After the beamformer computation has been initiated in the
'''Average tab of the Paradigm dialog box''', the source analysis window opens with an enlarged 3D image of the q-value computed with a bilateral beamformer. The result is
superimposed onto the MR image assigned to the data set (individual or standard).

[[File:MSBF44.png]]

''Beamformer image for auditory evoked data after starting the computation in the '''Average tab of the Paradigm dialog box'''. The bilateral beamformer manages to separate the
activities in auditory areas, while a traditional single-source beamformer would merge the two sources into one image maximum in the head center instead.''

'''Multiple-source beamformer in the Source Analysis window'''

The 3D imaging display is part of the source analysis window. In the Channel box, the averaged (evoked) data of the selected condition is shown. Selected covariance intervals in
the ERP module can be checked in the Channel box. The red, gray, and blue rectangles indicate signal, baseline, and common interval, respectively.

[[File:MSBF55.png]]

''Source Analysis window with beamformer image. The two beamformer virtual sensors have been added using the Switch to Maximum and Add Source toolbar buttons (see below).
Source waveforms are computed using the beamformer spatial weights and the displayed averaged data (the noise normalized weights (5% noise) option was used to compute the
beamformer image).''

When starting the beamformer from the '''Average tab of the Paradigm dialog box''', the bilateral beamformer scan is performed. In the source analysis window, the beamformer computation can be repeated taking into account possibly correlated sources that are specified in the current solution. Interfering activities generated by all sources in the current solution that are in the 'On' state are specifically suppressed (they enter the leadfield matrix L in the beamformer calculation). The computation can be started from the '''Image''' menu or from the Image selector button [[File:MSBF_Button.png|22px|Image: 22 pixels]] dropdown menu. The Image menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window.

[[File:MSBF66.png]]

''Multiple-source beamformer image calculated in the presence of a source in the left hemisphere. A single-source scan has been performed instead of a bilateral beamforemr. The
source set in the current solution accounts for the left-hemispheric q-maximum in the data. Accordingly, the beamformer scan reveals only the as yet unmodeled additional activity in
the right hemisphere (note the radiological convention in the 3D image display). The source waveform of the beamformer virtual sensor in the left hemisphere is not shown since the
location (blue square in the figure) is not considered for the multiple-source beamformer.''

The beamformer scan can be performed with a single or a bilateral source scan. The default scan type depends on the current solution:
When the beamformer is started from the '''Average tab of the Paradigm dialog box''' the Source Analysis window opens with a new solution and a bilateral beamformer scan is
performed.
When the beamformer is started within the Source Analysis window, the default is:

* a scan with a single source in addition to the sources in the current solution, if at least one source is active.
* a bilateral scan if no source in the current solution is active.
* a scan with a single source when scalar-type beamformer is selected in the '''beamformer option dialog box'''.

The default scan type is the multiple source beamformer. The non-default scan type can be enforced using the corresponding Volume Image / Beamformer entry in the Image main
menu or in the beamformer option dialog box (only for the time-domain beamformer).

===Inserting Sources as Beamformer Virtual Sensor out of the Beamformer Image===

This is similar to the inserting sources out of the beamformer image in Multiple Source Beamformer (MSBF) in the Time-frequency Domain section.
The beamformer image can be used to add beamformer virtual sensors to the current solution. A simple double-click anywhere in the 3D view (not in the 2D view) will generate a
source at the corresponding location. A better and easier way to create sources at image maxima and minima is to use the toolbar buttons '''Switch to Maximum''' [[Image:SA 3Dimaging (8).gif]] and '''Add Source''' [[Image:SA 3Dimaging (9).gif]].

This feature allows to use the beamformer as a tool to create a source montage for '''source coherence''' analysis. A source montage file (*.mtg) for beamformer virtual sensors can
be saved using File \ Save Source Montage As… entry.

The time-domain beamformer image can be also used to add regional or dipole sources to the current solution. Press '''N''' key when there is no source in the current source array or
there is more than one beamformer virtual sensor. To create a new source array for beamformer virtual sensor, press '''N''' key when there is more than one regional or dipole source in
the current source array.

===Notes===

* You can hide or re-display the last computed image by selecting ''Hide Image'' entry in the '''Image''' menu.
* The current image can be exported to ASCII, ANALYZE, or BrainVoyager (vmp) format from the '''Image''' menu.
* For scaling options, use [[Image:SA 3Dimaging (10).gif]] and [[Image:SA 3Dimaging (11).gif]] '''Image Scale toolbar''' buttons.
* Parameters used for the beamformer calculations can be set in the '''Standard Volume tab of the Image Settings dialog box'''.
* Note that Model, Residual, Order, and Residual variance are not shown for the beamformer virtual sensor type sources.

===References===

* Sekihara, K., Nagarajan, S. S., Poeppel, D., Marantz, A., & Miyashita, Y. (2001). Reconstructing spatio-temporal activities of neural sources using an MEG vector beamformer technique. IEEE Transactions on Biomedical Engineering, 48(7), 760–771.

* Van Veen, B. D., Van Drongelen, W., Yuchtman, M., & Suzuki, A. (1997). Localization of brain electrical activity via linearly constrained minimum variance spatial filtering. IEEE Transactions on Biomedical Engineering, 44(9), 867–880

== CLARA ==

CLARA ('Classical LORETA Analysis Recursively Applied') is an iterative application of weighted LORETA images with a reduced source space in each iteration.

In an initialization step, a LORETA image is calculated. Then in each iteration the following steps are performed:

# The obtained image is spatially smoothed (this step is left out in the first iteration).
# All grid points with amplitudes below a threshold of 1% of the maximum activity are set to zero, thus being effectively eliminated from the source space in the following step.
# The resulting image defines a spatial weighting term (for each voxel the corresponding image amplitude).
# A LORETA image is computed with an additional spatial weighting term for each voxel as computed in step 3. By the default settings in BESA Research, the regularization values used in the iteration steps are slightly higher than that of the initialization LORETA image.

The procedure stops after 2 iterations, and the image computed in the last iteration is displayed. Please note that you can change all parameters by creating a user-defined volume image.

The advantage of CLARA over non-focusing distributed imaging methods is visualized by the figure below. Both images are computed from the N100 response in an auditory oddball experiment (file '''Oddball.fsg''' in subfolder ''fMRI+EEG-RT-Experiment'' of the ''Examples'' folder). The CLARA image is much more focal than the sLORETA image, making it easier to determine the location of the image maxima.

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (24).gif|thumb|350px|sLORETA image]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (25).gif|thumb|350px|CLARA image]] </li>
</ul></div>

'''Notes:'''

* Starting CLARA: CLARA can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter ''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]'' for important information on regularization of distributed inverses.

== LAURA ==

LAURA (Local Auto Regressive Average) belongs to the distributed inverse method of the family of weighted minimum norm methods ([https://doi.org/10.1023/A:1012944913650 Grave de Peralta Menendeza et al., "Noninvasive Localization of Electromagnetic Epileptic Activity. I. Method Descriptions and Simulations", BrainTopography 14(2), 131-137, 2001]). LAURA uses a spatial weighting function that includes depth weighting and that term has the form of a local autoregressive function.

The source activity is estimated by applying the general formula for a weighted minimum norm:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T}\left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings.''

In LAURA, V contains both a depth weighting term W and a representation of a local autoregressive function A. V is computed as:

<math>\mathrm{V} = \left( \mathrm{U}^{T} \cdot \mathrm{U} \right)^{-1}</math>


Where

<math>\mathrm{U} = \left( \mathrm{W} \cdot \mathrm{A} \right) \otimes \mathrm{I}_{3}</math>


Here, <math>\otimes</math> denotes the Kronecker product. I3 is the [3×3] identity matrix. W is an [s×s] diagonal matrix (with s the number of source locations on the grid), where each diagonal element is the inverse of the maximum singular value of the corresponding regional source's leadfields. The formula for the diagonal components Aii and the off-diagonal components Aik are as follows:

<math>\mathrm{A}_{ii} = \frac{26}{\mathrm{N}_{i}}\sum_{k \subset V_{i}}^{}\frac{1}{\mathrm{d}_{ik}^{2}}</math>


<math>
\mathrm{A}_{ik} =
\begin{cases}
- 1/\operatorname{dist}\left( i,k \right)^{2}, & \text{if } k \subset V_{i} \\
0, & \text{otherwise}
\end{cases}
</math>


Here, Vi is the vicinity around grid point i that includes the 26 direct neighbors.

The LAURA image in BESA Research displays the norm of the 3 components of S at each location r. Using the menu function ''Image / Export Image As... ''you have the option to save this norm of S or alternatively all components separately to disk.

'''Notes:'''

* '''Grid spacing:''' Due to memory limitations, LAURA images require a grid spacing of 7 mm or more.
* '''Computation time:''' Computation speed during the first LAURA image calculation depends on the grid spacing (computation is faster with larger grid spacing). After the first computation of a LAURA image, a '''*.laura''' file is stored in the data folder, containing intermediate results of the LAURA inverse. This file is used during all subsequent LAURA image computations. Thereby, the time needed to obtain the image is substantially reduced.
* '''MEG:''' In the case of MEG data, an additional constraint is implemented in the LAURA algorithm that prevents solutions from containing radial source currents (compare Pascual-Marqui, ISBET Newsletter 1995, 22-29). In MEG, an additional source space regularization is necessary in the inverse matrix operation required compute V
* '''Starting LAURA:''' LAURA can be started from the''' Image''' menu or from the '''Image Selection''' button.
* '''Regularization:''' Please refer to Chapter'' “Regularization of distributed volume images” ''for important information on regularization of distributed inverses.

== LORETA ==

LORETA ("Low Resolution Electromagnetic Tomography") is a distributed inverse method of the family of ''weighted minimum norm'' methods. LORETA was suggested by R.D. Pascual-Marqui (International Journal of Psychophysiology. 1994, 18:49-65). LORETA is characterized by a smoothness constraint, represented by a discrete 3D Laplacian.

The source activity is estimated by applying the general formula for a weighted minimum norm:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T}\left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings.''

In LORETA, V contains both a depth weighting term and a representation of the 3D Laplacian matrix. V is computed as:

<math>\mathrm{V} = \left( \mathrm{U}^{T} \cdot \mathrm{U} \right)^{- 1}</math>


where

<math>\mathrm{U} = \left( \mathrm{W} \cdot \mathrm{A} \right) \otimes \mathrm{I}_{3}</math>


Here, <math>\otimes</math> denotes the Kronecker product. I3 is the [3x3] identity matrix. W is an [sxs] diagonal matrix (with s the number of source locations on the grid), where each diagonal element is the inverse of the maximum singular value of the corresponding regional source's leadfields. A contains the 3D Laplacian and is computed as

<math>\mathrm{A} = \mathrm{Y} - \mathrm{I}_{s}</math>


with Is the [sxs] identity matrix, where s is the number of sources (= three times the number of grid points) and

<math>\mathrm{Y} = \frac{1}{2}\left\{ \mathrm{I}_{s} + \left\lbrack \operatorname{diag}\left( \mathrm{Z} \cdot \left\lbrack 111 \ldots 1 \right\rbrack^{T} \right) \right\rbrack^{- 1} \right\} \cdot \mathrm{Z}</math>


where

<math>
\mathrm{Z}_{ik} =
\begin{cases}
1/6, & \text{if } \operatorname{dist}\left( i,k \right) = 1 \text{ grid point} \\
0, & \text{otherwise}
\end{cases}
</math>


The LORETA image in BESA Research displays the norm of the 3 components of S at each location r. Using the menu function ''Image / Export Image As... ''you have the option to save this norm of S or alternatively all components separately to disk.

'''Notes:'''
* '''Grid spacing:''' Due to memory limitations, LORETA images require a grid spacing of 5 mm or more.
* '''Computation time:''' Computation speed during the first LORETA image calculation depends on the grid spacing (computation is faster with larger grid spacing). After the first computation of a LORETA image, a '''<nowiki>*.loreta</nowiki>''' file is stored in the data folder, containing intermediate results of the LORETA inverse. This file is used during all subsequent LORETA image computations. Thereby, the time needed to obtain the image is substantially reduced.
* '''MEG''': In the case of MEG data, an additional constraint is implemented in the LORETA algorithm that prevents solutions from containing radial source currents (Pascual-Marqui, ISBET Newsletter 1995, 22-29). In MEG, an additional source space regularization is necessary in the inverse matrix operation required compute V.
* '''Starting LORETA:''' LORETA can be started from the''' Image''' menu or from the '''Image Selection '''button.
* '''Regularization:''' Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed source models.

== sLORETA ==

This distributed inverse method consists of a ''standardized, unweighted minimum norm''. The method was originally suggested by R.D. Pascual-Marqui (Methods & Findings in Experimental & Clinical Pharmacology 2002, 24D:5-12) Starting point is an unweighted minimum norm computation:

<math>\mathrm{S}_{\text{MN}}\left( t \right) = \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings''.

This minimum norm estimate is now standardized to produce the sLORETA activity at a certain brain location r:

<math>\mathrm{S}_{\text{sLORETA}, r} = \mathrm{R}_{rr}^{-1/2} \cdot \mathrm{S}_{\text{MN},r}</math>


SsMN,r is the [3x1] (MEG: [2x1]) minimum norm estimate of the 3 (MEG: 2) dipoles at location r. Rrr is the [3x3] (MEG: [2x2]) diagonal block of the resolution matrix R that corresponds to the source components at the target location r. The resolution matrix is defined as:

<math>\mathrm{R} = \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{L}^{T} + \lambda \cdot \mathrm{I} \right)^{-1} \cdot \mathrm{L}</math>


The sLORETA image in BESA Research displays the norm of SsLORETA, r at each location r. Using the menu function ''Image / Export Image As...'' you have the option to save this norm of SsLORETA, r or alternatively all components separately to disk.

'''Notes:'''

* sLORETA can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== swLORETA ==

This distributed inverse method is a ''standardized, depth-weighted minimum norm'' (E. Palmero-Soler et al 2007 Phys. Med. Biol. 52 1783-1800). It differs from sLORETA only by an additional depth weighting.

Starting point is a depth-weighted minimum norm computation:

<math>\mathrm{S}_{\text{MN}}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings''.

V is the diagonal depth weighting matrix. For s grid locations, V is of dimension [3s x 3s] (MEG: [2s x 2s]). Each diagonal element of V is the inverse of the first singular value of the leadfield of the corresponding regional source. Hence, the first 3 (MEG: 2) diagonal elements equal the inverse of the largest eigenvalue of the leadfield matrix of regional source 1, and so on.

This minimum norm estimate is now standardized to produce the swLORETA activity at a certain brain location r:

<math>\mathrm{S}_{\text{swLORETA},r} = \mathrm{R}_{rr}^{-1/2} \cdot \mathrm{S}_{\text{MN},r}</math>


SsMN,r is the [3x1] (MEG: [2x1]) depth-weighted minimum norm estimate of the regional source at location r. Rrr is the [3x3] (MEG: [2x2]) diagonal block of the resolution matrix R that corresponds to the source components at the target location r. The resolution matrix is defined as:

<math>\mathrm{R} = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} + \lambda \cdot \mathrm{I} \right)^{-1} \cdot \mathrm{L}</math>


The swLORETA image in BESA Research displays the norm of SswLORETA, r at each location r. Using the menu function ''Image / Export Image As...'' you have the option to save this norm of SswLORETA, r or alternatively all components separately to disk.

'''Notes:'''

* sLORETA can be started from the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== sSLOFO ==

SSLOFO (standardized shrinking LORETA-FOCUSS) is an iterative application of weighted distributed source images with a reduced source space in each iteration ([https://dx.doi.org/10.1109/TBME.2005.855720 Liu et al., "Standardized shrinking LORETA-FOCUSS (SSLOFO): a new algorithm for spatio-temporal EEG source reconstruction", IEEE Transactions on Biomedical Engineering 52(10), 1681-1691, 2005]).

In an initialization step, an [[#sLORETA | sLORETA]] image is calculated. Then in each iteration the following steps are performed:

# A weighted minimum norm solution is computed according to the formula <math display="inline">\mathrm{S} = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}</math> . Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D is the data at the time point under consideration. V is a diagonal spatial weighting matrix that is computed in the previous iteration step. In the first iteration, the elements of V contain the magnitudes of the initially computed LORETA image.
# Standardization of this weighted minimum norm image is performed with the resolution matrix as in [[#sLORETA | sLORETA]].
# The obtained standardized weighted minimum norm image is being smoothed to get Ssmooth.
# All voxels with amplitudes below a threshold of 1% of the maximum activity get a weight of zero in the next iteration step, thus being effectively eliminated from the source space in the next iteration step.
# For all other voxels, compute the elements of the spatial weighting matrix V to be used in the next iteration as follows: <math display="inline">\mathrm{V}_{ii,\text{next iteration}} = \frac{1}{\left\| \mathrm{L}_{i} \right\|} \cdot \mathrm{S}_{ii,\text{smooth}} \cdot \mathrm{V}_{ii,\text{current iteration}}</math>



The procedure stops after 3 iterations. Please note that you can change all parameters by creating a [[#User-Defined Volume Image | user-defined volume image]].

'''Notes:'''
* '''Starting sSLOFO''': sSLOFO can be started from the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter ''[[#Regularization of distributed volume images | Regularization of distributed volume images]]'' for important information on regularization of distributed inverses.

== User-Defined Volume Image ==

In addition to the predefined 3D imaging methods in BESA Research, it is possible to create user-defined imaging methods based on the general formula for distributed inverses:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. Custom-defined parameters are:* The spatial weighting matrix V: This may include depth weighting, image weighting, or cross-voxel weighting with a 3D Laplacian (as in LORETA) or an autoregressive function (as in LAURA).

* Regularization: The term in parentheses is generally regularized. Note that regularization has a strong effect on the obtained results. Please refer to chapter “''Regularization of Distributed Volume Images” ''for more information.
* Standardization: Optionally, the result of the distributed inverse can be standardized with the resolution matrix (as in sLORETA).
* Iterations: Inverse computations can be applied iteratively. Each iteration is weighted with the image obtained in the previous iteration.

All parameters for the user-defined volume image are specified in the User-Defined Volume Tab of the Image Settings dialog box. Please refer to chapter “''User-Defined Volume Tab”'' for details.

'''Notes:'''
* Starting the user-defined volume image: the image calculation can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== Regularization of distributed volume images ==

Distributed source images require the inversion of a term of the form L V LT. This term is generally regularized before its inversion. In BESA Research, selection can be made between two different regularization approaches (parameters are defined in the ''Image Settings dialog box''):

* '''Tikhonov regularization''': In Tikhonov regularization, the term L V LT is inverted as (L V LT +λ I)-1. Here, l is the regularization constant, and I is the identity matrix.
* One way of determining the optimum regularization constant is by minimizing the ''generalized cross'' ''validation error'' (CVE).
* Alternatively, the regularization constant can be specified manually as a percentage of the trace of the matrix L V LT.
* '''TSVD''': In the truncated singular value decomposition (TSVD) approach, an SVD decomposition of L V LT is computed as  L V LT = U S UT, where the diagonal matrix S contains the singular values. All singular values smaller than the specified percentage of the maximum singular values are set to zero. The inverse is computed as U S-1 UT, where the diagonal elements of S-1 are the inverse of the corresponding non-zero diagonal elements of S.

Regularization has a critical effect on the obtained distributed source images. The results may differ completely with different choices of the regularization parameter (see examples below). Therefore, it is important to evaluate the generated image critically with respect to the regularization constant, and to keep in mind the uncertainties resulting from this fact when interpreting the results. The default setting in BESA Research is a TSVD regularization with a 0.03% threshold. However, this value might need to be adjusted to the specific data set at hand.

The following example illustrates the influence of the regularization parameter on the obtained images. The data used here is condition '''St-Cor of dataset Examples \ TFC-Error-Related-Negativity \ Correct+Error.fsg''' at 176 ms following the visual stimulus. Discrete dipole analysis reveals the main activity in the left and right lateral visual cortex at this latency.

[[Image:SA 3Dimaging (42).gif]]

''Discrete source model at 176 ms: Main activity in the left and right lateral visual cortex, no visual midline activity.''

LORETA images computed at this latency depend critically on the choice of the regularization constant. The following 3D images are created with TSVD regularization with SVD cutoffs of 0.1%, 0.005%, and 0.0001%, respectively. The volume grid size was 9 mm. The example demonstrates the dramatic effect of regularization and demonstrates the typical tradeoff between too strong regularization (leading to too smeared 3D images that tend to show blurred maxima) and too small regularization (resulting in too superficial 3D images with multiple maxima).

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (43).gif|thumb|350px|'''SVD cutoff 0.1%''': Regularization too strong. No separation between sources, mislocalization towards the middle of the brain.]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (44).gif|thumb|350px|'''SVD cutoff 0.005%''': Appropriate regularization. Separation of the bilateral activities. Location in agreement with the discrete multiple source model.]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (45).gif|thumb|350px|'''SVD cutoff 0.0001%''': Too small regularization. Mislocalization, too superficial 3D image. ]] </li>
</ul></div>

The automatic determination of the regularization constant using the CVE approach does not necessarily result in the optimum regularization parameter either. In this example, the unscaled CVE approach rather resembles the TSVD image with a cutoff of 0.0001%, i.e. regularization is too small. Therefore, it is advisable to compare different settings of the regularization parameter and make the final choice based on the above-mentioned considerations.

== Cortical LORETA ==

Cortical LORETA is principally the same technique as LORETA, however, Cortical LORETA is not computed in a 3D volume, but on the cortical surface.

The cortical reconstruction in BESA Research fed from BESA MRI is a closed 2D surface with no boundaries and a very close approximation of the actual cortical form. It consists of an irregular triangulated grid.

The Laplace operator that is used for identifying a smooth solution in a three-dimensional space is exchanged with a Laplace operator that runs on the two-dimensional cortical surface.

There is a wide variety of 2D Laplace operators with different characteristics. The general form of the discrete Laplace operator is

<math>\Delta f\left( p_{i} \right) = \frac{1}{d_{i}}\sum_{j \in N(i)}^{}{w_{ij}\left\lbrack f\left( p_{i} \right) - f\left( p_{j} \right) \right\rbrack},</math>


where '''pi''' is the '''i-th''' node of the triangular mesh, '''f(pi) '''is the value of a function f defined on the cortical mesh at the node '''pi''', '''wij''' is the weight for the connection between the nodes '''pi''' and '''pj''' and '''di''' is a normalization factor for the '''i-th''' row of the operator. Furthermore, '''N(i)''' is the set of indices corresponding to the direct (also called "1-ring") neighbors of '''pi'''.

BESA offers the choice of three Laplace operators with slightly different characteristics.

* '''Unweighted Graph Laplacian''': This is the simplest operator. It takes into account only the adjacency of the nodes and not the geometry of the mesh:

<math>
w_{ij} =
\begin{cases}
1, & \text{if } p_{i} \text{ and } p_{j} \text{ are connected by an edge} \\
0, & \text{otherwise}
\end{cases}
</math>

<math>d_{i} = 1</math>


[[Image:SA 3Dimaging (4).jpg |450px]]

* '''Weighted Graph Laplacian:''' This operator is similar to the unweighted graph Laplacian but with different weights for the different connections. The connections between nearby nodes get larger weights than the connections between farther nodes:

<math>w_{ij} = \frac{1}{\operatorname{dist}\left( p_{i},p_{j} \right)}</math>

<math>d_{i} = \sum_{j \in N(i)}^{} {\operatorname{dist}\left(p_{i}, p_{j} \right)}</math>


where '''dist''' ('''pi''' , '''pj''') is the distance between the nodes '''pi '''and '''pj'''.

[[Image:SA 3Dimaging (6).jpg|450px]]

* '''Geometric Laplacian with mixed area weights''': This operator takes into account the angles in the corresponding triangles into account as well as the area around the nodes in order to determine the connection weights:

<math>w_{ij} = \frac{\cot\left( \alpha_{ij} \right) + \cot\left( \beta_{ij} \right)}{2}</math>

<math>d_{i} = A_{\text{mixed}}</math>


where '''αij''' and '''βij''' denote the two angles opposite to the edge ('''i , j''') and '''Amixed '''is either the Voronoi area, or 1/2 of the triangle area or 1/4 of the triangle area depending on the type of the triangle.

[[Image:SA 3Dimaging (8).jpg|450px]]

'''Regularization and other parameters:'''

[[Image:CorticalLOR.png‎]]

* '''SVD cutoff''': The regularization for the inverse operator as a percent of the largest singular value.
* '''Depth weighting''': Turn depth weighting on or off.
* '''Laplacian type''': Selection of Laplacian operators (see above).

'''Notes:'''
* '''Starting Cortical LORETA''': Cortical LORETA can be started from the sub-menu '''Surface Image''' of the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]''” for important information on regularization of distributed inverses.

== Cortical CLARA ==

Cortical CLARA is principally the same technique as CLARA, but Cortical CLARA is not computed in a 3D volume, but on the cortical surface. Instead of using a LORETA image as the basis for the iterative application, cortical CLARA uses cortical LORETA.

'''Regularization and other parameters:'''

[[Image:SA 3Dimaging (47).gif]]

* '''SVD cutoff''': The regularization for the inverse operator as a percent of the largest singular value.
* '''Depth weighting''': Turn depth weighting on or off.
* '''Laplacian type''': Selection of Laplacian operators (see Cortical LORETA).
* '''No of iterations''': Number of iterations for CLARA. The more iterations are used, the sparser becomes the solution.
* '''Automatic''': The algorithm tries to determine the number of iterations automatically. The goodness of fit (GOF) is calculated after every iteration and if there is a big jump in the GOF then the algorithm will stop. If no jumps appear during the calculations then CLARA iterates until the specified number of iterations is reached.
* '''Regularize iterations''': If one wants to use different regularization for the CLARA iterations than the value specified as "SVD cutoff", this option should be selected.
* '''Amount to clip from img (%)''': Cortical CLARA uses the solution from the previous iteration as an additional weighting matrix for the current iteration. That weighting matrix is constructed by cutting the "low" activity from the solution. This number specifies how much of the activity should be cut from the previous solution in order to construct the weighting matrix. This value is given as a percentage of the maximal activity. Default value is 10%.

'''Notes:'''

* '''Starting Cortical CLARA:''' Cortical CLARA can be started from the sub-menu '''Surface Image''' of the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]''” for important information on regularization of distributed inverses.

== Cortex Inflation ==

The inflated cortex is a smoothened version of the individual cortical surface with minimal metric distortions (Fischl, B. et al. (1999). Cortical Surface-Based Analysis: II: Inflation, Flattening, and a Surface-Based Coordinate System. ''NeuroImage'', 9(2), 195–207). Gyri and sulci are smoothened out. The original distances between each point on the cortex and its neighbors are, however, mostly preserved.

[[Image:SA 3Dimaging (48).gif]]

''Cortical LORETA map overlaid on top of the inflated cortical surface.''

A lighter gray color overlaid on top of the surface image indicates the location of a gyrus of the individual cortex surface, while a darker gray color indicates the location of a sulcus. The inflated cortical surface can be computed in '''BESA MRI 2.0'''. For more details please refer to the BESA MRI 2.0 help.

== Surface Minimum Norm Image ==

'''Introduction'''

The minimum norm approach is a common method to estimate a distributed electrical current image in the brain at each time sample (Hämäläinen & Ilmoniemi 1984). The source activities of a large number of regional sources are computed. The sources are evenly distributed using 1500 standard locations 10% and 30% below the smoothed standard brain surface (when using the standard MRI) or using between 3000-4000 locations on the individual brain surface defined by the gray-white-matter boundary.

Since the number of sources is much larger than the number of sensors in a minimum norm solution, the inverse problem is highly underdetermined and must be stabilized by a mathematical constraint, the minimum norm. Out of the many current distributions that can account for the recorded sensor data, the solution with the minimum L2 norm, i.e. the minimum total power of the current distribution is displayed in BESA Research.

First, the forward solution (leadfield matrix L) of all sources is calculated in the current head model. Then, the source activities S(t) of all source components are computed from the data matrix D(t) using an inverse regularized by the estimated noise covariance matrix:

<math>\mathrm{S}\left( t \right) = \mathrm{R} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{R} \cdot \mathrm{L}^{T} + \mathrm{C}_N \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed regional source model, CN denotes the noise correlation matrix in sensor space, and R is a weighting matrix in source space. R and CN can be designed in different ways in order to optimize the minimum norm result. The total activity of each regional source is computed as the root mean square of the source activities S(t) of its 3 (MEG:2) components. This total source activity is transformed to a color-coded image of the brain surface. (When the standard brain is used, two sources are assigned to each surface location, located 10% and 30% below the surface, respectively. The color that is displayed on the standard brain surface is the larger of the two corresponding source activities.)

'''Weighting options'''

The minimum norm current imaging techniques of BESA Research provide different weighting strategies. Two weighting approaches are available: Depth weighting and spatio-temporal approaches.
* '''Depth weighting:''' Without depth weighting, deep sources appear very smeared in a minimum-norm reconstruction. With depth weighting, both deep and superficial sources produce a similar, more focal result. If this weighting method is selected, the leadfield of each regional source is scaled with the largest singular value of the SVD (singular value decomposition) of the source's leadfield.
* '''Spatio-temporal weighting''': Spatio-temporal weighting tries to assign large weight to sources that are assumed to be more likely to contribute to the recorded data.
** '''Subspace correlation after single source scan''': This method divides the signal into a signal and a noise subspace. The correlation of the leadfield of a regional source i with the signal subspace (pi) is computed to find out if the source location contributes to the measured data. The weighting matrix R becomes a diagonal matrix. Each of the three (MEG: 2) components of a regional source get the same weighting value pi2. This approach is based on the signal subspace correlation measure introduced by J.C. Mosher, R. M. Leahy (Recursive MUSIC: A Framework for EEG and MEG Source Localization, IEEE Trans. On Biomed. Eng. Vol. 45, No. 11, November 1998)
** '''Dale & Sereno 1993:''' In the approach of Dale and Sereno (J Cogn Neurosci, 1993, 5: 162-176) a signal subspace needs not be defined. The correlation pi of the leadfield of regional source i with the inverse of the data covariance matrix is computed along with the largest singular value λmax of the data covariance matrix. The weighting matrix R is a diagonal matrix with weights: [[Image:SA 3Dimaging (50).gif]]. Each of the three (MEG: 2) components of a regional source receives the same weighting value.

'''Noise regularization'''

Two methods to estimate the channel noise correlation matrix CN are provided by the program:
* '''Use baseline:''' Select this option to estimate the noise from the user-definable baseline. The signal is computed from the data at non-baseline latencies.
* '''Use 15% lowest values:''' The baseline activity is computed from the data at those 15% of all displayed latencies that have the lowest global field power. The signal is computed from all displayed latencies.

In each case, the activity (noise or signal, respectively) is defined as root-mean-square across all respective latencies for each channel.

The noise covariance matrix CN is constructed as a diagonal matrix. The entries in the main diagonal are proportional to the noise activity of the individual channels (if selected) or are all equally proportional to the average noise activity over all channels. The noise covariance matrix CN is then scaled such that the ratio of the Frobenius norms of the weighted leadfield projector matrix (LRLT) and the noise covariance matrix CN equals the Signal-to-Noise ratio. This scaling can be multiplied by an additional factor (default=1) to sharpen (<1) or smoothen (>1) the minimum norm image.

'''Applying the Minimum Norm Image'''

The minimum-norm algorithm is started via the ''Surface minimum norm image dialog box'', which is opened from the''' Image''' menu, or by typing the shortcut '''Ctrl-M''': Please refer to Chapter ''“Surface'' ''Minimum Norm Tab”'' for more details.

As opposed to the other 3D images available from the '''Image '''menu, the surface minimum norm image is not computed on a volumetric grid, but rather for locations on the brain surface. Accordingly, the results of the minimum norm image are displayed superimposed to the brain surface mesh rather than to the volumetric MR image.

The figure below shows a minimum norm image computed from the file '''Examples\Epilepsy\Spikes\Spikes-Child4_EEG+MEG_averaged.fsg'''. The EEG spike peak was imaged using the individual brain surface of the subject. A baseline from -300 to -70 ms was used. Minimum norm was computed with depth weighting, Spatio-temporal weighting according to Dale & Sereno 1993 and individual noise weighting with a noise scale factor of 0.01. The minimum norm image reveals the location of the spike generator in the close vicinity of the frontal left-hemispheric lesion in this subject.

[[Image:SA 3Dimaging (51).gif]]

== Multiple Source Probe Scan (MSPS) ==

 
'''Introduction'''

The MSPS function provides a tool for the validation of a given solution. It is based on the following theoretical consideration: If the recorded EEG/MEG data has been modeled adequately, i.e. all active brain regions are represented by a source in the current solution, then any additional probe source added to the solution will not show any activity apart from noise. The only exception occurs if this probe source is placed in close vicinity to one of the sources in the current solution. In that case, the solution's source and the probe source will share the activity of the corresponding brain area. The MSPS applies these considerations by scanning the brain on a pre-defined grid with a regional probe added to the current solution. Grid extent and density can be specified in the Image settings. The power P of the probe source at location r in the signal interval is compared with the power of the probe source in a reference interval, defining a value q:

<math>\mathrm{q}\left( r \right) = \sqrt{\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}} - 1</math>


MSPS can be computed on time domain or time-frequency domain data:
* In the time domain, q(r) is computed from the source waveform of the probe source. Here, P(r) is the mean power of the probe source at location r in the marked latency range, and Pref(r) is the mean probe source power in the user-definable baseline interval.
* In the time-frequency domain, an MSPS image can be computed from the complex cross spectral density matrices. By applying the inverse operator for a source configuration consisting of the current solution and the probe source, the power of the probe source can be computed for the target interval [P(r)] and the reference time-frequency interval [Pref(r)]. In the resulting MSPS image, q-values are shown in %, where q[%] = q*100.

The inverse operator used to determine the probe source power uses different regularization constants for the probe source and the sources in the current solution. The regularization constant of the sources in the current solution can be specified in the Image settings (default 4%). The regularization constant of the probe source is internally set to 0%.

Alternatively to the definition above, q can also be displayed in units of dB:

<math>\mathrm{q}\left\lbrack \text{dB} \right\rbrack = 10 \cdot \log_{10}\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}</math>


Values of q smaller than zero are not shown in the MSPS image.

According to the considerations above, an MSPS of a correct source model should optimally yield image maxima around the sources in the current solution only. If the MSPS image is blurred or shows maxima at locations different from the modeled sources, this indicates a non-sufficient or incorrect solution.

'''Applying the MSPS'''

This chapter illustrates the application of the Multiple Source Probe Scan. The figures are generated with data from file '''Examples/Epilepsy/Spikes/Rolandic-Spike-Child.fsg''' (-300 : +200 ms, filtered from 3 Hz [forward] to 40 Hz [zero-phase]).

'''Time domain versus time-frequency domain MSPS'''

The multiple source probe scan can be computed in the time domain or the time-frequency domain. The latter is possible only when time-frequency domain data is available for the current condition, i.e. if the condition has been created by starting a multiple source beamformer (MSBF) computation from the source coherence window. In this case, evoking the MSPS calculation from the '''Imaging '''button or from the '''Image''' menu will bring up the following dialog window that allows to choose between time- or time-frequency MSPS. If only time domain data is available, this dialog window will not appear and MSPS will be computed in the time domain.

[[Image:SA 3Dimaging (53).gif]]

For a time-frequency domain MSPS, the target and the reference time-frequency interval have been specified already in the Time-Frequency window (see Chapter "''How To Create Beamformer Images''"). For a time-domain MSPS, the target and the reference epoch have to be specified in the Source Analysis window as described below.

'''Time domain MSPS'''

The time-domain MSPS image displays the ratio of the power of a regional probe source in the signal and the baseline interval. The currently set baseline is indicated by a horizontal line in the upper left corner of the channel box.

[[Image:SA 3Dimaging (54).gif|thumb|c|none|330px|The black horizontal bar in the upper part of the channel box (here circled in red) indicates the baseline interval.]]

By default, BESA Research defines the pre-stimulus interval of the current data segment as baseline. The baseline should represent a latency range in which no event-related activity is present in the data. There are several possibilities to modify the baseline interval: by clicking on the horizontal line with the left mouse button or by using the corresponding entry in the '''Condition '''menu or '''Fit Interval''' popup menu.

Mark an interval to define the target epoch, i.e. the time-interval for which the current solution is to be tested. Start the MSPS by selecting it from the '''Image selection '''button or from the '''Image''' menu to start the probe source scan. The''' Image '''menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window. The 3D window opens and displays the scan result.

<div><ul>
<li style="display: inline-block;"> [[Image:SA 3Dimaging (55).gif|thumb|c|none|650px|This figure shows the MSPS image applied on the three left-hemispheric sources in the solution ''''Rolandic-Spike-Child-RS2.bsa''''. The baseline is set from -300ms to -50 ms. The right-hemispheric sources have been switched off. The fit interval is set to the latency range of large overall activity in the data (-43 ms : 117 ms). A realistic FEM model appropriate for the subject's age (12 years, conductivity ratios (cr) 50) is applied. The MSPS image does not show maxima at the modeled source locations and rather shows a spread q-value distribution.]] </li>

<li style="display: inline-block;"> [[Image:SA 3Dimaging (56).gif|thumb|c|none|650px|The MSPS image for the same latency range when the right-hemispheric sources have been included. The MSPS image appears more focal and shows maxima around the modeled brain regions. This indicates the substantial improvement of the solution by adding the right-hemispheric sources that model the propagation of the epileptic spike from the left to the right hemisphere (note the radiological side convention in the 3D window).]] </li>
</ul></div>

'''Time-Resolved MSPS'''

If the MSPS has been computed on time domain data, the image can be shown separately for each latency in the selected interval. After the MSPS has been computed for the marked epoch, double-click anywhere within this epoch to display the ratio of the probe source magnitude at the selected latency and the mean probe source magnitude in the baseline. Scanning the latency range by moving the cursor (e.g. with the left and right arrow cursor keys) provides a time-resolved MSPS image.

Time-resolved MSPS images are not available if the MSPS has been computed on data in the time-frequency domain.

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (57).gif|thumb|450px|MSPS image of the spike peak activity at 0ms. The activity mainly occurs in the left hemisphere. This fact is illustrated by the source waveforms and confirmed in the MSPS image, which shows a focal maximum around the location of the red sources.]] </li>

<li style="display: inline-block;"> [[File:SA 3Dimaging (58).gif|thumb|450px|Around +27 ms, the spike has propagated to the right hemisphere. This becomes evident from the waveforms of the blue sources, which show a significant latency lag with respect to the first three sources, and from the MSPS image, which shows the maximum around blue sources at this latency.]] </li>
</ul></div>



'''Notes:'''

* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image''' menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the''' Image''' menu.
* For scaling options, please refer to the '''scaling buttons''' popup menu .
* Parameters used for the MSPS calculations can be set in the ''General Settings tab'' of the ''Image Settings dialog box.''

== Source Sensitivity ==

'''Introduction'''

The 'Source sensitivity' function displays the sensitivity of the selected source in the current source model to activity in other brain regions. Sensitivity is defined as the fraction of power at the scanned brain location that is mapped onto the selected source.

To compute the source sensitivity, unit brain activity is modeled at different locations (probe source) throughout the brain. To this data, the current source model is applied to compute the source waveforms SCM of all modeled sources:

<math>\mathrm{S}_{\text{CM}} = \mathrm{L}_{\text{CM}}^{-1} \cdot \mathrm{L}_{\text{PS}}</math>


Here LCM-1 is the regularized inverse operator for the current model, and LPS is the leadfield of the regional probe source (dimension [Nx3] for EEG and [Nx2] for MEG, respectively, where N is the number of sensors). The source amplitude SSS of the selected source in the model is a 3x3 (MEG: 2x2) sub-matrix of SCM (if the selected source is a regional source) or a 1x3-matrix (MEG: 1x2) (if the selected source is a dipole). The root mean square of the singular values of SCM is defined as the source sensitivity.

The 3D source sensitivity image displays this value for all locations on a grid specified under '''Image/Settings'''. Grid density can be specified in the Image Settings.

'''Applying the Source Sensitivity Image'''

The Source Sensitivity image is evoked from the '''Image''' menu or by pressing the corresponding hot key (default: '''V''').

This function is enabled only when a solution with an active selected source is present in the Source Analysis window. The source sensitivity image then displays the sensitivity of the selected source to activity in other brain regions.

[[Image:SA 3Dimaging (59).gif]]

''Source Sensitivity image for the selected frontal source (green) in model ''''''High_Intensity_3RS.bsa'''''' in folder 'Examples/ERP_Auditory_Intensity'. The data displayed is the '100dB' condition in file ''''''All_Subjects_cc.fsg''''''. The selected source is sensitive to activity in the frontal brain region (yellow/white), while it is not influenced by activity in the vicinity of the left and right auditory cortex areas, which are modeled by the red and blue source in the model (transparent/gray).''

'''Notes:'''

* The sensitivity image is independent of the recorded sensor signals. It only depends on the current source model, the sensor configuration, the head model, and the regularization constant.
* If the regularization constant is set to zero, each source has a sensitivity of 100% to activity around its own location. With increasing regularization, the spatial filter becomes less focused, and the sensitivity of a source to activity at its location decreases.
* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image''' menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the '''Image''' menu.

{{BESAManualNav}}

Source Analysis 3D Imaging

2019-03-28T12:41:08Z

Jamie:

{{BESAInfobox
|title = Module information
|module = BESA Research Standard or higher
|version = 6.1 or higher
}}


== Overview ==

BESA Research features a set of new functions that provide 3D images that are displayed superimposed to the individual subject's anatomy. This chapter introduces these different images and describe their properties and applications.

The 3D images can be divided into three categories:

'''Volume images:'''

* '''The Multiple Source Beamformer (MSBF)''' is a tool for imaging brain activity. It is applied in the time-domain or time-frequency domain. The beamformer technique in time-frequency domain can image not only evoked, but also induced activity, which is not visible in time-domain averages of the data.
* '''Dynamic Imaging of Coherent Sources (DICS)''' can find coherence between any two pairs of voxels in the brain or between an external source and brain voxels. DICS requires time-frequency-transformed data and can find coherence for evoked and induced activity.

The following imaging methods provide an image of brain activity based on a distributed multiple source model:
* '''CLARA''' is an iterative application of LORETA images, focusing the obtained 3D image in each iteration step.
* '''LAURA '''uses a spatial weighting function that has the form of a local autoregressive function.
* '''LORETA''' has the 3D Laplacian operator implemented as spatial weighting prior.
* '''sLORETA''' is an unweighted minimum norm that is standardized by the resolution matrix.
* '''swLORETA '''is equivalent to sLORETA, except for an additional depth weighting.
* '''SSLOFO '''is an iterative application of standardized minimum norm images with consecutive shrinkage of the source space.
* A '''User-defined volume image''' allows to experiment with the different imaging techniques. It is possible to specify user-defined parameters for the family of distributed source images to create a new imaging technique.
* Bayesian source imaging: '''SESAME''' uses a semi-automated Bayesian approach to estimate the number of dipoles along with their parameters.

'''Surface image:'''

* The '''Surface Minimum Norm Image'''. If no individual MRI is available, the minimum norm image is displayed on a standard brain surface and computed for standard source locations. If available, an individual brain surface is used to construct the distributed source model and to image the brain activity.
* '''Cortical LORETA'''. Unlike classical LORETA, cortical LORETA is not computed in a 3D volume, but on the cortical surface.
* '''Cortical CLARA'''. Unlike classical CLARA, cortical CLARA is not computed in a 3D volume, but on the cortical surface.

'''Discrete model probing:'''

These images do not visualize source activity. Rather, they visualize properties of the currently applied discrete source model:
* The '''Multiple Source Probe Scan (MSPS)''' is a tool for the validation of a discrete multiple source model.
* The '''Source Sensitivity image''' displays the sensitivity of a selected source in the current discrete source model and is therefore data independent.

== Multiple Source Beamformer (MSBF) in the Time-frequency Domain ==

 
'''Short mathematical introduction'''

The BESA beamformer is a modified version of the linearly constrained minimum variance vector beamformer in the time-frequency domain as described in [https://dx.doi.org/10.1073/pnas.98.2.694 Gross et al., "Dynamic imaging of coherent sources: Studying neural interactions in the human brain", PNAS 98, 694-699, 2001]. It allows to image evoked and induced oscillatory activity in a user-defined time-frequency range, where time is taken relative to a triggered event.

The computation is based on a transformation of each channel's single trial data from the time domain into the time-frequency domain. This transformation is performed by the BESA Research Source Coherence module and leads to the complex spectral density Si (f,t), where i is the channel index and f and t denote frequency and time, respectively. Complex cross spectral density matrices C are computed for each trial:

<math>\mathrm{C}_{ij}\left( f,t \right) = \mathrm{S}_{i}\left( f,t \right) \cdot \mathrm{S}_{j}^{*}\left( f,t \right)</math>


The output power P of the beamformer for a specific brain region at location r is then computed by the following equation:

<math>\mathrm{P}\left( r \right) = \operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{-1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{-1}</math>


Here, Cr-1 is the inverse of the SVD-regularized average of Cij(f,t) over trials and the time-frequency range of interest; L is the leadfield matrix of the model containing a regional source at target location r and, optionally, additional sources whose interference with the target source is to be minimized; tr'[] is the trace of the [3×3] (MEG:[2×2]) submatrix of the bracketed expression that corresponds to the source at target location r.

In BESA Research, the output power P(r) is normalized with the output power in a reference time-frequency interval Pref(r). A value q ist defined as follows:

<math> \mathrm{q}\left( r \right) =
\begin{cases}
\sqrt{\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}(r)}} - 1 = \sqrt{\frac{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{\text{ref},r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}} - 1, & \text{for }\mathrm{P}(r) \geq \mathrm{P}_{\text{ref}}(r) \\

1 - \sqrt{\frac{\mathrm{P}_{\text{ref}}\left( r \right)}{\mathrm{P}\left( r \right)}} = 1 - \sqrt{\frac{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{\text{ref},r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}}, & \text{for }\mathrm{P}(r) < \mathrm{P}_{\text{ref}}(r)
\end{cases} </math>


Pref can be computed either from the corresponding frequency range in the baseline of the same condition (i.e. the beamformer images event-related power increase or decrease) or from the corresponding time-frequency range in a control condition (i.e. the beamformer images differences between two conditions). The beamformer image is constructed from values q(r) computed for all locations on a grid specified in the '''General Settings tab'''. For MEG data, the innermost grid points within a sphere of approx. 12% of the head diameter are assigned interpolated rather than calculated values).
q-values are shown in %, where where q[%] = q*100. Alternatively to the definition above, q can also be displayed in units of dB:

<math>\mathrm{q}\left\lbrack \text{dB} \right\rbrack = 10 \cdot \log_{10}\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}</math>


A beamformer operator is designed to pass signals from the brain region of interest r without attenuation, while minimizing interference from activity in all other brain regions. Traditional single-source beamformers are known to mislocalize sources if several brain regions have highly correlated activity. Therefore, the BESA beamformer extends the traditional single-source beamformer in order to implicitly suppress activity from possibly correlated brain regions. This is achieved by using a multiple source beamformer calculation that contains not only the leadfields of the source at the location of interest r, but also those of possibly interfering sources. As a default, BESA Research uses a bilateral beamformer, where specifically contributions from the homologue source in the opposite hemisphere are taken into account (the matrix L thus being of dimension N×6 for EEG and N×4 for MEG, respectively, where N is the number of sensors). This allows for imaging of highly correlated bilateral activity in the two hemispheres that commonly occurs during processing of external stimuli.

In addition, the beamformer computation can take into account possibly correlated sources at arbitrary locations that are specified in the current solution. This is achieved by adding their leadfield vectors to the matrix L in the equation above.

'''Applying the Beamformer'''

This chapter illustrates the usage of the BESA beamformer. The displayed figures are generated using the file ''''Examples/Learn-by-Simulations/AC-Coherence/AC-Osc20.foc'''' (see BESA Tutorial 6: "''Time-frequency analysis and Source coherence''").

'''Starting the beamformer from the time-frequency window'''

The BESA beamformer is applied in the time-frequency domain and therefore requires the Source Coherence module to be enabled. The time-frequency beamformer is especially useful to image in- or decrease of induced oscillatory activity. Induced activity cannot be observed in the averaged data, but shows up as enhanced averaged power in the TSE (Temporal-Spectral Evolution) plot. For instructions on how to initiate a beamformer computation in the time-frequency window, please refer to Chapter '''[[Source_Coherence_How_to...#How_to_Start_the_Beamformer_from_the_Time-Frequency_Window|How to Create Beamformer Images]]'''.

After the beamformer computation has been initiated in the time-frequency window, the source analysis window opens with an enlarged 3D image of the q-value computed with a '''bilateral beamformer'''. The result is superimposed onto the MR image assigned to the data set (individual or standard).

[[Image:SA 3Dimaging (5).gif]]

''Beamformer image after starting the computation in the Time-Frequency window. A bilateral pair of sources in the auditory cortex accounts for the highly correlated oscillatory induced activity. Only the bilateral beamformer manages to separate these activities; a traditional single-source beamformer would merge the two sources into one image maximum in the head center instead.''

'''Multiple source beamformer in the Source Analysis window'''

The 3D imaging display is part of the source analysis window. If you press the '''Restore''' button at the right end of the title bar of the 3D window, the window appears at the bottom right of the source analysis window. In the channel box, the averaged (evoked) data of the selected condition is shown. When a control condition was selected, its average is appended to the average of the target condition.

[[Image:SA 3Dimaging (6).gif]]

''Source Analysis window with beamformer image. The two sources have been added using the '''''Switch to''''' '''''Maximum''''' and '''''Add Source '''''toolbar buttons (see below). Source waveforms are computed from the displayed averaged data. Therefore, they do not represent the activity displayed in the beamformer image, which in this simulation example is induced (i.e. not phase-locked to the trigger)!''

When starting the beamformer from the time-frequency window, a bilateral beamformer scan is performed. In the source analysis window, the beamformer computation can be repeated taking into account possibly correlated sources that are specified in the current solution. Interfering activities generated by all sources in the current solution that are in the 'On' state are specifically suppressed ('''they enter the matrix L in the beamformer calculation''', see Chapter ''Short mathematical description'' above). The computation can be started from the '''Image''' menu or from the '''Image selector button''' dropdown menu. The '''Image''' menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window.

[[Image:SA 3Dimaging (7).gif]]

''Multiple source beamformer image calculated in the presence of a source in the left hemisphere. A '''single''' source scan has been performed. The source set in the current solution accounts for the left-hemispheric q-maximum in the data. Accordingly, the beamformer scan reveals only the as yet unmodeled additional activity in the right hemisphere (note the radiological convention in the 3D image display).''

The beamformer scan can be performed with a '''single''' or a '''bilateral''' source scan. The default scan type depends on the current solution:
* When the beamformer is started from the Time-Frequency window, the Source Analysis window opens with a new solution and a '''bilateral''' beamformer scan is performed.
* When the beamformer is started within the Source Analysis window, the default is
** a scan with a '''single''' source in addition to the sources in the current solution, if at least one source is active.
** a '''bilateral''' scan if no source in the current solution is active.

The default scan type is the multiple source beamformer. The non-default scan type can be enforced using the corresponding ''Volume Image / Beamformer'' entry in the '''Image''' menu.

'''Inserting Sources out of the Beamformer Image'''

The beamformer image can be used to add sources to the current solution. A simple double-click anywhere in the 2D- or 3D-view will generate a non-oriented regional source at the corresponding location. However, a better and easier way to create sources at image maxima and minima is to use the toolbar buttons '''Switch to Maximum''' [[Image:SA 3Dimaging (8).gif]] and '''Add Source''' [[Image:SA 3Dimaging (9).gif]].

Use the '''Switch to Maximum''' button to place the red crosshair of the 3D window onto a local image maximum or minimum. Hitting the '''Add Source''' button creates a regional source at the location of the crosshair and therefore ensures the exact placement of the source at the image extremum. Moreover, the '''Add Source''' button generates an oriented regional source. BESA Research automatically estimates the source orientation that contributes most to the power in the target time-frequency interval (or the reference time-frequency interval, if its power is larger than that in the target interval). The accuracy of this orientation estimate depends largely on the noise content of the data. The smaller the signal-to-noise ratio of the data, the lower is the accuracy of the orientation estimate. '''This feature allows to use the beamformer as a tool to create a source montage for source coherence analysis, where it is of advantage to work with oriented sources'''.

'''Notes:'''

* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image '''menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the''' Image''' menu.
* For scaling options, use the [[Image:SA 3Dimaging (10).gif]] and [[Image:SA 3Dimaging (11).gif]] '''Image Scale toolbar''' buttons.
* Parameters used for the beamformer calculations can be set in the '''Standard Volumes''' of the ''Image Settings dialog box.''

== Dynamic Imaging of Coherent Sources (DICS) ==

 
'''Short mathematical introduction'''

Dynamic Imaging of Coherent Sources (DICS) is a sophisticated method for imaging cortico-cortical coherence in the brain, or coherence between an external reference (e.g. EMG channel) and cortical structures. DICS can be applied to localize evoked as well as induced coherent cortical activity in a user-defined time-frequency range.

DICS was implemented in BESA closely following [https://dx.doi.org/10.1073/pnas.98.2.694 Gross et al., "Dynamic imaging of coherent sources: Studying neural interactions in the human brain", PNAS 98, 694-699, 2001].

The computation is based on a transformation of each channel's single trial data from the time domain into the frequency domain. This transformation is performed by the BESA Research Coherence module and results in the complex spectral density matrix that is used for constructing the spatial filter similar to beamforming.

DICS computation yields a 3-D image, each voxel being assigned a coherence value. Coherence values can be described as a neural activity index and do not have a unit. The neural activity index contrasts coherence in a target time-frequency bin with coherence of the same time-frequency bin in a baseline.

'''DICS for cortico-cortical coherence is computed as follows:'''

Let L(r) be the leadfield in voxel r in the brain and C the complex cross-spectral density matrix. The spatial filter W(r) for the voxel r in the head is defined as follows:

<math>W\left( r \right) = \left\lbrack L^{T}\left( r \right) \cdot C^{- 1} \cdot L\left( r \right) \right\rbrack^{- 1} \cdot L^{T}(r) \cdot C^{- 1}</math>


The cross-spectrum between two locations (voxels) r1 and r2 in the head are calculated with the following equation:

<math>C_{s}\left( r_{1},r_{2} \right) = W\left( r_{1} \right) \cdot C \cdot W^{*T}\left( r_{2} \right),</math>


where <nowiki>*T</nowiki> means the transposed complex conjugate of a matrix. The cross-spectral density can then be calculated from the cross spectrum as follows:

<math>c_{s}\left( r_{1},r_{2} \right) = \lambda_{1}\left\{ C_{s}\left( r_{1},r_{2} \right) \right\},</math>


where λ1{} indicates the largest singular value of the cross spectrum. Once the cross spectral density is estimated, the connectivity¹(CON) between the two brain regions r1 and r2 are calculated as follows:

<math>\text{CON}\left( r_{1},r_{2} \right) = \frac{c_{s}^{\text{sig}}\left( r_{1},r_{2} \right) - c_{s}^{\text{bl}}(r_{1},r_{2})}{c_{s}^{\text{sig}}\left( r_{1},r_{2} \right) + c_{s}^{\text{bl}}(r_{1},r_{2})},</math>


where cssig is the cross-spectral density for the signal of interest between the two brain regions r1 and r2, and csbl is the corresponding cross spectral density for the baseline or the control condition, respectively. In the case DICS is computed with a cortical reference, r1 is the reference region (voxel) and remains constant while r2 scans all the grid points within the brain sequentially. In that way, the connectivity between the reference brain region and all other brain regions is estimated. The value of CON(r1, r2) falls in the interval [-1 1]. If the cross-spectral density for the baseline is 0 the connectivity value will be 1. If the cross-spectral density for the signal is 0 the connectivity value will be -1.

¹ Here, the term connectivity is used rather than coherence, as strictly speaking the coherence equation is defined slightly differently. For simplicity reasons the rest of the tutorial uses the term coherence.

'''DICS for cortico-muscular coherence is computed as follows:'''

When using an external reference, the equation for coherence calculation is slightly different compared to the equation for cortico-cortical coherence. First of all, the cross-spectral density matrix is not only computed for the MEG/EEG channels, but the external reference channel is added. This resulting matrix is Call. In this case, the cross-spectral density between the reference signal and all other MEG/EEG

channels is called cref. It is only one column of Call. Hence, the cross-spectrum in voxel r is calculated with the following equation:

<math>C_{s}\left( r \right) = W\left( r \right) \cdot c_{\text{ref}}</math>


and the corresponding cross-spectral density is calculated as the sum of squares of Cs:

<math>c_{s}\left( r \right) = \sum_{i = 1}^{n}{C_{s}\left( r \right)_{i}^{2}},</math>


where n is 2 for MEG and 3 for EEG. This equation can also be described as the squared Euclidean norm of the cross-spectrum:

<math>c_{s}\left( r \right) = \left\| C_{s} \right\|^{2},</math>


The power in voxel r is calculated as in the cortico-cortical case:

<math>p\left( r \right) = \lambda_{1}\left\{ C_{s}(r,r) \right\}.</math>


At last, coherence between the external reference and cortical activity is calculated with the equation:

<math>\text{CON}\left( r \right) = \frac{c_{s}(r)}{p\left( r \right) \cdot C_{\text{all}}(k,k)},</math>


where Call(k, k) is the (k,k)-th diagonal element of the matrix Call.

DICS is particularly useful, if coherence is to be calculated without an a-priory source model (in contrast to source coherence based on pre-defined source montages). However, the recommended analysis strategy for DICS is to use a brain source as a starting point for coherence calculation that is known to contribute to the EEG/MEG signal of interest. For example, one might first run a beamformer on the time-frequency range of interest and use the voxel with the strongest oscillatory activity as a starting point for DICS. The resulting coherence image will again lead to several maxima (ordered by magnitude), which in turn can serve as starting points for DICS calculation. This way, it is possible to detect even weak sources that show coherent activity in the given time-frequency range.

The other significant application for DICS is estimating coherence between an external source and voxels in the brain. For example, an external source can be muscle activity recoded by an electrode placed over the according peripheral region. This way, the direct relationship between muscle activity and brain activation can be measured.

'''Starting DICS computation from the Time-Frequency Window'''

DICS is particularly useful, if coherence in a user-defined time-frequency bin (evoked or induced) is to be calculated between any two brain regions or between an external reference and the brain. DICS runs only on time-frequency decomposed data, so time-frequency analysis needs to be run before starting DICS computation.

To start the DICS computation, left-drag a window over a selected time-frequency bin in the Time-Frequency Window. Right-click and select “Image”. A dialogue will open (see fig. 1) prompting you to specify time and frequency settings as well as the baseline period. It is recommended to use a baseline period of equal length as the data period of interest. Make sure to select “DICS” in the top row and press “'''Go'''”.

[[Image:SA 3Dimaging (21).gif|450px|thumb|c|none|Fig. 1: Time and frequency settings for DICS and MSBF]]

Next, a window will appear allowing you to specify the reference source for coherence calculation (see fig. 2). It is possible to select a channel (e.g. EMG) or a brain source. If a brain source is chosen and no source analysis was computed beforehand, the option “Use current cross-hair position” must be chosen. In case discrete source analysis was computed previously, the selected source can be chosen as the reference for DICS. Please note that DICS can be re-computed with any cross-hair or source position at a later stage.

[[Image:SA 3Dimaging (1).jpg|400px|thumb|c|none|Fig. 2: Possible options for choosing the reference]]

Confirming with “'''OK'''” will start computation of coherence between the selected channel/voxel and all other brain voxels. In case DICS is computed for a reference source in the brain, it can be advantageous to run a beamforming analysis in the selected time-frequency window first and use one of the beamforming maxima as reference for DICS. Fig. 3 shows an example for DICS calculation.

[[Image:SA 3Dimaging (22).gif|500px|thumb|c|none|Fig. 3: Coherence between left-hemispheric auditory areas and the selected voxel in the right auditory cortex.]]

Coherence values range between -1 and 1. If coherence in the signal is much larger than coherence in the baseline (control condition) then the DICS value is going to approach 1. Contrary, if coherence in the baseline is much larger than coherence in the signal, then the DICS value is going to approach -1. At last, if coherence in the signal is equal to coherence in the baseline, then the DICS value is 0.

In case DICS is to be re-computed with a different reference, simply mark the desired reference position by placing the cross-hair in the anatomical view and select “DICS” in the middle panel of the source analysis window (see Fig. 4). In case an external reference is to be selected, click on “DICS” in the middle panel to bring up the DICS dialogue (see. Fig. 2) and select the desired channel. Please note that DICS computation will only be available after running time-frequency analysis.

[[Image:SA 3Dimaging (23).gif|700px|thumb|c|none|Fig. 4: Integration of DICS in the Source Analysis window]]

== Multiple Source Beamformer (MSBF) in the Time Domain ==
''(requires Besa Research 7.0 or higher)''

===Short mathematical introduction===

Beamforming approach can be also applied in the time domain data. This approach was introduced as linearly constrained minimum variance (LCMV) beamformer (Van Veen et al., 1997). It allows to image evoked activity in a user-defined time range, where time is taken relative to a triggered event, and to estimate source waveforms using the calculated spatial weight at locations of interest. For an implementation of the beamformer in the time domain, data covariance matrices are required, while complex cross spectral density matrices are used for the beamformer approaches in the time-frequency domain as described in the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section.

The bilateral beamformer introduced in the ''[[Source_Analysis_3D_Imaging#Multiple_Source_Beamformer_.28MSBF.29_in_the_Time-frequency_Domain|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section is also implemented for the time-domain beamformer to take into account contributions from the homologue source in the opposite. This allows for imaging of highly correlated bilateral activity in the two hemispheres that commonly occurs during processing of external stimuli. In addition, the beamformer computation can take into account possibly correlated sources at arbitrary locations.
The beamformer spatial weight W(r) for the voxel r in the brain is defined as follows (Van Veen et al., 1997):

[[File:MSBF1.png]]

where '''C-1''' is the inversed regularized average of covariance matrix over trials, '''L''' is the leadfield matrix of the model containing a regional source at target location r and optionally
additional sources whose interference with the target source is to be minimized. The beamformer spatial weight '''W'''(r) can be applied to the measured data to estimate source
waveform at a location r (beamformer virtual sensor):

[[File:MSBF2.png]]

where '''S'''(r,t) represents the estimated source waveform and '''M'''(t) represents measured EEG or MEG signals.
The output power P of the beamformer for a specific brain region at location r is computed by the following equation:

[[File:MSBF3.png]]

where tr’[ ] is the trace of the [3×3] (MEG: [2×2]) submatrix of the bracketed expression that corresponds to the source at target location r.
Beamformer can suppress noise sources that are correlated across sensors. However, uncorrelated noise will be amplified in a spatially non-uniform manner, with increasing
distortion with increasing distance from the sensors (Van Veen et al., 1997; Sekihara et al., 2001). For this reason, estimated source power should be normalized by a noise power.
In BESA Research, the output power P(r) is normalized with the output power in a baseline interval or with the output power of a uncorrelated noise: P(r) / Pref (r).
The time-domain beamformer image is constructed from values q(r) computed for all locations on a grid specified in the '''General Settings''' tab. A value q(r) is defined as described in
the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section with data covariance matrices instead of cross-spectral density matrices.

===Applying the Beamformer===

This chapter illustrates the usage of the BESA beamformer in the time domain. The displayed figures are generated using the file ‘Examples/ERP-Auditory-Intensity/S1.cnt’.

'''Starting the time-domain beamformer from the Average tab of the Paradigm dialog box'''

The time-domain beamformer is needed data covariance matrices and therefore requires the ERP module to be enabled. After the beamformer computation has been initiated in the
'''Average tab of the Paradigm dialog box''', the source analysis window opens with an enlarged 3D image of the q-value computed with a bilateral beamformer. The result is
superimposed onto the MR image assigned to the data set (individual or standard).

[[File:MSBF44.png]]

''Beamformer image for auditory evoked data after starting the computation in the '''Average tab of the Paradigm dialog box'''. The bilateral beamformer manages to separate the
activities in auditory areas, while a traditional single-source beamformer would merge the two sources into one image maximum in the head center instead.''

'''Multiple-source beamformer in the Source Analysis window'''

The 3D imaging display is part of the source analysis window. In the Channel box, the averaged (evoked) data of the selected condition is shown. Selected covariance intervals in
the ERP module can be checked in the Channel box. The red, gray, and blue rectangles indicate signal, baseline, and common interval, respectively.

[[File:MSBF55.png]]

''Source Analysis window with beamformer image. The two beamformer virtual sensors have been added using the Switch to Maximum and Add Source toolbar buttons (see below).
Source waveforms are computed using the beamformer spatial weights and the displayed averaged data (the noise normalized weights (5% noise) option was used to compute the
beamformer image).''

When starting the beamformer from the '''Average tab of the Paradigm dialog box''', the bilateral beamformer scan is performed. In the source analysis window, the beamformer computation can be repeated taking into account possibly correlated sources that are specified in the current solution. Interfering activities generated by all sources in the current solution that are in the 'On' state are specifically suppressed (they enter the leadfield matrix L in the beamformer calculation). The computation can be started from the '''Image''' menu or from the Image selector button [[File:MSBF_Button.png|22px|Image: 22 pixels]] dropdown menu. The Image menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window.

[[File:MSBF66.png]]

''Multiple-source beamformer image calculated in the presence of a source in the left hemisphere. A single-source scan has been performed instead of a bilateral beamforemr. The
source set in the current solution accounts for the left-hemispheric q-maximum in the data. Accordingly, the beamformer scan reveals only the as yet unmodeled additional activity in
the right hemisphere (note the radiological convention in the 3D image display). The source waveform of the beamformer virtual sensor in the left hemisphere is not shown since the
location (blue square in the figure) is not considered for the multiple-source beamformer.''

The beamformer scan can be performed with a single or a bilateral source scan. The default scan type depends on the current solution:
When the beamformer is started from the '''Average tab of the Paradigm dialog box''' the Source Analysis window opens with a new solution and a bilateral beamformer scan is
performed.
When the beamformer is started within the Source Analysis window, the default is:

* a scan with a single source in addition to the sources in the current solution, if at least one source is active.
* a bilateral scan if no source in the current solution is active.
* a scan with a single source when scalar-type beamformer is selected in the '''beamformer option dialog box'''.

The default scan type is the multiple source beamformer. The non-default scan type can be enforced using the corresponding Volume Image / Beamformer entry in the Image main
menu or in the beamformer option dialog box (only for the time-domain beamformer).

===Inserting Sources as Beamformer Virtual Sensor out of the Beamformer Image===

This is similar to the inserting sources out of the beamformer image in Multiple Source Beamformer (MSBF) in the Time-frequency Domain section.
The beamformer image can be used to add beamformer virtual sensors to the current solution. A simple double-click anywhere in the 3D view (not in the 2D view) will generate a
source at the corresponding location. A better and easier way to create sources at image maxima and minima is to use the toolbar buttons '''Switch to Maximum''' [[Image:SA 3Dimaging (8).gif]] and '''Add Source''' [[Image:SA 3Dimaging (9).gif]].

This feature allows to use the beamformer as a tool to create a source montage for '''source coherence''' analysis. A source montage file (*.mtg) for beamformer virtual sensors can
be saved using File \ Save Source Montage As… entry.

The time-domain beamformer image can be also used to add regional or dipole sources to the current solution. Press '''N''' key when there is no source in the current source array or
there is more than one beamformer virtual sensor. To create a new source array for beamformer virtual sensor, press '''N''' key when there is more than one regional or dipole source in
the current source array.

===Notes===

* You can hide or re-display the last computed image by selecting ''Hide Image'' entry in the '''Image''' menu.
* The current image can be exported to ASCII, ANALYZE, or BrainVoyager (vmp) format from the '''Image''' menu.
* For scaling options, use [[Image:SA 3Dimaging (10).gif]] and [[Image:SA 3Dimaging (11).gif]] '''Image Scale toolbar''' buttons.
* Parameters used for the beamformer calculations can be set in the '''Standard Volume tab of the Image Settings dialog box'''.
* Note that Model, Residual, Order, and Residual variance are not shown for the beamformer virtual sensor type sources.

===References===

* Sekihara, K., Nagarajan, S. S., Poeppel, D., Marantz, A., & Miyashita, Y. (2001). Reconstructing spatio-temporal activities of neural sources using an MEG vector beamformer technique. IEEE Transactions on Biomedical Engineering, 48(7), 760–771.

* Van Veen, B. D., Van Drongelen, W., Yuchtman, M., & Suzuki, A. (1997). Localization of brain electrical activity via linearly constrained minimum variance spatial filtering. IEEE Transactions on Biomedical Engineering, 44(9), 867–880

== CLARA ==

CLARA ('Classical LORETA Analysis Recursively Applied') is an iterative application of weighted LORETA images with a reduced source space in each iteration.

In an initialization step, a LORETA image is calculated. Then in each iteration the following steps are performed:

# The obtained image is spatially smoothed (this step is left out in the first iteration).
# All grid points with amplitudes below a threshold of 1% of the maximum activity are set to zero, thus being effectively eliminated from the source space in the following step.
# The resulting image defines a spatial weighting term (for each voxel the corresponding image amplitude).
# A LORETA image is computed with an additional spatial weighting term for each voxel as computed in step 3. By the default settings in BESA Research, the regularization values used in the iteration steps are slightly higher than that of the initialization LORETA image.

The procedure stops after 2 iterations, and the image computed in the last iteration is displayed. Please note that you can change all parameters by creating a user-defined volume image.

The advantage of CLARA over non-focusing distributed imaging methods is visualized by the figure below. Both images are computed from the N100 response in an auditory oddball experiment (file '''Oddball.fsg''' in subfolder ''fMRI+EEG-RT-Experiment'' of the ''Examples'' folder). The CLARA image is much more focal than the sLORETA image, making it easier to determine the location of the image maxima.

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (24).gif|thumb|350px|sLORETA image]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (25).gif|thumb|350px|CLARA image]] </li>
</ul></div>

'''Notes:'''

* Starting CLARA: CLARA can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter ''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]'' for important information on regularization of distributed inverses.

== LAURA ==

LAURA (Local Auto Regressive Average) belongs to the distributed inverse method of the family of weighted minimum norm methods ([https://doi.org/10.1023/A:1012944913650 Grave de Peralta Menendeza et al., "Noninvasive Localization of Electromagnetic Epileptic Activity. I. Method Descriptions and Simulations", BrainTopography 14(2), 131-137, 2001]). LAURA uses a spatial weighting function that includes depth weighting and that term has the form of a local autoregressive function.

The source activity is estimated by applying the general formula for a weighted minimum norm:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T}\left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings.''

In LAURA, V contains both a depth weighting term W and a representation of a local autoregressive function A. V is computed as:

<math>\mathrm{V} = \left( \mathrm{U}^{T} \cdot \mathrm{U} \right)^{-1}</math>


Where

<math>\mathrm{U} = \left( \mathrm{W} \cdot \mathrm{A} \right) \otimes \mathrm{I}_{3}</math>


Here, <math>\otimes</math> denotes the Kronecker product. I3 is the [3×3] identity matrix. W is an [s×s] diagonal matrix (with s the number of source locations on the grid), where each diagonal element is the inverse of the maximum singular value of the corresponding regional source's leadfields. The formula for the diagonal components Aii and the off-diagonal components Aik are as follows:

<math>\mathrm{A}_{ii} = \frac{26}{\mathrm{N}_{i}}\sum_{k \subset V_{i}}^{}\frac{1}{\mathrm{d}_{ik}^{2}}</math>


<math>
\mathrm{A}_{ik} =
\begin{cases}
- 1/\operatorname{dist}\left( i,k \right)^{2}, & \text{if } k \subset V_{i} \\
0, & \text{otherwise}
\end{cases}
</math>


Here, Vi is the vicinity around grid point i that includes the 26 direct neighbors.

The LAURA image in BESA Research displays the norm of the 3 components of S at each location r. Using the menu function ''Image / Export Image As... ''you have the option to save this norm of S or alternatively all components separately to disk.

'''Notes:'''

* '''Grid spacing:''' Due to memory limitations, LAURA images require a grid spacing of 7 mm or more.
* '''Computation time:''' Computation speed during the first LAURA image calculation depends on the grid spacing (computation is faster with larger grid spacing). After the first computation of a LAURA image, a '''*.laura''' file is stored in the data folder, containing intermediate results of the LAURA inverse. This file is used during all subsequent LAURA image computations. Thereby, the time needed to obtain the image is substantially reduced.
* '''MEG:''' In the case of MEG data, an additional constraint is implemented in the LAURA algorithm that prevents solutions from containing radial source currents (compare Pascual-Marqui, ISBET Newsletter 1995, 22-29). In MEG, an additional source space regularization is necessary in the inverse matrix operation required compute V
* '''Starting LAURA:''' LAURA can be started from the''' Image''' menu or from the '''Image Selection''' button.
* '''Regularization:''' Please refer to Chapter'' “Regularization of distributed volume images” ''for important information on regularization of distributed inverses.

== LORETA ==

LORETA ("Low Resolution Electromagnetic Tomography") is a distributed inverse method of the family of ''weighted minimum norm'' methods. LORETA was suggested by R.D. Pascual-Marqui (International Journal of Psychophysiology. 1994, 18:49-65). LORETA is characterized by a smoothness constraint, represented by a discrete 3D Laplacian.

The source activity is estimated by applying the general formula for a weighted minimum norm:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T}\left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings.''

In LORETA, V contains both a depth weighting term and a representation of the 3D Laplacian matrix. V is computed as:

<math>\mathrm{V} = \left( \mathrm{U}^{T} \cdot \mathrm{U} \right)^{- 1}</math>


where

<math>\mathrm{U} = \left( \mathrm{W} \cdot \mathrm{A} \right) \otimes \mathrm{I}_{3}</math>


Here, <math>\otimes</math> denotes the Kronecker product. I3 is the [3x3] identity matrix. W is an [sxs] diagonal matrix (with s the number of source locations on the grid), where each diagonal element is the inverse of the maximum singular value of the corresponding regional source's leadfields. A contains the 3D Laplacian and is computed as

<math>\mathrm{A} = \mathrm{Y} - \mathrm{I}_{s}</math>


with Is the [sxs] identity matrix, where s is the number of sources (= three times the number of grid points) and

<math>\mathrm{Y} = \frac{1}{2}\left\{ \mathrm{I}_{s} + \left\lbrack \operatorname{diag}\left( \mathrm{Z} \cdot \left\lbrack 111 \ldots 1 \right\rbrack^{T} \right) \right\rbrack^{- 1} \right\} \cdot \mathrm{Z}</math>


where

<math>
\mathrm{Z}_{ik} =
\begin{cases}
1/6, & \text{if } \operatorname{dist}\left( i,k \right) = 1 \text{ grid point} \\
0, & \text{otherwise}
\end{cases}
</math>


The LORETA image in BESA Research displays the norm of the 3 components of S at each location r. Using the menu function ''Image / Export Image As... ''you have the option to save this norm of S or alternatively all components separately to disk.

'''Notes:'''
* '''Grid spacing:''' Due to memory limitations, LORETA images require a grid spacing of 5 mm or more.
* '''Computation time:''' Computation speed during the first LORETA image calculation depends on the grid spacing (computation is faster with larger grid spacing). After the first computation of a LORETA image, a '''<nowiki>*.loreta</nowiki>''' file is stored in the data folder, containing intermediate results of the LORETA inverse. This file is used during all subsequent LORETA image computations. Thereby, the time needed to obtain the image is substantially reduced.
* '''MEG''': In the case of MEG data, an additional constraint is implemented in the LORETA algorithm that prevents solutions from containing radial source currents (Pascual-Marqui, ISBET Newsletter 1995, 22-29). In MEG, an additional source space regularization is necessary in the inverse matrix operation required compute V.
* '''Starting LORETA:''' LORETA can be started from the''' Image''' menu or from the '''Image Selection '''button.
* '''Regularization:''' Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed source models.

== sLORETA ==

This distributed inverse method consists of a ''standardized, unweighted minimum norm''. The method was originally suggested by R.D. Pascual-Marqui (Methods & Findings in Experimental & Clinical Pharmacology 2002, 24D:5-12) Starting point is an unweighted minimum norm computation:

<math>\mathrm{S}_{\text{MN}}\left( t \right) = \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings''.

This minimum norm estimate is now standardized to produce the sLORETA activity at a certain brain location r:

<math>\mathrm{S}_{\text{sLORETA}, r} = \mathrm{R}_{rr}^{-1/2} \cdot \mathrm{S}_{\text{MN},r}</math>


SsMN,r is the [3x1] (MEG: [2x1]) minimum norm estimate of the 3 (MEG: 2) dipoles at location r. Rrr is the [3x3] (MEG: [2x2]) diagonal block of the resolution matrix R that corresponds to the source components at the target location r. The resolution matrix is defined as:

<math>\mathrm{R} = \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{L}^{T} + \lambda \cdot \mathrm{I} \right)^{-1} \cdot \mathrm{L}</math>


The sLORETA image in BESA Research displays the norm of SsLORETA, r at each location r. Using the menu function ''Image / Export Image As...'' you have the option to save this norm of SsLORETA, r or alternatively all components separately to disk.

'''Notes:'''

* sLORETA can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== swLORETA ==

This distributed inverse method is a ''standardized, depth-weighted minimum norm'' (E. Palmero-Soler et al 2007 Phys. Med. Biol. 52 1783-1800). It differs from sLORETA only by an additional depth weighting.

Starting point is a depth-weighted minimum norm computation:

<math>\mathrm{S}_{\text{MN}}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings''.

V is the diagonal depth weighting matrix. For s grid locations, V is of dimension [3s x 3s] (MEG: [2s x 2s]). Each diagonal element of V is the inverse of the first singular value of the leadfield of the corresponding regional source. Hence, the first 3 (MEG: 2) diagonal elements equal the inverse of the largest eigenvalue of the leadfield matrix of regional source 1, and so on.

This minimum norm estimate is now standardized to produce the swLORETA activity at a certain brain location r:

<math>\mathrm{S}_{\text{swLORETA},r} = \mathrm{R}_{rr}^{-1/2} \cdot \mathrm{S}_{\text{MN},r}</math>


SsMN,r is the [3x1] (MEG: [2x1]) depth-weighted minimum norm estimate of the regional source at location r. Rrr is the [3x3] (MEG: [2x2]) diagonal block of the resolution matrix R that corresponds to the source components at the target location r. The resolution matrix is defined as:

<math>\mathrm{R} = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} + \lambda \cdot \mathrm{I} \right)^{-1} \cdot \mathrm{L}</math>


The swLORETA image in BESA Research displays the norm of SswLORETA, r at each location r. Using the menu function ''Image / Export Image As...'' you have the option to save this norm of SswLORETA, r or alternatively all components separately to disk.

'''Notes:'''

* sLORETA can be started from the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== sSLOFO ==

SSLOFO (standardized shrinking LORETA-FOCUSS) is an iterative application of weighted distributed source images with a reduced source space in each iteration ([https://dx.doi.org/10.1109/TBME.2005.855720 Liu et al., "Standardized shrinking LORETA-FOCUSS (SSLOFO): a new algorithm for spatio-temporal EEG source reconstruction", IEEE Transactions on Biomedical Engineering 52(10), 1681-1691, 2005]).

In an initialization step, an [[#sLORETA | sLORETA]] image is calculated. Then in each iteration the following steps are performed:

# A weighted minimum norm solution is computed according to the formula <math display="inline">\mathrm{S} = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}</math> . Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D is the data at the time point under consideration. V is a diagonal spatial weighting matrix that is computed in the previous iteration step. In the first iteration, the elements of V contain the magnitudes of the initially computed LORETA image.
# Standardization of this weighted minimum norm image is performed with the resolution matrix as in [[#sLORETA | sLORETA]].
# The obtained standardized weighted minimum norm image is being smoothed to get Ssmooth.
# All voxels with amplitudes below a threshold of 1% of the maximum activity get a weight of zero in the next iteration step, thus being effectively eliminated from the source space in the next iteration step.
# For all other voxels, compute the elements of the spatial weighting matrix V to be used in the next iteration as follows: <math display="inline">\mathrm{V}_{ii,\text{next iteration}} = \frac{1}{\left\| \mathrm{L}_{i} \right\|} \cdot \mathrm{S}_{ii,\text{smooth}} \cdot \mathrm{V}_{ii,\text{current iteration}}</math>



The procedure stops after 3 iterations. Please note that you can change all parameters by creating a [[#User-Defined Volume Image | user-defined volume image]].

'''Notes:'''
* '''Starting sSLOFO''': sSLOFO can be started from the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter ''[[#Regularization of distributed volume images | Regularization of distributed volume images]]'' for important information on regularization of distributed inverses.

== User-Defined Volume Image ==

In addition to the predefined 3D imaging methods in BESA Research, it is possible to create user-defined imaging methods based on the general formula for distributed inverses:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. Custom-defined parameters are:* The spatial weighting matrix V: This may include depth weighting, image weighting, or cross-voxel weighting with a 3D Laplacian (as in LORETA) or an autoregressive function (as in LAURA).

* Regularization: The term in parentheses is generally regularized. Note that regularization has a strong effect on the obtained results. Please refer to chapter “''Regularization of Distributed Volume Images” ''for more information.
* Standardization: Optionally, the result of the distributed inverse can be standardized with the resolution matrix (as in sLORETA).
* Iterations: Inverse computations can be applied iteratively. Each iteration is weighted with the image obtained in the previous iteration.

All parameters for the user-defined volume image are specified in the User-Defined Volume Tab of the Image Settings dialog box. Please refer to chapter “''User-Defined Volume Tab”'' for details.

'''Notes:'''
* Starting the user-defined volume image: the image calculation can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== Regularization of distributed volume images ==

Distributed source images require the inversion of a term of the form L V LT. This term is generally regularized before its inversion. In BESA Research, selection can be made between two different regularization approaches (parameters are defined in the ''Image Settings dialog box''):

* '''Tikhonov regularization''': In Tikhonov regularization, the term L V LT is inverted as (L V LT +λ I)-1. Here, l is the regularization constant, and I is the identity matrix.
* One way of determining the optimum regularization constant is by minimizing the ''generalized cross'' ''validation error'' (CVE).
* Alternatively, the regularization constant can be specified manually as a percentage of the trace of the matrix L V LT.
* '''TSVD''': In the truncated singular value decomposition (TSVD) approach, an SVD decomposition of L V LT is computed as  L V LT = U S UT, where the diagonal matrix S contains the singular values. All singular values smaller than the specified percentage of the maximum singular values are set to zero. The inverse is computed as U S-1 UT, where the diagonal elements of S-1 are the inverse of the corresponding non-zero diagonal elements of S.

Regularization has a critical effect on the obtained distributed source images. The results may differ completely with different choices of the regularization parameter (see examples below). Therefore, it is important to evaluate the generated image critically with respect to the regularization constant, and to keep in mind the uncertainties resulting from this fact when interpreting the results. The default setting in BESA Research is a TSVD regularization with a 0.03% threshold. However, this value might need to be adjusted to the specific data set at hand.

The following example illustrates the influence of the regularization parameter on the obtained images. The data used here is condition '''St-Cor of dataset Examples \ TFC-Error-Related-Negativity \ Correct+Error.fsg''' at 176 ms following the visual stimulus. Discrete dipole analysis reveals the main activity in the left and right lateral visual cortex at this latency.

[[Image:SA 3Dimaging (42).gif]]

''Discrete source model at 176 ms: Main activity in the left and right lateral visual cortex, no visual midline activity.''

LORETA images computed at this latency depend critically on the choice of the regularization constant. The following 3D images are created with TSVD regularization with SVD cutoffs of 0.1%, 0.005%, and 0.0001%, respectively. The volume grid size was 9 mm. The example demonstrates the dramatic effect of regularization and demonstrates the typical tradeoff between too strong regularization (leading to too smeared 3D images that tend to show blurred maxima) and too small regularization (resulting in too superficial 3D images with multiple maxima).

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (43).gif|thumb|350px|'''SVD cutoff 0.1%''': Regularization too strong. No separation between sources, mislocalization towards the middle of the brain.]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (44).gif|thumb|350px|'''SVD cutoff 0.005%''': Appropriate regularization. Separation of the bilateral activities. Location in agreement with the discrete multiple source model.]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (45).gif|thumb|350px|'''SVD cutoff 0.0001%''': Too small regularization. Mislocalization, too superficial 3D image. ]] </li>
</ul></div>

The automatic determination of the regularization constant using the CVE approach does not necessarily result in the optimum regularization parameter either. In this example, the unscaled CVE approach rather resembles the TSVD image with a cutoff of 0.0001%, i.e. regularization is too small. Therefore, it is advisable to compare different settings of the regularization parameter and make the final choice based on the above-mentioned considerations.

== Cortical LORETA ==

Cortical LORETA is principally the same technique as LORETA, however, Cortical LORETA is not computed in a 3D volume, but on the cortical surface.

The cortical reconstruction in BESA Research fed from BESA MRI is a closed 2D surface with no boundaries and a very close approximation of the actual cortical form. It consists of an irregular triangulated grid.

The Laplace operator that is used for identifying a smooth solution in a three-dimensional space is exchanged with a Laplace operator that runs on the two-dimensional cortical surface.

There is a wide variety of 2D Laplace operators with different characteristics. The general form of the discrete Laplace operator is

<math>\Delta f\left( p_{i} \right) = \frac{1}{d_{i}}\sum_{j \in N(i)}^{}{w_{ij}\left\lbrack f\left( p_{i} \right) - f\left( p_{j} \right) \right\rbrack},</math>


where '''pi''' is the '''i-th''' node of the triangular mesh, '''f(pi) '''is the value of a function f defined on the cortical mesh at the node '''pi''', '''wij''' is the weight for the connection between the nodes '''pi''' and '''pj''' and '''di''' is a normalization factor for the '''i-th''' row of the operator. Furthermore, '''N(i)''' is the set of indices corresponding to the direct (also called "1-ring") neighbors of '''pi'''.

BESA offers the choice of three Laplace operators with slightly different characteristics.

* '''Unweighted Graph Laplacian''': This is the simplest operator. It takes into account only the adjacency of the nodes and not the geometry of the mesh:

<math>
w_{ij} =
\begin{cases}
1, & \text{if } p_{i} \text{ and } p_{j} \text{ are connected by an edge} \\
0, & \text{otherwise}
\end{cases}
</math>

<math>d_{i} = 1</math>


[[Image:SA 3Dimaging (4).jpg |450px]]

* '''Weighted Graph Laplacian:''' This operator is similar to the unweighted graph Laplacian but with different weights for the different connections. The connections between nearby nodes get larger weights than the connections between farther nodes:

<math>w_{ij} = \frac{1}{\operatorname{dist}\left( p_{i},p_{j} \right)}</math>

<math>d_{i} = \sum_{j \in N(i)}^{} {\operatorname{dist}\left(p_{i}, p_{j} \right)}</math>


where '''dist''' ('''pi''' , '''pj''') is the distance between the nodes '''pi '''and '''pj'''.

[[Image:SA 3Dimaging (6).jpg|450px]]

* '''Geometric Laplacian with mixed area weights''': This operator takes into account the angles in the corresponding triangles into account as well as the area around the nodes in order to determine the connection weights:

<math>w_{ij} = \frac{\cot\left( \alpha_{ij} \right) + \cot\left( \beta_{ij} \right)}{2}</math>

<math>d_{i} = A_{\text{mixed}}</math>


where '''αij''' and '''βij''' denote the two angles opposite to the edge ('''i , j''') and '''Amixed '''is either the Voronoi area, or 1/2 of the triangle area or 1/4 of the triangle area depending on the type of the triangle.

[[Image:SA 3Dimaging (8).jpg|450px]]

'''Regularization and other parameters:'''

[[Image:CorticalLOR.png‎]]

* '''SVD cutoff''': The regularization for the inverse operator as a percent of the largest singular value.
* '''Depth weighting''': Turn depth weighting on or off.
* '''Laplacian type''': Selection of Laplacian operators (see above).

'''Notes:'''
* '''Starting Cortical LORETA''': Cortical LORETA can be started from the sub-menu '''Surface Image''' of the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]''” for important information on regularization of distributed inverses.

== Cortical CLARA ==

Cortical CLARA is principally the same technique as CLARA, but Cortical CLARA is not computed in a 3D volume, but on the cortical surface. Instead of using a LORETA image as the basis for the iterative application, cortical CLARA uses cortical LORETA.

'''Regularization and other parameters:'''

[[Image:SA 3Dimaging (47).gif]]

* '''SVD cutoff''': The regularization for the inverse operator as a percent of the largest singular value.
* '''Depth weighting''': Turn depth weighting on or off.
* '''Laplacian type''': Selection of Laplacian operators (see Cortical LORETA).
* '''No of iterations''': Number of iterations for CLARA. The more iterations are used, the sparser becomes the solution.
* '''Automatic''': The algorithm tries to determine the number of iterations automatically. The goodness of fit (GOF) is calculated after every iteration and if there is a big jump in the GOF then the algorithm will stop. If no jumps appear during the calculations then CLARA iterates until the specified number of iterations is reached.
* '''Regularize iterations''': If one wants to use different regularization for the CLARA iterations than the value specified as "SVD cutoff", this option should be selected.
* '''Amount to clip from img (%)''': Cortical CLARA uses the solution from the previous iteration as an additional weighting matrix for the current iteration. That weighting matrix is constructed by cutting the "low" activity from the solution. This number specifies how much of the activity should be cut from the previous solution in order to construct the weighting matrix. This value is given as a percentage of the maximal activity. Default value is 10%.

'''Notes:'''

* '''Starting Cortical CLARA:''' Cortical CLARA can be started from the sub-menu '''Surface Image''' of the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]''” for important information on regularization of distributed inverses.

== Cortex Inflation ==

The inflated cortex is a smoothened version of the individual cortical surface with minimal metric distortions (Fischl, B. et al. (1999). Cortical Surface-Based Analysis: II: Inflation, Flattening, and a Surface-Based Coordinate System. ''NeuroImage'', 9(2), 195–207). Gyri and sulci are smoothened out. The original distances between each point on the cortex and its neighbors are, however, mostly preserved.

[[Image:SA 3Dimaging (48).gif]]

''Cortical LORETA map overlaid on top of the inflated cortical surface.''

A lighter gray color overlaid on top of the surface image indicates the location of a gyrus of the individual cortex surface, while a darker gray color indicates the location of a sulcus. The inflated cortical surface can be computed in '''BESA MRI 2.0'''. For more details please refer to the BESA MRI 2.0 help.

== Surface Minimum Norm Image ==

'''Introduction'''

The minimum norm approach is a common method to estimate a distributed electrical current image in the brain at each time sample (Hämäläinen & Ilmoniemi 1984). The source activities of a large number of regional sources are computed. The sources are evenly distributed using 1500 standard locations 10% and 30% below the smoothed standard brain surface (when using the standard MRI) or using between 3000-4000 locations on the individual brain surface defined by the gray-white-matter boundary.

Since the number of sources is much larger than the number of sensors in a minimum norm solution, the inverse problem is highly underdetermined and must be stabilized by a mathematical constraint, the minimum norm. Out of the many current distributions that can account for the recorded sensor data, the solution with the minimum L2 norm, i.e. the minimum total power of the current distribution is displayed in BESA Research.

First, the forward solution (leadfield matrix L) of all sources is calculated in the current head model. Then, the source activities S(t) of all source components are computed from the data matrix D(t) using an inverse regularized by the estimated noise covariance matrix:

<math>\mathrm{S}\left( t \right) = \mathrm{R} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{R} \cdot \mathrm{L}^{T} + \mathrm{C}_N \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed regional source model, CN denotes the noise correlation matrix in sensor space, and R is a weighting matrix in source space. R and CN can be designed in different ways in order to optimize the minimum norm result. The total activity of each regional source is computed as the root mean square of the source activities S(t) of its 3 (MEG:2) components. This total source activity is transformed to a color-coded image of the brain surface. (When the standard brain is used, two sources are assigned to each surface location, located 10% and 30% below the surface, respectively. The color that is displayed on the standard brain surface is the larger of the two corresponding source activities.)

'''Weighting options'''

The minimum norm current imaging techniques of BESA Research provide different weighting strategies. Two weighting approaches are available: Depth weighting and spatio-temporal approaches.
* '''Depth weighting:''' Without depth weighting, deep sources appear very smeared in a minimum-norm reconstruction. With depth weighting, both deep and superficial sources produce a similar, more focal result. If this weighting method is selected, the leadfield of each regional source is scaled with the largest singular value of the SVD (singular value decomposition) of the source's leadfield.
* '''Spatio-temporal weighting''': Spatio-temporal weighting tries to assign large weight to sources that are assumed to be more likely to contribute to the recorded data.
** '''Subspace correlation after single source scan''': This method divides the signal into a signal and a noise subspace. The correlation of the leadfield of a regional source i with the signal subspace (pi) is computed to find out if the source location contributes to the measured data. The weighting matrix R becomes a diagonal matrix. Each of the three (MEG: 2) components of a regional source get the same weighting value pi2. This approach is based on the signal subspace correlation measure introduced by J.C. Mosher, R. M. Leahy (Recursive MUSIC: A Framework for EEG and MEG Source Localization, IEEE Trans. On Biomed. Eng. Vol. 45, No. 11, November 1998)
** '''Dale & Sereno 1993:''' In the approach of Dale and Sereno (J Cogn Neurosci, 1993, 5: 162-176) a signal subspace needs not be defined. The correlation pi of the leadfield of regional source i with the inverse of the data covariance matrix is computed along with the largest singular value λmax of the data covariance matrix. The weighting matrix R is a diagonal matrix with weights: [[Image:SA 3Dimaging (50).gif]]. Each of the three (MEG: 2) components of a regional source receives the same weighting value.

'''Noise regularization'''

Two methods to estimate the channel noise correlation matrix CN are provided by the program:
* '''Use baseline:''' Select this option to estimate the noise from the user-definable baseline. The signal is computed from the data at non-baseline latencies.
* '''Use 15% lowest values:''' The baseline activity is computed from the data at those 15% of all displayed latencies that have the lowest global field power. The signal is computed from all displayed latencies.

In each case, the activity (noise or signal, respectively) is defined as root-mean-square across all respective latencies for each channel.

The noise covariance matrix CN is constructed as a diagonal matrix. The entries in the main diagonal are proportional to the noise activity of the individual channels (if selected) or are all equally proportional to the average noise activity over all channels. The noise covariance matrix CN is then scaled such that the ratio of the Frobenius norms of the weighted leadfield projector matrix (LRLT) and the noise covariance matrix CN equals the Signal-to-Noise ratio. This scaling can be multiplied by an additional factor (default=1) to sharpen (<1) or smoothen (>1) the minimum norm image.

'''Applying the Minimum Norm Image'''

The minimum-norm algorithm is started via the ''Surface minimum norm image dialog box'', which is opened from the''' Image''' menu, or by typing the shortcut '''Ctrl-M''': Please refer to Chapter ''“Surface'' ''Minimum Norm Tab”'' for more details.

As opposed to the other 3D images available from the '''Image '''menu, the surface minimum norm image is not computed on a volumetric grid, but rather for locations on the brain surface. Accordingly, the results of the minimum norm image are displayed superimposed to the brain surface mesh rather than to the volumetric MR image.

The figure below shows a minimum norm image computed from the file '''Examples\Epilepsy\Spikes\Spikes-Child4_EEG+MEG_averaged.fsg'''. The EEG spike peak was imaged using the individual brain surface of the subject. A baseline from -300 to -70 ms was used. Minimum norm was computed with depth weighting, Spatio-temporal weighting according to Dale & Sereno 1993 and individual noise weighting with a noise scale factor of 0.01. The minimum norm image reveals the location of the spike generator in the close vicinity of the frontal left-hemispheric lesion in this subject.

[[Image:SA 3Dimaging (51).gif]]

== Multiple Source Probe Scan (MSPS) ==

 
'''Introduction'''

The MSPS function provides a tool for the validation of a given solution. It is based on the following theoretical consideration: If the recorded EEG/MEG data has been modeled adequately, i.e. all active brain regions are represented by a source in the current solution, then any additional probe source added to the solution will not show any activity apart from noise. The only exception occurs if this probe source is placed in close vicinity to one of the sources in the current solution. In that case, the solution's source and the probe source will share the activity of the corresponding brain area. The MSPS applies these considerations by scanning the brain on a pre-defined grid with a regional probe added to the current solution. Grid extent and density can be specified in the Image settings. The power P of the probe source at location r in the signal interval is compared with the power of the probe source in a reference interval, defining a value q:

<math>\mathrm{q}\left( r \right) = \sqrt{\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}} - 1</math>


MSPS can be computed on time domain or time-frequency domain data:
* In the time domain, q(r) is computed from the source waveform of the probe source. Here, P(r) is the mean power of the probe source at location r in the marked latency range, and Pref(r) is the mean probe source power in the user-definable baseline interval.
* In the time-frequency domain, an MSPS image can be computed from the complex cross spectral density matrices. By applying the inverse operator for a source configuration consisting of the current solution and the probe source, the power of the probe source can be computed for the target interval [P(r)] and the reference time-frequency interval [Pref(r)]. In the resulting MSPS image, q-values are shown in %, where q[%] = q*100.

The inverse operator used to determine the probe source power uses different regularization constants for the probe source and the sources in the current solution. The regularization constant of the sources in the current solution can be specified in the Image settings (default 4%). The regularization constant of the probe source is internally set to 0%.

Alternatively to the definition above, q can also be displayed in units of dB:

<math>\mathrm{q}\left\lbrack \text{dB} \right\rbrack = 10 \cdot \log_{10}\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}</math>


Values of q smaller than zero are not shown in the MSPS image.

According to the considerations above, an MSPS of a correct source model should optimally yield image maxima around the sources in the current solution only. If the MSPS image is blurred or shows maxima at locations different from the modeled sources, this indicates a non-sufficient or incorrect solution.

'''Applying the MSPS'''

This chapter illustrates the application of the Multiple Source Probe Scan. The figures are generated with data from file '''Examples/Epilepsy/Spikes/Rolandic-Spike-Child.fsg''' (-300 : +200 ms, filtered from 3 Hz [forward] to 40 Hz [zero-phase]).

'''Time domain versus time-frequency domain MSPS'''

The multiple source probe scan can be computed in the time domain or the time-frequency domain. The latter is possible only when time-frequency domain data is available for the current condition, i.e. if the condition has been created by starting a multiple source beamformer (MSBF) computation from the source coherence window. In this case, evoking the MSPS calculation from the '''Imaging '''button or from the '''Image''' menu will bring up the following dialog window that allows to choose between time- or time-frequency MSPS. If only time domain data is available, this dialog window will not appear and MSPS will be computed in the time domain.

[[Image:SA 3Dimaging (53).gif]]

For a time-frequency domain MSPS, the target and the reference time-frequency interval have been specified already in the Time-Frequency window (see Chapter "''How To Create Beamformer Images''"). For a time-domain MSPS, the target and the reference epoch have to be specified in the Source Analysis window as described below.

'''Time domain MSPS'''

The time-domain MSPS image displays the ratio of the power of a regional probe source in the signal and the baseline interval. The currently set baseline is indicated by a horizontal line in the upper left corner of the channel box.

[[Image:SA 3Dimaging (54).gif|thumb|c|none|330px|The black horizontal bar in the upper part of the channel box (here circled in red) indicates the baseline interval.]]

By default, BESA Research defines the pre-stimulus interval of the current data segment as baseline. The baseline should represent a latency range in which no event-related activity is present in the data. There are several possibilities to modify the baseline interval: by clicking on the horizontal line with the left mouse button or by using the corresponding entry in the '''Condition '''menu or '''Fit Interval''' popup menu.

Mark an interval to define the target epoch, i.e. the time-interval for which the current solution is to be tested. Start the MSPS by selecting it from the '''Image selection '''button or from the '''Image''' menu to start the probe source scan. The''' Image '''menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window. The 3D window opens and displays the scan result.

<div><ul>
<li style="display: inline-block;"> [[Image:SA 3Dimaging (55).gif|thumb|c|none|650px|This figure shows the MSPS image applied on the three left-hemispheric sources in the solution ''''Rolandic-Spike-Child-RS2.bsa''''. The baseline is set from -300ms to -50 ms. The right-hemispheric sources have been switched off. The fit interval is set to the latency range of large overall activity in the data (-43 ms : 117 ms). A realistic FEM model appropriate for the subject's age (12 years, conductivity ratios (cr) 50) is applied. The MSPS image does not show maxima at the modeled source locations and rather shows a spread q-value distribution.]] </li>

<li style="display: inline-block;"> [[Image:SA 3Dimaging (56).gif|thumb|c|none|650px|The MSPS image for the same latency range when the right-hemispheric sources have been included. The MSPS image appears more focal and shows maxima around the modeled brain regions. This indicates the substantial improvement of the solution by adding the right-hemispheric sources that model the propagation of the epileptic spike from the left to the right hemisphere (note the radiological side convention in the 3D window).]] </li>
</ul></div>

'''Time-Resolved MSPS'''

If the MSPS has been computed on time domain data, the image can be shown separately for each latency in the selected interval. After the MSPS has been computed for the marked epoch, double-click anywhere within this epoch to display the ratio of the probe source magnitude at the selected latency and the mean probe source magnitude in the baseline. Scanning the latency range by moving the cursor (e.g. with the left and right arrow cursor keys) provides a time-resolved MSPS image.

Time-resolved MSPS images are not available if the MSPS has been computed on data in the time-frequency domain.

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (57).gif|thumb|450px|MSPS image of the spike peak activity at 0ms. The activity mainly occurs in the left hemisphere. This fact is illustrated by the source waveforms and confirmed in the MSPS image, which shows a focal maximum around the location of the red sources.]] </li>

<li style="display: inline-block;"> [[File:SA 3Dimaging (58).gif|thumb|450px|Around +27 ms, the spike has propagated to the right hemisphere. This becomes evident from the waveforms of the blue sources, which show a significant latency lag with respect to the first three sources, and from the MSPS image, which shows the maximum around blue sources at this latency.]] </li>
</ul></div>



'''Notes:'''

* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image''' menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the''' Image''' menu.
* For scaling options, please refer to the '''scaling buttons''' popup menu .
* Parameters used for the MSPS calculations can be set in the ''General Settings tab'' of the ''Image Settings dialog box.''

== Source Sensitivity ==

'''Introduction'''

The 'Source sensitivity' function displays the sensitivity of the selected source in the current source model to activity in other brain regions. Sensitivity is defined as the fraction of power at the scanned brain location that is mapped onto the selected source.

To compute the source sensitivity, unit brain activity is modeled at different locations (probe source) throughout the brain. To this data, the current source model is applied to compute the source waveforms SCM of all modeled sources:

<math>\mathrm{S}_{\text{CM}} = \mathrm{L}_{\text{CM}}^{-1} \cdot \mathrm{L}_{\text{PS}}</math>


Here LCM-1 is the regularized inverse operator for the current model, and LPS is the leadfield of the regional probe source (dimension [Nx3] for EEG and [Nx2] for MEG, respectively, where N is the number of sensors). The source amplitude SSS of the selected source in the model is a 3x3 (MEG: 2x2) sub-matrix of SCM (if the selected source is a regional source) or a 1x3-matrix (MEG: 1x2) (if the selected source is a dipole). The root mean square of the singular values of SCM is defined as the source sensitivity.

The 3D source sensitivity image displays this value for all locations on a grid specified under '''Image/Settings'''. Grid density can be specified in the Image Settings.

'''Applying the Source Sensitivity Image'''

The Source Sensitivity image is evoked from the '''Image''' menu or by pressing the corresponding hot key (default: '''V''').

This function is enabled only when a solution with an active selected source is present in the Source Analysis window. The source sensitivity image then displays the sensitivity of the selected source to activity in other brain regions.

[[Image:SA 3Dimaging (59).gif]]

''Source Sensitivity image for the selected frontal source (green) in model ''''''High_Intensity_3RS.bsa'''''' in folder 'Examples/ERP_Auditory_Intensity'. The data displayed is the '100dB' condition in file ''''''All_Subjects_cc.fsg''''''. The selected source is sensitive to activity in the frontal brain region (yellow/white), while it is not influenced by activity in the vicinity of the left and right auditory cortex areas, which are modeled by the red and blue source in the model (transparent/gray).''

'''Notes:'''

* The sensitivity image is independent of the recorded sensor signals. It only depends on the current source model, the sensor configuration, the head model, and the regularization constant.
* If the regularization constant is set to zero, each source has a sensitivity of 100% to activity around its own location. With increasing regularization, the spatial filter becomes less focused, and the sensitivity of a source to activity at its location decreases.
* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image''' menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the '''Image''' menu.

{{BESAManualNav}}

Source Analysis 3D Imaging

2019-03-28T12:04:51Z

Jamie: /* Multiple Source Beamformer (MSBF) in the Time Domain */

{{BESAInfobox
|title = Module information
|module = BESA Research Standard or higher
|version = 6.1 or higher
}}


== Overview ==

BESA Research features a set of new functions that provide 3D images that are displayed superimposed to the individual subject's anatomy. This chapter introduces these different images and describe their properties and applications.

The 3D images can be divided into three categories:

'''Volume images:'''

* '''The Multiple Source Beamformer (MSBF)''' is a tool for imaging brain activity. It is applied in the time-domain or time-frequency domain. The beamformer technique in time-frequency domain can image not only evoked, but also induced activity, which is not visible in time-domain averages of the data.
* '''Dynamic Imaging of Coherent Sources (DICS)''' can find coherence between any two pairs of voxels in the brain or between an external source and brain voxels. DICS requires time-frequency-transformed data and can find coherence for evoked and induced activity.

The following imaging methods provide an image of brain activity based on a distributed multiple source model:
* '''CLARA''' is an iterative application of LORETA images, focusing the obtained 3D image in each iteration step.
* '''LAURA '''uses a spatial weighting function that has the form of a local autoregressive function.
* '''LORETA''' has the 3D Laplacian operator implemented as spatial weighting prior.
* '''sLORETA''' is an unweighted minimum norm that is standardized by the resolution matrix.
* '''swLORETA '''is equivalent to sLORETA, except for an additional depth weighting.
* '''SSLOFO '''is an iterative application of standardized minimum norm images with consecutive shrinkage of the source space.
* A '''User-defined volume image''' allows to experiment with the different imaging techniques. It is possible to specify user-defined parameters for the family of distributed source images to create a new imaging technique.
* Bayesian source imaging: '''SESAME''' uses a semi-automated Bayesian approach to estimate the number of dipoles along with their parameters.

'''Surface image:'''

* The '''Surface Minimum Norm Image'''. If no individual MRI is available, the minimum norm image is displayed on a standard brain surface and computed for standard source locations. If available, an individual brain surface is used to construct the distributed source model and to image the brain activity.
* '''Cortical LORETA'''. Unlike classical LORETA, cortical LORETA is not computed in a 3D volume, but on the cortical surface.
* '''Cortical CLARA'''. Unlike classical CLARA, cortical CLARA is not computed in a 3D volume, but on the cortical surface.

'''Discrete model probing:'''

These images do not visualize source activity. Rather, they visualize properties of the currently applied discrete source model:
* The '''Multiple Source Probe Scan (MSPS)''' is a tool for the validation of a discrete multiple source model.
* The '''Source Sensitivity image''' displays the sensitivity of a selected source in the current discrete source model and is therefore data independent.

== Multiple Source Beamformer (MSBF) in the Time-frequency Domain ==

 
'''Short mathematical introduction'''

The BESA beamformer is a modified version of the linearly constrained minimum variance vector beamformer in the time-frequency domain as described in [https://dx.doi.org/10.1073/pnas.98.2.694 Gross et al., "Dynamic imaging of coherent sources: Studying neural interactions in the human brain", PNAS 98, 694-699, 2001]. It allows to image evoked and induced oscillatory activity in a user-defined time-frequency range, where time is taken relative to a triggered event.

The computation is based on a transformation of each channel's single trial data from the time domain into the time-frequency domain. This transformation is performed by the BESA Research Source Coherence module and leads to the complex spectral density Si (f,t), where i is the channel index and f and t denote frequency and time, respectively. Complex cross spectral density matrices C are computed for each trial:

<math>\mathrm{C}_{ij}\left( f,t \right) = \mathrm{S}_{i}\left( f,t \right) \cdot \mathrm{S}_{j}^{*}\left( f,t \right)</math>


The output power P of the beamformer for a specific brain region at location r is then computed by the following equation:

<math>\mathrm{P}\left( r \right) = \operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{-1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{-1}</math>


Here, Cr-1 is the inverse of the SVD-regularized average of Cij(f,t) over trials and the time-frequency range of interest; L is the leadfield matrix of the model containing a regional source at target location r and, optionally, additional sources whose interference with the target source is to be minimized; tr'[] is the trace of the [3×3] (MEG:[2×2]) submatrix of the bracketed expression that corresponds to the source at target location r.

In BESA Research, the output power P(r) is normalized with the output power in a reference time-frequency interval Pref(r). A value q ist defined as follows:

<math> \mathrm{q}\left( r \right) =
\begin{cases}
\sqrt{\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}(r)}} - 1 = \sqrt{\frac{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{\text{ref},r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}} - 1, & \text{for }\mathrm{P}(r) \geq \mathrm{P}_{\text{ref}}(r) \\

1 - \sqrt{\frac{\mathrm{P}_{\text{ref}}\left( r \right)}{\mathrm{P}\left( r \right)}} = 1 - \sqrt{\frac{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{\text{ref},r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}}, & \text{for }\mathrm{P}(r) < \mathrm{P}_{\text{ref}}(r)
\end{cases} </math>


Pref can be computed either from the corresponding frequency range in the baseline of the same condition (i.e. the beamformer images event-related power increase or decrease) or from the corresponding time-frequency range in a control condition (i.e. the beamformer images differences between two conditions). The beamformer image is constructed from values q(r) computed for all locations on a grid specified in the '''General Settings tab'''. For MEG data, the innermost grid points within a sphere of approx. 12% of the head diameter are assigned interpolated rather than calculated values).
q-values are shown in %, where where q[%] = q*100. Alternatively to the definition above, q can also be displayed in units of dB:

<math>\mathrm{q}\left\lbrack \text{dB} \right\rbrack = 10 \cdot \log_{10}\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}</math>


A beamformer operator is designed to pass signals from the brain region of interest r without attenuation, while minimizing interference from activity in all other brain regions. Traditional single-source beamformers are known to mislocalize sources if several brain regions have highly correlated activity. Therefore, the BESA beamformer extends the traditional single-source beamformer in order to implicitly suppress activity from possibly correlated brain regions. This is achieved by using a multiple source beamformer calculation that contains not only the leadfields of the source at the location of interest r, but also those of possibly interfering sources. As a default, BESA Research uses a bilateral beamformer, where specifically contributions from the homologue source in the opposite hemisphere are taken into account (the matrix L thus being of dimension N×6 for EEG and N×4 for MEG, respectively, where N is the number of sensors). This allows for imaging of highly correlated bilateral activity in the two hemispheres that commonly occurs during processing of external stimuli.

In addition, the beamformer computation can take into account possibly correlated sources at arbitrary locations that are specified in the current solution. This is achieved by adding their leadfield vectors to the matrix L in the equation above.

'''Applying the Beamformer'''

This chapter illustrates the usage of the BESA beamformer. The displayed figures are generated using the file ''''Examples/Learn-by-Simulations/AC-Coherence/AC-Osc20.foc'''' (see BESA Tutorial 6: "''Time-frequency analysis and Source coherence''").

'''Starting the beamformer from the time-frequency window'''

The BESA beamformer is applied in the time-frequency domain and therefore requires the Source Coherence module to be enabled. The time-frequency beamformer is especially useful to image in- or decrease of induced oscillatory activity. Induced activity cannot be observed in the averaged data, but shows up as enhanced averaged power in the TSE (Temporal-Spectral Evolution) plot. For instructions on how to initiate a beamformer computation in the time-frequency window, please refer to Chapter '''[[Source_Coherence_How_to...#How_to_Start_the_Beamformer_from_the_Time-Frequency_Window|How to Create Beamformer Images]]'''.

After the beamformer computation has been initiated in the time-frequency window, the source analysis window opens with an enlarged 3D image of the q-value computed with a '''bilateral beamformer'''. The result is superimposed onto the MR image assigned to the data set (individual or standard).

[[Image:SA 3Dimaging (5).gif]]

''Beamformer image after starting the computation in the Time-Frequency window. A bilateral pair of sources in the auditory cortex accounts for the highly correlated oscillatory induced activity. Only the bilateral beamformer manages to separate these activities; a traditional single-source beamformer would merge the two sources into one image maximum in the head center instead.''

'''Multiple source beamformer in the Source Analysis window'''

The 3D imaging display is part of the source analysis window. If you press the '''Restore''' button at the right end of the title bar of the 3D window, the window appears at the bottom right of the source analysis window. In the channel box, the averaged (evoked) data of the selected condition is shown. When a control condition was selected, its average is appended to the average of the target condition.

[[Image:SA 3Dimaging (6).gif]]

''Source Analysis window with beamformer image. The two sources have been added using the '''''Switch to''''' '''''Maximum''''' and '''''Add Source '''''toolbar buttons (see below). Source waveforms are computed from the displayed averaged data. Therefore, they do not represent the activity displayed in the beamformer image, which in this simulation example is induced (i.e. not phase-locked to the trigger)!''

When starting the beamformer from the time-frequency window, a bilateral beamformer scan is performed. In the source analysis window, the beamformer computation can be repeated taking into account possibly correlated sources that are specified in the current solution. Interfering activities generated by all sources in the current solution that are in the 'On' state are specifically suppressed ('''they enter the matrix L in the beamformer calculation''', see Chapter ''Short mathematical description'' above). The computation can be started from the '''Image''' menu or from the '''Image selector button''' dropdown menu. The '''Image''' menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window.

[[Image:SA 3Dimaging (7).gif]]

''Multiple source beamformer image calculated in the presence of a source in the left hemisphere. A '''single''' source scan has been performed. The source set in the current solution accounts for the left-hemispheric q-maximum in the data. Accordingly, the beamformer scan reveals only the as yet unmodeled additional activity in the right hemisphere (note the radiological convention in the 3D image display).''

The beamformer scan can be performed with a '''single''' or a '''bilateral''' source scan. The default scan type depends on the current solution:
* When the beamformer is started from the Time-Frequency window, the Source Analysis window opens with a new solution and a '''bilateral''' beamformer scan is performed.
* When the beamformer is started within the Source Analysis window, the default is
** a scan with a '''single''' source in addition to the sources in the current solution, if at least one source is active.
** a '''bilateral''' scan if no source in the current solution is active.

The default scan type is the multiple source beamformer. The non-default scan type can be enforced using the corresponding ''Volume Image / Beamformer'' entry in the '''Image''' menu.

'''Inserting Sources out of the Beamformer Image'''

The beamformer image can be used to add sources to the current solution. A simple double-click anywhere in the 2D- or 3D-view will generate a non-oriented regional source at the corresponding location. However, a better and easier way to create sources at image maxima and minima is to use the toolbar buttons '''Switch to Maximum''' [[Image:SA 3Dimaging (8).gif]] and '''Add Source''' [[Image:SA 3Dimaging (9).gif]].

Use the '''Switch to Maximum''' button to place the red crosshair of the 3D window onto a local image maximum or minimum. Hitting the '''Add Source''' button creates a regional source at the location of the crosshair and therefore ensures the exact placement of the source at the image extremum. Moreover, the '''Add Source''' button generates an oriented regional source. BESA Research automatically estimates the source orientation that contributes most to the power in the target time-frequency interval (or the reference time-frequency interval, if its power is larger than that in the target interval). The accuracy of this orientation estimate depends largely on the noise content of the data. The smaller the signal-to-noise ratio of the data, the lower is the accuracy of the orientation estimate. '''This feature allows to use the beamformer as a tool to create a source montage for source coherence analysis, where it is of advantage to work with oriented sources'''.

'''Notes:'''

* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image '''menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the''' Image''' menu.
* For scaling options, use the [[Image:SA 3Dimaging (10).gif]] and [[Image:SA 3Dimaging (11).gif]] '''Image Scale toolbar''' buttons.
* Parameters used for the beamformer calculations can be set in the '''Standard Volumes''' of the ''Image Settings dialog box.''

== Dynamic Imaging of Coherent Sources (DICS) ==

 
'''Short mathematical introduction'''

Dynamic Imaging of Coherent Sources (DICS) is a sophisticated method for imaging cortico-cortical coherence in the brain, or coherence between an external reference (e.g. EMG channel) and cortical structures. DICS can be applied to localize evoked as well as induced coherent cortical activity in a user-defined time-frequency range.

DICS was implemented in BESA closely following [https://dx.doi.org/10.1073/pnas.98.2.694 Gross et al., "Dynamic imaging of coherent sources: Studying neural interactions in the human brain", PNAS 98, 694-699, 2001].

The computation is based on a transformation of each channel's single trial data from the time domain into the frequency domain. This transformation is performed by the BESA Research Coherence module and results in the complex spectral density matrix that is used for constructing the spatial filter similar to beamforming.

DICS computation yields a 3-D image, each voxel being assigned a coherence value. Coherence values can be described as a neural activity index and do not have a unit. The neural activity index contrasts coherence in a target time-frequency bin with coherence of the same time-frequency bin in a baseline.

'''DICS for cortico-cortical coherence is computed as follows:'''

Let L(r) be the leadfield in voxel r in the brain and C the complex cross-spectral density matrix. The spatial filter W(r) for the voxel r in the head is defined as follows:

<math>W\left( r \right) = \left\lbrack L^{T}\left( r \right) \cdot C^{- 1} \cdot L\left( r \right) \right\rbrack^{- 1} \cdot L^{T}(r) \cdot C^{- 1}</math>


The cross-spectrum between two locations (voxels) r1 and r2 in the head are calculated with the following equation:

<math>C_{s}\left( r_{1},r_{2} \right) = W\left( r_{1} \right) \cdot C \cdot W^{*T}\left( r_{2} \right),</math>


where <nowiki>*T</nowiki> means the transposed complex conjugate of a matrix. The cross-spectral density can then be calculated from the cross spectrum as follows:

<math>c_{s}\left( r_{1},r_{2} \right) = \lambda_{1}\left\{ C_{s}\left( r_{1},r_{2} \right) \right\},</math>


where λ1{} indicates the largest singular value of the cross spectrum. Once the cross spectral density is estimated, the connectivity¹(CON) between the two brain regions r1 and r2 are calculated as follows:

<math>\text{CON}\left( r_{1},r_{2} \right) = \frac{c_{s}^{\text{sig}}\left( r_{1},r_{2} \right) - c_{s}^{\text{bl}}(r_{1},r_{2})}{c_{s}^{\text{sig}}\left( r_{1},r_{2} \right) + c_{s}^{\text{bl}}(r_{1},r_{2})},</math>


where cssig is the cross-spectral density for the signal of interest between the two brain regions r1 and r2, and csbl is the corresponding cross spectral density for the baseline or the control condition, respectively. In the case DICS is computed with a cortical reference, r1 is the reference region (voxel) and remains constant while r2 scans all the grid points within the brain sequentially. In that way, the connectivity between the reference brain region and all other brain regions is estimated. The value of CON(r1, r2) falls in the interval [-1 1]. If the cross-spectral density for the baseline is 0 the connectivity value will be 1. If the cross-spectral density for the signal is 0 the connectivity value will be -1.

¹ Here, the term connectivity is used rather than coherence, as strictly speaking the coherence equation is defined slightly differently. For simplicity reasons the rest of the tutorial uses the term coherence.

'''DICS for cortico-muscular coherence is computed as follows:'''

When using an external reference, the equation for coherence calculation is slightly different compared to the equation for cortico-cortical coherence. First of all, the cross-spectral density matrix is not only computed for the MEG/EEG channels, but the external reference channel is added. This resulting matrix is Call. In this case, the cross-spectral density between the reference signal and all other MEG/EEG

channels is called cref. It is only one column of Call. Hence, the cross-spectrum in voxel r is calculated with the following equation:

<math>C_{s}\left( r \right) = W\left( r \right) \cdot c_{\text{ref}}</math>


and the corresponding cross-spectral density is calculated as the sum of squares of Cs:

<math>c_{s}\left( r \right) = \sum_{i = 1}^{n}{C_{s}\left( r \right)_{i}^{2}},</math>


where n is 2 for MEG and 3 for EEG. This equation can also be described as the squared Euclidean norm of the cross-spectrum:

<math>c_{s}\left( r \right) = \left\| C_{s} \right\|^{2},</math>


The power in voxel r is calculated as in the cortico-cortical case:

<math>p\left( r \right) = \lambda_{1}\left\{ C_{s}(r,r) \right\}.</math>


At last, coherence between the external reference and cortical activity is calculated with the equation:

<math>\text{CON}\left( r \right) = \frac{c_{s}(r)}{p\left( r \right) \cdot C_{\text{all}}(k,k)},</math>


where Call(k, k) is the (k,k)-th diagonal element of the matrix Call.

DICS is particularly useful, if coherence is to be calculated without an a-priory source model (in contrast to source coherence based on pre-defined source montages). However, the recommended analysis strategy for DICS is to use a brain source as a starting point for coherence calculation that is known to contribute to the EEG/MEG signal of interest. For example, one might first run a beamformer on the time-frequency range of interest and use the voxel with the strongest oscillatory activity as a starting point for DICS. The resulting coherence image will again lead to several maxima (ordered by magnitude), which in turn can serve as starting points for DICS calculation. This way, it is possible to detect even weak sources that show coherent activity in the given time-frequency range.

The other significant application for DICS is estimating coherence between an external source and voxels in the brain. For example, an external source can be muscle activity recoded by an electrode placed over the according peripheral region. This way, the direct relationship between muscle activity and brain activation can be measured.

'''Starting DICS computation from the Time-Frequency Window'''

DICS is particularly useful, if coherence in a user-defined time-frequency bin (evoked or induced) is to be calculated between any two brain regions or between an external reference and the brain. DICS runs only on time-frequency decomposed data, so time-frequency analysis needs to be run before starting DICS computation.

To start the DICS computation, left-drag a window over a selected time-frequency bin in the Time-Frequency Window. Right-click and select “Image”. A dialogue will open (see fig. 1) prompting you to specify time and frequency settings as well as the baseline period. It is recommended to use a baseline period of equal length as the data period of interest. Make sure to select “DICS” in the top row and press “'''Go'''”.

[[Image:SA 3Dimaging (21).gif|450px|thumb|c|none|Fig. 1: Time and frequency settings for DICS and MSBF]]

Next, a window will appear allowing you to specify the reference source for coherence calculation (see fig. 2). It is possible to select a channel (e.g. EMG) or a brain source. If a brain source is chosen and no source analysis was computed beforehand, the option “Use current cross-hair position” must be chosen. In case discrete source analysis was computed previously, the selected source can be chosen as the reference for DICS. Please note that DICS can be re-computed with any cross-hair or source position at a later stage.

[[Image:SA 3Dimaging (1).jpg|400px|thumb|c|none|Fig. 2: Possible options for choosing the reference]]

Confirming with “'''OK'''” will start computation of coherence between the selected channel/voxel and all other brain voxels. In case DICS is computed for a reference source in the brain, it can be advantageous to run a beamforming analysis in the selected time-frequency window first and use one of the beamforming maxima as reference for DICS. Fig. 3 shows an example for DICS calculation.

[[Image:SA 3Dimaging (22).gif|500px|thumb|c|none|Fig. 3: Coherence between left-hemispheric auditory areas and the selected voxel in the right auditory cortex.]]

Coherence values range between -1 and 1. If coherence in the signal is much larger than coherence in the baseline (control condition) then the DICS value is going to approach 1. Contrary, if coherence in the baseline is much larger than coherence in the signal, then the DICS value is going to approach -1. At last, if coherence in the signal is equal to coherence in the baseline, then the DICS value is 0.

In case DICS is to be re-computed with a different reference, simply mark the desired reference position by placing the cross-hair in the anatomical view and select “DICS” in the middle panel of the source analysis window (see Fig. 4). In case an external reference is to be selected, click on “DICS” in the middle panel to bring up the DICS dialogue (see. Fig. 2) and select the desired channel. Please note that DICS computation will only be available after running time-frequency analysis.

[[Image:SA 3Dimaging (23).gif|700px|thumb|c|none|Fig. 4: Integration of DICS in the Source Analysis window]]

== Multiple Source Beamformer (MSBF) in the Time Domain ==
''(requires Besa Research 7.0 or higher)''

===Short mathematical introduction===

Beamforming approach can be also applied in the time domain data. This approach was introduced as linearly constrained minimum variance (LCMV) beamformer (Van Veen et al., 1997). It allows to image evoked activity in a user-defined time range, where time is taken relative to a triggered event, and to estimate source waveforms using the calculated spatial weight at locations of interest. For an implementation of the beamformer in the time domain, data covariance matrices are required, while complex cross spectral density matrices are used for the beamformer approaches in the time-frequency domain as described in the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section.

The bilateral beamformer introduced in the ''[[Source_Analysis_3D_Imaging#Categories|Multiple_Source_Beamformer_(MSBF)_in_the_Time-frequency_Domain]]'' section is also implemented for the time-domain beamformer to take into account contributions from the homologue source in the opposite. This allows for imaging of highly correlated bilateral activity in the two hemispheres that commonly occurs during processing of external stimuli. In addition, the beamformer computation can take into account possibly correlated sources at arbitrary locations.
The beamformer spatial weight W(r) for the voxel r in the brain is defined as follows (Van Veen et al., 1997):

[[File:MSBF1.png]]

where '''C-1''' is the inversed regularized average of covariance matrix over trials, '''L''' is the leadfield matrix of the model containing a regional source at target location r and optionally
additional sources whose interference with the target source is to be minimized. The beamformer spatial weight '''W'''(r) can be applied to the measured data to estimate source
waveform at a location r (beamformer virtual sensor):

[[File:MSBF2.png]]

where '''S'''(r,t) represents the estimated source waveform and '''M'''(t) represents measured EEG or MEG signals.
The output power P of the beamformer for a specific brain region at location r is computed by the following equation:

[[File:MSBF3.png]]

where tr’[ ] is the trace of the [3×3] (MEG: [2×2]) submatrix of the bracketed expression that corresponds to the source at target location r.
Beamformer can suppress noise sources that are correlated across sensors. However, uncorrelated noise will be amplified in a spatially non-uniform manner, with increasing
distortion with increasing distance from the sensors (Van Veen et al., 1997; Sekihara et al., 2001). For this reason, estimated source power should be normalized by a noise power.
In BESA Research, the output power P(r) is normalized with the output power in a baseline interval or with the output power of a uncorrelated noise: P(r) / Pref (r).
The time-domain beamformer image is constructed from values q(r) computed for all locations on a grid specified in the '''General Settings''' tab. A value q(r) is defined as described in
the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section with data covariance matrices instead of cross-spectral density matrices.

===Applying the Beamformer===

This chapter illustrates the usage of the BESA beamformer in the time domain. The displayed figures are generated using the file ‘Examples/ERP-Auditory-Intensity/S1.cnt’.

'''Starting the time-domain beamformer from the Average tab of the Paradigm dialog box'''

The time-domain beamformer is needed data covariance matrices and therefore requires the ERP module to be enabled. After the beamformer computation has been initiated in the
'''Average tab of the Paradigm dialog box''', the source analysis window opens with an enlarged 3D image of the q-value computed with a bilateral beamformer. The result is
superimposed onto the MR image assigned to the data set (individual or standard).

[[File:MSBF44.png]]

''Beamformer image for auditory evoked data after starting the computation in the '''Average tab of the Paradigm dialog box'''. The bilateral beamformer manages to separate the
activities in auditory areas, while a traditional single-source beamformer would merge the two sources into one image maximum in the head center instead.''

'''Multiple-source beamformer in the Source Analysis window'''

The 3D imaging display is part of the source analysis window. In the Channel box, the averaged (evoked) data of the selected condition is shown. Selected covariance intervals in
the ERP module can be checked in the Channel box. The red, gray, and blue rectangles indicate signal, baseline, and common interval, respectively.

[[File:MSBF55.png]]

''Source Analysis window with beamformer image. The two beamformer virtual sensors have been added using the Switch to Maximum and Add Source toolbar buttons (see below).
Source waveforms are computed using the beamformer spatial weights and the displayed averaged data (the noise normalized weights (5% noise) option was used to compute the
beamformer image).''

When starting the beamformer from the '''Average tab of the Paradigm dialog box''', the bilateral beamformer scan is performed. In the source analysis window, the beamformer computation can be repeated taking into account possibly correlated sources that are specified in the current solution. Interfering activities generated by all sources in the current solution that are in the 'On' state are specifically suppressed (they enter the leadfield matrix L in the beamformer calculation). The computation can be started from the '''Image''' menu or from the Image selector button [[File:MSBF_Button.png|22px|Image: 22 pixels]] dropdown menu. The Image menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window.

[[File:MSBF66.png]]

''Multiple-source beamformer image calculated in the presence of a source in the left hemisphere. A single-source scan has been performed instead of a bilateral beamforemr. The
source set in the current solution accounts for the left-hemispheric q-maximum in the data. Accordingly, the beamformer scan reveals only the as yet unmodeled additional activity in
the right hemisphere (note the radiological convention in the 3D image display). The source waveform of the beamformer virtual sensor in the left hemisphere is not shown since the
location (blue square in the figure) is not considered for the multiple-source beamformer.''

The beamformer scan can be performed with a single or a bilateral source scan. The default scan type depends on the current solution:
When the beamformer is started from the '''Average tab of the Paradigm dialog box''' the Source Analysis window opens with a new solution and a bilateral beamformer scan is
performed.
When the beamformer is started within the Source Analysis window, the default is:

* a scan with a single source in addition to the sources in the current solution, if at least one source is active.
* a bilateral scan if no source in the current solution is active.
* a scan with a single source when scalar-type beamformer is selected in the '''beamformer option dialog box'''.

The default scan type is the multiple source beamformer. The non-default scan type can be enforced using the corresponding Volume Image / Beamformer entry in the Image main
menu or in the beamformer option dialog box (only for the time-domain beamformer).

===Inserting Sources as Beamformer Virtual Sensor out of the Beamformer Image===

This is similar to the inserting sources out of the beamformer image in Multiple Source Beamformer (MSBF) in the Time-frequency Domain section.
The beamformer image can be used to add beamformer virtual sensors to the current solution. A simple double-click anywhere in the 3D view (not in the 2D view) will generate a
source at the corresponding location. A better and easier way to create sources at image maxima and minima is to use the toolbar buttons '''Switch to Maximum''' [[Image:SA 3Dimaging (8).gif]] and '''Add Source''' [[Image:SA 3Dimaging (9).gif]].

This feature allows to use the beamformer as a tool to create a source montage for '''source coherence''' analysis. A source montage file (*.mtg) for beamformer virtual sensors can
be saved using File \ Save Source Montage As… entry.

The time-domain beamformer image can be also used to add regional or dipole sources to the current solution. Press '''N''' key when there is no source in the current source array or
there is more than one beamformer virtual sensor. To create a new source array for beamformer virtual sensor, press '''N''' key when there is more than one regional or dipole source in
the current source array.

===Notes===

* You can hide or re-display the last computed image by selecting ''Hide Image'' entry in the '''Image''' menu.
* The current image can be exported to ASCII, ANALYZE, or BrainVoyager (vmp) format from the '''Image''' menu.
* For scaling options, use [[Image:SA 3Dimaging (10).gif]] and [[Image:SA 3Dimaging (11).gif]] '''Image Scale toolbar''' buttons.
* Parameters used for the beamformer calculations can be set in the '''Standard Volume tab of the Image Settings dialog box'''.
* Note that Model, Residual, Order, and Residual variance are not shown for the beamformer virtual sensor type sources.

===References===

* Sekihara, K., Nagarajan, S. S., Poeppel, D., Marantz, A., & Miyashita, Y. (2001). Reconstructing spatio-temporal activities of neural sources using an MEG vector beamformer technique. IEEE Transactions on Biomedical Engineering, 48(7), 760–771.

* Van Veen, B. D., Van Drongelen, W., Yuchtman, M., & Suzuki, A. (1997). Localization of brain electrical activity via linearly constrained minimum variance spatial filtering. IEEE Transactions on Biomedical Engineering, 44(9), 867–880

== CLARA ==

CLARA ('Classical LORETA Analysis Recursively Applied') is an iterative application of weighted LORETA images with a reduced source space in each iteration.

In an initialization step, a LORETA image is calculated. Then in each iteration the following steps are performed:

# The obtained image is spatially smoothed (this step is left out in the first iteration).
# All grid points with amplitudes below a threshold of 1% of the maximum activity are set to zero, thus being effectively eliminated from the source space in the following step.
# The resulting image defines a spatial weighting term (for each voxel the corresponding image amplitude).
# A LORETA image is computed with an additional spatial weighting term for each voxel as computed in step 3. By the default settings in BESA Research, the regularization values used in the iteration steps are slightly higher than that of the initialization LORETA image.

The procedure stops after 2 iterations, and the image computed in the last iteration is displayed. Please note that you can change all parameters by creating a user-defined volume image.

The advantage of CLARA over non-focusing distributed imaging methods is visualized by the figure below. Both images are computed from the N100 response in an auditory oddball experiment (file '''Oddball.fsg''' in subfolder ''fMRI+EEG-RT-Experiment'' of the ''Examples'' folder). The CLARA image is much more focal than the sLORETA image, making it easier to determine the location of the image maxima.

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (24).gif|thumb|350px|sLORETA image]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (25).gif|thumb|350px|CLARA image]] </li>
</ul></div>

'''Notes:'''

* Starting CLARA: CLARA can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter ''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]'' for important information on regularization of distributed inverses.

== LAURA ==

LAURA (Local Auto Regressive Average) belongs to the distributed inverse method of the family of weighted minimum norm methods ([https://doi.org/10.1023/A:1012944913650 Grave de Peralta Menendeza et al., "Noninvasive Localization of Electromagnetic Epileptic Activity. I. Method Descriptions and Simulations", BrainTopography 14(2), 131-137, 2001]). LAURA uses a spatial weighting function that includes depth weighting and that term has the form of a local autoregressive function.

The source activity is estimated by applying the general formula for a weighted minimum norm:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T}\left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings.''

In LAURA, V contains both a depth weighting term W and a representation of a local autoregressive function A. V is computed as:

<math>\mathrm{V} = \left( \mathrm{U}^{T} \cdot \mathrm{U} \right)^{-1}</math>


Where

<math>\mathrm{U} = \left( \mathrm{W} \cdot \mathrm{A} \right) \otimes \mathrm{I}_{3}</math>


Here, <math>\otimes</math> denotes the Kronecker product. I3 is the [3×3] identity matrix. W is an [s×s] diagonal matrix (with s the number of source locations on the grid), where each diagonal element is the inverse of the maximum singular value of the corresponding regional source's leadfields. The formula for the diagonal components Aii and the off-diagonal components Aik are as follows:

<math>\mathrm{A}_{ii} = \frac{26}{\mathrm{N}_{i}}\sum_{k \subset V_{i}}^{}\frac{1}{\mathrm{d}_{ik}^{2}}</math>


<math>
\mathrm{A}_{ik} =
\begin{cases}
- 1/\operatorname{dist}\left( i,k \right)^{2}, & \text{if } k \subset V_{i} \\
0, & \text{otherwise}
\end{cases}
</math>


Here, Vi is the vicinity around grid point i that includes the 26 direct neighbors.

The LAURA image in BESA Research displays the norm of the 3 components of S at each location r. Using the menu function ''Image / Export Image As... ''you have the option to save this norm of S or alternatively all components separately to disk.

'''Notes:'''

* '''Grid spacing:''' Due to memory limitations, LAURA images require a grid spacing of 7 mm or more.
* '''Computation time:''' Computation speed during the first LAURA image calculation depends on the grid spacing (computation is faster with larger grid spacing). After the first computation of a LAURA image, a '''*.laura''' file is stored in the data folder, containing intermediate results of the LAURA inverse. This file is used during all subsequent LAURA image computations. Thereby, the time needed to obtain the image is substantially reduced.
* '''MEG:''' In the case of MEG data, an additional constraint is implemented in the LAURA algorithm that prevents solutions from containing radial source currents (compare Pascual-Marqui, ISBET Newsletter 1995, 22-29). In MEG, an additional source space regularization is necessary in the inverse matrix operation required compute V
* '''Starting LAURA:''' LAURA can be started from the''' Image''' menu or from the '''Image Selection''' button.
* '''Regularization:''' Please refer to Chapter'' “Regularization of distributed volume images” ''for important information on regularization of distributed inverses.

== LORETA ==

LORETA ("Low Resolution Electromagnetic Tomography") is a distributed inverse method of the family of ''weighted minimum norm'' methods. LORETA was suggested by R.D. Pascual-Marqui (International Journal of Psychophysiology. 1994, 18:49-65). LORETA is characterized by a smoothness constraint, represented by a discrete 3D Laplacian.

The source activity is estimated by applying the general formula for a weighted minimum norm:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T}\left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings.''

In LORETA, V contains both a depth weighting term and a representation of the 3D Laplacian matrix. V is computed as:

<math>\mathrm{V} = \left( \mathrm{U}^{T} \cdot \mathrm{U} \right)^{- 1}</math>


where

<math>\mathrm{U} = \left( \mathrm{W} \cdot \mathrm{A} \right) \otimes \mathrm{I}_{3}</math>


Here, <math>\otimes</math> denotes the Kronecker product. I3 is the [3x3] identity matrix. W is an [sxs] diagonal matrix (with s the number of source locations on the grid), where each diagonal element is the inverse of the maximum singular value of the corresponding regional source's leadfields. A contains the 3D Laplacian and is computed as

<math>\mathrm{A} = \mathrm{Y} - \mathrm{I}_{s}</math>


with Is the [sxs] identity matrix, where s is the number of sources (= three times the number of grid points) and

<math>\mathrm{Y} = \frac{1}{2}\left\{ \mathrm{I}_{s} + \left\lbrack \operatorname{diag}\left( \mathrm{Z} \cdot \left\lbrack 111 \ldots 1 \right\rbrack^{T} \right) \right\rbrack^{- 1} \right\} \cdot \mathrm{Z}</math>


where

<math>
\mathrm{Z}_{ik} =
\begin{cases}
1/6, & \text{if } \operatorname{dist}\left( i,k \right) = 1 \text{ grid point} \\
0, & \text{otherwise}
\end{cases}
</math>


The LORETA image in BESA Research displays the norm of the 3 components of S at each location r. Using the menu function ''Image / Export Image As... ''you have the option to save this norm of S or alternatively all components separately to disk.

'''Notes:'''
* '''Grid spacing:''' Due to memory limitations, LORETA images require a grid spacing of 5 mm or more.
* '''Computation time:''' Computation speed during the first LORETA image calculation depends on the grid spacing (computation is faster with larger grid spacing). After the first computation of a LORETA image, a '''<nowiki>*.loreta</nowiki>''' file is stored in the data folder, containing intermediate results of the LORETA inverse. This file is used during all subsequent LORETA image computations. Thereby, the time needed to obtain the image is substantially reduced.
* '''MEG''': In the case of MEG data, an additional constraint is implemented in the LORETA algorithm that prevents solutions from containing radial source currents (Pascual-Marqui, ISBET Newsletter 1995, 22-29). In MEG, an additional source space regularization is necessary in the inverse matrix operation required compute V.
* '''Starting LORETA:''' LORETA can be started from the''' Image''' menu or from the '''Image Selection '''button.
* '''Regularization:''' Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed source models.

== sLORETA ==

This distributed inverse method consists of a ''standardized, unweighted minimum norm''. The method was originally suggested by R.D. Pascual-Marqui (Methods & Findings in Experimental & Clinical Pharmacology 2002, 24D:5-12) Starting point is an unweighted minimum norm computation:

<math>\mathrm{S}_{\text{MN}}\left( t \right) = \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings''.

This minimum norm estimate is now standardized to produce the sLORETA activity at a certain brain location r:

<math>\mathrm{S}_{\text{sLORETA}, r} = \mathrm{R}_{rr}^{-1/2} \cdot \mathrm{S}_{\text{MN},r}</math>


SsMN,r is the [3x1] (MEG: [2x1]) minimum norm estimate of the 3 (MEG: 2) dipoles at location r. Rrr is the [3x3] (MEG: [2x2]) diagonal block of the resolution matrix R that corresponds to the source components at the target location r. The resolution matrix is defined as:

<math>\mathrm{R} = \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{L}^{T} + \lambda \cdot \mathrm{I} \right)^{-1} \cdot \mathrm{L}</math>


The sLORETA image in BESA Research displays the norm of SsLORETA, r at each location r. Using the menu function ''Image / Export Image As...'' you have the option to save this norm of SsLORETA, r or alternatively all components separately to disk.

'''Notes:'''

* sLORETA can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== swLORETA ==

This distributed inverse method is a ''standardized, depth-weighted minimum norm'' (E. Palmero-Soler et al 2007 Phys. Med. Biol. 52 1783-1800). It differs from sLORETA only by an additional depth weighting.

Starting point is a depth-weighted minimum norm computation:

<math>\mathrm{S}_{\text{MN}}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings''.

V is the diagonal depth weighting matrix. For s grid locations, V is of dimension [3s x 3s] (MEG: [2s x 2s]). Each diagonal element of V is the inverse of the first singular value of the leadfield of the corresponding regional source. Hence, the first 3 (MEG: 2) diagonal elements equal the inverse of the largest eigenvalue of the leadfield matrix of regional source 1, and so on.

This minimum norm estimate is now standardized to produce the swLORETA activity at a certain brain location r:

<math>\mathrm{S}_{\text{swLORETA},r} = \mathrm{R}_{rr}^{-1/2} \cdot \mathrm{S}_{\text{MN},r}</math>


SsMN,r is the [3x1] (MEG: [2x1]) depth-weighted minimum norm estimate of the regional source at location r. Rrr is the [3x3] (MEG: [2x2]) diagonal block of the resolution matrix R that corresponds to the source components at the target location r. The resolution matrix is defined as:

<math>\mathrm{R} = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} + \lambda \cdot \mathrm{I} \right)^{-1} \cdot \mathrm{L}</math>


The swLORETA image in BESA Research displays the norm of SswLORETA, r at each location r. Using the menu function ''Image / Export Image As...'' you have the option to save this norm of SswLORETA, r or alternatively all components separately to disk.

'''Notes:'''

* sLORETA can be started from the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== sSLOFO ==

SSLOFO (standardized shrinking LORETA-FOCUSS) is an iterative application of weighted distributed source images with a reduced source space in each iteration ([https://dx.doi.org/10.1109/TBME.2005.855720 Liu et al., "Standardized shrinking LORETA-FOCUSS (SSLOFO): a new algorithm for spatio-temporal EEG source reconstruction", IEEE Transactions on Biomedical Engineering 52(10), 1681-1691, 2005]).

In an initialization step, an [[#sLORETA | sLORETA]] image is calculated. Then in each iteration the following steps are performed:

# A weighted minimum norm solution is computed according to the formula <math display="inline">\mathrm{S} = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}</math> . Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D is the data at the time point under consideration. V is a diagonal spatial weighting matrix that is computed in the previous iteration step. In the first iteration, the elements of V contain the magnitudes of the initially computed LORETA image.
# Standardization of this weighted minimum norm image is performed with the resolution matrix as in [[#sLORETA | sLORETA]].
# The obtained standardized weighted minimum norm image is being smoothed to get Ssmooth.
# All voxels with amplitudes below a threshold of 1% of the maximum activity get a weight of zero in the next iteration step, thus being effectively eliminated from the source space in the next iteration step.
# For all other voxels, compute the elements of the spatial weighting matrix V to be used in the next iteration as follows: <math display="inline">\mathrm{V}_{ii,\text{next iteration}} = \frac{1}{\left\| \mathrm{L}_{i} \right\|} \cdot \mathrm{S}_{ii,\text{smooth}} \cdot \mathrm{V}_{ii,\text{current iteration}}</math>



The procedure stops after 3 iterations. Please note that you can change all parameters by creating a [[#User-Defined Volume Image | user-defined volume image]].

'''Notes:'''
* '''Starting sSLOFO''': sSLOFO can be started from the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter ''[[#Regularization of distributed volume images | Regularization of distributed volume images]]'' for important information on regularization of distributed inverses.

== User-Defined Volume Image ==

In addition to the predefined 3D imaging methods in BESA Research, it is possible to create user-defined imaging methods based on the general formula for distributed inverses:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. Custom-defined parameters are:* The spatial weighting matrix V: This may include depth weighting, image weighting, or cross-voxel weighting with a 3D Laplacian (as in LORETA) or an autoregressive function (as in LAURA).

* Regularization: The term in parentheses is generally regularized. Note that regularization has a strong effect on the obtained results. Please refer to chapter “''Regularization of Distributed Volume Images” ''for more information.
* Standardization: Optionally, the result of the distributed inverse can be standardized with the resolution matrix (as in sLORETA).
* Iterations: Inverse computations can be applied iteratively. Each iteration is weighted with the image obtained in the previous iteration.

All parameters for the user-defined volume image are specified in the User-Defined Volume Tab of the Image Settings dialog box. Please refer to chapter “''User-Defined Volume Tab”'' for details.

'''Notes:'''
* Starting the user-defined volume image: the image calculation can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== Regularization of distributed volume images ==

Distributed source images require the inversion of a term of the form L V LT. This term is generally regularized before its inversion. In BESA Research, selection can be made between two different regularization approaches (parameters are defined in the ''Image Settings dialog box''):

* '''Tikhonov regularization''': In Tikhonov regularization, the term L V LT is inverted as (L V LT +λ I)-1. Here, l is the regularization constant, and I is the identity matrix.
* One way of determining the optimum regularization constant is by minimizing the ''generalized cross'' ''validation error'' (CVE).
* Alternatively, the regularization constant can be specified manually as a percentage of the trace of the matrix L V LT.
* '''TSVD''': In the truncated singular value decomposition (TSVD) approach, an SVD decomposition of L V LT is computed as  L V LT = U S UT, where the diagonal matrix S contains the singular values. All singular values smaller than the specified percentage of the maximum singular values are set to zero. The inverse is computed as U S-1 UT, where the diagonal elements of S-1 are the inverse of the corresponding non-zero diagonal elements of S.

Regularization has a critical effect on the obtained distributed source images. The results may differ completely with different choices of the regularization parameter (see examples below). Therefore, it is important to evaluate the generated image critically with respect to the regularization constant, and to keep in mind the uncertainties resulting from this fact when interpreting the results. The default setting in BESA Research is a TSVD regularization with a 0.03% threshold. However, this value might need to be adjusted to the specific data set at hand.

The following example illustrates the influence of the regularization parameter on the obtained images. The data used here is condition '''St-Cor of dataset Examples \ TFC-Error-Related-Negativity \ Correct+Error.fsg''' at 176 ms following the visual stimulus. Discrete dipole analysis reveals the main activity in the left and right lateral visual cortex at this latency.

[[Image:SA 3Dimaging (42).gif]]

''Discrete source model at 176 ms: Main activity in the left and right lateral visual cortex, no visual midline activity.''

LORETA images computed at this latency depend critically on the choice of the regularization constant. The following 3D images are created with TSVD regularization with SVD cutoffs of 0.1%, 0.005%, and 0.0001%, respectively. The volume grid size was 9 mm. The example demonstrates the dramatic effect of regularization and demonstrates the typical tradeoff between too strong regularization (leading to too smeared 3D images that tend to show blurred maxima) and too small regularization (resulting in too superficial 3D images with multiple maxima).

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (43).gif|thumb|350px|'''SVD cutoff 0.1%''': Regularization too strong. No separation between sources, mislocalization towards the middle of the brain.]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (44).gif|thumb|350px|'''SVD cutoff 0.005%''': Appropriate regularization. Separation of the bilateral activities. Location in agreement with the discrete multiple source model.]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (45).gif|thumb|350px|'''SVD cutoff 0.0001%''': Too small regularization. Mislocalization, too superficial 3D image. ]] </li>
</ul></div>

The automatic determination of the regularization constant using the CVE approach does not necessarily result in the optimum regularization parameter either. In this example, the unscaled CVE approach rather resembles the TSVD image with a cutoff of 0.0001%, i.e. regularization is too small. Therefore, it is advisable to compare different settings of the regularization parameter and make the final choice based on the above-mentioned considerations.

== Cortical LORETA ==

Cortical LORETA is principally the same technique as LORETA, however, Cortical LORETA is not computed in a 3D volume, but on the cortical surface.

The cortical reconstruction in BESA Research fed from BESA MRI is a closed 2D surface with no boundaries and a very close approximation of the actual cortical form. It consists of an irregular triangulated grid.

The Laplace operator that is used for identifying a smooth solution in a three-dimensional space is exchanged with a Laplace operator that runs on the two-dimensional cortical surface.

There is a wide variety of 2D Laplace operators with different characteristics. The general form of the discrete Laplace operator is

<math>\Delta f\left( p_{i} \right) = \frac{1}{d_{i}}\sum_{j \in N(i)}^{}{w_{ij}\left\lbrack f\left( p_{i} \right) - f\left( p_{j} \right) \right\rbrack},</math>


where '''pi''' is the '''i-th''' node of the triangular mesh, '''f(pi) '''is the value of a function f defined on the cortical mesh at the node '''pi''', '''wij''' is the weight for the connection between the nodes '''pi''' and '''pj''' and '''di''' is a normalization factor for the '''i-th''' row of the operator. Furthermore, '''N(i)''' is the set of indices corresponding to the direct (also called "1-ring") neighbors of '''pi'''.

BESA offers the choice of three Laplace operators with slightly different characteristics.

* '''Unweighted Graph Laplacian''': This is the simplest operator. It takes into account only the adjacency of the nodes and not the geometry of the mesh:

<math>
w_{ij} =
\begin{cases}
1, & \text{if } p_{i} \text{ and } p_{j} \text{ are connected by an edge} \\
0, & \text{otherwise}
\end{cases}
</math>

<math>d_{i} = 1</math>


[[Image:SA 3Dimaging (4).jpg |450px]]

* '''Weighted Graph Laplacian:''' This operator is similar to the unweighted graph Laplacian but with different weights for the different connections. The connections between nearby nodes get larger weights than the connections between farther nodes:

<math>w_{ij} = \frac{1}{\operatorname{dist}\left( p_{i},p_{j} \right)}</math>

<math>d_{i} = \sum_{j \in N(i)}^{} {\operatorname{dist}\left(p_{i}, p_{j} \right)}</math>


where '''dist''' ('''pi''' , '''pj''') is the distance between the nodes '''pi '''and '''pj'''.

[[Image:SA 3Dimaging (6).jpg|450px]]

* '''Geometric Laplacian with mixed area weights''': This operator takes into account the angles in the corresponding triangles into account as well as the area around the nodes in order to determine the connection weights:

<math>w_{ij} = \frac{\cot\left( \alpha_{ij} \right) + \cot\left( \beta_{ij} \right)}{2}</math>

<math>d_{i} = A_{\text{mixed}}</math>


where '''αij''' and '''βij''' denote the two angles opposite to the edge ('''i , j''') and '''Amixed '''is either the Voronoi area, or 1/2 of the triangle area or 1/4 of the triangle area depending on the type of the triangle.

[[Image:SA 3Dimaging (8).jpg|450px]]

'''Regularization and other parameters:'''

[[Image:CorticalLOR.png‎]]

* '''SVD cutoff''': The regularization for the inverse operator as a percent of the largest singular value.
* '''Depth weighting''': Turn depth weighting on or off.
* '''Laplacian type''': Selection of Laplacian operators (see above).

'''Notes:'''
* '''Starting Cortical LORETA''': Cortical LORETA can be started from the sub-menu '''Surface Image''' of the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]''” for important information on regularization of distributed inverses.

== Cortical CLARA ==

Cortical CLARA is principally the same technique as CLARA, but Cortical CLARA is not computed in a 3D volume, but on the cortical surface. Instead of using a LORETA image as the basis for the iterative application, cortical CLARA uses cortical LORETA.

'''Regularization and other parameters:'''

[[Image:SA 3Dimaging (47).gif]]

* '''SVD cutoff''': The regularization for the inverse operator as a percent of the largest singular value.
* '''Depth weighting''': Turn depth weighting on or off.
* '''Laplacian type''': Selection of Laplacian operators (see Cortical LORETA).
* '''No of iterations''': Number of iterations for CLARA. The more iterations are used, the sparser becomes the solution.
* '''Automatic''': The algorithm tries to determine the number of iterations automatically. The goodness of fit (GOF) is calculated after every iteration and if there is a big jump in the GOF then the algorithm will stop. If no jumps appear during the calculations then CLARA iterates until the specified number of iterations is reached.
* '''Regularize iterations''': If one wants to use different regularization for the CLARA iterations than the value specified as "SVD cutoff", this option should be selected.
* '''Amount to clip from img (%)''': Cortical CLARA uses the solution from the previous iteration as an additional weighting matrix for the current iteration. That weighting matrix is constructed by cutting the "low" activity from the solution. This number specifies how much of the activity should be cut from the previous solution in order to construct the weighting matrix. This value is given as a percentage of the maximal activity. Default value is 10%.

'''Notes:'''

* '''Starting Cortical CLARA:''' Cortical CLARA can be started from the sub-menu '''Surface Image''' of the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]''” for important information on regularization of distributed inverses.

== Cortex Inflation ==

The inflated cortex is a smoothened version of the individual cortical surface with minimal metric distortions (Fischl, B. et al. (1999). Cortical Surface-Based Analysis: II: Inflation, Flattening, and a Surface-Based Coordinate System. ''NeuroImage'', 9(2), 195–207). Gyri and sulci are smoothened out. The original distances between each point on the cortex and its neighbors are, however, mostly preserved.

[[Image:SA 3Dimaging (48).gif]]

''Cortical LORETA map overlaid on top of the inflated cortical surface.''

A lighter gray color overlaid on top of the surface image indicates the location of a gyrus of the individual cortex surface, while a darker gray color indicates the location of a sulcus. The inflated cortical surface can be computed in '''BESA MRI 2.0'''. For more details please refer to the BESA MRI 2.0 help.

== Surface Minimum Norm Image ==

'''Introduction'''

The minimum norm approach is a common method to estimate a distributed electrical current image in the brain at each time sample (Hämäläinen & Ilmoniemi 1984). The source activities of a large number of regional sources are computed. The sources are evenly distributed using 1500 standard locations 10% and 30% below the smoothed standard brain surface (when using the standard MRI) or using between 3000-4000 locations on the individual brain surface defined by the gray-white-matter boundary.

Since the number of sources is much larger than the number of sensors in a minimum norm solution, the inverse problem is highly underdetermined and must be stabilized by a mathematical constraint, the minimum norm. Out of the many current distributions that can account for the recorded sensor data, the solution with the minimum L2 norm, i.e. the minimum total power of the current distribution is displayed in BESA Research.

First, the forward solution (leadfield matrix L) of all sources is calculated in the current head model. Then, the source activities S(t) of all source components are computed from the data matrix D(t) using an inverse regularized by the estimated noise covariance matrix:

<math>\mathrm{S}\left( t \right) = \mathrm{R} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{R} \cdot \mathrm{L}^{T} + \mathrm{C}_N \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed regional source model, CN denotes the noise correlation matrix in sensor space, and R is a weighting matrix in source space. R and CN can be designed in different ways in order to optimize the minimum norm result. The total activity of each regional source is computed as the root mean square of the source activities S(t) of its 3 (MEG:2) components. This total source activity is transformed to a color-coded image of the brain surface. (When the standard brain is used, two sources are assigned to each surface location, located 10% and 30% below the surface, respectively. The color that is displayed on the standard brain surface is the larger of the two corresponding source activities.)

'''Weighting options'''

The minimum norm current imaging techniques of BESA Research provide different weighting strategies. Two weighting approaches are available: Depth weighting and spatio-temporal approaches.
* '''Depth weighting:''' Without depth weighting, deep sources appear very smeared in a minimum-norm reconstruction. With depth weighting, both deep and superficial sources produce a similar, more focal result. If this weighting method is selected, the leadfield of each regional source is scaled with the largest singular value of the SVD (singular value decomposition) of the source's leadfield.
* '''Spatio-temporal weighting''': Spatio-temporal weighting tries to assign large weight to sources that are assumed to be more likely to contribute to the recorded data.
** '''Subspace correlation after single source scan''': This method divides the signal into a signal and a noise subspace. The correlation of the leadfield of a regional source i with the signal subspace (pi) is computed to find out if the source location contributes to the measured data. The weighting matrix R becomes a diagonal matrix. Each of the three (MEG: 2) components of a regional source get the same weighting value pi2. This approach is based on the signal subspace correlation measure introduced by J.C. Mosher, R. M. Leahy (Recursive MUSIC: A Framework for EEG and MEG Source Localization, IEEE Trans. On Biomed. Eng. Vol. 45, No. 11, November 1998)
** '''Dale & Sereno 1993:''' In the approach of Dale and Sereno (J Cogn Neurosci, 1993, 5: 162-176) a signal subspace needs not be defined. The correlation pi of the leadfield of regional source i with the inverse of the data covariance matrix is computed along with the largest singular value λmax of the data covariance matrix. The weighting matrix R is a diagonal matrix with weights: [[Image:SA 3Dimaging (50).gif]]. Each of the three (MEG: 2) components of a regional source receives the same weighting value.

'''Noise regularization'''

Two methods to estimate the channel noise correlation matrix CN are provided by the program:
* '''Use baseline:''' Select this option to estimate the noise from the user-definable baseline. The signal is computed from the data at non-baseline latencies.
* '''Use 15% lowest values:''' The baseline activity is computed from the data at those 15% of all displayed latencies that have the lowest global field power. The signal is computed from all displayed latencies.

In each case, the activity (noise or signal, respectively) is defined as root-mean-square across all respective latencies for each channel.

The noise covariance matrix CN is constructed as a diagonal matrix. The entries in the main diagonal are proportional to the noise activity of the individual channels (if selected) or are all equally proportional to the average noise activity over all channels. The noise covariance matrix CN is then scaled such that the ratio of the Frobenius norms of the weighted leadfield projector matrix (LRLT) and the noise covariance matrix CN equals the Signal-to-Noise ratio. This scaling can be multiplied by an additional factor (default=1) to sharpen (<1) or smoothen (>1) the minimum norm image.

'''Applying the Minimum Norm Image'''

The minimum-norm algorithm is started via the ''Surface minimum norm image dialog box'', which is opened from the''' Image''' menu, or by typing the shortcut '''Ctrl-M''': Please refer to Chapter ''“Surface'' ''Minimum Norm Tab”'' for more details.

As opposed to the other 3D images available from the '''Image '''menu, the surface minimum norm image is not computed on a volumetric grid, but rather for locations on the brain surface. Accordingly, the results of the minimum norm image are displayed superimposed to the brain surface mesh rather than to the volumetric MR image.

The figure below shows a minimum norm image computed from the file '''Examples\Epilepsy\Spikes\Spikes-Child4_EEG+MEG_averaged.fsg'''. The EEG spike peak was imaged using the individual brain surface of the subject. A baseline from -300 to -70 ms was used. Minimum norm was computed with depth weighting, Spatio-temporal weighting according to Dale & Sereno 1993 and individual noise weighting with a noise scale factor of 0.01. The minimum norm image reveals the location of the spike generator in the close vicinity of the frontal left-hemispheric lesion in this subject.

[[Image:SA 3Dimaging (51).gif]]

== Multiple Source Probe Scan (MSPS) ==

 
'''Introduction'''

The MSPS function provides a tool for the validation of a given solution. It is based on the following theoretical consideration: If the recorded EEG/MEG data has been modeled adequately, i.e. all active brain regions are represented by a source in the current solution, then any additional probe source added to the solution will not show any activity apart from noise. The only exception occurs if this probe source is placed in close vicinity to one of the sources in the current solution. In that case, the solution's source and the probe source will share the activity of the corresponding brain area. The MSPS applies these considerations by scanning the brain on a pre-defined grid with a regional probe added to the current solution. Grid extent and density can be specified in the Image settings. The power P of the probe source at location r in the signal interval is compared with the power of the probe source in a reference interval, defining a value q:

<math>\mathrm{q}\left( r \right) = \sqrt{\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}} - 1</math>


MSPS can be computed on time domain or time-frequency domain data:
* In the time domain, q(r) is computed from the source waveform of the probe source. Here, P(r) is the mean power of the probe source at location r in the marked latency range, and Pref(r) is the mean probe source power in the user-definable baseline interval.
* In the time-frequency domain, an MSPS image can be computed from the complex cross spectral density matrices. By applying the inverse operator for a source configuration consisting of the current solution and the probe source, the power of the probe source can be computed for the target interval [P(r)] and the reference time-frequency interval [Pref(r)]. In the resulting MSPS image, q-values are shown in %, where q[%] = q*100.

The inverse operator used to determine the probe source power uses different regularization constants for the probe source and the sources in the current solution. The regularization constant of the sources in the current solution can be specified in the Image settings (default 4%). The regularization constant of the probe source is internally set to 0%.

Alternatively to the definition above, q can also be displayed in units of dB:

<math>\mathrm{q}\left\lbrack \text{dB} \right\rbrack = 10 \cdot \log_{10}\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}</math>


Values of q smaller than zero are not shown in the MSPS image.

According to the considerations above, an MSPS of a correct source model should optimally yield image maxima around the sources in the current solution only. If the MSPS image is blurred or shows maxima at locations different from the modeled sources, this indicates a non-sufficient or incorrect solution.

'''Applying the MSPS'''

This chapter illustrates the application of the Multiple Source Probe Scan. The figures are generated with data from file '''Examples/Epilepsy/Spikes/Rolandic-Spike-Child.fsg''' (-300 : +200 ms, filtered from 3 Hz [forward] to 40 Hz [zero-phase]).

'''Time domain versus time-frequency domain MSPS'''

The multiple source probe scan can be computed in the time domain or the time-frequency domain. The latter is possible only when time-frequency domain data is available for the current condition, i.e. if the condition has been created by starting a multiple source beamformer (MSBF) computation from the source coherence window. In this case, evoking the MSPS calculation from the '''Imaging '''button or from the '''Image''' menu will bring up the following dialog window that allows to choose between time- or time-frequency MSPS. If only time domain data is available, this dialog window will not appear and MSPS will be computed in the time domain.

[[Image:SA 3Dimaging (53).gif]]

For a time-frequency domain MSPS, the target and the reference time-frequency interval have been specified already in the Time-Frequency window (see Chapter "''How To Create Beamformer Images''"). For a time-domain MSPS, the target and the reference epoch have to be specified in the Source Analysis window as described below.

'''Time domain MSPS'''

The time-domain MSPS image displays the ratio of the power of a regional probe source in the signal and the baseline interval. The currently set baseline is indicated by a horizontal line in the upper left corner of the channel box.

[[Image:SA 3Dimaging (54).gif|thumb|c|none|330px|The black horizontal bar in the upper part of the channel box (here circled in red) indicates the baseline interval.]]

By default, BESA Research defines the pre-stimulus interval of the current data segment as baseline. The baseline should represent a latency range in which no event-related activity is present in the data. There are several possibilities to modify the baseline interval: by clicking on the horizontal line with the left mouse button or by using the corresponding entry in the '''Condition '''menu or '''Fit Interval''' popup menu.

Mark an interval to define the target epoch, i.e. the time-interval for which the current solution is to be tested. Start the MSPS by selecting it from the '''Image selection '''button or from the '''Image''' menu to start the probe source scan. The''' Image '''menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window. The 3D window opens and displays the scan result.

<div><ul>
<li style="display: inline-block;"> [[Image:SA 3Dimaging (55).gif|thumb|c|none|650px|This figure shows the MSPS image applied on the three left-hemispheric sources in the solution ''''Rolandic-Spike-Child-RS2.bsa''''. The baseline is set from -300ms to -50 ms. The right-hemispheric sources have been switched off. The fit interval is set to the latency range of large overall activity in the data (-43 ms : 117 ms). A realistic FEM model appropriate for the subject's age (12 years, conductivity ratios (cr) 50) is applied. The MSPS image does not show maxima at the modeled source locations and rather shows a spread q-value distribution.]] </li>

<li style="display: inline-block;"> [[Image:SA 3Dimaging (56).gif|thumb|c|none|650px|The MSPS image for the same latency range when the right-hemispheric sources have been included. The MSPS image appears more focal and shows maxima around the modeled brain regions. This indicates the substantial improvement of the solution by adding the right-hemispheric sources that model the propagation of the epileptic spike from the left to the right hemisphere (note the radiological side convention in the 3D window).]] </li>
</ul></div>

'''Time-Resolved MSPS'''

If the MSPS has been computed on time domain data, the image can be shown separately for each latency in the selected interval. After the MSPS has been computed for the marked epoch, double-click anywhere within this epoch to display the ratio of the probe source magnitude at the selected latency and the mean probe source magnitude in the baseline. Scanning the latency range by moving the cursor (e.g. with the left and right arrow cursor keys) provides a time-resolved MSPS image.

Time-resolved MSPS images are not available if the MSPS has been computed on data in the time-frequency domain.

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (57).gif|thumb|450px|MSPS image of the spike peak activity at 0ms. The activity mainly occurs in the left hemisphere. This fact is illustrated by the source waveforms and confirmed in the MSPS image, which shows a focal maximum around the location of the red sources.]] </li>

<li style="display: inline-block;"> [[File:SA 3Dimaging (58).gif|thumb|450px|Around +27 ms, the spike has propagated to the right hemisphere. This becomes evident from the waveforms of the blue sources, which show a significant latency lag with respect to the first three sources, and from the MSPS image, which shows the maximum around blue sources at this latency.]] </li>
</ul></div>



'''Notes:'''

* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image''' menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the''' Image''' menu.
* For scaling options, please refer to the '''scaling buttons''' popup menu .
* Parameters used for the MSPS calculations can be set in the ''General Settings tab'' of the ''Image Settings dialog box.''

== Source Sensitivity ==

'''Introduction'''

The 'Source sensitivity' function displays the sensitivity of the selected source in the current source model to activity in other brain regions. Sensitivity is defined as the fraction of power at the scanned brain location that is mapped onto the selected source.

To compute the source sensitivity, unit brain activity is modeled at different locations (probe source) throughout the brain. To this data, the current source model is applied to compute the source waveforms SCM of all modeled sources:

<math>\mathrm{S}_{\text{CM}} = \mathrm{L}_{\text{CM}}^{-1} \cdot \mathrm{L}_{\text{PS}}</math>


Here LCM-1 is the regularized inverse operator for the current model, and LPS is the leadfield of the regional probe source (dimension [Nx3] for EEG and [Nx2] for MEG, respectively, where N is the number of sensors). The source amplitude SSS of the selected source in the model is a 3x3 (MEG: 2x2) sub-matrix of SCM (if the selected source is a regional source) or a 1x3-matrix (MEG: 1x2) (if the selected source is a dipole). The root mean square of the singular values of SCM is defined as the source sensitivity.

The 3D source sensitivity image displays this value for all locations on a grid specified under '''Image/Settings'''. Grid density can be specified in the Image Settings.

'''Applying the Source Sensitivity Image'''

The Source Sensitivity image is evoked from the '''Image''' menu or by pressing the corresponding hot key (default: '''V''').

This function is enabled only when a solution with an active selected source is present in the Source Analysis window. The source sensitivity image then displays the sensitivity of the selected source to activity in other brain regions.

[[Image:SA 3Dimaging (59).gif]]

''Source Sensitivity image for the selected frontal source (green) in model ''''''High_Intensity_3RS.bsa'''''' in folder 'Examples/ERP_Auditory_Intensity'. The data displayed is the '100dB' condition in file ''''''All_Subjects_cc.fsg''''''. The selected source is sensitive to activity in the frontal brain region (yellow/white), while it is not influenced by activity in the vicinity of the left and right auditory cortex areas, which are modeled by the red and blue source in the model (transparent/gray).''

'''Notes:'''

* The sensitivity image is independent of the recorded sensor signals. It only depends on the current source model, the sensor configuration, the head model, and the regularization constant.
* If the regularization constant is set to zero, each source has a sensitivity of 100% to activity around its own location. With increasing regularization, the spatial filter becomes less focused, and the sensitivity of a source to activity at its location decreases.
* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image''' menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the '''Image''' menu.

{{BESAManualNav}}

Source Analysis 3D Imaging

2019-03-28T09:38:43Z

Jamie: /* Notes */

{{BESAInfobox
|title = Module information
|module = BESA Research Standard or higher
|version = 6.1 or higher
}}


== Overview ==

BESA Research features a set of new functions that provide 3D images that are displayed superimposed to the individual subject's anatomy. This chapter introduces these different images and describe their properties and applications.

The 3D images can be divided into three categories:

'''Volume images:'''

* '''The Multiple Source Beamformer (MSBF)''' is a tool for imaging brain activity. It is applied in the time-domain or time-frequency domain. The beamformer technique in time-frequency domain can image not only evoked, but also induced activity, which is not visible in time-domain averages of the data.
* '''Dynamic Imaging of Coherent Sources (DICS)''' can find coherence between any two pairs of voxels in the brain or between an external source and brain voxels. DICS requires time-frequency-transformed data and can find coherence for evoked and induced activity.

The following imaging methods provide an image of brain activity based on a distributed multiple source model:
* '''CLARA''' is an iterative application of LORETA images, focusing the obtained 3D image in each iteration step.
* '''LAURA '''uses a spatial weighting function that has the form of a local autoregressive function.
* '''LORETA''' has the 3D Laplacian operator implemented as spatial weighting prior.
* '''sLORETA''' is an unweighted minimum norm that is standardized by the resolution matrix.
* '''swLORETA '''is equivalent to sLORETA, except for an additional depth weighting.
* '''SSLOFO '''is an iterative application of standardized minimum norm images with consecutive shrinkage of the source space.
* A '''User-defined volume image''' allows to experiment with the different imaging techniques. It is possible to specify user-defined parameters for the family of distributed source images to create a new imaging technique.
* Bayesian source imaging: '''SESAME''' uses a semi-automated Bayesian approach to estimate the number of dipoles along with their parameters.

'''Surface image:'''

* The '''Surface Minimum Norm Image'''. If no individual MRI is available, the minimum norm image is displayed on a standard brain surface and computed for standard source locations. If available, an individual brain surface is used to construct the distributed source model and to image the brain activity.
* '''Cortical LORETA'''. Unlike classical LORETA, cortical LORETA is not computed in a 3D volume, but on the cortical surface.
* '''Cortical CLARA'''. Unlike classical CLARA, cortical CLARA is not computed in a 3D volume, but on the cortical surface.

'''Discrete model probing:'''

These images do not visualize source activity. Rather, they visualize properties of the currently applied discrete source model:
* The '''Multiple Source Probe Scan (MSPS)''' is a tool for the validation of a discrete multiple source model.
* The '''Source Sensitivity image''' displays the sensitivity of a selected source in the current discrete source model and is therefore data independent.

== Multiple Source Beamformer (MSBF) in the Time-frequency Domain ==

 
'''Short mathematical introduction'''

The BESA beamformer is a modified version of the linearly constrained minimum variance vector beamformer in the time-frequency domain as described in [https://dx.doi.org/10.1073/pnas.98.2.694 Gross et al., "Dynamic imaging of coherent sources: Studying neural interactions in the human brain", PNAS 98, 694-699, 2001]. It allows to image evoked and induced oscillatory activity in a user-defined time-frequency range, where time is taken relative to a triggered event.

The computation is based on a transformation of each channel's single trial data from the time domain into the time-frequency domain. This transformation is performed by the BESA Research Source Coherence module and leads to the complex spectral density Si (f,t), where i is the channel index and f and t denote frequency and time, respectively. Complex cross spectral density matrices C are computed for each trial:

<math>\mathrm{C}_{ij}\left( f,t \right) = \mathrm{S}_{i}\left( f,t \right) \cdot \mathrm{S}_{j}^{*}\left( f,t \right)</math>


The output power P of the beamformer for a specific brain region at location r is then computed by the following equation:

<math>\mathrm{P}\left( r \right) = \operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{-1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{-1}</math>


Here, Cr-1 is the inverse of the SVD-regularized average of Cij(f,t) over trials and the time-frequency range of interest; L is the leadfield matrix of the model containing a regional source at target location r and, optionally, additional sources whose interference with the target source is to be minimized; tr'[] is the trace of the [3×3] (MEG:[2×2]) submatrix of the bracketed expression that corresponds to the source at target location r.

In BESA Research, the output power P(r) is normalized with the output power in a reference time-frequency interval Pref(r). A value q ist defined as follows:

<math> \mathrm{q}\left( r \right) =
\begin{cases}
\sqrt{\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}(r)}} - 1 = \sqrt{\frac{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{\text{ref},r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}} - 1, & \text{for }\mathrm{P}(r) \geq \mathrm{P}_{\text{ref}}(r) \\

1 - \sqrt{\frac{\mathrm{P}_{\text{ref}}\left( r \right)}{\mathrm{P}\left( r \right)}} = 1 - \sqrt{\frac{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{\text{ref},r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}}, & \text{for }\mathrm{P}(r) < \mathrm{P}_{\text{ref}}(r)
\end{cases} </math>


Pref can be computed either from the corresponding frequency range in the baseline of the same condition (i.e. the beamformer images event-related power increase or decrease) or from the corresponding time-frequency range in a control condition (i.e. the beamformer images differences between two conditions). The beamformer image is constructed from values q(r) computed for all locations on a grid specified in the '''General Settings tab'''. For MEG data, the innermost grid points within a sphere of approx. 12% of the head diameter are assigned interpolated rather than calculated values).
q-values are shown in %, where where q[%] = q*100. Alternatively to the definition above, q can also be displayed in units of dB:

<math>\mathrm{q}\left\lbrack \text{dB} \right\rbrack = 10 \cdot \log_{10}\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}</math>


A beamformer operator is designed to pass signals from the brain region of interest r without attenuation, while minimizing interference from activity in all other brain regions. Traditional single-source beamformers are known to mislocalize sources if several brain regions have highly correlated activity. Therefore, the BESA beamformer extends the traditional single-source beamformer in order to implicitly suppress activity from possibly correlated brain regions. This is achieved by using a multiple source beamformer calculation that contains not only the leadfields of the source at the location of interest r, but also those of possibly interfering sources. As a default, BESA Research uses a bilateral beamformer, where specifically contributions from the homologue source in the opposite hemisphere are taken into account (the matrix L thus being of dimension N×6 for EEG and N×4 for MEG, respectively, where N is the number of sensors). This allows for imaging of highly correlated bilateral activity in the two hemispheres that commonly occurs during processing of external stimuli.

In addition, the beamformer computation can take into account possibly correlated sources at arbitrary locations that are specified in the current solution. This is achieved by adding their leadfield vectors to the matrix L in the equation above.

'''Applying the Beamformer'''

This chapter illustrates the usage of the BESA beamformer. The displayed figures are generated using the file ''''Examples/Learn-by-Simulations/AC-Coherence/AC-Osc20.foc'''' (see BESA Tutorial 6: "''Time-frequency analysis and Source coherence''").

'''Starting the beamformer from the time-frequency window'''

The BESA beamformer is applied in the time-frequency domain and therefore requires the Source Coherence module to be enabled. The time-frequency beamformer is especially useful to image in- or decrease of induced oscillatory activity. Induced activity cannot be observed in the averaged data, but shows up as enhanced averaged power in the TSE (Temporal-Spectral Evolution) plot. For instructions on how to initiate a beamformer computation in the time-frequency window, please refer to Chapter '''[[Source_Coherence_How_to...#How_to_Start_the_Beamformer_from_the_Time-Frequency_Window|How to Create Beamformer Images]]'''.

After the beamformer computation has been initiated in the time-frequency window, the source analysis window opens with an enlarged 3D image of the q-value computed with a '''bilateral beamformer'''. The result is superimposed onto the MR image assigned to the data set (individual or standard).

[[Image:SA 3Dimaging (5).gif]]

''Beamformer image after starting the computation in the Time-Frequency window. A bilateral pair of sources in the auditory cortex accounts for the highly correlated oscillatory induced activity. Only the bilateral beamformer manages to separate these activities; a traditional single-source beamformer would merge the two sources into one image maximum in the head center instead.''

'''Multiple source beamformer in the Source Analysis window'''

The 3D imaging display is part of the source analysis window. If you press the '''Restore''' button at the right end of the title bar of the 3D window, the window appears at the bottom right of the source analysis window. In the channel box, the averaged (evoked) data of the selected condition is shown. When a control condition was selected, its average is appended to the average of the target condition.

[[Image:SA 3Dimaging (6).gif]]

''Source Analysis window with beamformer image. The two sources have been added using the '''''Switch to''''' '''''Maximum''''' and '''''Add Source '''''toolbar buttons (see below). Source waveforms are computed from the displayed averaged data. Therefore, they do not represent the activity displayed in the beamformer image, which in this simulation example is induced (i.e. not phase-locked to the trigger)!''

When starting the beamformer from the time-frequency window, a bilateral beamformer scan is performed. In the source analysis window, the beamformer computation can be repeated taking into account possibly correlated sources that are specified in the current solution. Interfering activities generated by all sources in the current solution that are in the 'On' state are specifically suppressed ('''they enter the matrix L in the beamformer calculation''', see Chapter ''Short mathematical description'' above). The computation can be started from the '''Image''' menu or from the '''Image selector button''' dropdown menu. The '''Image''' menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window.

[[Image:SA 3Dimaging (7).gif]]

''Multiple source beamformer image calculated in the presence of a source in the left hemisphere. A '''single''' source scan has been performed. The source set in the current solution accounts for the left-hemispheric q-maximum in the data. Accordingly, the beamformer scan reveals only the as yet unmodeled additional activity in the right hemisphere (note the radiological convention in the 3D image display).''

The beamformer scan can be performed with a '''single''' or a '''bilateral''' source scan. The default scan type depends on the current solution:
* When the beamformer is started from the Time-Frequency window, the Source Analysis window opens with a new solution and a '''bilateral''' beamformer scan is performed.
* When the beamformer is started within the Source Analysis window, the default is
** a scan with a '''single''' source in addition to the sources in the current solution, if at least one source is active.
** a '''bilateral''' scan if no source in the current solution is active.

The default scan type is the multiple source beamformer. The non-default scan type can be enforced using the corresponding ''Volume Image / Beamformer'' entry in the '''Image''' menu.

'''Inserting Sources out of the Beamformer Image'''

The beamformer image can be used to add sources to the current solution. A simple double-click anywhere in the 2D- or 3D-view will generate a non-oriented regional source at the corresponding location. However, a better and easier way to create sources at image maxima and minima is to use the toolbar buttons '''Switch to Maximum''' [[Image:SA 3Dimaging (8).gif]] and '''Add Source''' [[Image:SA 3Dimaging (9).gif]].

Use the '''Switch to Maximum''' button to place the red crosshair of the 3D window onto a local image maximum or minimum. Hitting the '''Add Source''' button creates a regional source at the location of the crosshair and therefore ensures the exact placement of the source at the image extremum. Moreover, the '''Add Source''' button generates an oriented regional source. BESA Research automatically estimates the source orientation that contributes most to the power in the target time-frequency interval (or the reference time-frequency interval, if its power is larger than that in the target interval). The accuracy of this orientation estimate depends largely on the noise content of the data. The smaller the signal-to-noise ratio of the data, the lower is the accuracy of the orientation estimate. '''This feature allows to use the beamformer as a tool to create a source montage for source coherence analysis, where it is of advantage to work with oriented sources'''.

'''Notes:'''

* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image '''menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the''' Image''' menu.
* For scaling options, use the [[Image:SA 3Dimaging (10).gif]] and [[Image:SA 3Dimaging (11).gif]] '''Image Scale toolbar''' buttons.
* Parameters used for the beamformer calculations can be set in the '''Standard Volumes''' of the ''Image Settings dialog box.''

== Dynamic Imaging of Coherent Sources (DICS) ==

 
'''Short mathematical introduction'''

Dynamic Imaging of Coherent Sources (DICS) is a sophisticated method for imaging cortico-cortical coherence in the brain, or coherence between an external reference (e.g. EMG channel) and cortical structures. DICS can be applied to localize evoked as well as induced coherent cortical activity in a user-defined time-frequency range.

DICS was implemented in BESA closely following [https://dx.doi.org/10.1073/pnas.98.2.694 Gross et al., "Dynamic imaging of coherent sources: Studying neural interactions in the human brain", PNAS 98, 694-699, 2001].

The computation is based on a transformation of each channel's single trial data from the time domain into the frequency domain. This transformation is performed by the BESA Research Coherence module and results in the complex spectral density matrix that is used for constructing the spatial filter similar to beamforming.

DICS computation yields a 3-D image, each voxel being assigned a coherence value. Coherence values can be described as a neural activity index and do not have a unit. The neural activity index contrasts coherence in a target time-frequency bin with coherence of the same time-frequency bin in a baseline.

'''DICS for cortico-cortical coherence is computed as follows:'''

Let L(r) be the leadfield in voxel r in the brain and C the complex cross-spectral density matrix. The spatial filter W(r) for the voxel r in the head is defined as follows:

<math>W\left( r \right) = \left\lbrack L^{T}\left( r \right) \cdot C^{- 1} \cdot L\left( r \right) \right\rbrack^{- 1} \cdot L^{T}(r) \cdot C^{- 1}</math>


The cross-spectrum between two locations (voxels) r1 and r2 in the head are calculated with the following equation:

<math>C_{s}\left( r_{1},r_{2} \right) = W\left( r_{1} \right) \cdot C \cdot W^{*T}\left( r_{2} \right),</math>


where <nowiki>*T</nowiki> means the transposed complex conjugate of a matrix. The cross-spectral density can then be calculated from the cross spectrum as follows:

<math>c_{s}\left( r_{1},r_{2} \right) = \lambda_{1}\left\{ C_{s}\left( r_{1},r_{2} \right) \right\},</math>


where λ1{} indicates the largest singular value of the cross spectrum. Once the cross spectral density is estimated, the connectivity¹(CON) between the two brain regions r1 and r2 are calculated as follows:

<math>\text{CON}\left( r_{1},r_{2} \right) = \frac{c_{s}^{\text{sig}}\left( r_{1},r_{2} \right) - c_{s}^{\text{bl}}(r_{1},r_{2})}{c_{s}^{\text{sig}}\left( r_{1},r_{2} \right) + c_{s}^{\text{bl}}(r_{1},r_{2})},</math>


where cssig is the cross-spectral density for the signal of interest between the two brain regions r1 and r2, and csbl is the corresponding cross spectral density for the baseline or the control condition, respectively. In the case DICS is computed with a cortical reference, r1 is the reference region (voxel) and remains constant while r2 scans all the grid points within the brain sequentially. In that way, the connectivity between the reference brain region and all other brain regions is estimated. The value of CON(r1, r2) falls in the interval [-1 1]. If the cross-spectral density for the baseline is 0 the connectivity value will be 1. If the cross-spectral density for the signal is 0 the connectivity value will be -1.

¹ Here, the term connectivity is used rather than coherence, as strictly speaking the coherence equation is defined slightly differently. For simplicity reasons the rest of the tutorial uses the term coherence.

'''DICS for cortico-muscular coherence is computed as follows:'''

When using an external reference, the equation for coherence calculation is slightly different compared to the equation for cortico-cortical coherence. First of all, the cross-spectral density matrix is not only computed for the MEG/EEG channels, but the external reference channel is added. This resulting matrix is Call. In this case, the cross-spectral density between the reference signal and all other MEG/EEG

channels is called cref. It is only one column of Call. Hence, the cross-spectrum in voxel r is calculated with the following equation:

<math>C_{s}\left( r \right) = W\left( r \right) \cdot c_{\text{ref}}</math>


and the corresponding cross-spectral density is calculated as the sum of squares of Cs:

<math>c_{s}\left( r \right) = \sum_{i = 1}^{n}{C_{s}\left( r \right)_{i}^{2}},</math>


where n is 2 for MEG and 3 for EEG. This equation can also be described as the squared Euclidean norm of the cross-spectrum:

<math>c_{s}\left( r \right) = \left\| C_{s} \right\|^{2},</math>


The power in voxel r is calculated as in the cortico-cortical case:

<math>p\left( r \right) = \lambda_{1}\left\{ C_{s}(r,r) \right\}.</math>


At last, coherence between the external reference and cortical activity is calculated with the equation:

<math>\text{CON}\left( r \right) = \frac{c_{s}(r)}{p\left( r \right) \cdot C_{\text{all}}(k,k)},</math>


where Call(k, k) is the (k,k)-th diagonal element of the matrix Call.

DICS is particularly useful, if coherence is to be calculated without an a-priory source model (in contrast to source coherence based on pre-defined source montages). However, the recommended analysis strategy for DICS is to use a brain source as a starting point for coherence calculation that is known to contribute to the EEG/MEG signal of interest. For example, one might first run a beamformer on the time-frequency range of interest and use the voxel with the strongest oscillatory activity as a starting point for DICS. The resulting coherence image will again lead to several maxima (ordered by magnitude), which in turn can serve as starting points for DICS calculation. This way, it is possible to detect even weak sources that show coherent activity in the given time-frequency range.

The other significant application for DICS is estimating coherence between an external source and voxels in the brain. For example, an external source can be muscle activity recoded by an electrode placed over the according peripheral region. This way, the direct relationship between muscle activity and brain activation can be measured.

'''Starting DICS computation from the Time-Frequency Window'''

DICS is particularly useful, if coherence in a user-defined time-frequency bin (evoked or induced) is to be calculated between any two brain regions or between an external reference and the brain. DICS runs only on time-frequency decomposed data, so time-frequency analysis needs to be run before starting DICS computation.

To start the DICS computation, left-drag a window over a selected time-frequency bin in the Time-Frequency Window. Right-click and select “Image”. A dialogue will open (see fig. 1) prompting you to specify time and frequency settings as well as the baseline period. It is recommended to use a baseline period of equal length as the data period of interest. Make sure to select “DICS” in the top row and press “'''Go'''”.

[[Image:SA 3Dimaging (21).gif|450px|thumb|c|none|Fig. 1: Time and frequency settings for DICS and MSBF]]

Next, a window will appear allowing you to specify the reference source for coherence calculation (see fig. 2). It is possible to select a channel (e.g. EMG) or a brain source. If a brain source is chosen and no source analysis was computed beforehand, the option “Use current cross-hair position” must be chosen. In case discrete source analysis was computed previously, the selected source can be chosen as the reference for DICS. Please note that DICS can be re-computed with any cross-hair or source position at a later stage.

[[Image:SA 3Dimaging (1).jpg|400px|thumb|c|none|Fig. 2: Possible options for choosing the reference]]

Confirming with “'''OK'''” will start computation of coherence between the selected channel/voxel and all other brain voxels. In case DICS is computed for a reference source in the brain, it can be advantageous to run a beamforming analysis in the selected time-frequency window first and use one of the beamforming maxima as reference for DICS. Fig. 3 shows an example for DICS calculation.

[[Image:SA 3Dimaging (22).gif|500px|thumb|c|none|Fig. 3: Coherence between left-hemispheric auditory areas and the selected voxel in the right auditory cortex.]]

Coherence values range between -1 and 1. If coherence in the signal is much larger than coherence in the baseline (control condition) then the DICS value is going to approach 1. Contrary, if coherence in the baseline is much larger than coherence in the signal, then the DICS value is going to approach -1. At last, if coherence in the signal is equal to coherence in the baseline, then the DICS value is 0.

In case DICS is to be re-computed with a different reference, simply mark the desired reference position by placing the cross-hair in the anatomical view and select “DICS” in the middle panel of the source analysis window (see Fig. 4). In case an external reference is to be selected, click on “DICS” in the middle panel to bring up the DICS dialogue (see. Fig. 2) and select the desired channel. Please note that DICS computation will only be available after running time-frequency analysis.

[[Image:SA 3Dimaging (23).gif|700px|thumb|c|none|Fig. 4: Integration of DICS in the Source Analysis window]]

== Multiple Source Beamformer (MSBF) in the Time Domain ==
''(requires Besa Research 7.0 or higher)''

===Short mathematical introduction===

Beamforming approach can be also applied in the time domain data. This approach was introduced as linearly constrained minimum variance (LCMV) beamformer (Van Veen et al., 1997). It allows to image evoked activity in a user-defined time range, where time is taken relative to a triggered event, and to estimate source waveforms using the calculated spatial weight at locations of interest. For an implementation of the beamformer in the time domain, data covariance matrices are required, while complex cross spectral density matrices are used for the beamformer approaches in the time-frequency domain as described in the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section.

The bilateral beamformer introduced in the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section is also implemented for the time-domain beamformer to take into account contributions from the homologue source in the opposite. This allows for imaging of highly correlated bilateral activity in the two hemispheres that commonly occurs during processing of external stimuli. In addition, the beamformer computation can take into account possibly correlated sources at arbitrary locations.
The beamformer spatial weight W(r) for the voxel r in the brain is defined as follows (Van Veen et al., 1997):

[[File:MSBF1.png]]

where '''C-1''' is the inversed regularized average of covariance matrix over trials, '''L''' is the leadfield matrix of the model containing a regional source at target location r and optionally
additional sources whose interference with the target source is to be minimized. The beamformer spatial weight '''W'''(r) can be applied to the measured data to estimate source
waveform at a location r (beamformer virtual sensor):

[[File:MSBF2.png]]

where '''S'''(r,t) represents the estimated source waveform and '''M'''(t) represents measured EEG or MEG signals.
The output power P of the beamformer for a specific brain region at location r is computed by the following equation:

[[File:MSBF3.png]]

where tr’[ ] is the trace of the [3×3] (MEG: [2×2]) submatrix of the bracketed expression that corresponds to the source at target location r.
Beamformer can suppress noise sources that are correlated across sensors. However, uncorrelated noise will be amplified in a spatially non-uniform manner, with increasing
distortion with increasing distance from the sensors (Van Veen et al., 1997; Sekihara et al., 2001). For this reason, estimated source power should be normalized by a noise power.
In BESA Research, the output power P(r) is normalized with the output power in a baseline interval or with the output power of a uncorrelated noise: P(r) / Pref (r).
The time-domain beamformer image is constructed from values q(r) computed for all locations on a grid specified in the '''General Settings''' tab. A value q(r) is defined as described in
the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section with data covariance matrices instead of cross-spectral density matrices.

===Applying the Beamformer===

This chapter illustrates the usage of the BESA beamformer in the time domain. The displayed figures are generated using the file ‘Examples/ERP-Auditory-Intensity/S1.cnt’.

'''Starting the time-domain beamformer from the Average tab of the Paradigm dialog box'''

The time-domain beamformer is needed data covariance matrices and therefore requires the ERP module to be enabled. After the beamformer computation has been initiated in the
'''Average tab of the Paradigm dialog box''', the source analysis window opens with an enlarged 3D image of the q-value computed with a bilateral beamformer. The result is
superimposed onto the MR image assigned to the data set (individual or standard).

[[File:MSBF44.png]]

''Beamformer image for auditory evoked data after starting the computation in the '''Average tab of the Paradigm dialog box'''. The bilateral beamformer manages to separate the
activities in auditory areas, while a traditional single-source beamformer would merge the two sources into one image maximum in the head center instead.''

'''Multiple-source beamformer in the Source Analysis window'''

The 3D imaging display is part of the source analysis window. In the Channel box, the averaged (evoked) data of the selected condition is shown. Selected covariance intervals in
the ERP module can be checked in the Channel box. The red, gray, and blue rectangles indicate signal, baseline, and common interval, respectively.

[[File:MSBF55.png]]

''Source Analysis window with beamformer image. The two beamformer virtual sensors have been added using the Switch to Maximum and Add Source toolbar buttons (see below).
Source waveforms are computed using the beamformer spatial weights and the displayed averaged data (the noise normalized weights (5% noise) option was used to compute the
beamformer image).''

When starting the beamformer from the '''Average tab of the Paradigm dialog box''', the bilateral beamformer scan is performed. In the source analysis window, the beamformer computation can be repeated taking into account possibly correlated sources that are specified in the current solution. Interfering activities generated by all sources in the current solution that are in the 'On' state are specifically suppressed (they enter the leadfield matrix L in the beamformer calculation). The computation can be started from the '''Image''' menu or from the Image selector button [[File:MSBF_Button.png|22px|Image: 22 pixels]] dropdown menu. The Image menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window.

[[File:MSBF66.png]]

''Multiple-source beamformer image calculated in the presence of a source in the left hemisphere. A single-source scan has been performed instead of a bilateral beamforemr. The
source set in the current solution accounts for the left-hemispheric q-maximum in the data. Accordingly, the beamformer scan reveals only the as yet unmodeled additional activity in
the right hemisphere (note the radiological convention in the 3D image display). The source waveform of the beamformer virtual sensor in the left hemisphere is not shown since the
location (blue square in the figure) is not considered for the multiple-source beamformer.''

The beamformer scan can be performed with a single or a bilateral source scan. The default scan type depends on the current solution:
When the beamformer is started from the '''Average tab of the Paradigm dialog box''' the Source Analysis window opens with a new solution and a bilateral beamformer scan is
performed.
When the beamformer is started within the Source Analysis window, the default is:

* a scan with a single source in addition to the sources in the current solution, if at least one source is active.
* a bilateral scan if no source in the current solution is active.
* a scan with a single source when scalar-type beamformer is selected in the '''beamformer option dialog box'''.

The default scan type is the multiple source beamformer. The non-default scan type can be enforced using the corresponding Volume Image / Beamformer entry in the Image main
menu or in the beamformer option dialog box (only for the time-domain beamformer).

===Inserting Sources as Beamformer Virtual Sensor out of the Beamformer Image===

This is similar to the inserting sources out of the beamformer image in Multiple Source Beamformer (MSBF) in the Time-frequency Domain section.
The beamformer image can be used to add beamformer virtual sensors to the current solution. A simple double-click anywhere in the 3D view (not in the 2D view) will generate a
source at the corresponding location. A better and easier way to create sources at image maxima and minima is to use the toolbar buttons '''Switch to Maximum''' [[Image:SA 3Dimaging (8).gif]] and '''Add Source''' [[Image:SA 3Dimaging (9).gif]].

This feature allows to use the beamformer as a tool to create a source montage for '''source coherence''' analysis. A source montage file (*.mtg) for beamformer virtual sensors can
be saved using File \ Save Source Montage As… entry.

The time-domain beamformer image can be also used to add regional or dipole sources to the current solution. Press '''N''' key when there is no source in the current source array or
there is more than one beamformer virtual sensor. To create a new source array for beamformer virtual sensor, press '''N''' key when there is more than one regional or dipole source in
the current source array.

===Notes===

* You can hide or re-display the last computed image by selecting ''Hide Image'' entry in the '''Image''' menu.
* The current image can be exported to ASCII, ANALYZE, or BrainVoyager (vmp) format from the '''Image''' menu.
* For scaling options, use [[Image:SA 3Dimaging (10).gif]] and [[Image:SA 3Dimaging (11).gif]] '''Image Scale toolbar''' buttons.
* Parameters used for the beamformer calculations can be set in the '''Standard Volume tab of the Image Settings dialog box'''.
* Note that Model, Residual, Order, and Residual variance are not shown for the beamformer virtual sensor type sources.

===References===

* Sekihara, K., Nagarajan, S. S., Poeppel, D., Marantz, A., & Miyashita, Y. (2001). Reconstructing spatio-temporal activities of neural sources using an MEG vector beamformer technique. IEEE Transactions on Biomedical Engineering, 48(7), 760–771.

* Van Veen, B. D., Van Drongelen, W., Yuchtman, M., & Suzuki, A. (1997). Localization of brain electrical activity via linearly constrained minimum variance spatial filtering. IEEE Transactions on Biomedical Engineering, 44(9), 867–880

== CLARA ==

CLARA ('Classical LORETA Analysis Recursively Applied') is an iterative application of weighted LORETA images with a reduced source space in each iteration.

In an initialization step, a LORETA image is calculated. Then in each iteration the following steps are performed:

# The obtained image is spatially smoothed (this step is left out in the first iteration).
# All grid points with amplitudes below a threshold of 1% of the maximum activity are set to zero, thus being effectively eliminated from the source space in the following step.
# The resulting image defines a spatial weighting term (for each voxel the corresponding image amplitude).
# A LORETA image is computed with an additional spatial weighting term for each voxel as computed in step 3. By the default settings in BESA Research, the regularization values used in the iteration steps are slightly higher than that of the initialization LORETA image.

The procedure stops after 2 iterations, and the image computed in the last iteration is displayed. Please note that you can change all parameters by creating a user-defined volume image.

The advantage of CLARA over non-focusing distributed imaging methods is visualized by the figure below. Both images are computed from the N100 response in an auditory oddball experiment (file '''Oddball.fsg''' in subfolder ''fMRI+EEG-RT-Experiment'' of the ''Examples'' folder). The CLARA image is much more focal than the sLORETA image, making it easier to determine the location of the image maxima.

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (24).gif|thumb|350px|sLORETA image]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (25).gif|thumb|350px|CLARA image]] </li>
</ul></div>

'''Notes:'''

* Starting CLARA: CLARA can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter ''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]'' for important information on regularization of distributed inverses.

== LAURA ==

LAURA (Local Auto Regressive Average) belongs to the distributed inverse method of the family of weighted minimum norm methods ([https://doi.org/10.1023/A:1012944913650 Grave de Peralta Menendeza et al., "Noninvasive Localization of Electromagnetic Epileptic Activity. I. Method Descriptions and Simulations", BrainTopography 14(2), 131-137, 2001]). LAURA uses a spatial weighting function that includes depth weighting and that term has the form of a local autoregressive function.

The source activity is estimated by applying the general formula for a weighted minimum norm:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T}\left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings.''

In LAURA, V contains both a depth weighting term W and a representation of a local autoregressive function A. V is computed as:

<math>\mathrm{V} = \left( \mathrm{U}^{T} \cdot \mathrm{U} \right)^{-1}</math>


Where

<math>\mathrm{U} = \left( \mathrm{W} \cdot \mathrm{A} \right) \otimes \mathrm{I}_{3}</math>


Here, <math>\otimes</math> denotes the Kronecker product. I3 is the [3×3] identity matrix. W is an [s×s] diagonal matrix (with s the number of source locations on the grid), where each diagonal element is the inverse of the maximum singular value of the corresponding regional source's leadfields. The formula for the diagonal components Aii and the off-diagonal components Aik are as follows:

<math>\mathrm{A}_{ii} = \frac{26}{\mathrm{N}_{i}}\sum_{k \subset V_{i}}^{}\frac{1}{\mathrm{d}_{ik}^{2}}</math>


<math>
\mathrm{A}_{ik} =
\begin{cases}
- 1/\operatorname{dist}\left( i,k \right)^{2}, & \text{if } k \subset V_{i} \\
0, & \text{otherwise}
\end{cases}
</math>


Here, Vi is the vicinity around grid point i that includes the 26 direct neighbors.

The LAURA image in BESA Research displays the norm of the 3 components of S at each location r. Using the menu function ''Image / Export Image As... ''you have the option to save this norm of S or alternatively all components separately to disk.

'''Notes:'''

* '''Grid spacing:''' Due to memory limitations, LAURA images require a grid spacing of 7 mm or more.
* '''Computation time:''' Computation speed during the first LAURA image calculation depends on the grid spacing (computation is faster with larger grid spacing). After the first computation of a LAURA image, a '''*.laura''' file is stored in the data folder, containing intermediate results of the LAURA inverse. This file is used during all subsequent LAURA image computations. Thereby, the time needed to obtain the image is substantially reduced.
* '''MEG:''' In the case of MEG data, an additional constraint is implemented in the LAURA algorithm that prevents solutions from containing radial source currents (compare Pascual-Marqui, ISBET Newsletter 1995, 22-29). In MEG, an additional source space regularization is necessary in the inverse matrix operation required compute V
* '''Starting LAURA:''' LAURA can be started from the''' Image''' menu or from the '''Image Selection''' button.
* '''Regularization:''' Please refer to Chapter'' “Regularization of distributed volume images” ''for important information on regularization of distributed inverses.

== LORETA ==

LORETA ("Low Resolution Electromagnetic Tomography") is a distributed inverse method of the family of ''weighted minimum norm'' methods. LORETA was suggested by R.D. Pascual-Marqui (International Journal of Psychophysiology. 1994, 18:49-65). LORETA is characterized by a smoothness constraint, represented by a discrete 3D Laplacian.

The source activity is estimated by applying the general formula for a weighted minimum norm:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T}\left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings.''

In LORETA, V contains both a depth weighting term and a representation of the 3D Laplacian matrix. V is computed as:

<math>\mathrm{V} = \left( \mathrm{U}^{T} \cdot \mathrm{U} \right)^{- 1}</math>


where

<math>\mathrm{U} = \left( \mathrm{W} \cdot \mathrm{A} \right) \otimes \mathrm{I}_{3}</math>


Here, <math>\otimes</math> denotes the Kronecker product. I3 is the [3x3] identity matrix. W is an [sxs] diagonal matrix (with s the number of source locations on the grid), where each diagonal element is the inverse of the maximum singular value of the corresponding regional source's leadfields. A contains the 3D Laplacian and is computed as

<math>\mathrm{A} = \mathrm{Y} - \mathrm{I}_{s}</math>


with Is the [sxs] identity matrix, where s is the number of sources (= three times the number of grid points) and

<math>\mathrm{Y} = \frac{1}{2}\left\{ \mathrm{I}_{s} + \left\lbrack \operatorname{diag}\left( \mathrm{Z} \cdot \left\lbrack 111 \ldots 1 \right\rbrack^{T} \right) \right\rbrack^{- 1} \right\} \cdot \mathrm{Z}</math>


where

<math>
\mathrm{Z}_{ik} =
\begin{cases}
1/6, & \text{if } \operatorname{dist}\left( i,k \right) = 1 \text{ grid point} \\
0, & \text{otherwise}
\end{cases}
</math>


The LORETA image in BESA Research displays the norm of the 3 components of S at each location r. Using the menu function ''Image / Export Image As... ''you have the option to save this norm of S or alternatively all components separately to disk.

'''Notes:'''
* '''Grid spacing:''' Due to memory limitations, LORETA images require a grid spacing of 5 mm or more.
* '''Computation time:''' Computation speed during the first LORETA image calculation depends on the grid spacing (computation is faster with larger grid spacing). After the first computation of a LORETA image, a '''<nowiki>*.loreta</nowiki>''' file is stored in the data folder, containing intermediate results of the LORETA inverse. This file is used during all subsequent LORETA image computations. Thereby, the time needed to obtain the image is substantially reduced.
* '''MEG''': In the case of MEG data, an additional constraint is implemented in the LORETA algorithm that prevents solutions from containing radial source currents (Pascual-Marqui, ISBET Newsletter 1995, 22-29). In MEG, an additional source space regularization is necessary in the inverse matrix operation required compute V.
* '''Starting LORETA:''' LORETA can be started from the''' Image''' menu or from the '''Image Selection '''button.
* '''Regularization:''' Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed source models.

== sLORETA ==

This distributed inverse method consists of a ''standardized, unweighted minimum norm''. The method was originally suggested by R.D. Pascual-Marqui (Methods & Findings in Experimental & Clinical Pharmacology 2002, 24D:5-12) Starting point is an unweighted minimum norm computation:

<math>\mathrm{S}_{\text{MN}}\left( t \right) = \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings''.

This minimum norm estimate is now standardized to produce the sLORETA activity at a certain brain location r:

<math>\mathrm{S}_{\text{sLORETA}, r} = \mathrm{R}_{rr}^{-1/2} \cdot \mathrm{S}_{\text{MN},r}</math>


SsMN,r is the [3x1] (MEG: [2x1]) minimum norm estimate of the 3 (MEG: 2) dipoles at location r. Rrr is the [3x3] (MEG: [2x2]) diagonal block of the resolution matrix R that corresponds to the source components at the target location r. The resolution matrix is defined as:

<math>\mathrm{R} = \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{L}^{T} + \lambda \cdot \mathrm{I} \right)^{-1} \cdot \mathrm{L}</math>


The sLORETA image in BESA Research displays the norm of SsLORETA, r at each location r. Using the menu function ''Image / Export Image As...'' you have the option to save this norm of SsLORETA, r or alternatively all components separately to disk.

'''Notes:'''

* sLORETA can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== swLORETA ==

This distributed inverse method is a ''standardized, depth-weighted minimum norm'' (E. Palmero-Soler et al 2007 Phys. Med. Biol. 52 1783-1800). It differs from sLORETA only by an additional depth weighting.

Starting point is a depth-weighted minimum norm computation:

<math>\mathrm{S}_{\text{MN}}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings''.

V is the diagonal depth weighting matrix. For s grid locations, V is of dimension [3s x 3s] (MEG: [2s x 2s]). Each diagonal element of V is the inverse of the first singular value of the leadfield of the corresponding regional source. Hence, the first 3 (MEG: 2) diagonal elements equal the inverse of the largest eigenvalue of the leadfield matrix of regional source 1, and so on.

This minimum norm estimate is now standardized to produce the swLORETA activity at a certain brain location r:

<math>\mathrm{S}_{\text{swLORETA},r} = \mathrm{R}_{rr}^{-1/2} \cdot \mathrm{S}_{\text{MN},r}</math>


SsMN,r is the [3x1] (MEG: [2x1]) depth-weighted minimum norm estimate of the regional source at location r. Rrr is the [3x3] (MEG: [2x2]) diagonal block of the resolution matrix R that corresponds to the source components at the target location r. The resolution matrix is defined as:

<math>\mathrm{R} = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} + \lambda \cdot \mathrm{I} \right)^{-1} \cdot \mathrm{L}</math>


The swLORETA image in BESA Research displays the norm of SswLORETA, r at each location r. Using the menu function ''Image / Export Image As...'' you have the option to save this norm of SswLORETA, r or alternatively all components separately to disk.

'''Notes:'''

* sLORETA can be started from the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== sSLOFO ==

SSLOFO (standardized shrinking LORETA-FOCUSS) is an iterative application of weighted distributed source images with a reduced source space in each iteration ([https://dx.doi.org/10.1109/TBME.2005.855720 Liu et al., "Standardized shrinking LORETA-FOCUSS (SSLOFO): a new algorithm for spatio-temporal EEG source reconstruction", IEEE Transactions on Biomedical Engineering 52(10), 1681-1691, 2005]).

In an initialization step, an [[#sLORETA | sLORETA]] image is calculated. Then in each iteration the following steps are performed:

# A weighted minimum norm solution is computed according to the formula <math display="inline">\mathrm{S} = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}</math> . Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D is the data at the time point under consideration. V is a diagonal spatial weighting matrix that is computed in the previous iteration step. In the first iteration, the elements of V contain the magnitudes of the initially computed LORETA image.
# Standardization of this weighted minimum norm image is performed with the resolution matrix as in [[#sLORETA | sLORETA]].
# The obtained standardized weighted minimum norm image is being smoothed to get Ssmooth.
# All voxels with amplitudes below a threshold of 1% of the maximum activity get a weight of zero in the next iteration step, thus being effectively eliminated from the source space in the next iteration step.
# For all other voxels, compute the elements of the spatial weighting matrix V to be used in the next iteration as follows: <math display="inline">\mathrm{V}_{ii,\text{next iteration}} = \frac{1}{\left\| \mathrm{L}_{i} \right\|} \cdot \mathrm{S}_{ii,\text{smooth}} \cdot \mathrm{V}_{ii,\text{current iteration}}</math>



The procedure stops after 3 iterations. Please note that you can change all parameters by creating a [[#User-Defined Volume Image | user-defined volume image]].

'''Notes:'''
* '''Starting sSLOFO''': sSLOFO can be started from the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter ''[[#Regularization of distributed volume images | Regularization of distributed volume images]]'' for important information on regularization of distributed inverses.

== User-Defined Volume Image ==

In addition to the predefined 3D imaging methods in BESA Research, it is possible to create user-defined imaging methods based on the general formula for distributed inverses:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. Custom-defined parameters are:* The spatial weighting matrix V: This may include depth weighting, image weighting, or cross-voxel weighting with a 3D Laplacian (as in LORETA) or an autoregressive function (as in LAURA).

* Regularization: The term in parentheses is generally regularized. Note that regularization has a strong effect on the obtained results. Please refer to chapter “''Regularization of Distributed Volume Images” ''for more information.
* Standardization: Optionally, the result of the distributed inverse can be standardized with the resolution matrix (as in sLORETA).
* Iterations: Inverse computations can be applied iteratively. Each iteration is weighted with the image obtained in the previous iteration.

All parameters for the user-defined volume image are specified in the User-Defined Volume Tab of the Image Settings dialog box. Please refer to chapter “''User-Defined Volume Tab”'' for details.

'''Notes:'''
* Starting the user-defined volume image: the image calculation can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== Regularization of distributed volume images ==

Distributed source images require the inversion of a term of the form L V LT. This term is generally regularized before its inversion. In BESA Research, selection can be made between two different regularization approaches (parameters are defined in the ''Image Settings dialog box''):

* '''Tikhonov regularization''': In Tikhonov regularization, the term L V LT is inverted as (L V LT +λ I)-1. Here, l is the regularization constant, and I is the identity matrix.
* One way of determining the optimum regularization constant is by minimizing the ''generalized cross'' ''validation error'' (CVE).
* Alternatively, the regularization constant can be specified manually as a percentage of the trace of the matrix L V LT.
* '''TSVD''': In the truncated singular value decomposition (TSVD) approach, an SVD decomposition of L V LT is computed as  L V LT = U S UT, where the diagonal matrix S contains the singular values. All singular values smaller than the specified percentage of the maximum singular values are set to zero. The inverse is computed as U S-1 UT, where the diagonal elements of S-1 are the inverse of the corresponding non-zero diagonal elements of S.

Regularization has a critical effect on the obtained distributed source images. The results may differ completely with different choices of the regularization parameter (see examples below). Therefore, it is important to evaluate the generated image critically with respect to the regularization constant, and to keep in mind the uncertainties resulting from this fact when interpreting the results. The default setting in BESA Research is a TSVD regularization with a 0.03% threshold. However, this value might need to be adjusted to the specific data set at hand.

The following example illustrates the influence of the regularization parameter on the obtained images. The data used here is condition '''St-Cor of dataset Examples \ TFC-Error-Related-Negativity \ Correct+Error.fsg''' at 176 ms following the visual stimulus. Discrete dipole analysis reveals the main activity in the left and right lateral visual cortex at this latency.

[[Image:SA 3Dimaging (42).gif]]

''Discrete source model at 176 ms: Main activity in the left and right lateral visual cortex, no visual midline activity.''

LORETA images computed at this latency depend critically on the choice of the regularization constant. The following 3D images are created with TSVD regularization with SVD cutoffs of 0.1%, 0.005%, and 0.0001%, respectively. The volume grid size was 9 mm. The example demonstrates the dramatic effect of regularization and demonstrates the typical tradeoff between too strong regularization (leading to too smeared 3D images that tend to show blurred maxima) and too small regularization (resulting in too superficial 3D images with multiple maxima).

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (43).gif|thumb|350px|'''SVD cutoff 0.1%''': Regularization too strong. No separation between sources, mislocalization towards the middle of the brain.]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (44).gif|thumb|350px|'''SVD cutoff 0.005%''': Appropriate regularization. Separation of the bilateral activities. Location in agreement with the discrete multiple source model.]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (45).gif|thumb|350px|'''SVD cutoff 0.0001%''': Too small regularization. Mislocalization, too superficial 3D image. ]] </li>
</ul></div>

The automatic determination of the regularization constant using the CVE approach does not necessarily result in the optimum regularization parameter either. In this example, the unscaled CVE approach rather resembles the TSVD image with a cutoff of 0.0001%, i.e. regularization is too small. Therefore, it is advisable to compare different settings of the regularization parameter and make the final choice based on the above-mentioned considerations.

== Cortical LORETA ==

Cortical LORETA is principally the same technique as LORETA, however, Cortical LORETA is not computed in a 3D volume, but on the cortical surface.

The cortical reconstruction in BESA Research fed from BESA MRI is a closed 2D surface with no boundaries and a very close approximation of the actual cortical form. It consists of an irregular triangulated grid.

The Laplace operator that is used for identifying a smooth solution in a three-dimensional space is exchanged with a Laplace operator that runs on the two-dimensional cortical surface.

There is a wide variety of 2D Laplace operators with different characteristics. The general form of the discrete Laplace operator is

<math>\Delta f\left( p_{i} \right) = \frac{1}{d_{i}}\sum_{j \in N(i)}^{}{w_{ij}\left\lbrack f\left( p_{i} \right) - f\left( p_{j} \right) \right\rbrack},</math>


where '''pi''' is the '''i-th''' node of the triangular mesh, '''f(pi) '''is the value of a function f defined on the cortical mesh at the node '''pi''', '''wij''' is the weight for the connection between the nodes '''pi''' and '''pj''' and '''di''' is a normalization factor for the '''i-th''' row of the operator. Furthermore, '''N(i)''' is the set of indices corresponding to the direct (also called "1-ring") neighbors of '''pi'''.

BESA offers the choice of three Laplace operators with slightly different characteristics.

* '''Unweighted Graph Laplacian''': This is the simplest operator. It takes into account only the adjacency of the nodes and not the geometry of the mesh:

<math>
w_{ij} =
\begin{cases}
1, & \text{if } p_{i} \text{ and } p_{j} \text{ are connected by an edge} \\
0, & \text{otherwise}
\end{cases}
</math>

<math>d_{i} = 1</math>


[[Image:SA 3Dimaging (4).jpg |450px]]

* '''Weighted Graph Laplacian:''' This operator is similar to the unweighted graph Laplacian but with different weights for the different connections. The connections between nearby nodes get larger weights than the connections between farther nodes:

<math>w_{ij} = \frac{1}{\operatorname{dist}\left( p_{i},p_{j} \right)}</math>

<math>d_{i} = \sum_{j \in N(i)}^{} {\operatorname{dist}\left(p_{i}, p_{j} \right)}</math>


where '''dist''' ('''pi''' , '''pj''') is the distance between the nodes '''pi '''and '''pj'''.

[[Image:SA 3Dimaging (6).jpg|450px]]

* '''Geometric Laplacian with mixed area weights''': This operator takes into account the angles in the corresponding triangles into account as well as the area around the nodes in order to determine the connection weights:

<math>w_{ij} = \frac{\cot\left( \alpha_{ij} \right) + \cot\left( \beta_{ij} \right)}{2}</math>

<math>d_{i} = A_{\text{mixed}}</math>


where '''αij''' and '''βij''' denote the two angles opposite to the edge ('''i , j''') and '''Amixed '''is either the Voronoi area, or 1/2 of the triangle area or 1/4 of the triangle area depending on the type of the triangle.

[[Image:SA 3Dimaging (8).jpg|450px]]

'''Regularization and other parameters:'''

[[Image:CorticalLOR.png‎]]

* '''SVD cutoff''': The regularization for the inverse operator as a percent of the largest singular value.
* '''Depth weighting''': Turn depth weighting on or off.
* '''Laplacian type''': Selection of Laplacian operators (see above).

'''Notes:'''
* '''Starting Cortical LORETA''': Cortical LORETA can be started from the sub-menu '''Surface Image''' of the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]''” for important information on regularization of distributed inverses.

== Cortical CLARA ==

Cortical CLARA is principally the same technique as CLARA, but Cortical CLARA is not computed in a 3D volume, but on the cortical surface. Instead of using a LORETA image as the basis for the iterative application, cortical CLARA uses cortical LORETA.

'''Regularization and other parameters:'''

[[Image:SA 3Dimaging (47).gif]]

* '''SVD cutoff''': The regularization for the inverse operator as a percent of the largest singular value.
* '''Depth weighting''': Turn depth weighting on or off.
* '''Laplacian type''': Selection of Laplacian operators (see Cortical LORETA).
* '''No of iterations''': Number of iterations for CLARA. The more iterations are used, the sparser becomes the solution.
* '''Automatic''': The algorithm tries to determine the number of iterations automatically. The goodness of fit (GOF) is calculated after every iteration and if there is a big jump in the GOF then the algorithm will stop. If no jumps appear during the calculations then CLARA iterates until the specified number of iterations is reached.
* '''Regularize iterations''': If one wants to use different regularization for the CLARA iterations than the value specified as "SVD cutoff", this option should be selected.
* '''Amount to clip from img (%)''': Cortical CLARA uses the solution from the previous iteration as an additional weighting matrix for the current iteration. That weighting matrix is constructed by cutting the "low" activity from the solution. This number specifies how much of the activity should be cut from the previous solution in order to construct the weighting matrix. This value is given as a percentage of the maximal activity. Default value is 10%.

'''Notes:'''

* '''Starting Cortical CLARA:''' Cortical CLARA can be started from the sub-menu '''Surface Image''' of the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]''” for important information on regularization of distributed inverses.

== Cortex Inflation ==

The inflated cortex is a smoothened version of the individual cortical surface with minimal metric distortions (Fischl, B. et al. (1999). Cortical Surface-Based Analysis: II: Inflation, Flattening, and a Surface-Based Coordinate System. ''NeuroImage'', 9(2), 195–207). Gyri and sulci are smoothened out. The original distances between each point on the cortex and its neighbors are, however, mostly preserved.

[[Image:SA 3Dimaging (48).gif]]

''Cortical LORETA map overlaid on top of the inflated cortical surface.''

A lighter gray color overlaid on top of the surface image indicates the location of a gyrus of the individual cortex surface, while a darker gray color indicates the location of a sulcus. The inflated cortical surface can be computed in '''BESA MRI 2.0'''. For more details please refer to the BESA MRI 2.0 help.

== Surface Minimum Norm Image ==

'''Introduction'''

The minimum norm approach is a common method to estimate a distributed electrical current image in the brain at each time sample (Hämäläinen & Ilmoniemi 1984). The source activities of a large number of regional sources are computed. The sources are evenly distributed using 1500 standard locations 10% and 30% below the smoothed standard brain surface (when using the standard MRI) or using between 3000-4000 locations on the individual brain surface defined by the gray-white-matter boundary.

Since the number of sources is much larger than the number of sensors in a minimum norm solution, the inverse problem is highly underdetermined and must be stabilized by a mathematical constraint, the minimum norm. Out of the many current distributions that can account for the recorded sensor data, the solution with the minimum L2 norm, i.e. the minimum total power of the current distribution is displayed in BESA Research.

First, the forward solution (leadfield matrix L) of all sources is calculated in the current head model. Then, the source activities S(t) of all source components are computed from the data matrix D(t) using an inverse regularized by the estimated noise covariance matrix:

<math>\mathrm{S}\left( t \right) = \mathrm{R} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{R} \cdot \mathrm{L}^{T} + \mathrm{C}_N \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed regional source model, CN denotes the noise correlation matrix in sensor space, and R is a weighting matrix in source space. R and CN can be designed in different ways in order to optimize the minimum norm result. The total activity of each regional source is computed as the root mean square of the source activities S(t) of its 3 (MEG:2) components. This total source activity is transformed to a color-coded image of the brain surface. (When the standard brain is used, two sources are assigned to each surface location, located 10% and 30% below the surface, respectively. The color that is displayed on the standard brain surface is the larger of the two corresponding source activities.)

'''Weighting options'''

The minimum norm current imaging techniques of BESA Research provide different weighting strategies. Two weighting approaches are available: Depth weighting and spatio-temporal approaches.
* '''Depth weighting:''' Without depth weighting, deep sources appear very smeared in a minimum-norm reconstruction. With depth weighting, both deep and superficial sources produce a similar, more focal result. If this weighting method is selected, the leadfield of each regional source is scaled with the largest singular value of the SVD (singular value decomposition) of the source's leadfield.
* '''Spatio-temporal weighting''': Spatio-temporal weighting tries to assign large weight to sources that are assumed to be more likely to contribute to the recorded data.
** '''Subspace correlation after single source scan''': This method divides the signal into a signal and a noise subspace. The correlation of the leadfield of a regional source i with the signal subspace (pi) is computed to find out if the source location contributes to the measured data. The weighting matrix R becomes a diagonal matrix. Each of the three (MEG: 2) components of a regional source get the same weighting value pi2. This approach is based on the signal subspace correlation measure introduced by J.C. Mosher, R. M. Leahy (Recursive MUSIC: A Framework for EEG and MEG Source Localization, IEEE Trans. On Biomed. Eng. Vol. 45, No. 11, November 1998)
** '''Dale & Sereno 1993:''' In the approach of Dale and Sereno (J Cogn Neurosci, 1993, 5: 162-176) a signal subspace needs not be defined. The correlation pi of the leadfield of regional source i with the inverse of the data covariance matrix is computed along with the largest singular value λmax of the data covariance matrix. The weighting matrix R is a diagonal matrix with weights: [[Image:SA 3Dimaging (50).gif]]. Each of the three (MEG: 2) components of a regional source receives the same weighting value.

'''Noise regularization'''

Two methods to estimate the channel noise correlation matrix CN are provided by the program:
* '''Use baseline:''' Select this option to estimate the noise from the user-definable baseline. The signal is computed from the data at non-baseline latencies.
* '''Use 15% lowest values:''' The baseline activity is computed from the data at those 15% of all displayed latencies that have the lowest global field power. The signal is computed from all displayed latencies.

In each case, the activity (noise or signal, respectively) is defined as root-mean-square across all respective latencies for each channel.

The noise covariance matrix CN is constructed as a diagonal matrix. The entries in the main diagonal are proportional to the noise activity of the individual channels (if selected) or are all equally proportional to the average noise activity over all channels. The noise covariance matrix CN is then scaled such that the ratio of the Frobenius norms of the weighted leadfield projector matrix (LRLT) and the noise covariance matrix CN equals the Signal-to-Noise ratio. This scaling can be multiplied by an additional factor (default=1) to sharpen (<1) or smoothen (>1) the minimum norm image.

'''Applying the Minimum Norm Image'''

The minimum-norm algorithm is started via the ''Surface minimum norm image dialog box'', which is opened from the''' Image''' menu, or by typing the shortcut '''Ctrl-M''': Please refer to Chapter ''“Surface'' ''Minimum Norm Tab”'' for more details.

As opposed to the other 3D images available from the '''Image '''menu, the surface minimum norm image is not computed on a volumetric grid, but rather for locations on the brain surface. Accordingly, the results of the minimum norm image are displayed superimposed to the brain surface mesh rather than to the volumetric MR image.

The figure below shows a minimum norm image computed from the file '''Examples\Epilepsy\Spikes\Spikes-Child4_EEG+MEG_averaged.fsg'''. The EEG spike peak was imaged using the individual brain surface of the subject. A baseline from -300 to -70 ms was used. Minimum norm was computed with depth weighting, Spatio-temporal weighting according to Dale & Sereno 1993 and individual noise weighting with a noise scale factor of 0.01. The minimum norm image reveals the location of the spike generator in the close vicinity of the frontal left-hemispheric lesion in this subject.

[[Image:SA 3Dimaging (51).gif]]

== Multiple Source Probe Scan (MSPS) ==

 
'''Introduction'''

The MSPS function provides a tool for the validation of a given solution. It is based on the following theoretical consideration: If the recorded EEG/MEG data has been modeled adequately, i.e. all active brain regions are represented by a source in the current solution, then any additional probe source added to the solution will not show any activity apart from noise. The only exception occurs if this probe source is placed in close vicinity to one of the sources in the current solution. In that case, the solution's source and the probe source will share the activity of the corresponding brain area. The MSPS applies these considerations by scanning the brain on a pre-defined grid with a regional probe added to the current solution. Grid extent and density can be specified in the Image settings. The power P of the probe source at location r in the signal interval is compared with the power of the probe source in a reference interval, defining a value q:

<math>\mathrm{q}\left( r \right) = \sqrt{\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}} - 1</math>


MSPS can be computed on time domain or time-frequency domain data:
* In the time domain, q(r) is computed from the source waveform of the probe source. Here, P(r) is the mean power of the probe source at location r in the marked latency range, and Pref(r) is the mean probe source power in the user-definable baseline interval.
* In the time-frequency domain, an MSPS image can be computed from the complex cross spectral density matrices. By applying the inverse operator for a source configuration consisting of the current solution and the probe source, the power of the probe source can be computed for the target interval [P(r)] and the reference time-frequency interval [Pref(r)]. In the resulting MSPS image, q-values are shown in %, where q[%] = q*100.

The inverse operator used to determine the probe source power uses different regularization constants for the probe source and the sources in the current solution. The regularization constant of the sources in the current solution can be specified in the Image settings (default 4%). The regularization constant of the probe source is internally set to 0%.

Alternatively to the definition above, q can also be displayed in units of dB:

<math>\mathrm{q}\left\lbrack \text{dB} \right\rbrack = 10 \cdot \log_{10}\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}</math>


Values of q smaller than zero are not shown in the MSPS image.

According to the considerations above, an MSPS of a correct source model should optimally yield image maxima around the sources in the current solution only. If the MSPS image is blurred or shows maxima at locations different from the modeled sources, this indicates a non-sufficient or incorrect solution.

'''Applying the MSPS'''

This chapter illustrates the application of the Multiple Source Probe Scan. The figures are generated with data from file '''Examples/Epilepsy/Spikes/Rolandic-Spike-Child.fsg''' (-300 : +200 ms, filtered from 3 Hz [forward] to 40 Hz [zero-phase]).

'''Time domain versus time-frequency domain MSPS'''

The multiple source probe scan can be computed in the time domain or the time-frequency domain. The latter is possible only when time-frequency domain data is available for the current condition, i.e. if the condition has been created by starting a multiple source beamformer (MSBF) computation from the source coherence window. In this case, evoking the MSPS calculation from the '''Imaging '''button or from the '''Image''' menu will bring up the following dialog window that allows to choose between time- or time-frequency MSPS. If only time domain data is available, this dialog window will not appear and MSPS will be computed in the time domain.

[[Image:SA 3Dimaging (53).gif]]

For a time-frequency domain MSPS, the target and the reference time-frequency interval have been specified already in the Time-Frequency window (see Chapter "''How To Create Beamformer Images''"). For a time-domain MSPS, the target and the reference epoch have to be specified in the Source Analysis window as described below.

'''Time domain MSPS'''

The time-domain MSPS image displays the ratio of the power of a regional probe source in the signal and the baseline interval. The currently set baseline is indicated by a horizontal line in the upper left corner of the channel box.

[[Image:SA 3Dimaging (54).gif|thumb|c|none|330px|The black horizontal bar in the upper part of the channel box (here circled in red) indicates the baseline interval.]]

By default, BESA Research defines the pre-stimulus interval of the current data segment as baseline. The baseline should represent a latency range in which no event-related activity is present in the data. There are several possibilities to modify the baseline interval: by clicking on the horizontal line with the left mouse button or by using the corresponding entry in the '''Condition '''menu or '''Fit Interval''' popup menu.

Mark an interval to define the target epoch, i.e. the time-interval for which the current solution is to be tested. Start the MSPS by selecting it from the '''Image selection '''button or from the '''Image''' menu to start the probe source scan. The''' Image '''menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window. The 3D window opens and displays the scan result.

<div><ul>
<li style="display: inline-block;"> [[Image:SA 3Dimaging (55).gif|thumb|c|none|650px|This figure shows the MSPS image applied on the three left-hemispheric sources in the solution ''''Rolandic-Spike-Child-RS2.bsa''''. The baseline is set from -300ms to -50 ms. The right-hemispheric sources have been switched off. The fit interval is set to the latency range of large overall activity in the data (-43 ms : 117 ms). A realistic FEM model appropriate for the subject's age (12 years, conductivity ratios (cr) 50) is applied. The MSPS image does not show maxima at the modeled source locations and rather shows a spread q-value distribution.]] </li>

<li style="display: inline-block;"> [[Image:SA 3Dimaging (56).gif|thumb|c|none|650px|The MSPS image for the same latency range when the right-hemispheric sources have been included. The MSPS image appears more focal and shows maxima around the modeled brain regions. This indicates the substantial improvement of the solution by adding the right-hemispheric sources that model the propagation of the epileptic spike from the left to the right hemisphere (note the radiological side convention in the 3D window).]] </li>
</ul></div>

'''Time-Resolved MSPS'''

If the MSPS has been computed on time domain data, the image can be shown separately for each latency in the selected interval. After the MSPS has been computed for the marked epoch, double-click anywhere within this epoch to display the ratio of the probe source magnitude at the selected latency and the mean probe source magnitude in the baseline. Scanning the latency range by moving the cursor (e.g. with the left and right arrow cursor keys) provides a time-resolved MSPS image.

Time-resolved MSPS images are not available if the MSPS has been computed on data in the time-frequency domain.

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (57).gif|thumb|450px|MSPS image of the spike peak activity at 0ms. The activity mainly occurs in the left hemisphere. This fact is illustrated by the source waveforms and confirmed in the MSPS image, which shows a focal maximum around the location of the red sources.]] </li>

<li style="display: inline-block;"> [[File:SA 3Dimaging (58).gif|thumb|450px|Around +27 ms, the spike has propagated to the right hemisphere. This becomes evident from the waveforms of the blue sources, which show a significant latency lag with respect to the first three sources, and from the MSPS image, which shows the maximum around blue sources at this latency.]] </li>
</ul></div>



'''Notes:'''

* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image''' menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the''' Image''' menu.
* For scaling options, please refer to the '''scaling buttons''' popup menu .
* Parameters used for the MSPS calculations can be set in the ''General Settings tab'' of the ''Image Settings dialog box.''

== Source Sensitivity ==

'''Introduction'''

The 'Source sensitivity' function displays the sensitivity of the selected source in the current source model to activity in other brain regions. Sensitivity is defined as the fraction of power at the scanned brain location that is mapped onto the selected source.

To compute the source sensitivity, unit brain activity is modeled at different locations (probe source) throughout the brain. To this data, the current source model is applied to compute the source waveforms SCM of all modeled sources:

<math>\mathrm{S}_{\text{CM}} = \mathrm{L}_{\text{CM}}^{-1} \cdot \mathrm{L}_{\text{PS}}</math>


Here LCM-1 is the regularized inverse operator for the current model, and LPS is the leadfield of the regional probe source (dimension [Nx3] for EEG and [Nx2] for MEG, respectively, where N is the number of sensors). The source amplitude SSS of the selected source in the model is a 3x3 (MEG: 2x2) sub-matrix of SCM (if the selected source is a regional source) or a 1x3-matrix (MEG: 1x2) (if the selected source is a dipole). The root mean square of the singular values of SCM is defined as the source sensitivity.

The 3D source sensitivity image displays this value for all locations on a grid specified under '''Image/Settings'''. Grid density can be specified in the Image Settings.

'''Applying the Source Sensitivity Image'''

The Source Sensitivity image is evoked from the '''Image''' menu or by pressing the corresponding hot key (default: '''V''').

This function is enabled only when a solution with an active selected source is present in the Source Analysis window. The source sensitivity image then displays the sensitivity of the selected source to activity in other brain regions.

[[Image:SA 3Dimaging (59).gif]]

''Source Sensitivity image for the selected frontal source (green) in model ''''''High_Intensity_3RS.bsa'''''' in folder 'Examples/ERP_Auditory_Intensity'. The data displayed is the '100dB' condition in file ''''''All_Subjects_cc.fsg''''''. The selected source is sensitive to activity in the frontal brain region (yellow/white), while it is not influenced by activity in the vicinity of the left and right auditory cortex areas, which are modeled by the red and blue source in the model (transparent/gray).''

'''Notes:'''

* The sensitivity image is independent of the recorded sensor signals. It only depends on the current source model, the sensor configuration, the head model, and the regularization constant.
* If the regularization constant is set to zero, each source has a sensitivity of 100% to activity around its own location. With increasing regularization, the spatial filter becomes less focused, and the sensitivity of a source to activity at its location decreases.
* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image''' menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the '''Image''' menu.

{{BESAManualNav}}

Source Analysis 3D Imaging

2019-03-28T09:37:41Z

Jamie: /* Inserting Sources as Beamformer Virtual Sensor out of the Beamformer Image */

{{BESAInfobox
|title = Module information
|module = BESA Research Standard or higher
|version = 6.1 or higher
}}


== Overview ==

BESA Research features a set of new functions that provide 3D images that are displayed superimposed to the individual subject's anatomy. This chapter introduces these different images and describe their properties and applications.

The 3D images can be divided into three categories:

'''Volume images:'''

* '''The Multiple Source Beamformer (MSBF)''' is a tool for imaging brain activity. It is applied in the time-domain or time-frequency domain. The beamformer technique in time-frequency domain can image not only evoked, but also induced activity, which is not visible in time-domain averages of the data.
* '''Dynamic Imaging of Coherent Sources (DICS)''' can find coherence between any two pairs of voxels in the brain or between an external source and brain voxels. DICS requires time-frequency-transformed data and can find coherence for evoked and induced activity.

The following imaging methods provide an image of brain activity based on a distributed multiple source model:
* '''CLARA''' is an iterative application of LORETA images, focusing the obtained 3D image in each iteration step.
* '''LAURA '''uses a spatial weighting function that has the form of a local autoregressive function.
* '''LORETA''' has the 3D Laplacian operator implemented as spatial weighting prior.
* '''sLORETA''' is an unweighted minimum norm that is standardized by the resolution matrix.
* '''swLORETA '''is equivalent to sLORETA, except for an additional depth weighting.
* '''SSLOFO '''is an iterative application of standardized minimum norm images with consecutive shrinkage of the source space.
* A '''User-defined volume image''' allows to experiment with the different imaging techniques. It is possible to specify user-defined parameters for the family of distributed source images to create a new imaging technique.
* Bayesian source imaging: '''SESAME''' uses a semi-automated Bayesian approach to estimate the number of dipoles along with their parameters.

'''Surface image:'''

* The '''Surface Minimum Norm Image'''. If no individual MRI is available, the minimum norm image is displayed on a standard brain surface and computed for standard source locations. If available, an individual brain surface is used to construct the distributed source model and to image the brain activity.
* '''Cortical LORETA'''. Unlike classical LORETA, cortical LORETA is not computed in a 3D volume, but on the cortical surface.
* '''Cortical CLARA'''. Unlike classical CLARA, cortical CLARA is not computed in a 3D volume, but on the cortical surface.

'''Discrete model probing:'''

These images do not visualize source activity. Rather, they visualize properties of the currently applied discrete source model:
* The '''Multiple Source Probe Scan (MSPS)''' is a tool for the validation of a discrete multiple source model.
* The '''Source Sensitivity image''' displays the sensitivity of a selected source in the current discrete source model and is therefore data independent.

== Multiple Source Beamformer (MSBF) in the Time-frequency Domain ==

 
'''Short mathematical introduction'''

The BESA beamformer is a modified version of the linearly constrained minimum variance vector beamformer in the time-frequency domain as described in [https://dx.doi.org/10.1073/pnas.98.2.694 Gross et al., "Dynamic imaging of coherent sources: Studying neural interactions in the human brain", PNAS 98, 694-699, 2001]. It allows to image evoked and induced oscillatory activity in a user-defined time-frequency range, where time is taken relative to a triggered event.

The computation is based on a transformation of each channel's single trial data from the time domain into the time-frequency domain. This transformation is performed by the BESA Research Source Coherence module and leads to the complex spectral density Si (f,t), where i is the channel index and f and t denote frequency and time, respectively. Complex cross spectral density matrices C are computed for each trial:

<math>\mathrm{C}_{ij}\left( f,t \right) = \mathrm{S}_{i}\left( f,t \right) \cdot \mathrm{S}_{j}^{*}\left( f,t \right)</math>


The output power P of the beamformer for a specific brain region at location r is then computed by the following equation:

<math>\mathrm{P}\left( r \right) = \operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{-1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{-1}</math>


Here, Cr-1 is the inverse of the SVD-regularized average of Cij(f,t) over trials and the time-frequency range of interest; L is the leadfield matrix of the model containing a regional source at target location r and, optionally, additional sources whose interference with the target source is to be minimized; tr'[] is the trace of the [3×3] (MEG:[2×2]) submatrix of the bracketed expression that corresponds to the source at target location r.

In BESA Research, the output power P(r) is normalized with the output power in a reference time-frequency interval Pref(r). A value q ist defined as follows:

<math> \mathrm{q}\left( r \right) =
\begin{cases}
\sqrt{\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}(r)}} - 1 = \sqrt{\frac{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{\text{ref},r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}} - 1, & \text{for }\mathrm{P}(r) \geq \mathrm{P}_{\text{ref}}(r) \\

1 - \sqrt{\frac{\mathrm{P}_{\text{ref}}\left( r \right)}{\mathrm{P}\left( r \right)}} = 1 - \sqrt{\frac{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{\text{ref},r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}}, & \text{for }\mathrm{P}(r) < \mathrm{P}_{\text{ref}}(r)
\end{cases} </math>


Pref can be computed either from the corresponding frequency range in the baseline of the same condition (i.e. the beamformer images event-related power increase or decrease) or from the corresponding time-frequency range in a control condition (i.e. the beamformer images differences between two conditions). The beamformer image is constructed from values q(r) computed for all locations on a grid specified in the '''General Settings tab'''. For MEG data, the innermost grid points within a sphere of approx. 12% of the head diameter are assigned interpolated rather than calculated values).
q-values are shown in %, where where q[%] = q*100. Alternatively to the definition above, q can also be displayed in units of dB:

<math>\mathrm{q}\left\lbrack \text{dB} \right\rbrack = 10 \cdot \log_{10}\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}</math>


A beamformer operator is designed to pass signals from the brain region of interest r without attenuation, while minimizing interference from activity in all other brain regions. Traditional single-source beamformers are known to mislocalize sources if several brain regions have highly correlated activity. Therefore, the BESA beamformer extends the traditional single-source beamformer in order to implicitly suppress activity from possibly correlated brain regions. This is achieved by using a multiple source beamformer calculation that contains not only the leadfields of the source at the location of interest r, but also those of possibly interfering sources. As a default, BESA Research uses a bilateral beamformer, where specifically contributions from the homologue source in the opposite hemisphere are taken into account (the matrix L thus being of dimension N×6 for EEG and N×4 for MEG, respectively, where N is the number of sensors). This allows for imaging of highly correlated bilateral activity in the two hemispheres that commonly occurs during processing of external stimuli.

In addition, the beamformer computation can take into account possibly correlated sources at arbitrary locations that are specified in the current solution. This is achieved by adding their leadfield vectors to the matrix L in the equation above.

'''Applying the Beamformer'''

This chapter illustrates the usage of the BESA beamformer. The displayed figures are generated using the file ''''Examples/Learn-by-Simulations/AC-Coherence/AC-Osc20.foc'''' (see BESA Tutorial 6: "''Time-frequency analysis and Source coherence''").

'''Starting the beamformer from the time-frequency window'''

The BESA beamformer is applied in the time-frequency domain and therefore requires the Source Coherence module to be enabled. The time-frequency beamformer is especially useful to image in- or decrease of induced oscillatory activity. Induced activity cannot be observed in the averaged data, but shows up as enhanced averaged power in the TSE (Temporal-Spectral Evolution) plot. For instructions on how to initiate a beamformer computation in the time-frequency window, please refer to Chapter '''[[Source_Coherence_How_to...#How_to_Start_the_Beamformer_from_the_Time-Frequency_Window|How to Create Beamformer Images]]'''.

After the beamformer computation has been initiated in the time-frequency window, the source analysis window opens with an enlarged 3D image of the q-value computed with a '''bilateral beamformer'''. The result is superimposed onto the MR image assigned to the data set (individual or standard).

[[Image:SA 3Dimaging (5).gif]]

''Beamformer image after starting the computation in the Time-Frequency window. A bilateral pair of sources in the auditory cortex accounts for the highly correlated oscillatory induced activity. Only the bilateral beamformer manages to separate these activities; a traditional single-source beamformer would merge the two sources into one image maximum in the head center instead.''

'''Multiple source beamformer in the Source Analysis window'''

The 3D imaging display is part of the source analysis window. If you press the '''Restore''' button at the right end of the title bar of the 3D window, the window appears at the bottom right of the source analysis window. In the channel box, the averaged (evoked) data of the selected condition is shown. When a control condition was selected, its average is appended to the average of the target condition.

[[Image:SA 3Dimaging (6).gif]]

''Source Analysis window with beamformer image. The two sources have been added using the '''''Switch to''''' '''''Maximum''''' and '''''Add Source '''''toolbar buttons (see below). Source waveforms are computed from the displayed averaged data. Therefore, they do not represent the activity displayed in the beamformer image, which in this simulation example is induced (i.e. not phase-locked to the trigger)!''

When starting the beamformer from the time-frequency window, a bilateral beamformer scan is performed. In the source analysis window, the beamformer computation can be repeated taking into account possibly correlated sources that are specified in the current solution. Interfering activities generated by all sources in the current solution that are in the 'On' state are specifically suppressed ('''they enter the matrix L in the beamformer calculation''', see Chapter ''Short mathematical description'' above). The computation can be started from the '''Image''' menu or from the '''Image selector button''' dropdown menu. The '''Image''' menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window.

[[Image:SA 3Dimaging (7).gif]]

''Multiple source beamformer image calculated in the presence of a source in the left hemisphere. A '''single''' source scan has been performed. The source set in the current solution accounts for the left-hemispheric q-maximum in the data. Accordingly, the beamformer scan reveals only the as yet unmodeled additional activity in the right hemisphere (note the radiological convention in the 3D image display).''

The beamformer scan can be performed with a '''single''' or a '''bilateral''' source scan. The default scan type depends on the current solution:
* When the beamformer is started from the Time-Frequency window, the Source Analysis window opens with a new solution and a '''bilateral''' beamformer scan is performed.
* When the beamformer is started within the Source Analysis window, the default is
** a scan with a '''single''' source in addition to the sources in the current solution, if at least one source is active.
** a '''bilateral''' scan if no source in the current solution is active.

The default scan type is the multiple source beamformer. The non-default scan type can be enforced using the corresponding ''Volume Image / Beamformer'' entry in the '''Image''' menu.

'''Inserting Sources out of the Beamformer Image'''

The beamformer image can be used to add sources to the current solution. A simple double-click anywhere in the 2D- or 3D-view will generate a non-oriented regional source at the corresponding location. However, a better and easier way to create sources at image maxima and minima is to use the toolbar buttons '''Switch to Maximum''' [[Image:SA 3Dimaging (8).gif]] and '''Add Source''' [[Image:SA 3Dimaging (9).gif]].

Use the '''Switch to Maximum''' button to place the red crosshair of the 3D window onto a local image maximum or minimum. Hitting the '''Add Source''' button creates a regional source at the location of the crosshair and therefore ensures the exact placement of the source at the image extremum. Moreover, the '''Add Source''' button generates an oriented regional source. BESA Research automatically estimates the source orientation that contributes most to the power in the target time-frequency interval (or the reference time-frequency interval, if its power is larger than that in the target interval). The accuracy of this orientation estimate depends largely on the noise content of the data. The smaller the signal-to-noise ratio of the data, the lower is the accuracy of the orientation estimate. '''This feature allows to use the beamformer as a tool to create a source montage for source coherence analysis, where it is of advantage to work with oriented sources'''.

'''Notes:'''

* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image '''menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the''' Image''' menu.
* For scaling options, use the [[Image:SA 3Dimaging (10).gif]] and [[Image:SA 3Dimaging (11).gif]] '''Image Scale toolbar''' buttons.
* Parameters used for the beamformer calculations can be set in the '''Standard Volumes''' of the ''Image Settings dialog box.''

== Dynamic Imaging of Coherent Sources (DICS) ==

 
'''Short mathematical introduction'''

Dynamic Imaging of Coherent Sources (DICS) is a sophisticated method for imaging cortico-cortical coherence in the brain, or coherence between an external reference (e.g. EMG channel) and cortical structures. DICS can be applied to localize evoked as well as induced coherent cortical activity in a user-defined time-frequency range.

DICS was implemented in BESA closely following [https://dx.doi.org/10.1073/pnas.98.2.694 Gross et al., "Dynamic imaging of coherent sources: Studying neural interactions in the human brain", PNAS 98, 694-699, 2001].

The computation is based on a transformation of each channel's single trial data from the time domain into the frequency domain. This transformation is performed by the BESA Research Coherence module and results in the complex spectral density matrix that is used for constructing the spatial filter similar to beamforming.

DICS computation yields a 3-D image, each voxel being assigned a coherence value. Coherence values can be described as a neural activity index and do not have a unit. The neural activity index contrasts coherence in a target time-frequency bin with coherence of the same time-frequency bin in a baseline.

'''DICS for cortico-cortical coherence is computed as follows:'''

Let L(r) be the leadfield in voxel r in the brain and C the complex cross-spectral density matrix. The spatial filter W(r) for the voxel r in the head is defined as follows:

<math>W\left( r \right) = \left\lbrack L^{T}\left( r \right) \cdot C^{- 1} \cdot L\left( r \right) \right\rbrack^{- 1} \cdot L^{T}(r) \cdot C^{- 1}</math>


The cross-spectrum between two locations (voxels) r1 and r2 in the head are calculated with the following equation:

<math>C_{s}\left( r_{1},r_{2} \right) = W\left( r_{1} \right) \cdot C \cdot W^{*T}\left( r_{2} \right),</math>


where <nowiki>*T</nowiki> means the transposed complex conjugate of a matrix. The cross-spectral density can then be calculated from the cross spectrum as follows:

<math>c_{s}\left( r_{1},r_{2} \right) = \lambda_{1}\left\{ C_{s}\left( r_{1},r_{2} \right) \right\},</math>


where λ1{} indicates the largest singular value of the cross spectrum. Once the cross spectral density is estimated, the connectivity¹(CON) between the two brain regions r1 and r2 are calculated as follows:

<math>\text{CON}\left( r_{1},r_{2} \right) = \frac{c_{s}^{\text{sig}}\left( r_{1},r_{2} \right) - c_{s}^{\text{bl}}(r_{1},r_{2})}{c_{s}^{\text{sig}}\left( r_{1},r_{2} \right) + c_{s}^{\text{bl}}(r_{1},r_{2})},</math>


where cssig is the cross-spectral density for the signal of interest between the two brain regions r1 and r2, and csbl is the corresponding cross spectral density for the baseline or the control condition, respectively. In the case DICS is computed with a cortical reference, r1 is the reference region (voxel) and remains constant while r2 scans all the grid points within the brain sequentially. In that way, the connectivity between the reference brain region and all other brain regions is estimated. The value of CON(r1, r2) falls in the interval [-1 1]. If the cross-spectral density for the baseline is 0 the connectivity value will be 1. If the cross-spectral density for the signal is 0 the connectivity value will be -1.

¹ Here, the term connectivity is used rather than coherence, as strictly speaking the coherence equation is defined slightly differently. For simplicity reasons the rest of the tutorial uses the term coherence.

'''DICS for cortico-muscular coherence is computed as follows:'''

When using an external reference, the equation for coherence calculation is slightly different compared to the equation for cortico-cortical coherence. First of all, the cross-spectral density matrix is not only computed for the MEG/EEG channels, but the external reference channel is added. This resulting matrix is Call. In this case, the cross-spectral density between the reference signal and all other MEG/EEG

channels is called cref. It is only one column of Call. Hence, the cross-spectrum in voxel r is calculated with the following equation:

<math>C_{s}\left( r \right) = W\left( r \right) \cdot c_{\text{ref}}</math>


and the corresponding cross-spectral density is calculated as the sum of squares of Cs:

<math>c_{s}\left( r \right) = \sum_{i = 1}^{n}{C_{s}\left( r \right)_{i}^{2}},</math>


where n is 2 for MEG and 3 for EEG. This equation can also be described as the squared Euclidean norm of the cross-spectrum:

<math>c_{s}\left( r \right) = \left\| C_{s} \right\|^{2},</math>


The power in voxel r is calculated as in the cortico-cortical case:

<math>p\left( r \right) = \lambda_{1}\left\{ C_{s}(r,r) \right\}.</math>


At last, coherence between the external reference and cortical activity is calculated with the equation:

<math>\text{CON}\left( r \right) = \frac{c_{s}(r)}{p\left( r \right) \cdot C_{\text{all}}(k,k)},</math>


where Call(k, k) is the (k,k)-th diagonal element of the matrix Call.

DICS is particularly useful, if coherence is to be calculated without an a-priory source model (in contrast to source coherence based on pre-defined source montages). However, the recommended analysis strategy for DICS is to use a brain source as a starting point for coherence calculation that is known to contribute to the EEG/MEG signal of interest. For example, one might first run a beamformer on the time-frequency range of interest and use the voxel with the strongest oscillatory activity as a starting point for DICS. The resulting coherence image will again lead to several maxima (ordered by magnitude), which in turn can serve as starting points for DICS calculation. This way, it is possible to detect even weak sources that show coherent activity in the given time-frequency range.

The other significant application for DICS is estimating coherence between an external source and voxels in the brain. For example, an external source can be muscle activity recoded by an electrode placed over the according peripheral region. This way, the direct relationship between muscle activity and brain activation can be measured.

'''Starting DICS computation from the Time-Frequency Window'''

DICS is particularly useful, if coherence in a user-defined time-frequency bin (evoked or induced) is to be calculated between any two brain regions or between an external reference and the brain. DICS runs only on time-frequency decomposed data, so time-frequency analysis needs to be run before starting DICS computation.

To start the DICS computation, left-drag a window over a selected time-frequency bin in the Time-Frequency Window. Right-click and select “Image”. A dialogue will open (see fig. 1) prompting you to specify time and frequency settings as well as the baseline period. It is recommended to use a baseline period of equal length as the data period of interest. Make sure to select “DICS” in the top row and press “'''Go'''”.

[[Image:SA 3Dimaging (21).gif|450px|thumb|c|none|Fig. 1: Time and frequency settings for DICS and MSBF]]

Next, a window will appear allowing you to specify the reference source for coherence calculation (see fig. 2). It is possible to select a channel (e.g. EMG) or a brain source. If a brain source is chosen and no source analysis was computed beforehand, the option “Use current cross-hair position” must be chosen. In case discrete source analysis was computed previously, the selected source can be chosen as the reference for DICS. Please note that DICS can be re-computed with any cross-hair or source position at a later stage.

[[Image:SA 3Dimaging (1).jpg|400px|thumb|c|none|Fig. 2: Possible options for choosing the reference]]

Confirming with “'''OK'''” will start computation of coherence between the selected channel/voxel and all other brain voxels. In case DICS is computed for a reference source in the brain, it can be advantageous to run a beamforming analysis in the selected time-frequency window first and use one of the beamforming maxima as reference for DICS. Fig. 3 shows an example for DICS calculation.

[[Image:SA 3Dimaging (22).gif|500px|thumb|c|none|Fig. 3: Coherence between left-hemispheric auditory areas and the selected voxel in the right auditory cortex.]]

Coherence values range between -1 and 1. If coherence in the signal is much larger than coherence in the baseline (control condition) then the DICS value is going to approach 1. Contrary, if coherence in the baseline is much larger than coherence in the signal, then the DICS value is going to approach -1. At last, if coherence in the signal is equal to coherence in the baseline, then the DICS value is 0.

In case DICS is to be re-computed with a different reference, simply mark the desired reference position by placing the cross-hair in the anatomical view and select “DICS” in the middle panel of the source analysis window (see Fig. 4). In case an external reference is to be selected, click on “DICS” in the middle panel to bring up the DICS dialogue (see. Fig. 2) and select the desired channel. Please note that DICS computation will only be available after running time-frequency analysis.

[[Image:SA 3Dimaging (23).gif|700px|thumb|c|none|Fig. 4: Integration of DICS in the Source Analysis window]]

== Multiple Source Beamformer (MSBF) in the Time Domain ==
''(requires Besa Research 7.0 or higher)''

===Short mathematical introduction===

Beamforming approach can be also applied in the time domain data. This approach was introduced as linearly constrained minimum variance (LCMV) beamformer (Van Veen et al., 1997). It allows to image evoked activity in a user-defined time range, where time is taken relative to a triggered event, and to estimate source waveforms using the calculated spatial weight at locations of interest. For an implementation of the beamformer in the time domain, data covariance matrices are required, while complex cross spectral density matrices are used for the beamformer approaches in the time-frequency domain as described in the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section.

The bilateral beamformer introduced in the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section is also implemented for the time-domain beamformer to take into account contributions from the homologue source in the opposite. This allows for imaging of highly correlated bilateral activity in the two hemispheres that commonly occurs during processing of external stimuli. In addition, the beamformer computation can take into account possibly correlated sources at arbitrary locations.
The beamformer spatial weight W(r) for the voxel r in the brain is defined as follows (Van Veen et al., 1997):

[[File:MSBF1.png]]

where '''C-1''' is the inversed regularized average of covariance matrix over trials, '''L''' is the leadfield matrix of the model containing a regional source at target location r and optionally
additional sources whose interference with the target source is to be minimized. The beamformer spatial weight '''W'''(r) can be applied to the measured data to estimate source
waveform at a location r (beamformer virtual sensor):

[[File:MSBF2.png]]

where '''S'''(r,t) represents the estimated source waveform and '''M'''(t) represents measured EEG or MEG signals.
The output power P of the beamformer for a specific brain region at location r is computed by the following equation:

[[File:MSBF3.png]]

where tr’[ ] is the trace of the [3×3] (MEG: [2×2]) submatrix of the bracketed expression that corresponds to the source at target location r.
Beamformer can suppress noise sources that are correlated across sensors. However, uncorrelated noise will be amplified in a spatially non-uniform manner, with increasing
distortion with increasing distance from the sensors (Van Veen et al., 1997; Sekihara et al., 2001). For this reason, estimated source power should be normalized by a noise power.
In BESA Research, the output power P(r) is normalized with the output power in a baseline interval or with the output power of a uncorrelated noise: P(r) / Pref (r).
The time-domain beamformer image is constructed from values q(r) computed for all locations on a grid specified in the '''General Settings''' tab. A value q(r) is defined as described in
the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section with data covariance matrices instead of cross-spectral density matrices.

===Applying the Beamformer===

This chapter illustrates the usage of the BESA beamformer in the time domain. The displayed figures are generated using the file ‘Examples/ERP-Auditory-Intensity/S1.cnt’.

'''Starting the time-domain beamformer from the Average tab of the Paradigm dialog box'''

The time-domain beamformer is needed data covariance matrices and therefore requires the ERP module to be enabled. After the beamformer computation has been initiated in the
'''Average tab of the Paradigm dialog box''', the source analysis window opens with an enlarged 3D image of the q-value computed with a bilateral beamformer. The result is
superimposed onto the MR image assigned to the data set (individual or standard).

[[File:MSBF44.png]]

''Beamformer image for auditory evoked data after starting the computation in the '''Average tab of the Paradigm dialog box'''. The bilateral beamformer manages to separate the
activities in auditory areas, while a traditional single-source beamformer would merge the two sources into one image maximum in the head center instead.''

'''Multiple-source beamformer in the Source Analysis window'''

The 3D imaging display is part of the source analysis window. In the Channel box, the averaged (evoked) data of the selected condition is shown. Selected covariance intervals in
the ERP module can be checked in the Channel box. The red, gray, and blue rectangles indicate signal, baseline, and common interval, respectively.

[[File:MSBF55.png]]

''Source Analysis window with beamformer image. The two beamformer virtual sensors have been added using the Switch to Maximum and Add Source toolbar buttons (see below).
Source waveforms are computed using the beamformer spatial weights and the displayed averaged data (the noise normalized weights (5% noise) option was used to compute the
beamformer image).''

When starting the beamformer from the '''Average tab of the Paradigm dialog box''', the bilateral beamformer scan is performed. In the source analysis window, the beamformer computation can be repeated taking into account possibly correlated sources that are specified in the current solution. Interfering activities generated by all sources in the current solution that are in the 'On' state are specifically suppressed (they enter the leadfield matrix L in the beamformer calculation). The computation can be started from the '''Image''' menu or from the Image selector button [[File:MSBF_Button.png|22px|Image: 22 pixels]] dropdown menu. The Image menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window.

[[File:MSBF66.png]]

''Multiple-source beamformer image calculated in the presence of a source in the left hemisphere. A single-source scan has been performed instead of a bilateral beamforemr. The
source set in the current solution accounts for the left-hemispheric q-maximum in the data. Accordingly, the beamformer scan reveals only the as yet unmodeled additional activity in
the right hemisphere (note the radiological convention in the 3D image display). The source waveform of the beamformer virtual sensor in the left hemisphere is not shown since the
location (blue square in the figure) is not considered for the multiple-source beamformer.''

The beamformer scan can be performed with a single or a bilateral source scan. The default scan type depends on the current solution:
When the beamformer is started from the '''Average tab of the Paradigm dialog box''' the Source Analysis window opens with a new solution and a bilateral beamformer scan is
performed.
When the beamformer is started within the Source Analysis window, the default is:

* a scan with a single source in addition to the sources in the current solution, if at least one source is active.
* a bilateral scan if no source in the current solution is active.
* a scan with a single source when scalar-type beamformer is selected in the '''beamformer option dialog box'''.

The default scan type is the multiple source beamformer. The non-default scan type can be enforced using the corresponding Volume Image / Beamformer entry in the Image main
menu or in the beamformer option dialog box (only for the time-domain beamformer).

===Inserting Sources as Beamformer Virtual Sensor out of the Beamformer Image===

This is similar to the inserting sources out of the beamformer image in Multiple Source Beamformer (MSBF) in the Time-frequency Domain section.
The beamformer image can be used to add beamformer virtual sensors to the current solution. A simple double-click anywhere in the 3D view (not in the 2D view) will generate a
source at the corresponding location. A better and easier way to create sources at image maxima and minima is to use the toolbar buttons '''Switch to Maximum''' [[Image:SA 3Dimaging (8).gif]] and '''Add Source''' [[Image:SA 3Dimaging (9).gif]].

This feature allows to use the beamformer as a tool to create a source montage for '''source coherence''' analysis. A source montage file (*.mtg) for beamformer virtual sensors can
be saved using File \ Save Source Montage As… entry.

The time-domain beamformer image can be also used to add regional or dipole sources to the current solution. Press '''N''' key when there is no source in the current source array or
there is more than one beamformer virtual sensor. To create a new source array for beamformer virtual sensor, press '''N''' key when there is more than one regional or dipole source in
the current source array.

===Notes===

* You can hide or re-display the last computed image by selecting ''Hide Image'' entry in the '''Image''' menu.
* The current image can be exported to ASCII, ANALYZE, or BrainVoyager (vmp) format from the '''Image''' menu.
* For scaling options, use the and Image Scale toolbar buttons.
* Parameters used for the beamformer calculations can be set in the '''Standard Volume tab of the Image Settings dialog box'''.
* Note that Model, Residual, Order, and Residual variance are not shown for the beamformer virtual sensor type sources.

===References===

* Sekihara, K., Nagarajan, S. S., Poeppel, D., Marantz, A., & Miyashita, Y. (2001). Reconstructing spatio-temporal activities of neural sources using an MEG vector beamformer technique. IEEE Transactions on Biomedical Engineering, 48(7), 760–771.

* Van Veen, B. D., Van Drongelen, W., Yuchtman, M., & Suzuki, A. (1997). Localization of brain electrical activity via linearly constrained minimum variance spatial filtering. IEEE Transactions on Biomedical Engineering, 44(9), 867–880

== CLARA ==

CLARA ('Classical LORETA Analysis Recursively Applied') is an iterative application of weighted LORETA images with a reduced source space in each iteration.

In an initialization step, a LORETA image is calculated. Then in each iteration the following steps are performed:

# The obtained image is spatially smoothed (this step is left out in the first iteration).
# All grid points with amplitudes below a threshold of 1% of the maximum activity are set to zero, thus being effectively eliminated from the source space in the following step.
# The resulting image defines a spatial weighting term (for each voxel the corresponding image amplitude).
# A LORETA image is computed with an additional spatial weighting term for each voxel as computed in step 3. By the default settings in BESA Research, the regularization values used in the iteration steps are slightly higher than that of the initialization LORETA image.

The procedure stops after 2 iterations, and the image computed in the last iteration is displayed. Please note that you can change all parameters by creating a user-defined volume image.

The advantage of CLARA over non-focusing distributed imaging methods is visualized by the figure below. Both images are computed from the N100 response in an auditory oddball experiment (file '''Oddball.fsg''' in subfolder ''fMRI+EEG-RT-Experiment'' of the ''Examples'' folder). The CLARA image is much more focal than the sLORETA image, making it easier to determine the location of the image maxima.

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (24).gif|thumb|350px|sLORETA image]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (25).gif|thumb|350px|CLARA image]] </li>
</ul></div>

'''Notes:'''

* Starting CLARA: CLARA can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter ''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]'' for important information on regularization of distributed inverses.

== LAURA ==

LAURA (Local Auto Regressive Average) belongs to the distributed inverse method of the family of weighted minimum norm methods ([https://doi.org/10.1023/A:1012944913650 Grave de Peralta Menendeza et al., "Noninvasive Localization of Electromagnetic Epileptic Activity. I. Method Descriptions and Simulations", BrainTopography 14(2), 131-137, 2001]). LAURA uses a spatial weighting function that includes depth weighting and that term has the form of a local autoregressive function.

The source activity is estimated by applying the general formula for a weighted minimum norm:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T}\left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings.''

In LAURA, V contains both a depth weighting term W and a representation of a local autoregressive function A. V is computed as:

<math>\mathrm{V} = \left( \mathrm{U}^{T} \cdot \mathrm{U} \right)^{-1}</math>


Where

<math>\mathrm{U} = \left( \mathrm{W} \cdot \mathrm{A} \right) \otimes \mathrm{I}_{3}</math>


Here, <math>\otimes</math> denotes the Kronecker product. I3 is the [3×3] identity matrix. W is an [s×s] diagonal matrix (with s the number of source locations on the grid), where each diagonal element is the inverse of the maximum singular value of the corresponding regional source's leadfields. The formula for the diagonal components Aii and the off-diagonal components Aik are as follows:

<math>\mathrm{A}_{ii} = \frac{26}{\mathrm{N}_{i}}\sum_{k \subset V_{i}}^{}\frac{1}{\mathrm{d}_{ik}^{2}}</math>


<math>
\mathrm{A}_{ik} =
\begin{cases}
- 1/\operatorname{dist}\left( i,k \right)^{2}, & \text{if } k \subset V_{i} \\
0, & \text{otherwise}
\end{cases}
</math>


Here, Vi is the vicinity around grid point i that includes the 26 direct neighbors.

The LAURA image in BESA Research displays the norm of the 3 components of S at each location r. Using the menu function ''Image / Export Image As... ''you have the option to save this norm of S or alternatively all components separately to disk.

'''Notes:'''

* '''Grid spacing:''' Due to memory limitations, LAURA images require a grid spacing of 7 mm or more.
* '''Computation time:''' Computation speed during the first LAURA image calculation depends on the grid spacing (computation is faster with larger grid spacing). After the first computation of a LAURA image, a '''*.laura''' file is stored in the data folder, containing intermediate results of the LAURA inverse. This file is used during all subsequent LAURA image computations. Thereby, the time needed to obtain the image is substantially reduced.
* '''MEG:''' In the case of MEG data, an additional constraint is implemented in the LAURA algorithm that prevents solutions from containing radial source currents (compare Pascual-Marqui, ISBET Newsletter 1995, 22-29). In MEG, an additional source space regularization is necessary in the inverse matrix operation required compute V
* '''Starting LAURA:''' LAURA can be started from the''' Image''' menu or from the '''Image Selection''' button.
* '''Regularization:''' Please refer to Chapter'' “Regularization of distributed volume images” ''for important information on regularization of distributed inverses.

== LORETA ==

LORETA ("Low Resolution Electromagnetic Tomography") is a distributed inverse method of the family of ''weighted minimum norm'' methods. LORETA was suggested by R.D. Pascual-Marqui (International Journal of Psychophysiology. 1994, 18:49-65). LORETA is characterized by a smoothness constraint, represented by a discrete 3D Laplacian.

The source activity is estimated by applying the general formula for a weighted minimum norm:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T}\left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings.''

In LORETA, V contains both a depth weighting term and a representation of the 3D Laplacian matrix. V is computed as:

<math>\mathrm{V} = \left( \mathrm{U}^{T} \cdot \mathrm{U} \right)^{- 1}</math>


where

<math>\mathrm{U} = \left( \mathrm{W} \cdot \mathrm{A} \right) \otimes \mathrm{I}_{3}</math>


Here, <math>\otimes</math> denotes the Kronecker product. I3 is the [3x3] identity matrix. W is an [sxs] diagonal matrix (with s the number of source locations on the grid), where each diagonal element is the inverse of the maximum singular value of the corresponding regional source's leadfields. A contains the 3D Laplacian and is computed as

<math>\mathrm{A} = \mathrm{Y} - \mathrm{I}_{s}</math>


with Is the [sxs] identity matrix, where s is the number of sources (= three times the number of grid points) and

<math>\mathrm{Y} = \frac{1}{2}\left\{ \mathrm{I}_{s} + \left\lbrack \operatorname{diag}\left( \mathrm{Z} \cdot \left\lbrack 111 \ldots 1 \right\rbrack^{T} \right) \right\rbrack^{- 1} \right\} \cdot \mathrm{Z}</math>


where

<math>
\mathrm{Z}_{ik} =
\begin{cases}
1/6, & \text{if } \operatorname{dist}\left( i,k \right) = 1 \text{ grid point} \\
0, & \text{otherwise}
\end{cases}
</math>


The LORETA image in BESA Research displays the norm of the 3 components of S at each location r. Using the menu function ''Image / Export Image As... ''you have the option to save this norm of S or alternatively all components separately to disk.

'''Notes:'''
* '''Grid spacing:''' Due to memory limitations, LORETA images require a grid spacing of 5 mm or more.
* '''Computation time:''' Computation speed during the first LORETA image calculation depends on the grid spacing (computation is faster with larger grid spacing). After the first computation of a LORETA image, a '''<nowiki>*.loreta</nowiki>''' file is stored in the data folder, containing intermediate results of the LORETA inverse. This file is used during all subsequent LORETA image computations. Thereby, the time needed to obtain the image is substantially reduced.
* '''MEG''': In the case of MEG data, an additional constraint is implemented in the LORETA algorithm that prevents solutions from containing radial source currents (Pascual-Marqui, ISBET Newsletter 1995, 22-29). In MEG, an additional source space regularization is necessary in the inverse matrix operation required compute V.
* '''Starting LORETA:''' LORETA can be started from the''' Image''' menu or from the '''Image Selection '''button.
* '''Regularization:''' Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed source models.

== sLORETA ==

This distributed inverse method consists of a ''standardized, unweighted minimum norm''. The method was originally suggested by R.D. Pascual-Marqui (Methods & Findings in Experimental & Clinical Pharmacology 2002, 24D:5-12) Starting point is an unweighted minimum norm computation:

<math>\mathrm{S}_{\text{MN}}\left( t \right) = \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings''.

This minimum norm estimate is now standardized to produce the sLORETA activity at a certain brain location r:

<math>\mathrm{S}_{\text{sLORETA}, r} = \mathrm{R}_{rr}^{-1/2} \cdot \mathrm{S}_{\text{MN},r}</math>


SsMN,r is the [3x1] (MEG: [2x1]) minimum norm estimate of the 3 (MEG: 2) dipoles at location r. Rrr is the [3x3] (MEG: [2x2]) diagonal block of the resolution matrix R that corresponds to the source components at the target location r. The resolution matrix is defined as:

<math>\mathrm{R} = \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{L}^{T} + \lambda \cdot \mathrm{I} \right)^{-1} \cdot \mathrm{L}</math>


The sLORETA image in BESA Research displays the norm of SsLORETA, r at each location r. Using the menu function ''Image / Export Image As...'' you have the option to save this norm of SsLORETA, r or alternatively all components separately to disk.

'''Notes:'''

* sLORETA can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== swLORETA ==

This distributed inverse method is a ''standardized, depth-weighted minimum norm'' (E. Palmero-Soler et al 2007 Phys. Med. Biol. 52 1783-1800). It differs from sLORETA only by an additional depth weighting.

Starting point is a depth-weighted minimum norm computation:

<math>\mathrm{S}_{\text{MN}}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings''.

V is the diagonal depth weighting matrix. For s grid locations, V is of dimension [3s x 3s] (MEG: [2s x 2s]). Each diagonal element of V is the inverse of the first singular value of the leadfield of the corresponding regional source. Hence, the first 3 (MEG: 2) diagonal elements equal the inverse of the largest eigenvalue of the leadfield matrix of regional source 1, and so on.

This minimum norm estimate is now standardized to produce the swLORETA activity at a certain brain location r:

<math>\mathrm{S}_{\text{swLORETA},r} = \mathrm{R}_{rr}^{-1/2} \cdot \mathrm{S}_{\text{MN},r}</math>


SsMN,r is the [3x1] (MEG: [2x1]) depth-weighted minimum norm estimate of the regional source at location r. Rrr is the [3x3] (MEG: [2x2]) diagonal block of the resolution matrix R that corresponds to the source components at the target location r. The resolution matrix is defined as:

<math>\mathrm{R} = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} + \lambda \cdot \mathrm{I} \right)^{-1} \cdot \mathrm{L}</math>


The swLORETA image in BESA Research displays the norm of SswLORETA, r at each location r. Using the menu function ''Image / Export Image As...'' you have the option to save this norm of SswLORETA, r or alternatively all components separately to disk.

'''Notes:'''

* sLORETA can be started from the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== sSLOFO ==

SSLOFO (standardized shrinking LORETA-FOCUSS) is an iterative application of weighted distributed source images with a reduced source space in each iteration ([https://dx.doi.org/10.1109/TBME.2005.855720 Liu et al., "Standardized shrinking LORETA-FOCUSS (SSLOFO): a new algorithm for spatio-temporal EEG source reconstruction", IEEE Transactions on Biomedical Engineering 52(10), 1681-1691, 2005]).

In an initialization step, an [[#sLORETA | sLORETA]] image is calculated. Then in each iteration the following steps are performed:

# A weighted minimum norm solution is computed according to the formula <math display="inline">\mathrm{S} = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}</math> . Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D is the data at the time point under consideration. V is a diagonal spatial weighting matrix that is computed in the previous iteration step. In the first iteration, the elements of V contain the magnitudes of the initially computed LORETA image.
# Standardization of this weighted minimum norm image is performed with the resolution matrix as in [[#sLORETA | sLORETA]].
# The obtained standardized weighted minimum norm image is being smoothed to get Ssmooth.
# All voxels with amplitudes below a threshold of 1% of the maximum activity get a weight of zero in the next iteration step, thus being effectively eliminated from the source space in the next iteration step.
# For all other voxels, compute the elements of the spatial weighting matrix V to be used in the next iteration as follows: <math display="inline">\mathrm{V}_{ii,\text{next iteration}} = \frac{1}{\left\| \mathrm{L}_{i} \right\|} \cdot \mathrm{S}_{ii,\text{smooth}} \cdot \mathrm{V}_{ii,\text{current iteration}}</math>



The procedure stops after 3 iterations. Please note that you can change all parameters by creating a [[#User-Defined Volume Image | user-defined volume image]].

'''Notes:'''
* '''Starting sSLOFO''': sSLOFO can be started from the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter ''[[#Regularization of distributed volume images | Regularization of distributed volume images]]'' for important information on regularization of distributed inverses.

== User-Defined Volume Image ==

In addition to the predefined 3D imaging methods in BESA Research, it is possible to create user-defined imaging methods based on the general formula for distributed inverses:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. Custom-defined parameters are:* The spatial weighting matrix V: This may include depth weighting, image weighting, or cross-voxel weighting with a 3D Laplacian (as in LORETA) or an autoregressive function (as in LAURA).

* Regularization: The term in parentheses is generally regularized. Note that regularization has a strong effect on the obtained results. Please refer to chapter “''Regularization of Distributed Volume Images” ''for more information.
* Standardization: Optionally, the result of the distributed inverse can be standardized with the resolution matrix (as in sLORETA).
* Iterations: Inverse computations can be applied iteratively. Each iteration is weighted with the image obtained in the previous iteration.

All parameters for the user-defined volume image are specified in the User-Defined Volume Tab of the Image Settings dialog box. Please refer to chapter “''User-Defined Volume Tab”'' for details.

'''Notes:'''
* Starting the user-defined volume image: the image calculation can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== Regularization of distributed volume images ==

Distributed source images require the inversion of a term of the form L V LT. This term is generally regularized before its inversion. In BESA Research, selection can be made between two different regularization approaches (parameters are defined in the ''Image Settings dialog box''):

* '''Tikhonov regularization''': In Tikhonov regularization, the term L V LT is inverted as (L V LT +λ I)-1. Here, l is the regularization constant, and I is the identity matrix.
* One way of determining the optimum regularization constant is by minimizing the ''generalized cross'' ''validation error'' (CVE).
* Alternatively, the regularization constant can be specified manually as a percentage of the trace of the matrix L V LT.
* '''TSVD''': In the truncated singular value decomposition (TSVD) approach, an SVD decomposition of L V LT is computed as  L V LT = U S UT, where the diagonal matrix S contains the singular values. All singular values smaller than the specified percentage of the maximum singular values are set to zero. The inverse is computed as U S-1 UT, where the diagonal elements of S-1 are the inverse of the corresponding non-zero diagonal elements of S.

Regularization has a critical effect on the obtained distributed source images. The results may differ completely with different choices of the regularization parameter (see examples below). Therefore, it is important to evaluate the generated image critically with respect to the regularization constant, and to keep in mind the uncertainties resulting from this fact when interpreting the results. The default setting in BESA Research is a TSVD regularization with a 0.03% threshold. However, this value might need to be adjusted to the specific data set at hand.

The following example illustrates the influence of the regularization parameter on the obtained images. The data used here is condition '''St-Cor of dataset Examples \ TFC-Error-Related-Negativity \ Correct+Error.fsg''' at 176 ms following the visual stimulus. Discrete dipole analysis reveals the main activity in the left and right lateral visual cortex at this latency.

[[Image:SA 3Dimaging (42).gif]]

''Discrete source model at 176 ms: Main activity in the left and right lateral visual cortex, no visual midline activity.''

LORETA images computed at this latency depend critically on the choice of the regularization constant. The following 3D images are created with TSVD regularization with SVD cutoffs of 0.1%, 0.005%, and 0.0001%, respectively. The volume grid size was 9 mm. The example demonstrates the dramatic effect of regularization and demonstrates the typical tradeoff between too strong regularization (leading to too smeared 3D images that tend to show blurred maxima) and too small regularization (resulting in too superficial 3D images with multiple maxima).

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (43).gif|thumb|350px|'''SVD cutoff 0.1%''': Regularization too strong. No separation between sources, mislocalization towards the middle of the brain.]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (44).gif|thumb|350px|'''SVD cutoff 0.005%''': Appropriate regularization. Separation of the bilateral activities. Location in agreement with the discrete multiple source model.]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (45).gif|thumb|350px|'''SVD cutoff 0.0001%''': Too small regularization. Mislocalization, too superficial 3D image. ]] </li>
</ul></div>

The automatic determination of the regularization constant using the CVE approach does not necessarily result in the optimum regularization parameter either. In this example, the unscaled CVE approach rather resembles the TSVD image with a cutoff of 0.0001%, i.e. regularization is too small. Therefore, it is advisable to compare different settings of the regularization parameter and make the final choice based on the above-mentioned considerations.

== Cortical LORETA ==

Cortical LORETA is principally the same technique as LORETA, however, Cortical LORETA is not computed in a 3D volume, but on the cortical surface.

The cortical reconstruction in BESA Research fed from BESA MRI is a closed 2D surface with no boundaries and a very close approximation of the actual cortical form. It consists of an irregular triangulated grid.

The Laplace operator that is used for identifying a smooth solution in a three-dimensional space is exchanged with a Laplace operator that runs on the two-dimensional cortical surface.

There is a wide variety of 2D Laplace operators with different characteristics. The general form of the discrete Laplace operator is

<math>\Delta f\left( p_{i} \right) = \frac{1}{d_{i}}\sum_{j \in N(i)}^{}{w_{ij}\left\lbrack f\left( p_{i} \right) - f\left( p_{j} \right) \right\rbrack},</math>


where '''pi''' is the '''i-th''' node of the triangular mesh, '''f(pi) '''is the value of a function f defined on the cortical mesh at the node '''pi''', '''wij''' is the weight for the connection between the nodes '''pi''' and '''pj''' and '''di''' is a normalization factor for the '''i-th''' row of the operator. Furthermore, '''N(i)''' is the set of indices corresponding to the direct (also called "1-ring") neighbors of '''pi'''.

BESA offers the choice of three Laplace operators with slightly different characteristics.

* '''Unweighted Graph Laplacian''': This is the simplest operator. It takes into account only the adjacency of the nodes and not the geometry of the mesh:

<math>
w_{ij} =
\begin{cases}
1, & \text{if } p_{i} \text{ and } p_{j} \text{ are connected by an edge} \\
0, & \text{otherwise}
\end{cases}
</math>

<math>d_{i} = 1</math>


[[Image:SA 3Dimaging (4).jpg |450px]]

* '''Weighted Graph Laplacian:''' This operator is similar to the unweighted graph Laplacian but with different weights for the different connections. The connections between nearby nodes get larger weights than the connections between farther nodes:

<math>w_{ij} = \frac{1}{\operatorname{dist}\left( p_{i},p_{j} \right)}</math>

<math>d_{i} = \sum_{j \in N(i)}^{} {\operatorname{dist}\left(p_{i}, p_{j} \right)}</math>


where '''dist''' ('''pi''' , '''pj''') is the distance between the nodes '''pi '''and '''pj'''.

[[Image:SA 3Dimaging (6).jpg|450px]]

* '''Geometric Laplacian with mixed area weights''': This operator takes into account the angles in the corresponding triangles into account as well as the area around the nodes in order to determine the connection weights:

<math>w_{ij} = \frac{\cot\left( \alpha_{ij} \right) + \cot\left( \beta_{ij} \right)}{2}</math>

<math>d_{i} = A_{\text{mixed}}</math>


where '''αij''' and '''βij''' denote the two angles opposite to the edge ('''i , j''') and '''Amixed '''is either the Voronoi area, or 1/2 of the triangle area or 1/4 of the triangle area depending on the type of the triangle.

[[Image:SA 3Dimaging (8).jpg|450px]]

'''Regularization and other parameters:'''

[[Image:CorticalLOR.png‎]]

* '''SVD cutoff''': The regularization for the inverse operator as a percent of the largest singular value.
* '''Depth weighting''': Turn depth weighting on or off.
* '''Laplacian type''': Selection of Laplacian operators (see above).

'''Notes:'''
* '''Starting Cortical LORETA''': Cortical LORETA can be started from the sub-menu '''Surface Image''' of the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]''” for important information on regularization of distributed inverses.

== Cortical CLARA ==

Cortical CLARA is principally the same technique as CLARA, but Cortical CLARA is not computed in a 3D volume, but on the cortical surface. Instead of using a LORETA image as the basis for the iterative application, cortical CLARA uses cortical LORETA.

'''Regularization and other parameters:'''

[[Image:SA 3Dimaging (47).gif]]

* '''SVD cutoff''': The regularization for the inverse operator as a percent of the largest singular value.
* '''Depth weighting''': Turn depth weighting on or off.
* '''Laplacian type''': Selection of Laplacian operators (see Cortical LORETA).
* '''No of iterations''': Number of iterations for CLARA. The more iterations are used, the sparser becomes the solution.
* '''Automatic''': The algorithm tries to determine the number of iterations automatically. The goodness of fit (GOF) is calculated after every iteration and if there is a big jump in the GOF then the algorithm will stop. If no jumps appear during the calculations then CLARA iterates until the specified number of iterations is reached.
* '''Regularize iterations''': If one wants to use different regularization for the CLARA iterations than the value specified as "SVD cutoff", this option should be selected.
* '''Amount to clip from img (%)''': Cortical CLARA uses the solution from the previous iteration as an additional weighting matrix for the current iteration. That weighting matrix is constructed by cutting the "low" activity from the solution. This number specifies how much of the activity should be cut from the previous solution in order to construct the weighting matrix. This value is given as a percentage of the maximal activity. Default value is 10%.

'''Notes:'''

* '''Starting Cortical CLARA:''' Cortical CLARA can be started from the sub-menu '''Surface Image''' of the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]''” for important information on regularization of distributed inverses.

== Cortex Inflation ==

The inflated cortex is a smoothened version of the individual cortical surface with minimal metric distortions (Fischl, B. et al. (1999). Cortical Surface-Based Analysis: II: Inflation, Flattening, and a Surface-Based Coordinate System. ''NeuroImage'', 9(2), 195–207). Gyri and sulci are smoothened out. The original distances between each point on the cortex and its neighbors are, however, mostly preserved.

[[Image:SA 3Dimaging (48).gif]]

''Cortical LORETA map overlaid on top of the inflated cortical surface.''

A lighter gray color overlaid on top of the surface image indicates the location of a gyrus of the individual cortex surface, while a darker gray color indicates the location of a sulcus. The inflated cortical surface can be computed in '''BESA MRI 2.0'''. For more details please refer to the BESA MRI 2.0 help.

== Surface Minimum Norm Image ==

'''Introduction'''

The minimum norm approach is a common method to estimate a distributed electrical current image in the brain at each time sample (Hämäläinen & Ilmoniemi 1984). The source activities of a large number of regional sources are computed. The sources are evenly distributed using 1500 standard locations 10% and 30% below the smoothed standard brain surface (when using the standard MRI) or using between 3000-4000 locations on the individual brain surface defined by the gray-white-matter boundary.

Since the number of sources is much larger than the number of sensors in a minimum norm solution, the inverse problem is highly underdetermined and must be stabilized by a mathematical constraint, the minimum norm. Out of the many current distributions that can account for the recorded sensor data, the solution with the minimum L2 norm, i.e. the minimum total power of the current distribution is displayed in BESA Research.

First, the forward solution (leadfield matrix L) of all sources is calculated in the current head model. Then, the source activities S(t) of all source components are computed from the data matrix D(t) using an inverse regularized by the estimated noise covariance matrix:

<math>\mathrm{S}\left( t \right) = \mathrm{R} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{R} \cdot \mathrm{L}^{T} + \mathrm{C}_N \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed regional source model, CN denotes the noise correlation matrix in sensor space, and R is a weighting matrix in source space. R and CN can be designed in different ways in order to optimize the minimum norm result. The total activity of each regional source is computed as the root mean square of the source activities S(t) of its 3 (MEG:2) components. This total source activity is transformed to a color-coded image of the brain surface. (When the standard brain is used, two sources are assigned to each surface location, located 10% and 30% below the surface, respectively. The color that is displayed on the standard brain surface is the larger of the two corresponding source activities.)

'''Weighting options'''

The minimum norm current imaging techniques of BESA Research provide different weighting strategies. Two weighting approaches are available: Depth weighting and spatio-temporal approaches.
* '''Depth weighting:''' Without depth weighting, deep sources appear very smeared in a minimum-norm reconstruction. With depth weighting, both deep and superficial sources produce a similar, more focal result. If this weighting method is selected, the leadfield of each regional source is scaled with the largest singular value of the SVD (singular value decomposition) of the source's leadfield.
* '''Spatio-temporal weighting''': Spatio-temporal weighting tries to assign large weight to sources that are assumed to be more likely to contribute to the recorded data.
** '''Subspace correlation after single source scan''': This method divides the signal into a signal and a noise subspace. The correlation of the leadfield of a regional source i with the signal subspace (pi) is computed to find out if the source location contributes to the measured data. The weighting matrix R becomes a diagonal matrix. Each of the three (MEG: 2) components of a regional source get the same weighting value pi2. This approach is based on the signal subspace correlation measure introduced by J.C. Mosher, R. M. Leahy (Recursive MUSIC: A Framework for EEG and MEG Source Localization, IEEE Trans. On Biomed. Eng. Vol. 45, No. 11, November 1998)
** '''Dale & Sereno 1993:''' In the approach of Dale and Sereno (J Cogn Neurosci, 1993, 5: 162-176) a signal subspace needs not be defined. The correlation pi of the leadfield of regional source i with the inverse of the data covariance matrix is computed along with the largest singular value λmax of the data covariance matrix. The weighting matrix R is a diagonal matrix with weights: [[Image:SA 3Dimaging (50).gif]]. Each of the three (MEG: 2) components of a regional source receives the same weighting value.

'''Noise regularization'''

Two methods to estimate the channel noise correlation matrix CN are provided by the program:
* '''Use baseline:''' Select this option to estimate the noise from the user-definable baseline. The signal is computed from the data at non-baseline latencies.
* '''Use 15% lowest values:''' The baseline activity is computed from the data at those 15% of all displayed latencies that have the lowest global field power. The signal is computed from all displayed latencies.

In each case, the activity (noise or signal, respectively) is defined as root-mean-square across all respective latencies for each channel.

The noise covariance matrix CN is constructed as a diagonal matrix. The entries in the main diagonal are proportional to the noise activity of the individual channels (if selected) or are all equally proportional to the average noise activity over all channels. The noise covariance matrix CN is then scaled such that the ratio of the Frobenius norms of the weighted leadfield projector matrix (LRLT) and the noise covariance matrix CN equals the Signal-to-Noise ratio. This scaling can be multiplied by an additional factor (default=1) to sharpen (<1) or smoothen (>1) the minimum norm image.

'''Applying the Minimum Norm Image'''

The minimum-norm algorithm is started via the ''Surface minimum norm image dialog box'', which is opened from the''' Image''' menu, or by typing the shortcut '''Ctrl-M''': Please refer to Chapter ''“Surface'' ''Minimum Norm Tab”'' for more details.

As opposed to the other 3D images available from the '''Image '''menu, the surface minimum norm image is not computed on a volumetric grid, but rather for locations on the brain surface. Accordingly, the results of the minimum norm image are displayed superimposed to the brain surface mesh rather than to the volumetric MR image.

The figure below shows a minimum norm image computed from the file '''Examples\Epilepsy\Spikes\Spikes-Child4_EEG+MEG_averaged.fsg'''. The EEG spike peak was imaged using the individual brain surface of the subject. A baseline from -300 to -70 ms was used. Minimum norm was computed with depth weighting, Spatio-temporal weighting according to Dale & Sereno 1993 and individual noise weighting with a noise scale factor of 0.01. The minimum norm image reveals the location of the spike generator in the close vicinity of the frontal left-hemispheric lesion in this subject.

[[Image:SA 3Dimaging (51).gif]]

== Multiple Source Probe Scan (MSPS) ==

 
'''Introduction'''

The MSPS function provides a tool for the validation of a given solution. It is based on the following theoretical consideration: If the recorded EEG/MEG data has been modeled adequately, i.e. all active brain regions are represented by a source in the current solution, then any additional probe source added to the solution will not show any activity apart from noise. The only exception occurs if this probe source is placed in close vicinity to one of the sources in the current solution. In that case, the solution's source and the probe source will share the activity of the corresponding brain area. The MSPS applies these considerations by scanning the brain on a pre-defined grid with a regional probe added to the current solution. Grid extent and density can be specified in the Image settings. The power P of the probe source at location r in the signal interval is compared with the power of the probe source in a reference interval, defining a value q:

<math>\mathrm{q}\left( r \right) = \sqrt{\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}} - 1</math>


MSPS can be computed on time domain or time-frequency domain data:
* In the time domain, q(r) is computed from the source waveform of the probe source. Here, P(r) is the mean power of the probe source at location r in the marked latency range, and Pref(r) is the mean probe source power in the user-definable baseline interval.
* In the time-frequency domain, an MSPS image can be computed from the complex cross spectral density matrices. By applying the inverse operator for a source configuration consisting of the current solution and the probe source, the power of the probe source can be computed for the target interval [P(r)] and the reference time-frequency interval [Pref(r)]. In the resulting MSPS image, q-values are shown in %, where q[%] = q*100.

The inverse operator used to determine the probe source power uses different regularization constants for the probe source and the sources in the current solution. The regularization constant of the sources in the current solution can be specified in the Image settings (default 4%). The regularization constant of the probe source is internally set to 0%.

Alternatively to the definition above, q can also be displayed in units of dB:

<math>\mathrm{q}\left\lbrack \text{dB} \right\rbrack = 10 \cdot \log_{10}\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}</math>


Values of q smaller than zero are not shown in the MSPS image.

According to the considerations above, an MSPS of a correct source model should optimally yield image maxima around the sources in the current solution only. If the MSPS image is blurred or shows maxima at locations different from the modeled sources, this indicates a non-sufficient or incorrect solution.

'''Applying the MSPS'''

This chapter illustrates the application of the Multiple Source Probe Scan. The figures are generated with data from file '''Examples/Epilepsy/Spikes/Rolandic-Spike-Child.fsg''' (-300 : +200 ms, filtered from 3 Hz [forward] to 40 Hz [zero-phase]).

'''Time domain versus time-frequency domain MSPS'''

The multiple source probe scan can be computed in the time domain or the time-frequency domain. The latter is possible only when time-frequency domain data is available for the current condition, i.e. if the condition has been created by starting a multiple source beamformer (MSBF) computation from the source coherence window. In this case, evoking the MSPS calculation from the '''Imaging '''button or from the '''Image''' menu will bring up the following dialog window that allows to choose between time- or time-frequency MSPS. If only time domain data is available, this dialog window will not appear and MSPS will be computed in the time domain.

[[Image:SA 3Dimaging (53).gif]]

For a time-frequency domain MSPS, the target and the reference time-frequency interval have been specified already in the Time-Frequency window (see Chapter "''How To Create Beamformer Images''"). For a time-domain MSPS, the target and the reference epoch have to be specified in the Source Analysis window as described below.

'''Time domain MSPS'''

The time-domain MSPS image displays the ratio of the power of a regional probe source in the signal and the baseline interval. The currently set baseline is indicated by a horizontal line in the upper left corner of the channel box.

[[Image:SA 3Dimaging (54).gif|thumb|c|none|330px|The black horizontal bar in the upper part of the channel box (here circled in red) indicates the baseline interval.]]

By default, BESA Research defines the pre-stimulus interval of the current data segment as baseline. The baseline should represent a latency range in which no event-related activity is present in the data. There are several possibilities to modify the baseline interval: by clicking on the horizontal line with the left mouse button or by using the corresponding entry in the '''Condition '''menu or '''Fit Interval''' popup menu.

Mark an interval to define the target epoch, i.e. the time-interval for which the current solution is to be tested. Start the MSPS by selecting it from the '''Image selection '''button or from the '''Image''' menu to start the probe source scan. The''' Image '''menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window. The 3D window opens and displays the scan result.

<div><ul>
<li style="display: inline-block;"> [[Image:SA 3Dimaging (55).gif|thumb|c|none|650px|This figure shows the MSPS image applied on the three left-hemispheric sources in the solution ''''Rolandic-Spike-Child-RS2.bsa''''. The baseline is set from -300ms to -50 ms. The right-hemispheric sources have been switched off. The fit interval is set to the latency range of large overall activity in the data (-43 ms : 117 ms). A realistic FEM model appropriate for the subject's age (12 years, conductivity ratios (cr) 50) is applied. The MSPS image does not show maxima at the modeled source locations and rather shows a spread q-value distribution.]] </li>

<li style="display: inline-block;"> [[Image:SA 3Dimaging (56).gif|thumb|c|none|650px|The MSPS image for the same latency range when the right-hemispheric sources have been included. The MSPS image appears more focal and shows maxima around the modeled brain regions. This indicates the substantial improvement of the solution by adding the right-hemispheric sources that model the propagation of the epileptic spike from the left to the right hemisphere (note the radiological side convention in the 3D window).]] </li>
</ul></div>

'''Time-Resolved MSPS'''

If the MSPS has been computed on time domain data, the image can be shown separately for each latency in the selected interval. After the MSPS has been computed for the marked epoch, double-click anywhere within this epoch to display the ratio of the probe source magnitude at the selected latency and the mean probe source magnitude in the baseline. Scanning the latency range by moving the cursor (e.g. with the left and right arrow cursor keys) provides a time-resolved MSPS image.

Time-resolved MSPS images are not available if the MSPS has been computed on data in the time-frequency domain.

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (57).gif|thumb|450px|MSPS image of the spike peak activity at 0ms. The activity mainly occurs in the left hemisphere. This fact is illustrated by the source waveforms and confirmed in the MSPS image, which shows a focal maximum around the location of the red sources.]] </li>

<li style="display: inline-block;"> [[File:SA 3Dimaging (58).gif|thumb|450px|Around +27 ms, the spike has propagated to the right hemisphere. This becomes evident from the waveforms of the blue sources, which show a significant latency lag with respect to the first three sources, and from the MSPS image, which shows the maximum around blue sources at this latency.]] </li>
</ul></div>



'''Notes:'''

* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image''' menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the''' Image''' menu.
* For scaling options, please refer to the '''scaling buttons''' popup menu .
* Parameters used for the MSPS calculations can be set in the ''General Settings tab'' of the ''Image Settings dialog box.''

== Source Sensitivity ==

'''Introduction'''

The 'Source sensitivity' function displays the sensitivity of the selected source in the current source model to activity in other brain regions. Sensitivity is defined as the fraction of power at the scanned brain location that is mapped onto the selected source.

To compute the source sensitivity, unit brain activity is modeled at different locations (probe source) throughout the brain. To this data, the current source model is applied to compute the source waveforms SCM of all modeled sources:

<math>\mathrm{S}_{\text{CM}} = \mathrm{L}_{\text{CM}}^{-1} \cdot \mathrm{L}_{\text{PS}}</math>


Here LCM-1 is the regularized inverse operator for the current model, and LPS is the leadfield of the regional probe source (dimension [Nx3] for EEG and [Nx2] for MEG, respectively, where N is the number of sensors). The source amplitude SSS of the selected source in the model is a 3x3 (MEG: 2x2) sub-matrix of SCM (if the selected source is a regional source) or a 1x3-matrix (MEG: 1x2) (if the selected source is a dipole). The root mean square of the singular values of SCM is defined as the source sensitivity.

The 3D source sensitivity image displays this value for all locations on a grid specified under '''Image/Settings'''. Grid density can be specified in the Image Settings.

'''Applying the Source Sensitivity Image'''

The Source Sensitivity image is evoked from the '''Image''' menu or by pressing the corresponding hot key (default: '''V''').

This function is enabled only when a solution with an active selected source is present in the Source Analysis window. The source sensitivity image then displays the sensitivity of the selected source to activity in other brain regions.

[[Image:SA 3Dimaging (59).gif]]

''Source Sensitivity image for the selected frontal source (green) in model ''''''High_Intensity_3RS.bsa'''''' in folder 'Examples/ERP_Auditory_Intensity'. The data displayed is the '100dB' condition in file ''''''All_Subjects_cc.fsg''''''. The selected source is sensitive to activity in the frontal brain region (yellow/white), while it is not influenced by activity in the vicinity of the left and right auditory cortex areas, which are modeled by the red and blue source in the model (transparent/gray).''

'''Notes:'''

* The sensitivity image is independent of the recorded sensor signals. It only depends on the current source model, the sensor configuration, the head model, and the regularization constant.
* If the regularization constant is set to zero, each source has a sensitivity of 100% to activity around its own location. With increasing regularization, the spatial filter becomes less focused, and the sensitivity of a source to activity at its location decreases.
* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image''' menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the '''Image''' menu.

{{BESAManualNav}}

File:Msbfpic4.png

2019-03-27T13:58:11Z

Jamie:

File:Msbfpic3.png

2019-03-27T13:58:02Z

Jamie:

File:Msbfpic2.png

2019-03-27T13:57:50Z

Jamie:

File:MsbfPic1.png

2019-03-27T13:57:41Z

Jamie:

The Initialization File: BESA.ini

2019-03-27T13:46:08Z

Jamie: /* FMRI */

{{BESAInfobox
|title = Module information
|module = BESA Research Basic or higher
|version = 6.1 or higher
}}

== Introduction ==

'''BESA.ini File'''

BESA Research uses settings provided in the initialization file '''BESA.ini''' whenever BESA Research is started or a new file is opened for the first time. The format of this file conforms with standard initialization files ('''<nowiki>*.ini</nowiki>''') of Windows. You may change the settings in '''BESA.ini''' using NOTEPAD.exe from the ACCESSORIES group, or other plain text editors to adapt BESA Research to '''your own everyday needs'''. The default settings provided in '''BESA.ini''' will be used by BESA Research whenever BESA Research or the launch program is started. It is advised that you make a backup copy of '''BESA.ini''' before you change the default settings.

'''Location of BESA.ini'''

You can place '''BESA.ini''' at three possible locations:

# '''Private''': each user on a PC should have his/her own private settings. This is normally in ''My Documents/BESA/Research_6_1''
# '''Public''': all users should use one setting, but they can edit '''BESA.ini''' to change the settings. This is normally in ''Public Documents/BESA/Research_6_1''
# '''Administrator''': the PC administrator determines the settings. This is normally in ''C:Program Files(x86)/BESA/Research_6_1''

The actual folder names depend on the operating system and the system language.

When BESA starts, it first looks for the '''administrator''' version of '''BESA.ini'''. If this is not found, it looks for the '''private''' version. If this is not found, it looks for the '''public''' version. If this is not found, internal default values are used.

'''There are 13 general sections, and several reader-specific sections:'''

[Defaults]                    General settings (filters, scaling, and various other settings)

[Folders]                     Folders used by BESA Research (Examples, Montages, Scripts, Settings,...)

[Electrodes]                Electrode renaming

[Patterns]                   Rename patterns in the '''Tags''' menu

[Artifacts]                   Settings for artifact correction

[KEYCONTROLS]      Function key definitions

[Search]                     Default parameters for search

[FFT]                           Frequency band definitions

[Printer]                      Printer control

[Calibration]              Calibration control

[Video]                       Digital video control

[Mapping]                  Mapping control

[Updates]                   Options for program updates

[Matlab]                      Settings for the Matlab interface

[fMRI]                   Settings for the fMRI arfifact removal

[Montages]                   A setting for a default source montage

'''Reader-specific settings'''

[BrainLab]

[Bio-Logic]

[EDF+] [BDF] [Trackit]

[EGI]

[Harmonie]

[NeuroScan Keys]

[NKT2100]

[Vangard]

[XLTEK]

== Defaults ==

'''Default settings provided for section [Defaults]:'''

'''DatabaseAllowLocalFiles=Yes''' (If set to "Yes", BESA Research will write filenames "'''datafilename.ftg'''" and "'''datafilename.fst"''' to the data folder, saving current file tag and display settings there. If set to "No", these files are only written to the database. If set to "Yes", you can copy these files along with the data to a new folder, and display settings and tags will be preserved.)

'''DataBuffering=Off''' (If set to "On", an internal buffer of length 180 s of data is kept to speed up paging). This can speed up paging, particularly when the data are in a network folder.

'''DisplayedTime=10''' displayed time window [s] on the screen

'''Montage=Org''' montage used when opening a new file

'''ScpScale=50''' scale of scalp channels in [mV]

'''PgrScale=500''' scale of polygraphic channels in [mV]

'''IcrScale=500''' scale of intracranial channels in [mV]

'''MegScale=500''' scale of MEG/marker channels in [fT]

'''SrcScale=100''' scale of source of source montages

'''BaselineCorrection=On''' baseline correction, do not switch off in AC systems

'''ClippingPercent= '''set from 100 to 200 if you want to clip artifacts in displayed EEG (not used if empty or 0)

'''LowFilter=''' low filter cutoff frequency [Hz] (variable filter)

'''TimeConstant=0.3''' time constant for low filter cutoff frequency [sec] (fixed forward filter, 0.3 sec is equivalent to 0.53 Hz)

'''HighFilter=70''' high filter cutoff frequency [Hz] (variable filter)

'''NotchFilter=50''' notch filter center frequency [Hz]

'''NotchFilterStatus=Off''' notch filter is off, set=On if you want to use as default

'''BandFilter=12''' band pass filter center frequency [Hz]

'''BandFilterStatus=Off''' band pass is off, set=On if you want to use as default

'''AdditionalChannelFile=''' defines the full path and name of an additional channels montage file, e.g. '''C:\Program Files\BESA\Research_x\Montages\AdditionalChannels\EKG.sel'''

'''ColoredWaveforms=On''' scalp waveforms are (not) colored according to region

'''WriteSegmentPath=''' defines default path for saving segments/averages. If blank, the path of the current data file is used.

'''ShowSubjectInfo=Off''' subject info will (not) be displayed.

The following optional parameters are not defined as default and can be set manually in''' BESA.ini''':

'''TextEditor="Notepad.exe"''' defines the path to your preferred text editor. This will be used when you press the '''Edit''' button the ''Load Coordinate Files dialog box''.

'''NeuroScanDataNumberOfBits=32''' defines the format of NeuroScan data files ('16' for 16-bit, '32' for 32-bit). If this variable is not specified, BESA uses a heuristic to (try to) decide which of the two data formats is used. This variable overrides the heuristic. If you want to specify the NeuroScan data format for specific files, create a file, named "16bit" or "32bit", and place it in the data folder.

'''ScaleAmplitudesForNNChannels=25''' Scale waveforms as if a fixed number of channels were displayed in the window (here: 25). A minimum of 10 channels can be used for the scaling. This parameter is superseded if the parameter "''ScaleAmplitudesFixedPixelHeight"'' is specified.

'''ScaleAmplitudesFixedPixelHeight=70''' Set the scale bar for amplitudes to a fixed pixel height (here: 70). If this parameter is set in the '''.ini''' file, it supersedes the parameter "''ScaleAmplitudesForNNChannels''".

'''Notes'''

Check the Menu descriptions for the various definitions of filters, montages etc. For montage preselection, use the labels as visible on the montage push-buttons.

The additional channels file should contain all polygraphic channels (e.g. EKG, EOG, respiratory) that you want to view regularly along with the scalp channels. The entry AdditionalChannelFile must specify the full path pointing to the location of additional channel files (recommended: ''Montages\AdditionalChannels''). If no drive is specified, the installation drive of BESA is used.

If BaselineCorrection is set to 'On', before displaying a screen of data, BESA subtracts for each channel the mean over its displayed time points. This optimizes viewing, because it ensures that the vertical position of each channel is not shifted upward or downward from the channel label at the left of the screen. There are some cases in which you will not want baseline correction, i.e. when the DC level in the data is already correctly defined. This is usually the case, for instance, when reading in files that have been processed by BESA. In this case, BaselineCorrection should be set to 'Off', because otherwise maps and source montage displays may be distorted.

== Folders ==

'''The [Folders] section defines where BESA Research places its files. In versions 5.1 and earlier, files were located in various subfolders of the program folder. This led to problems if the user did not have administrator rights, e.g. to create or write to a file. For compatibility with Windows 7 and higher versions, many folders are now located by default in locations where normal users can create and write files. If you wish, you can also specify paths in the [Folders] section to use the previous locations. The previous location is given for each variable.'''

These settings allow some flexibility that can be useful if you want to tune BESA Research for use by several users, or on a network. For instance, the Examples and Montages folders might be located on a network disk. For the current defaults, the database, Examples, Montages, and Scripts are set up for use by all users on the PC on which BESA Research is installed. The settings files ('''Besa.set''', '''Besa.cfg''', etc.) are located in private folders so that each user retains his or her own settings.

The '''default''' settings (i.e. settings that BESA Research uses if the entries are omitted in the '''.ini''' file) are shown for each variable definition.

The folder definitions can use '''placeholders''', labels enclosed by a % sign (e.g. %localapp%), to define paths that vary depending on the language version and on the Windows system. These are defined below.

'''The Variables'''

'''Database=%localapp%''' The path of the BESA Research database folder (used to be ''%progdir%System\DB'' in BESA versions up to 5.1.x). Unless the provided path ends with ''\DB'' or ''\Database'', BESA Research will automatically create a folder named ''Database'' in the provided path.

'''Settings=%privatprog%Settings''' The path of the BESA Research settings folder (used to be ''%progdir%System'' in BESA versions up to 5.1.x)

'''Montages=%publicprog%Montages''' The path of the BESA Research montages folder (used to be ''%progdir%Montages'' in BESA versions up to 5.1.x)

'''Scripts=%publicprog%Scripts''' The path of the BESA Research Scripts folder (used to be ''%progdir%Scripts'' in BESA versions up to 5.1.x)

'''Examples=%publicprog%Examples''' The path of the BESA Research Examples folder (used to be ''%progdir%Examples'' in BESA versions up to 5.1.x)

'''User=%privatprog%Settings''' The path for user defined settings (used to be ''%progdir%System\Userdirs'' in BESA versions up to 5.1.x)

'''Placeholders'''

The strings enclosed by percent signs (%) are placeholders for the following folders in English-language versions of Windows. Folder names differ depending on Windows version, and for other language settings. BESA Research will substitute the placeholders by the appropriate folder name for the system and the system language:

* '''Windows 7 and higher (English):'''

'''%localapp%''' = "''C:\Users\[user]\AppData\Local\BESA\Research_6_1''", where [user] is the logon name of the current user. This folder is directly accessible from the Desktop as "''Desktop\[user]\AppData\Local\BESA\Research_6_1''".

'''%publicprog%''' = "''C:\Users\Public\Public Documents\BESA\Research_6_1''". This folder is directly accessible from the Windows Explorer under "''Libraries\Documents\Public'' ''Documents\BESA\Research_6_1''".

'''%privateprog%''' = "''C:\Users\[user]\Documents\BESA\Research_6_1''", where [user] is the logon name of the current user. This folder is directly accessible from the Windows Explorer as "''Libraries\Documents\My'' ''Documents\Research_6_1''" or "''Desktop\[User]\My Documents\BESA\Research_6_1''.

'''%progdir%''' = the BESA Research root folder. In a default installation, this is "''C:\Program'' ''Files\BESA\Research_6_1''".

'''%besaroot%''' is the same as '''%progdir%'''

* '''Windows Vista (English'''):

'''%localapp% '''<nowiki>= "</nowiki>''C:\Users\[user]\AppData\Local\BESA\Research_6_1''", where [user] is the logon name of the current user. This folder is directly accessible from the Windows Explorer as "''Desktop\[user]\AppData\Local\BESA\Research_6_1''".

'''%publicprog%''' = "''C:\Users\Public\Public Documents\BESA\Research_6_1''". This folder is directly accessible from the Windows Explorer under "''Desktop\Public\Public Documents\BESA\Research_6_1''".

'''%privateprog%''' = "''C:\Users\[user]\Documents\BESA\Research_6_1''", where [user] is the logon name of the current user. This folder is directly accessible from the Windows Explorer as "''Desktop\[user]\Documents\BESA\Research_6_1''".

'''%progdir%''' = the BESA Research root folder. In a default installation, this is "''C:\Program'' ''Files\BESA\Research_6_1''".

'''%besaroot%''' is the same as '''%progdir%'''  

* '''Windows XP (English) (note: not supported by BESA Research 6.1 and higher):'''

'''%localapp% '''<nowiki>= "</nowiki>''C:\Documents and Settings\[user]\Local Settings\Application Data\BESA\Research_6_0''", where [user] is the logon name of the current user.

'''%publicprog%''' = "''C:\Documents and Settings\All Users\Documents\BESA\Research_6_0". ''This folder is directly accessible from the Windows Explorer under "''My Computer\Shared'' ''Documents\BESA\Research_6_0''".

'''%privateprog%''' = "''C:\Documents and Settings\[user]\My Documents\BESA\Research_6_0''", where [user] is the logon name of the current user. This folder is directly accessible from the Windows Explorer as "''My Documents\BESA\Research_6_0''".

'''%progdir%''' = the BESA Research root folder. In a default installation, this is "''C:\Program'' ''Files\BESA\Research_6_0''".

'''%besaroot%''' is the same as '''%progdir%  '''

* '''Windows 2000 (English) (note: not supported by BESA Research 6.1 and higher):'''

'''%localapp%''' = "''C:\Documents and Settings\[user]\Local Settings\Application Data\BESA\Research_6_0''", where [user] is the logon name of the current user.

'''%publicprog%''' = "''C:\Documents and Settings\All Users\Documents\BESA\Research_6_0''".

'''%privateprog%''' = "''C:\Documents and Settings\[user]\My Documents\BESA\Research_6_0''", where [user] is the logon name of the current user. This folder is directly accessible from the Windows Explorer '''as "'''''My Documents\BESA\Research_6_0'''''". '''

'''%progdir%''' = the BESA Research root folder. In a default installation, this is "''C:\Program'' ''Files\BESA\\Research_6_0''".

'''%besaroot%''' is the same as '''%progdir%'''

== Electrodes ==

'''This section allows for automatic relabeling of electrodes. For instance, the 10-20 label "T3" can be replaced by the 10-10 convention "T7".'''

'''Default settings provided for section [Electrodes]:'''

T7=T3 replace 10-10 label with old 10-20 convention

T8=T4 replace 10-10 label with old 10-20 convention

P7=T5 replace 10-10 label with old 10-20 convention

P8=T6 replace 10-10 label with old 10-20 convention

X1=ECG1 define X1 channel to be ECG1

X2=ECG2 define X2 channel to be ECG2

Other examples, depending on your electrode input box definition, could be:

PG1=LO1 define X3 as lateral orbital eye electrode left

PG2=LO2 bipolar LO1-LO2 defines horizontal EOG (additional channel)

X3=IO1 infraorbital, e.g. use with FP1 as additional channel for VEOG

X9=Rsp define X9 channel to be a respiratory channel

Relabeling of channel names (as stored in the EEG file header) is helpful to predefine your standard sequence of channels and to avoid the need for reading and/or editing a Channel Configuration file for every EEG file.

'''Note 1''': For polygraphic channels, or if your EKG has been recorded differentially, you should edit and define an ''Additional Channels Montage'' according to your recording channel configuration (e.g. Fp1-IO1=vertical EOG). The Additional Channels group permits to display these channels regularly below the scalp montages with individual scales.

'''Note 2''': EOG channels record both eye and scalp activity. In digital EEG systems, EOG electrodes should be labeled according to their position in the 10-10 system (see "''Electrode Conventions''"). This permits use of these electrodes for mapping and suppression of eye artifacts. The standard definitions above give an example of how to relabel extra channels (X1...X10, PG1, PG2) for the use of EOG, EKG and respiratory (Rsp) channels. Use an ''Additional Channels'' file to define horizontal and vertical EOG channels by using the appropriate electrodes in a bipolar montage (an example is provided in '''eog-ecg.mtg''' in ''Montages\AdditionalChannels''). Differentially recorded EKG and respiratory channel can be defined in the same file.

== Patterns ==

'''Default settings provided for section [Patterns]:'''

These settings define labels for each of the five patterns. The labels are shown* in the''' Tags''' menu,
* in the '''TAG push-button''' popup menu, and
* when displaying tag info clicking with the right mouse on a tag at the bottom of the EEG or on the event bar.

By default, no labels are defined. Define a label, e.g. for Pattern1 and Pattern2, as in the following example:

Pattern1=Spike

Pattern2=Sharp Wave

== Artifacts ==

'''Artifact default settings:'''

See the chapter "''Artifact Correction / Reference / Artifact settings in the BESA.ini file''" in the online help.

== Search ==

Default settings for pattern search.

'''Default Settings for the ''Search/Options ''Dialog box:'''

'''CorrelationThreshold''' = '''75%'''

'''AmplitudeThreshold = 100 µV'''

'''GradientThreshold = 25'''

'''Default Settings for the ''Search/Average/View'' (SAV) Dialog box:'''

'''PreCursor = -250 ms'''

'''PostCursor = 150 ms'''

'''HighPassFreq = 2 Hz'''

'''HighPassSlope = 12 dB/Octave'''

'''HighPassType = 0 (0 = zero phase, 1 = forward, 2 = backward'''

'''LowPassFreq = 35 Hz'''

'''LowPassSlope = 24 dB/Octave'''

'''LowPassType = 0 (0 = zero phase, 1 = forward, 2 = backward)'''

'''CorrelationThresholdNoMarked = 60%'''

Default correlation threshold if no channel labels are marked when the SAV Dialog is opened.

'''CorrelationThresholdOneMarked = 85%'''

Default correlation threshold if one channel label is marked when the SAV Dialog is opened.

'''CorrelationThresholdFourMarked = 65%'''

Default correlation threshold if between two channel labels are marked when the SAV Dialog is opened.

'''SelectedViewWindowWidthMultiplier = 300%'''

'''WriteAfterSearch = No'''

If set to "Yes", a File Save dialog will open, to allow to save the search average to a file (as with the SAW function).

'''WriteAfterSearchCheckBox = No'''

If set to "Yes", an additional checkbox "Write after search" is displayed at the bottom of the SAV Dialog, allowing to choose whether or not to write the search average after a search:

[[Image:ST Besa ini (1).gif ‎ ]]

'''PreserveDefaults = Yes'''

If set to "No", the SAV Dialog will open with the same boxes checked as the last time the dialog was opened during the current session.

If set to "Yes", the default frequency, buffer width, selected view after search, and default threshold are always checked when the dialog is opened.

== KeyControls ==

In the [KeyControls] section you can specify functions that can be allocated to '''function keys''' or to the ''Del'' key. Specify using the form:

'''Fn=function''' or

'''Del=function'''

where "''n''" is a number between 2 and 12 (F1 is reserved for Help). For example:

    F2 = Batch1

Possible functions are:

'''Setting or removing events:'''

'''Pattern''n''''', where ''n''<nowiki>=1-5: Sets the tag number </nowiki>''n'' at the cursor latency.

'''Epochfast:''' sets one boundary of an epoch at the cursor latency, but does not open the epoch text box to define a label.

'''Marker:'''  sets a marker at the cursor latency.

'''Comment:''' sets a comment at the cursor latency and opens the comment box to enter text.

'''Epoch:''' sets one boundary of an epoch at the cursor latency and opens the epoch text box to enter a label.

'''Artifact:''' sets one boundary of an artifact segment at the cursor latency.

'''Delete:'''  deletes a tag at the cursor latency

'''Batches and Montages:'''

'''Batch''n''''', where n=1-12: Runs a predefined batch file corresponding to the number ''n''.

<div style="margin-left:0.953cm;margin-right:0cm;">If a key has not yet been associated with a batch, pressing it will open a ''File Open Dialog'' to select a batch. The setting you have chosen will be retained across BESA Research sessions. Holding the '''<shift>''' key while pressing the '''function key''' will always open the dialog. Hold the''' <ctrl> '''key with the function key to open the associated batch in the batch edit dialog.</div>

'''Montage''n''''', where n=1-12: Sets a montage corresponding to the number'' n''.

<div style="margin-left:0.953cm;margin-right:0cm;">If a key has not yet been associated with a montage, pressing it will generate a message asking you to associate a montage as follows: Holding the '''<shift> '''key while pressing the '''function key''' will remove the current association, and substitute it with the current montage.</div>

The default settings after program installation are listed in the online help chapter ''Review / Reference / Controls / Mouse and Keyboard / Keyboard Controls''.

== FFT ==

'''Default settings provided for section [FFT]:'''

These settings define the setup in the Spectral Analysis section of the BESA Research program (FFT window, see the chapter "''Spectral Analysis / FFT''"). Up to 7 frequency bands may be defined. Five are defined by default.

'''FFTBand1=On''' FFT Bands 1-5 are defined

'''FFTBand2=On'''

'''FFTBand3=On'''

'''FFTBand4=On'''

'''FFTBand5=On'''

'''FFTBand6=Off''' FFT Bands 6-7 are not defined

'''FFTBand7=Off'''

'''FFTNameBand1=Delta''' Names of the defined bands

'''FFTNameBand2=Theta'''

'''FFTNameBand3=Alpha'''

'''FFTNameBand4=Beta'''

'''FFTNameBand5=Gamma'''

'''FFTColorBand1=RGB(0,0,0)'''  Default color of each band

'''FFTColorBand2=RGB(0,128,64)'''

'''FFTColorBand3=RGB(128,0,0)'''

'''FFTColorBand4=RGB(255,0,0)'''

'''FFTColorBand5=RGB(255,128,0)'''

'''FFTColorBand6=RGB(255,192,0)'''

'''FFTColorBand7=RGB(255,255,0)'''

'''FFTLowBand1=1''' Delta from 1-4 Hz

'''FFTHighBand1=4'''

'''FFTLowBand2=4''' Theta from 4-8 Hz

'''FFTHighBand2=8'''

'''FFTLowBand3=8''' Alpha from 8-14 Hz

'''FFTHighBand3=14'''

'''FFTLowBand4=14''' Beta from 14-30 Hz

'''FFTHighBand4=30'''

'''FFTLowBand5=30''' Gamma from 30-50 Hz

'''FFTHighBand5=50'''

These values are best set from within BESA Research, using the '''Options''' menu in the FFT window (see the chapter "''Spectral Analysis / FFT / FFT Options Menu''"). Current settings are stored after each session and retrieved in the next session.

== Printer ==

'''Default settings provided for section [Printer]:'''

'''PrinterMarginPercent=100''' controls size of printout

'''PrinterColors=256''' set to 1/2 for black&white, 0/256 for color printers

'''PrinterLineMode=1''' set to 2 for thicker lines and to save printer memory

'''PrinterMapResolution=1''' set to 2, 3, 4 to save printer memory and increase speed

== Calibration ==

'''Default settings provided for section [Calibration]:'''

'''AutoCalibration=Off''' On: automatic calibration of signals >= 4 cycles

'''MicrovoltCalibration=50''' peak voltage of calibration signal

If calibration is set to'' On'', the menu item ''Calibration ''will appear in the''' Process '''menu. Position your current screen at an epoch containing at least 4 regular cycles of the calibration signal (in all channels!) and select Calibration.

== Video ==

'''Default settings provided for section [Video]:'''

'''DVCFilePath=C:\DVC\DVPlay.exe''' holds the path to the digital video player

'''DVCCommandLineArguments=/S:3 /M:P /T:M'''  arguments to be passed to the digital video player

'''CursorPagingOffsetLeft=0.2  '''

'''CursorPagingOffsetRight=0.8'''

'''CursorMinDistToBorderBeforePaging=0.02'''

'''PageDisplayIfCursorIsBelowVideo=1'''

'''MappingRepetitionRateWithVideoInMS=100'''  gives the number of milliseconds between two maps if the mapping window is open while the video is running. If the graphics board encounters problems during the display, this value should be increased.

== Mapping ==

'''Default settings provided for section [Mapping]:'''

'''UseBitmapDrawing=Off'''

Set this to "On" if 3D maps show a strange pattern of black triangular shapes (this is frequently observed with modern Intel On-Board graphics controllers, and is a result of inadequate drivers for Open-GL).

'''Use3DVBlending=Auto'''

Set this to "Off" if the 3D view in the Montage Editor or the Source Analysis window does not show up properly (this may happen with some older graphics cards).

Set this to "On" if the 3D view in the Montage Editor or the Source Analysis window shows a ragged surface boundary.

'''MapSmoothing=0 '''

Set a non-zero value to specify a default map smoothing parameter (normally specified in ''Options/Mapping/Spline Interpolation Smoothing Constant'').

== Matlab ==

'''Default settings for the [Matlab] section:'''

'''Platform=32'''

'''Set Platform=64''' if you want to use the 64-bit version of Matlab

== Updates ==

This section is not normally required, but the variables here can be altered or defined to determine how BESA Research checks for dongle and program updates.

'''DaysBetweenUpdateChecks=7'''

Sets the number of days between automatic checks for updates. Set the value to 0 to check every time BESA Research is started. Set to -1 to turn off automatic update checks.

'''CheckNetworkDongle=Off'''

For the network administrator: If set to "On", BESA Research will check the dongle on the network for updates. Otherwise the state of the network dongle will be ignored.

'''LocalPath'''

For the network administrator. This can be set to a path on the local network to the BESA update files, so that users can obtain their updates locally. The path is given to the text file "'''UpdateVersions.txt'''" (e.g. ''LocalPath=\\transtec-sak\zarascratch\BESA\Updates\UpdateVersions.txt''), which contains further details for the program to obtain its updates. If you want to use this feature, please contact us at [mailto:support@besa.de support@besa.de].

The following variables are not required, because BESA Research has the paths hardwired:

'''FTP1 (also FTP2, FTP3)'''

ftp download server

'''Path1 (also Path2, Path3)'''

Path on the server to UpdateVersions.txt.

'''HaspPath1 (also HaspPath2, HaspPath3)'''

Path on the server to HASP (dongle) update files.

'''History'''

Path on the server to general history file

== FMRI ==

These settings define the default parameters for the fMRI artifact removal in the BESA Research (see fMRI artifact removal chapter for
further details).

For example:

[FMRI]

FMRIRemovalMode=1

TRDelay=200

TRLength=800

NumberOfAverages=21

fMRImoveThreshold=0.15

FMRITRID=8015

ScansToSkip=0

These values indicate:

'''FMRIRemovalMode''' ''Removal method (0: Turned off; 1: Allen et al, 2000; 2: Allen et al., 2000 Modified; 3: Moosmann et al.,2003)''

'''TRDelay''' ''Delay between marker and start of volume acquisition [ms]''

'''NumberOfAverages''' ''Number of artifact occurrence averages''

'''fMRImoveThreshold''' ''Movement threshold [mm]''

'''FMRITRID''' ''fMRI Trigger code''

'''ScansToSkip''' ''Number of scans to skip''

== Reader-Specific Settings ==

=== BrainLab ===

'''Default settings provided for section [BrainLab]:'''

'''BrainLabFormat=New''' this entry ensures that the newer BrainLab file format can be read by BESA Research.

=== Bio-Logic ===

'''FileSelect=Yes'''

If there are several Bio-Logic files in a data folder, the reader can check if the files have the same settings. There are three possible options:

* Open a dialog to ask if the files should be treated as a single data set, or as individual, separate files.

[[Image:ST Besa ini (2).jpg ‎]]

<div style="margin-left:0.953cm;margin-right:0cm;">in this case, use '''FileSelect=Yes''' (this is the default setting) Note that the choice made in the dialog will apply to the file(s) within a BESA Research session. For a given file and session, the dialog will only be opened once, even if the file is closed and reopened.</div>

* Always concatenate such files into a single data set. In this case use '''FileSelect=All'''
* Always open the files as single, separate files. In this case use '''FileSelect=Single'''

=== EDF+/BDF/Trackit ===

'''TriggerScan=On'''

Set '''TriggerScan=Off '''to prevent BESA Research from scanning the file for triggers. This is done separately for EDF+, BDF, and Trackit files in sections '''[EDF+], [BDF],''' and '''[Trackit]''' in the '''BESA.ini''' file.

=== EGI ===

The treatment of DIN events can be modified in the''' [EGI] '''section:

'''CombineDINevents'''<nowiki>=yes/no    (default is “yes”)</nowiki>

Set to “no” if you want to treat DIN events separately, and not generate combined values.

'''SeparateDINevents'''<nowiki>=yes/no    (default is “yes”)</nowiki>

Set to “no” if you don’t want to treat DIN events separately.

Thus, using the above two parameters, you can choose whether you want to treat DIN events as combined, separate, both, or completely ignored.

'''CombineDINeventsPrefix'''<nowiki>=dinComb</nowiki>

<div style="margin-left:0.953cm;margin-right:0cm;">This defines the text preceding the number when DIN events are combined. The default is “dinComb”.</div>

=== Harmonie ===

'''Default settings provided for section [Harmonie] (Stellate Harmonie systems):'''

'''SeizurePreEpoch=60''' length of the epoch preceding a seizure detection in s

'''SeizurePostEpoch=60''' length of the epoch following a seizure detection in s

'''PushButtonPreEpoch=60''' length of the epoch preceding a push button detection

'''PushButtonPostEpoch=60''' length of the epoch following a push button detection

When BESA Research encounters a seizure detection event or a push button detection event in a Stellate Harmonie file, it automatically sets an epoch around the event, which makes it convenient to view just those epochs for analysis. The length of the epochs preceding and following the events can be adjusted in the '''.ini''' file.

=== Neuroscan Keys ===

'''Note that there is a setting "NeuroScanDataNumberOfBits" in the [Defaults] section of BESA.ini that is used for distinguishing the data format of Neuroscan files (16 or 32-bit).'''

'''Default settings provided for section [NeuroScan Keys] (NeuroScan systems):'''

Event1=Movement Text corresponding to keyboard events 1 through 10

Event2=Blink

Event3=Talking

Event4=Cough

Event5=Muscle

Event6=Jaw

Event7=Sneeze

Event8=Swallow

Event9=Eye movement

Event10=Hiccup

=== NKT2100 ===

'''Default settings provided for section [NKT2100] (Nihon Kohden EEG 21xx systems):'''

'''TriggerScan=On'''   Set to "Off" to prevent a scan for trigger events.

'''Country=NotKanji''' set to NotKanji for non-Kanji characters else to Kanji

'''KanjiCharSize=16''' Kanji character size

'''KanjiPrinterCharSize=32''' Kanji printer character size

'''EEG_Sensitivity=50''' default sensitivity of Nihon Kohden EEG-2100 system

'''DC_Sensitivity=50''' default sensitivity of Nihon Kohden DAE-2100 system

'''QJ_Sensitivity=100''' default sensitivity of Nihon Kohden QJ-403 system

'''Mark_Sensitivity=100''' default sensitivity of EEG-2100 marker channels

These settings need to be changed only if the manufacturer has specified different gains for your system. Otherwise do not alter these settings.

=== Vangard ===

'''AlwaysOpenFileSelect=Yes'''

If "Yes" is selected, each time a Vangard file is opened, a dialog box will open, asking for a selection of the segment type to display.

If "No" is selected, the selection dialog is opened whenever a Vangard file is opened for the first time, or if the ''Channel and digitized head surface point information dialog box'' is opened (e.g. with '''ctrl-L''' or ''File/Head Surface Points and Sensors/Load Coordinate Files...'' ).

=== XLTEK ===

'''TriggerScan=Off '''Set to "On" to scan the data file for trigger events

'''MontageNo=2''' Set to 1 or 2. If two montages for the data file are defined, this variable determines whether the first or the second alternative should be used.

[[Category:Research Manual]]

{{BESAManualNav}}

The Initialization File: BESA.ini

2019-03-27T13:44:15Z

Jamie: /* Updates */

{{BESAInfobox
|title = Module information
|module = BESA Research Basic or higher
|version = 6.1 or higher
}}

== Introduction ==

'''BESA.ini File'''

BESA Research uses settings provided in the initialization file '''BESA.ini''' whenever BESA Research is started or a new file is opened for the first time. The format of this file conforms with standard initialization files ('''<nowiki>*.ini</nowiki>''') of Windows. You may change the settings in '''BESA.ini''' using NOTEPAD.exe from the ACCESSORIES group, or other plain text editors to adapt BESA Research to '''your own everyday needs'''. The default settings provided in '''BESA.ini''' will be used by BESA Research whenever BESA Research or the launch program is started. It is advised that you make a backup copy of '''BESA.ini''' before you change the default settings.

'''Location of BESA.ini'''

You can place '''BESA.ini''' at three possible locations:

# '''Private''': each user on a PC should have his/her own private settings. This is normally in ''My Documents/BESA/Research_6_1''
# '''Public''': all users should use one setting, but they can edit '''BESA.ini''' to change the settings. This is normally in ''Public Documents/BESA/Research_6_1''
# '''Administrator''': the PC administrator determines the settings. This is normally in ''C:Program Files(x86)/BESA/Research_6_1''

The actual folder names depend on the operating system and the system language.

When BESA starts, it first looks for the '''administrator''' version of '''BESA.ini'''. If this is not found, it looks for the '''private''' version. If this is not found, it looks for the '''public''' version. If this is not found, internal default values are used.

'''There are 13 general sections, and several reader-specific sections:'''

[Defaults]                    General settings (filters, scaling, and various other settings)

[Folders]                     Folders used by BESA Research (Examples, Montages, Scripts, Settings,...)

[Electrodes]                Electrode renaming

[Patterns]                   Rename patterns in the '''Tags''' menu

[Artifacts]                   Settings for artifact correction

[KEYCONTROLS]      Function key definitions

[Search]                     Default parameters for search

[FFT]                           Frequency band definitions

[Printer]                      Printer control

[Calibration]              Calibration control

[Video]                       Digital video control

[Mapping]                  Mapping control

[Updates]                   Options for program updates

[Matlab]                      Settings for the Matlab interface

[fMRI]                   Settings for the fMRI arfifact removal

[Montages]                   A setting for a default source montage

'''Reader-specific settings'''

[BrainLab]

[Bio-Logic]

[EDF+] [BDF] [Trackit]

[EGI]

[Harmonie]

[NeuroScan Keys]

[NKT2100]

[Vangard]

[XLTEK]

== Defaults ==

'''Default settings provided for section [Defaults]:'''

'''DatabaseAllowLocalFiles=Yes''' (If set to "Yes", BESA Research will write filenames "'''datafilename.ftg'''" and "'''datafilename.fst"''' to the data folder, saving current file tag and display settings there. If set to "No", these files are only written to the database. If set to "Yes", you can copy these files along with the data to a new folder, and display settings and tags will be preserved.)

'''DataBuffering=Off''' (If set to "On", an internal buffer of length 180 s of data is kept to speed up paging). This can speed up paging, particularly when the data are in a network folder.

'''DisplayedTime=10''' displayed time window [s] on the screen

'''Montage=Org''' montage used when opening a new file

'''ScpScale=50''' scale of scalp channels in [mV]

'''PgrScale=500''' scale of polygraphic channels in [mV]

'''IcrScale=500''' scale of intracranial channels in [mV]

'''MegScale=500''' scale of MEG/marker channels in [fT]

'''SrcScale=100''' scale of source of source montages

'''BaselineCorrection=On''' baseline correction, do not switch off in AC systems

'''ClippingPercent= '''set from 100 to 200 if you want to clip artifacts in displayed EEG (not used if empty or 0)

'''LowFilter=''' low filter cutoff frequency [Hz] (variable filter)

'''TimeConstant=0.3''' time constant for low filter cutoff frequency [sec] (fixed forward filter, 0.3 sec is equivalent to 0.53 Hz)

'''HighFilter=70''' high filter cutoff frequency [Hz] (variable filter)

'''NotchFilter=50''' notch filter center frequency [Hz]

'''NotchFilterStatus=Off''' notch filter is off, set=On if you want to use as default

'''BandFilter=12''' band pass filter center frequency [Hz]

'''BandFilterStatus=Off''' band pass is off, set=On if you want to use as default

'''AdditionalChannelFile=''' defines the full path and name of an additional channels montage file, e.g. '''C:\Program Files\BESA\Research_x\Montages\AdditionalChannels\EKG.sel'''

'''ColoredWaveforms=On''' scalp waveforms are (not) colored according to region

'''WriteSegmentPath=''' defines default path for saving segments/averages. If blank, the path of the current data file is used.

'''ShowSubjectInfo=Off''' subject info will (not) be displayed.

The following optional parameters are not defined as default and can be set manually in''' BESA.ini''':

'''TextEditor="Notepad.exe"''' defines the path to your preferred text editor. This will be used when you press the '''Edit''' button the ''Load Coordinate Files dialog box''.

'''NeuroScanDataNumberOfBits=32''' defines the format of NeuroScan data files ('16' for 16-bit, '32' for 32-bit). If this variable is not specified, BESA uses a heuristic to (try to) decide which of the two data formats is used. This variable overrides the heuristic. If you want to specify the NeuroScan data format for specific files, create a file, named "16bit" or "32bit", and place it in the data folder.

'''ScaleAmplitudesForNNChannels=25''' Scale waveforms as if a fixed number of channels were displayed in the window (here: 25). A minimum of 10 channels can be used for the scaling. This parameter is superseded if the parameter "''ScaleAmplitudesFixedPixelHeight"'' is specified.

'''ScaleAmplitudesFixedPixelHeight=70''' Set the scale bar for amplitudes to a fixed pixel height (here: 70). If this parameter is set in the '''.ini''' file, it supersedes the parameter "''ScaleAmplitudesForNNChannels''".

'''Notes'''

Check the Menu descriptions for the various definitions of filters, montages etc. For montage preselection, use the labels as visible on the montage push-buttons.

The additional channels file should contain all polygraphic channels (e.g. EKG, EOG, respiratory) that you want to view regularly along with the scalp channels. The entry AdditionalChannelFile must specify the full path pointing to the location of additional channel files (recommended: ''Montages\AdditionalChannels''). If no drive is specified, the installation drive of BESA is used.

If BaselineCorrection is set to 'On', before displaying a screen of data, BESA subtracts for each channel the mean over its displayed time points. This optimizes viewing, because it ensures that the vertical position of each channel is not shifted upward or downward from the channel label at the left of the screen. There are some cases in which you will not want baseline correction, i.e. when the DC level in the data is already correctly defined. This is usually the case, for instance, when reading in files that have been processed by BESA. In this case, BaselineCorrection should be set to 'Off', because otherwise maps and source montage displays may be distorted.

== Folders ==

'''The [Folders] section defines where BESA Research places its files. In versions 5.1 and earlier, files were located in various subfolders of the program folder. This led to problems if the user did not have administrator rights, e.g. to create or write to a file. For compatibility with Windows 7 and higher versions, many folders are now located by default in locations where normal users can create and write files. If you wish, you can also specify paths in the [Folders] section to use the previous locations. The previous location is given for each variable.'''

These settings allow some flexibility that can be useful if you want to tune BESA Research for use by several users, or on a network. For instance, the Examples and Montages folders might be located on a network disk. For the current defaults, the database, Examples, Montages, and Scripts are set up for use by all users on the PC on which BESA Research is installed. The settings files ('''Besa.set''', '''Besa.cfg''', etc.) are located in private folders so that each user retains his or her own settings.

The '''default''' settings (i.e. settings that BESA Research uses if the entries are omitted in the '''.ini''' file) are shown for each variable definition.

The folder definitions can use '''placeholders''', labels enclosed by a % sign (e.g. %localapp%), to define paths that vary depending on the language version and on the Windows system. These are defined below.

'''The Variables'''

'''Database=%localapp%''' The path of the BESA Research database folder (used to be ''%progdir%System\DB'' in BESA versions up to 5.1.x). Unless the provided path ends with ''\DB'' or ''\Database'', BESA Research will automatically create a folder named ''Database'' in the provided path.

'''Settings=%privatprog%Settings''' The path of the BESA Research settings folder (used to be ''%progdir%System'' in BESA versions up to 5.1.x)

'''Montages=%publicprog%Montages''' The path of the BESA Research montages folder (used to be ''%progdir%Montages'' in BESA versions up to 5.1.x)

'''Scripts=%publicprog%Scripts''' The path of the BESA Research Scripts folder (used to be ''%progdir%Scripts'' in BESA versions up to 5.1.x)

'''Examples=%publicprog%Examples''' The path of the BESA Research Examples folder (used to be ''%progdir%Examples'' in BESA versions up to 5.1.x)

'''User=%privatprog%Settings''' The path for user defined settings (used to be ''%progdir%System\Userdirs'' in BESA versions up to 5.1.x)

'''Placeholders'''

The strings enclosed by percent signs (%) are placeholders for the following folders in English-language versions of Windows. Folder names differ depending on Windows version, and for other language settings. BESA Research will substitute the placeholders by the appropriate folder name for the system and the system language:

* '''Windows 7 and higher (English):'''

'''%localapp%''' = "''C:\Users\[user]\AppData\Local\BESA\Research_6_1''", where [user] is the logon name of the current user. This folder is directly accessible from the Desktop as "''Desktop\[user]\AppData\Local\BESA\Research_6_1''".

'''%publicprog%''' = "''C:\Users\Public\Public Documents\BESA\Research_6_1''". This folder is directly accessible from the Windows Explorer under "''Libraries\Documents\Public'' ''Documents\BESA\Research_6_1''".

'''%privateprog%''' = "''C:\Users\[user]\Documents\BESA\Research_6_1''", where [user] is the logon name of the current user. This folder is directly accessible from the Windows Explorer as "''Libraries\Documents\My'' ''Documents\Research_6_1''" or "''Desktop\[User]\My Documents\BESA\Research_6_1''.

'''%progdir%''' = the BESA Research root folder. In a default installation, this is "''C:\Program'' ''Files\BESA\Research_6_1''".

'''%besaroot%''' is the same as '''%progdir%'''

* '''Windows Vista (English'''):

'''%localapp% '''<nowiki>= "</nowiki>''C:\Users\[user]\AppData\Local\BESA\Research_6_1''", where [user] is the logon name of the current user. This folder is directly accessible from the Windows Explorer as "''Desktop\[user]\AppData\Local\BESA\Research_6_1''".

'''%publicprog%''' = "''C:\Users\Public\Public Documents\BESA\Research_6_1''". This folder is directly accessible from the Windows Explorer under "''Desktop\Public\Public Documents\BESA\Research_6_1''".

'''%privateprog%''' = "''C:\Users\[user]\Documents\BESA\Research_6_1''", where [user] is the logon name of the current user. This folder is directly accessible from the Windows Explorer as "''Desktop\[user]\Documents\BESA\Research_6_1''".

'''%progdir%''' = the BESA Research root folder. In a default installation, this is "''C:\Program'' ''Files\BESA\Research_6_1''".

'''%besaroot%''' is the same as '''%progdir%'''  

* '''Windows XP (English) (note: not supported by BESA Research 6.1 and higher):'''

'''%localapp% '''<nowiki>= "</nowiki>''C:\Documents and Settings\[user]\Local Settings\Application Data\BESA\Research_6_0''", where [user] is the logon name of the current user.

'''%publicprog%''' = "''C:\Documents and Settings\All Users\Documents\BESA\Research_6_0". ''This folder is directly accessible from the Windows Explorer under "''My Computer\Shared'' ''Documents\BESA\Research_6_0''".

'''%privateprog%''' = "''C:\Documents and Settings\[user]\My Documents\BESA\Research_6_0''", where [user] is the logon name of the current user. This folder is directly accessible from the Windows Explorer as "''My Documents\BESA\Research_6_0''".

'''%progdir%''' = the BESA Research root folder. In a default installation, this is "''C:\Program'' ''Files\BESA\Research_6_0''".

'''%besaroot%''' is the same as '''%progdir%  '''

* '''Windows 2000 (English) (note: not supported by BESA Research 6.1 and higher):'''

'''%localapp%''' = "''C:\Documents and Settings\[user]\Local Settings\Application Data\BESA\Research_6_0''", where [user] is the logon name of the current user.

'''%publicprog%''' = "''C:\Documents and Settings\All Users\Documents\BESA\Research_6_0''".

'''%privateprog%''' = "''C:\Documents and Settings\[user]\My Documents\BESA\Research_6_0''", where [user] is the logon name of the current user. This folder is directly accessible from the Windows Explorer '''as "'''''My Documents\BESA\Research_6_0'''''". '''

'''%progdir%''' = the BESA Research root folder. In a default installation, this is "''C:\Program'' ''Files\BESA\\Research_6_0''".

'''%besaroot%''' is the same as '''%progdir%'''

== Electrodes ==

'''This section allows for automatic relabeling of electrodes. For instance, the 10-20 label "T3" can be replaced by the 10-10 convention "T7".'''

'''Default settings provided for section [Electrodes]:'''

T7=T3 replace 10-10 label with old 10-20 convention

T8=T4 replace 10-10 label with old 10-20 convention

P7=T5 replace 10-10 label with old 10-20 convention

P8=T6 replace 10-10 label with old 10-20 convention

X1=ECG1 define X1 channel to be ECG1

X2=ECG2 define X2 channel to be ECG2

Other examples, depending on your electrode input box definition, could be:

PG1=LO1 define X3 as lateral orbital eye electrode left

PG2=LO2 bipolar LO1-LO2 defines horizontal EOG (additional channel)

X3=IO1 infraorbital, e.g. use with FP1 as additional channel for VEOG

X9=Rsp define X9 channel to be a respiratory channel

Relabeling of channel names (as stored in the EEG file header) is helpful to predefine your standard sequence of channels and to avoid the need for reading and/or editing a Channel Configuration file for every EEG file.

'''Note 1''': For polygraphic channels, or if your EKG has been recorded differentially, you should edit and define an ''Additional Channels Montage'' according to your recording channel configuration (e.g. Fp1-IO1=vertical EOG). The Additional Channels group permits to display these channels regularly below the scalp montages with individual scales.

'''Note 2''': EOG channels record both eye and scalp activity. In digital EEG systems, EOG electrodes should be labeled according to their position in the 10-10 system (see "''Electrode Conventions''"). This permits use of these electrodes for mapping and suppression of eye artifacts. The standard definitions above give an example of how to relabel extra channels (X1...X10, PG1, PG2) for the use of EOG, EKG and respiratory (Rsp) channels. Use an ''Additional Channels'' file to define horizontal and vertical EOG channels by using the appropriate electrodes in a bipolar montage (an example is provided in '''eog-ecg.mtg''' in ''Montages\AdditionalChannels''). Differentially recorded EKG and respiratory channel can be defined in the same file.

== Patterns ==

'''Default settings provided for section [Patterns]:'''

These settings define labels for each of the five patterns. The labels are shown* in the''' Tags''' menu,
* in the '''TAG push-button''' popup menu, and
* when displaying tag info clicking with the right mouse on a tag at the bottom of the EEG or on the event bar.

By default, no labels are defined. Define a label, e.g. for Pattern1 and Pattern2, as in the following example:

Pattern1=Spike

Pattern2=Sharp Wave

== Artifacts ==

'''Artifact default settings:'''

See the chapter "''Artifact Correction / Reference / Artifact settings in the BESA.ini file''" in the online help.

== Search ==

Default settings for pattern search.

'''Default Settings for the ''Search/Options ''Dialog box:'''

'''CorrelationThreshold''' = '''75%'''

'''AmplitudeThreshold = 100 µV'''

'''GradientThreshold = 25'''

'''Default Settings for the ''Search/Average/View'' (SAV) Dialog box:'''

'''PreCursor = -250 ms'''

'''PostCursor = 150 ms'''

'''HighPassFreq = 2 Hz'''

'''HighPassSlope = 12 dB/Octave'''

'''HighPassType = 0 (0 = zero phase, 1 = forward, 2 = backward'''

'''LowPassFreq = 35 Hz'''

'''LowPassSlope = 24 dB/Octave'''

'''LowPassType = 0 (0 = zero phase, 1 = forward, 2 = backward)'''

'''CorrelationThresholdNoMarked = 60%'''

Default correlation threshold if no channel labels are marked when the SAV Dialog is opened.

'''CorrelationThresholdOneMarked = 85%'''

Default correlation threshold if one channel label is marked when the SAV Dialog is opened.

'''CorrelationThresholdFourMarked = 65%'''

Default correlation threshold if between two channel labels are marked when the SAV Dialog is opened.

'''SelectedViewWindowWidthMultiplier = 300%'''

'''WriteAfterSearch = No'''

If set to "Yes", a File Save dialog will open, to allow to save the search average to a file (as with the SAW function).

'''WriteAfterSearchCheckBox = No'''

If set to "Yes", an additional checkbox "Write after search" is displayed at the bottom of the SAV Dialog, allowing to choose whether or not to write the search average after a search:

[[Image:ST Besa ini (1).gif ‎ ]]

'''PreserveDefaults = Yes'''

If set to "No", the SAV Dialog will open with the same boxes checked as the last time the dialog was opened during the current session.

If set to "Yes", the default frequency, buffer width, selected view after search, and default threshold are always checked when the dialog is opened.

== KeyControls ==

In the [KeyControls] section you can specify functions that can be allocated to '''function keys''' or to the ''Del'' key. Specify using the form:

'''Fn=function''' or

'''Del=function'''

where "''n''" is a number between 2 and 12 (F1 is reserved for Help). For example:

    F2 = Batch1

Possible functions are:

'''Setting or removing events:'''

'''Pattern''n''''', where ''n''<nowiki>=1-5: Sets the tag number </nowiki>''n'' at the cursor latency.

'''Epochfast:''' sets one boundary of an epoch at the cursor latency, but does not open the epoch text box to define a label.

'''Marker:'''  sets a marker at the cursor latency.

'''Comment:''' sets a comment at the cursor latency and opens the comment box to enter text.

'''Epoch:''' sets one boundary of an epoch at the cursor latency and opens the epoch text box to enter a label.

'''Artifact:''' sets one boundary of an artifact segment at the cursor latency.

'''Delete:'''  deletes a tag at the cursor latency

'''Batches and Montages:'''

'''Batch''n''''', where n=1-12: Runs a predefined batch file corresponding to the number ''n''.

<div style="margin-left:0.953cm;margin-right:0cm;">If a key has not yet been associated with a batch, pressing it will open a ''File Open Dialog'' to select a batch. The setting you have chosen will be retained across BESA Research sessions. Holding the '''<shift>''' key while pressing the '''function key''' will always open the dialog. Hold the''' <ctrl> '''key with the function key to open the associated batch in the batch edit dialog.</div>

'''Montage''n''''', where n=1-12: Sets a montage corresponding to the number'' n''.

<div style="margin-left:0.953cm;margin-right:0cm;">If a key has not yet been associated with a montage, pressing it will generate a message asking you to associate a montage as follows: Holding the '''<shift> '''key while pressing the '''function key''' will remove the current association, and substitute it with the current montage.</div>

The default settings after program installation are listed in the online help chapter ''Review / Reference / Controls / Mouse and Keyboard / Keyboard Controls''.

== FFT ==

'''Default settings provided for section [FFT]:'''

These settings define the setup in the Spectral Analysis section of the BESA Research program (FFT window, see the chapter "''Spectral Analysis / FFT''"). Up to 7 frequency bands may be defined. Five are defined by default.

'''FFTBand1=On''' FFT Bands 1-5 are defined

'''FFTBand2=On'''

'''FFTBand3=On'''

'''FFTBand4=On'''

'''FFTBand5=On'''

'''FFTBand6=Off''' FFT Bands 6-7 are not defined

'''FFTBand7=Off'''

'''FFTNameBand1=Delta''' Names of the defined bands

'''FFTNameBand2=Theta'''

'''FFTNameBand3=Alpha'''

'''FFTNameBand4=Beta'''

'''FFTNameBand5=Gamma'''

'''FFTColorBand1=RGB(0,0,0)'''  Default color of each band

'''FFTColorBand2=RGB(0,128,64)'''

'''FFTColorBand3=RGB(128,0,0)'''

'''FFTColorBand4=RGB(255,0,0)'''

'''FFTColorBand5=RGB(255,128,0)'''

'''FFTColorBand6=RGB(255,192,0)'''

'''FFTColorBand7=RGB(255,255,0)'''

'''FFTLowBand1=1''' Delta from 1-4 Hz

'''FFTHighBand1=4'''

'''FFTLowBand2=4''' Theta from 4-8 Hz

'''FFTHighBand2=8'''

'''FFTLowBand3=8''' Alpha from 8-14 Hz

'''FFTHighBand3=14'''

'''FFTLowBand4=14''' Beta from 14-30 Hz

'''FFTHighBand4=30'''

'''FFTLowBand5=30''' Gamma from 30-50 Hz

'''FFTHighBand5=50'''

These values are best set from within BESA Research, using the '''Options''' menu in the FFT window (see the chapter "''Spectral Analysis / FFT / FFT Options Menu''"). Current settings are stored after each session and retrieved in the next session.

== Printer ==

'''Default settings provided for section [Printer]:'''

'''PrinterMarginPercent=100''' controls size of printout

'''PrinterColors=256''' set to 1/2 for black&white, 0/256 for color printers

'''PrinterLineMode=1''' set to 2 for thicker lines and to save printer memory

'''PrinterMapResolution=1''' set to 2, 3, 4 to save printer memory and increase speed

== Calibration ==

'''Default settings provided for section [Calibration]:'''

'''AutoCalibration=Off''' On: automatic calibration of signals >= 4 cycles

'''MicrovoltCalibration=50''' peak voltage of calibration signal

If calibration is set to'' On'', the menu item ''Calibration ''will appear in the''' Process '''menu. Position your current screen at an epoch containing at least 4 regular cycles of the calibration signal (in all channels!) and select Calibration.

== Video ==

'''Default settings provided for section [Video]:'''

'''DVCFilePath=C:\DVC\DVPlay.exe''' holds the path to the digital video player

'''DVCCommandLineArguments=/S:3 /M:P /T:M'''  arguments to be passed to the digital video player

'''CursorPagingOffsetLeft=0.2  '''

'''CursorPagingOffsetRight=0.8'''

'''CursorMinDistToBorderBeforePaging=0.02'''

'''PageDisplayIfCursorIsBelowVideo=1'''

'''MappingRepetitionRateWithVideoInMS=100'''  gives the number of milliseconds between two maps if the mapping window is open while the video is running. If the graphics board encounters problems during the display, this value should be increased.

== Mapping ==

'''Default settings provided for section [Mapping]:'''

'''UseBitmapDrawing=Off'''

Set this to "On" if 3D maps show a strange pattern of black triangular shapes (this is frequently observed with modern Intel On-Board graphics controllers, and is a result of inadequate drivers for Open-GL).

'''Use3DVBlending=Auto'''

Set this to "Off" if the 3D view in the Montage Editor or the Source Analysis window does not show up properly (this may happen with some older graphics cards).

Set this to "On" if the 3D view in the Montage Editor or the Source Analysis window shows a ragged surface boundary.

'''MapSmoothing=0 '''

Set a non-zero value to specify a default map smoothing parameter (normally specified in ''Options/Mapping/Spline Interpolation Smoothing Constant'').

== Matlab ==

'''Default settings for the [Matlab] section:'''

'''Platform=32'''

'''Set Platform=64''' if you want to use the 64-bit version of Matlab

== Updates ==

This section is not normally required, but the variables here can be altered or defined to determine how BESA Research checks for dongle and program updates.

'''DaysBetweenUpdateChecks=7'''

Sets the number of days between automatic checks for updates. Set the value to 0 to check every time BESA Research is started. Set to -1 to turn off automatic update checks.

'''CheckNetworkDongle=Off'''

For the network administrator: If set to "On", BESA Research will check the dongle on the network for updates. Otherwise the state of the network dongle will be ignored.

'''LocalPath'''

For the network administrator. This can be set to a path on the local network to the BESA update files, so that users can obtain their updates locally. The path is given to the text file "'''UpdateVersions.txt'''" (e.g. ''LocalPath=\\transtec-sak\zarascratch\BESA\Updates\UpdateVersions.txt''), which contains further details for the program to obtain its updates. If you want to use this feature, please contact us at [mailto:support@besa.de support@besa.de].

The following variables are not required, because BESA Research has the paths hardwired:

'''FTP1 (also FTP2, FTP3)'''

ftp download server

'''Path1 (also Path2, Path3)'''

Path on the server to UpdateVersions.txt.

'''HaspPath1 (also HaspPath2, HaspPath3)'''

Path on the server to HASP (dongle) update files.

'''History'''

Path on the server to general history file

== FMRI ==

These settings define the default parameters for the fMRI artifact removal in the BESA Research (see fMRI artifact removal chapter for
further details).

For example:

[FMRI]

FMRIRemovalMode=1

TRDelay=200

TRLength=800

NumberOfAverages=21

fMRImoveThreshold=0.15

FMRITRID=8015

ScansToSkip=0

These values indicate:

FMRIRemovalMode Removal method (0: Turned off; 1: Allen et al, 2000; 2: Allen et al., 2000 Modified; 3: Moosmann et al.,2003)

TRDelay Delay between marker and start of volume acquisition [ms]

NumberOfAverages Number of artifact occurrence averages

fMRImoveThreshold Movement threshold [mm]

FMRITRID fMRI Trigger code

ScansToSkip Number of scans to skip

== Reader-Specific Settings ==

=== BrainLab ===

'''Default settings provided for section [BrainLab]:'''

'''BrainLabFormat=New''' this entry ensures that the newer BrainLab file format can be read by BESA Research.

=== Bio-Logic ===

'''FileSelect=Yes'''

If there are several Bio-Logic files in a data folder, the reader can check if the files have the same settings. There are three possible options:

* Open a dialog to ask if the files should be treated as a single data set, or as individual, separate files.

[[Image:ST Besa ini (2).jpg ‎]]

<div style="margin-left:0.953cm;margin-right:0cm;">in this case, use '''FileSelect=Yes''' (this is the default setting) Note that the choice made in the dialog will apply to the file(s) within a BESA Research session. For a given file and session, the dialog will only be opened once, even if the file is closed and reopened.</div>

* Always concatenate such files into a single data set. In this case use '''FileSelect=All'''
* Always open the files as single, separate files. In this case use '''FileSelect=Single'''

=== EDF+/BDF/Trackit ===

'''TriggerScan=On'''

Set '''TriggerScan=Off '''to prevent BESA Research from scanning the file for triggers. This is done separately for EDF+, BDF, and Trackit files in sections '''[EDF+], [BDF],''' and '''[Trackit]''' in the '''BESA.ini''' file.

=== EGI ===

The treatment of DIN events can be modified in the''' [EGI] '''section:

'''CombineDINevents'''<nowiki>=yes/no    (default is “yes”)</nowiki>

Set to “no” if you want to treat DIN events separately, and not generate combined values.

'''SeparateDINevents'''<nowiki>=yes/no    (default is “yes”)</nowiki>

Set to “no” if you don’t want to treat DIN events separately.

Thus, using the above two parameters, you can choose whether you want to treat DIN events as combined, separate, both, or completely ignored.

'''CombineDINeventsPrefix'''<nowiki>=dinComb</nowiki>

<div style="margin-left:0.953cm;margin-right:0cm;">This defines the text preceding the number when DIN events are combined. The default is “dinComb”.</div>

=== Harmonie ===

'''Default settings provided for section [Harmonie] (Stellate Harmonie systems):'''

'''SeizurePreEpoch=60''' length of the epoch preceding a seizure detection in s

'''SeizurePostEpoch=60''' length of the epoch following a seizure detection in s

'''PushButtonPreEpoch=60''' length of the epoch preceding a push button detection

'''PushButtonPostEpoch=60''' length of the epoch following a push button detection

When BESA Research encounters a seizure detection event or a push button detection event in a Stellate Harmonie file, it automatically sets an epoch around the event, which makes it convenient to view just those epochs for analysis. The length of the epochs preceding and following the events can be adjusted in the '''.ini''' file.

=== Neuroscan Keys ===

'''Note that there is a setting "NeuroScanDataNumberOfBits" in the [Defaults] section of BESA.ini that is used for distinguishing the data format of Neuroscan files (16 or 32-bit).'''

'''Default settings provided for section [NeuroScan Keys] (NeuroScan systems):'''

Event1=Movement Text corresponding to keyboard events 1 through 10

Event2=Blink

Event3=Talking

Event4=Cough

Event5=Muscle

Event6=Jaw

Event7=Sneeze

Event8=Swallow

Event9=Eye movement

Event10=Hiccup

=== NKT2100 ===

'''Default settings provided for section [NKT2100] (Nihon Kohden EEG 21xx systems):'''

'''TriggerScan=On'''   Set to "Off" to prevent a scan for trigger events.

'''Country=NotKanji''' set to NotKanji for non-Kanji characters else to Kanji

'''KanjiCharSize=16''' Kanji character size

'''KanjiPrinterCharSize=32''' Kanji printer character size

'''EEG_Sensitivity=50''' default sensitivity of Nihon Kohden EEG-2100 system

'''DC_Sensitivity=50''' default sensitivity of Nihon Kohden DAE-2100 system

'''QJ_Sensitivity=100''' default sensitivity of Nihon Kohden QJ-403 system

'''Mark_Sensitivity=100''' default sensitivity of EEG-2100 marker channels

These settings need to be changed only if the manufacturer has specified different gains for your system. Otherwise do not alter these settings.

=== Vangard ===

'''AlwaysOpenFileSelect=Yes'''

If "Yes" is selected, each time a Vangard file is opened, a dialog box will open, asking for a selection of the segment type to display.

If "No" is selected, the selection dialog is opened whenever a Vangard file is opened for the first time, or if the ''Channel and digitized head surface point information dialog box'' is opened (e.g. with '''ctrl-L''' or ''File/Head Surface Points and Sensors/Load Coordinate Files...'' ).

=== XLTEK ===

'''TriggerScan=Off '''Set to "On" to scan the data file for trigger events

'''MontageNo=2''' Set to 1 or 2. If two montages for the data file are defined, this variable determines whether the first or the second alternative should be used.

[[Category:Research Manual]]

{{BESAManualNav}}

The Initialization File: BESA.ini

2019-03-27T13:29:46Z

Jamie: /* Defaults */

{{BESAInfobox
|title = Module information
|module = BESA Research Basic or higher
|version = 6.1 or higher
}}

== Introduction ==

'''BESA.ini File'''

BESA Research uses settings provided in the initialization file '''BESA.ini''' whenever BESA Research is started or a new file is opened for the first time. The format of this file conforms with standard initialization files ('''<nowiki>*.ini</nowiki>''') of Windows. You may change the settings in '''BESA.ini''' using NOTEPAD.exe from the ACCESSORIES group, or other plain text editors to adapt BESA Research to '''your own everyday needs'''. The default settings provided in '''BESA.ini''' will be used by BESA Research whenever BESA Research or the launch program is started. It is advised that you make a backup copy of '''BESA.ini''' before you change the default settings.

'''Location of BESA.ini'''

You can place '''BESA.ini''' at three possible locations:

# '''Private''': each user on a PC should have his/her own private settings. This is normally in ''My Documents/BESA/Research_6_1''
# '''Public''': all users should use one setting, but they can edit '''BESA.ini''' to change the settings. This is normally in ''Public Documents/BESA/Research_6_1''
# '''Administrator''': the PC administrator determines the settings. This is normally in ''C:Program Files(x86)/BESA/Research_6_1''

The actual folder names depend on the operating system and the system language.

When BESA starts, it first looks for the '''administrator''' version of '''BESA.ini'''. If this is not found, it looks for the '''private''' version. If this is not found, it looks for the '''public''' version. If this is not found, internal default values are used.

'''There are 13 general sections, and several reader-specific sections:'''

[Defaults]                    General settings (filters, scaling, and various other settings)

[Folders]                     Folders used by BESA Research (Examples, Montages, Scripts, Settings,...)

[Electrodes]                Electrode renaming

[Patterns]                   Rename patterns in the '''Tags''' menu

[Artifacts]                   Settings for artifact correction

[KEYCONTROLS]      Function key definitions

[Search]                     Default parameters for search

[FFT]                           Frequency band definitions

[Printer]                      Printer control

[Calibration]              Calibration control

[Video]                       Digital video control

[Mapping]                  Mapping control

[Updates]                   Options for program updates

[Matlab]                      Settings for the Matlab interface

[fMRI]                   Settings for the fMRI arfifact removal

[Montages]                   A setting for a default source montage

'''Reader-specific settings'''

[BrainLab]

[Bio-Logic]

[EDF+] [BDF] [Trackit]

[EGI]

[Harmonie]

[NeuroScan Keys]

[NKT2100]

[Vangard]

[XLTEK]

== Defaults ==

'''Default settings provided for section [Defaults]:'''

'''DatabaseAllowLocalFiles=Yes''' (If set to "Yes", BESA Research will write filenames "'''datafilename.ftg'''" and "'''datafilename.fst"''' to the data folder, saving current file tag and display settings there. If set to "No", these files are only written to the database. If set to "Yes", you can copy these files along with the data to a new folder, and display settings and tags will be preserved.)

'''DataBuffering=Off''' (If set to "On", an internal buffer of length 180 s of data is kept to speed up paging). This can speed up paging, particularly when the data are in a network folder.

'''DisplayedTime=10''' displayed time window [s] on the screen

'''Montage=Org''' montage used when opening a new file

'''ScpScale=50''' scale of scalp channels in [mV]

'''PgrScale=500''' scale of polygraphic channels in [mV]

'''IcrScale=500''' scale of intracranial channels in [mV]

'''MegScale=500''' scale of MEG/marker channels in [fT]

'''SrcScale=100''' scale of source of source montages

'''BaselineCorrection=On''' baseline correction, do not switch off in AC systems

'''ClippingPercent= '''set from 100 to 200 if you want to clip artifacts in displayed EEG (not used if empty or 0)

'''LowFilter=''' low filter cutoff frequency [Hz] (variable filter)

'''TimeConstant=0.3''' time constant for low filter cutoff frequency [sec] (fixed forward filter, 0.3 sec is equivalent to 0.53 Hz)

'''HighFilter=70''' high filter cutoff frequency [Hz] (variable filter)

'''NotchFilter=50''' notch filter center frequency [Hz]

'''NotchFilterStatus=Off''' notch filter is off, set=On if you want to use as default

'''BandFilter=12''' band pass filter center frequency [Hz]

'''BandFilterStatus=Off''' band pass is off, set=On if you want to use as default

'''AdditionalChannelFile=''' defines the full path and name of an additional channels montage file, e.g. '''C:\Program Files\BESA\Research_x\Montages\AdditionalChannels\EKG.sel'''

'''ColoredWaveforms=On''' scalp waveforms are (not) colored according to region

'''WriteSegmentPath=''' defines default path for saving segments/averages. If blank, the path of the current data file is used.

'''ShowSubjectInfo=Off''' subject info will (not) be displayed.

The following optional parameters are not defined as default and can be set manually in''' BESA.ini''':

'''TextEditor="Notepad.exe"''' defines the path to your preferred text editor. This will be used when you press the '''Edit''' button the ''Load Coordinate Files dialog box''.

'''NeuroScanDataNumberOfBits=32''' defines the format of NeuroScan data files ('16' for 16-bit, '32' for 32-bit). If this variable is not specified, BESA uses a heuristic to (try to) decide which of the two data formats is used. This variable overrides the heuristic. If you want to specify the NeuroScan data format for specific files, create a file, named "16bit" or "32bit", and place it in the data folder.

'''ScaleAmplitudesForNNChannels=25''' Scale waveforms as if a fixed number of channels were displayed in the window (here: 25). A minimum of 10 channels can be used for the scaling. This parameter is superseded if the parameter "''ScaleAmplitudesFixedPixelHeight"'' is specified.

'''ScaleAmplitudesFixedPixelHeight=70''' Set the scale bar for amplitudes to a fixed pixel height (here: 70). If this parameter is set in the '''.ini''' file, it supersedes the parameter "''ScaleAmplitudesForNNChannels''".

'''Notes'''

Check the Menu descriptions for the various definitions of filters, montages etc. For montage preselection, use the labels as visible on the montage push-buttons.

The additional channels file should contain all polygraphic channels (e.g. EKG, EOG, respiratory) that you want to view regularly along with the scalp channels. The entry AdditionalChannelFile must specify the full path pointing to the location of additional channel files (recommended: ''Montages\AdditionalChannels''). If no drive is specified, the installation drive of BESA is used.

If BaselineCorrection is set to 'On', before displaying a screen of data, BESA subtracts for each channel the mean over its displayed time points. This optimizes viewing, because it ensures that the vertical position of each channel is not shifted upward or downward from the channel label at the left of the screen. There are some cases in which you will not want baseline correction, i.e. when the DC level in the data is already correctly defined. This is usually the case, for instance, when reading in files that have been processed by BESA. In this case, BaselineCorrection should be set to 'Off', because otherwise maps and source montage displays may be distorted.

== Folders ==

'''The [Folders] section defines where BESA Research places its files. In versions 5.1 and earlier, files were located in various subfolders of the program folder. This led to problems if the user did not have administrator rights, e.g. to create or write to a file. For compatibility with Windows 7 and higher versions, many folders are now located by default in locations where normal users can create and write files. If you wish, you can also specify paths in the [Folders] section to use the previous locations. The previous location is given for each variable.'''

These settings allow some flexibility that can be useful if you want to tune BESA Research for use by several users, or on a network. For instance, the Examples and Montages folders might be located on a network disk. For the current defaults, the database, Examples, Montages, and Scripts are set up for use by all users on the PC on which BESA Research is installed. The settings files ('''Besa.set''', '''Besa.cfg''', etc.) are located in private folders so that each user retains his or her own settings.

The '''default''' settings (i.e. settings that BESA Research uses if the entries are omitted in the '''.ini''' file) are shown for each variable definition.

The folder definitions can use '''placeholders''', labels enclosed by a % sign (e.g. %localapp%), to define paths that vary depending on the language version and on the Windows system. These are defined below.

'''The Variables'''

'''Database=%localapp%''' The path of the BESA Research database folder (used to be ''%progdir%System\DB'' in BESA versions up to 5.1.x). Unless the provided path ends with ''\DB'' or ''\Database'', BESA Research will automatically create a folder named ''Database'' in the provided path.

'''Settings=%privatprog%Settings''' The path of the BESA Research settings folder (used to be ''%progdir%System'' in BESA versions up to 5.1.x)

'''Montages=%publicprog%Montages''' The path of the BESA Research montages folder (used to be ''%progdir%Montages'' in BESA versions up to 5.1.x)

'''Scripts=%publicprog%Scripts''' The path of the BESA Research Scripts folder (used to be ''%progdir%Scripts'' in BESA versions up to 5.1.x)

'''Examples=%publicprog%Examples''' The path of the BESA Research Examples folder (used to be ''%progdir%Examples'' in BESA versions up to 5.1.x)

'''User=%privatprog%Settings''' The path for user defined settings (used to be ''%progdir%System\Userdirs'' in BESA versions up to 5.1.x)

'''Placeholders'''

The strings enclosed by percent signs (%) are placeholders for the following folders in English-language versions of Windows. Folder names differ depending on Windows version, and for other language settings. BESA Research will substitute the placeholders by the appropriate folder name for the system and the system language:

* '''Windows 7 and higher (English):'''

'''%localapp%''' = "''C:\Users\[user]\AppData\Local\BESA\Research_6_1''", where [user] is the logon name of the current user. This folder is directly accessible from the Desktop as "''Desktop\[user]\AppData\Local\BESA\Research_6_1''".

'''%publicprog%''' = "''C:\Users\Public\Public Documents\BESA\Research_6_1''". This folder is directly accessible from the Windows Explorer under "''Libraries\Documents\Public'' ''Documents\BESA\Research_6_1''".

'''%privateprog%''' = "''C:\Users\[user]\Documents\BESA\Research_6_1''", where [user] is the logon name of the current user. This folder is directly accessible from the Windows Explorer as "''Libraries\Documents\My'' ''Documents\Research_6_1''" or "''Desktop\[User]\My Documents\BESA\Research_6_1''.

'''%progdir%''' = the BESA Research root folder. In a default installation, this is "''C:\Program'' ''Files\BESA\Research_6_1''".

'''%besaroot%''' is the same as '''%progdir%'''

* '''Windows Vista (English'''):

'''%localapp% '''<nowiki>= "</nowiki>''C:\Users\[user]\AppData\Local\BESA\Research_6_1''", where [user] is the logon name of the current user. This folder is directly accessible from the Windows Explorer as "''Desktop\[user]\AppData\Local\BESA\Research_6_1''".

'''%publicprog%''' = "''C:\Users\Public\Public Documents\BESA\Research_6_1''". This folder is directly accessible from the Windows Explorer under "''Desktop\Public\Public Documents\BESA\Research_6_1''".

'''%privateprog%''' = "''C:\Users\[user]\Documents\BESA\Research_6_1''", where [user] is the logon name of the current user. This folder is directly accessible from the Windows Explorer as "''Desktop\[user]\Documents\BESA\Research_6_1''".

'''%progdir%''' = the BESA Research root folder. In a default installation, this is "''C:\Program'' ''Files\BESA\Research_6_1''".

'''%besaroot%''' is the same as '''%progdir%'''  

* '''Windows XP (English) (note: not supported by BESA Research 6.1 and higher):'''

'''%localapp% '''<nowiki>= "</nowiki>''C:\Documents and Settings\[user]\Local Settings\Application Data\BESA\Research_6_0''", where [user] is the logon name of the current user.

'''%publicprog%''' = "''C:\Documents and Settings\All Users\Documents\BESA\Research_6_0". ''This folder is directly accessible from the Windows Explorer under "''My Computer\Shared'' ''Documents\BESA\Research_6_0''".

'''%privateprog%''' = "''C:\Documents and Settings\[user]\My Documents\BESA\Research_6_0''", where [user] is the logon name of the current user. This folder is directly accessible from the Windows Explorer as "''My Documents\BESA\Research_6_0''".

'''%progdir%''' = the BESA Research root folder. In a default installation, this is "''C:\Program'' ''Files\BESA\Research_6_0''".

'''%besaroot%''' is the same as '''%progdir%  '''

* '''Windows 2000 (English) (note: not supported by BESA Research 6.1 and higher):'''

'''%localapp%''' = "''C:\Documents and Settings\[user]\Local Settings\Application Data\BESA\Research_6_0''", where [user] is the logon name of the current user.

'''%publicprog%''' = "''C:\Documents and Settings\All Users\Documents\BESA\Research_6_0''".

'''%privateprog%''' = "''C:\Documents and Settings\[user]\My Documents\BESA\Research_6_0''", where [user] is the logon name of the current user. This folder is directly accessible from the Windows Explorer '''as "'''''My Documents\BESA\Research_6_0'''''". '''

'''%progdir%''' = the BESA Research root folder. In a default installation, this is "''C:\Program'' ''Files\BESA\\Research_6_0''".

'''%besaroot%''' is the same as '''%progdir%'''

== Electrodes ==

'''This section allows for automatic relabeling of electrodes. For instance, the 10-20 label "T3" can be replaced by the 10-10 convention "T7".'''

'''Default settings provided for section [Electrodes]:'''

T7=T3 replace 10-10 label with old 10-20 convention

T8=T4 replace 10-10 label with old 10-20 convention

P7=T5 replace 10-10 label with old 10-20 convention

P8=T6 replace 10-10 label with old 10-20 convention

X1=ECG1 define X1 channel to be ECG1

X2=ECG2 define X2 channel to be ECG2

Other examples, depending on your electrode input box definition, could be:

PG1=LO1 define X3 as lateral orbital eye electrode left

PG2=LO2 bipolar LO1-LO2 defines horizontal EOG (additional channel)

X3=IO1 infraorbital, e.g. use with FP1 as additional channel for VEOG

X9=Rsp define X9 channel to be a respiratory channel

Relabeling of channel names (as stored in the EEG file header) is helpful to predefine your standard sequence of channels and to avoid the need for reading and/or editing a Channel Configuration file for every EEG file.

'''Note 1''': For polygraphic channels, or if your EKG has been recorded differentially, you should edit and define an ''Additional Channels Montage'' according to your recording channel configuration (e.g. Fp1-IO1=vertical EOG). The Additional Channels group permits to display these channels regularly below the scalp montages with individual scales.

'''Note 2''': EOG channels record both eye and scalp activity. In digital EEG systems, EOG electrodes should be labeled according to their position in the 10-10 system (see "''Electrode Conventions''"). This permits use of these electrodes for mapping and suppression of eye artifacts. The standard definitions above give an example of how to relabel extra channels (X1...X10, PG1, PG2) for the use of EOG, EKG and respiratory (Rsp) channels. Use an ''Additional Channels'' file to define horizontal and vertical EOG channels by using the appropriate electrodes in a bipolar montage (an example is provided in '''eog-ecg.mtg''' in ''Montages\AdditionalChannels''). Differentially recorded EKG and respiratory channel can be defined in the same file.

== Patterns ==

'''Default settings provided for section [Patterns]:'''

These settings define labels for each of the five patterns. The labels are shown* in the''' Tags''' menu,
* in the '''TAG push-button''' popup menu, and
* when displaying tag info clicking with the right mouse on a tag at the bottom of the EEG or on the event bar.

By default, no labels are defined. Define a label, e.g. for Pattern1 and Pattern2, as in the following example:

Pattern1=Spike

Pattern2=Sharp Wave

== Artifacts ==

'''Artifact default settings:'''

See the chapter "''Artifact Correction / Reference / Artifact settings in the BESA.ini file''" in the online help.

== Search ==

Default settings for pattern search.

'''Default Settings for the ''Search/Options ''Dialog box:'''

'''CorrelationThreshold''' = '''75%'''

'''AmplitudeThreshold = 100 µV'''

'''GradientThreshold = 25'''

'''Default Settings for the ''Search/Average/View'' (SAV) Dialog box:'''

'''PreCursor = -250 ms'''

'''PostCursor = 150 ms'''

'''HighPassFreq = 2 Hz'''

'''HighPassSlope = 12 dB/Octave'''

'''HighPassType = 0 (0 = zero phase, 1 = forward, 2 = backward'''

'''LowPassFreq = 35 Hz'''

'''LowPassSlope = 24 dB/Octave'''

'''LowPassType = 0 (0 = zero phase, 1 = forward, 2 = backward)'''

'''CorrelationThresholdNoMarked = 60%'''

Default correlation threshold if no channel labels are marked when the SAV Dialog is opened.

'''CorrelationThresholdOneMarked = 85%'''

Default correlation threshold if one channel label is marked when the SAV Dialog is opened.

'''CorrelationThresholdFourMarked = 65%'''

Default correlation threshold if between two channel labels are marked when the SAV Dialog is opened.

'''SelectedViewWindowWidthMultiplier = 300%'''

'''WriteAfterSearch = No'''

If set to "Yes", a File Save dialog will open, to allow to save the search average to a file (as with the SAW function).

'''WriteAfterSearchCheckBox = No'''

If set to "Yes", an additional checkbox "Write after search" is displayed at the bottom of the SAV Dialog, allowing to choose whether or not to write the search average after a search:

[[Image:ST Besa ini (1).gif ‎ ]]

'''PreserveDefaults = Yes'''

If set to "No", the SAV Dialog will open with the same boxes checked as the last time the dialog was opened during the current session.

If set to "Yes", the default frequency, buffer width, selected view after search, and default threshold are always checked when the dialog is opened.

== KeyControls ==

In the [KeyControls] section you can specify functions that can be allocated to '''function keys''' or to the ''Del'' key. Specify using the form:

'''Fn=function''' or

'''Del=function'''

where "''n''" is a number between 2 and 12 (F1 is reserved for Help). For example:

    F2 = Batch1

Possible functions are:

'''Setting or removing events:'''

'''Pattern''n''''', where ''n''<nowiki>=1-5: Sets the tag number </nowiki>''n'' at the cursor latency.

'''Epochfast:''' sets one boundary of an epoch at the cursor latency, but does not open the epoch text box to define a label.

'''Marker:'''  sets a marker at the cursor latency.

'''Comment:''' sets a comment at the cursor latency and opens the comment box to enter text.

'''Epoch:''' sets one boundary of an epoch at the cursor latency and opens the epoch text box to enter a label.

'''Artifact:''' sets one boundary of an artifact segment at the cursor latency.

'''Delete:'''  deletes a tag at the cursor latency

'''Batches and Montages:'''

'''Batch''n''''', where n=1-12: Runs a predefined batch file corresponding to the number ''n''.

<div style="margin-left:0.953cm;margin-right:0cm;">If a key has not yet been associated with a batch, pressing it will open a ''File Open Dialog'' to select a batch. The setting you have chosen will be retained across BESA Research sessions. Holding the '''<shift>''' key while pressing the '''function key''' will always open the dialog. Hold the''' <ctrl> '''key with the function key to open the associated batch in the batch edit dialog.</div>

'''Montage''n''''', where n=1-12: Sets a montage corresponding to the number'' n''.

<div style="margin-left:0.953cm;margin-right:0cm;">If a key has not yet been associated with a montage, pressing it will generate a message asking you to associate a montage as follows: Holding the '''<shift> '''key while pressing the '''function key''' will remove the current association, and substitute it with the current montage.</div>

The default settings after program installation are listed in the online help chapter ''Review / Reference / Controls / Mouse and Keyboard / Keyboard Controls''.

== FFT ==

'''Default settings provided for section [FFT]:'''

These settings define the setup in the Spectral Analysis section of the BESA Research program (FFT window, see the chapter "''Spectral Analysis / FFT''"). Up to 7 frequency bands may be defined. Five are defined by default.

'''FFTBand1=On''' FFT Bands 1-5 are defined

'''FFTBand2=On'''

'''FFTBand3=On'''

'''FFTBand4=On'''

'''FFTBand5=On'''

'''FFTBand6=Off''' FFT Bands 6-7 are not defined

'''FFTBand7=Off'''

'''FFTNameBand1=Delta''' Names of the defined bands

'''FFTNameBand2=Theta'''

'''FFTNameBand3=Alpha'''

'''FFTNameBand4=Beta'''

'''FFTNameBand5=Gamma'''

'''FFTColorBand1=RGB(0,0,0)'''  Default color of each band

'''FFTColorBand2=RGB(0,128,64)'''

'''FFTColorBand3=RGB(128,0,0)'''

'''FFTColorBand4=RGB(255,0,0)'''

'''FFTColorBand5=RGB(255,128,0)'''

'''FFTColorBand6=RGB(255,192,0)'''

'''FFTColorBand7=RGB(255,255,0)'''

'''FFTLowBand1=1''' Delta from 1-4 Hz

'''FFTHighBand1=4'''

'''FFTLowBand2=4''' Theta from 4-8 Hz

'''FFTHighBand2=8'''

'''FFTLowBand3=8''' Alpha from 8-14 Hz

'''FFTHighBand3=14'''

'''FFTLowBand4=14''' Beta from 14-30 Hz

'''FFTHighBand4=30'''

'''FFTLowBand5=30''' Gamma from 30-50 Hz

'''FFTHighBand5=50'''

These values are best set from within BESA Research, using the '''Options''' menu in the FFT window (see the chapter "''Spectral Analysis / FFT / FFT Options Menu''"). Current settings are stored after each session and retrieved in the next session.

== Printer ==

'''Default settings provided for section [Printer]:'''

'''PrinterMarginPercent=100''' controls size of printout

'''PrinterColors=256''' set to 1/2 for black&white, 0/256 for color printers

'''PrinterLineMode=1''' set to 2 for thicker lines and to save printer memory

'''PrinterMapResolution=1''' set to 2, 3, 4 to save printer memory and increase speed

== Calibration ==

'''Default settings provided for section [Calibration]:'''

'''AutoCalibration=Off''' On: automatic calibration of signals >= 4 cycles

'''MicrovoltCalibration=50''' peak voltage of calibration signal

If calibration is set to'' On'', the menu item ''Calibration ''will appear in the''' Process '''menu. Position your current screen at an epoch containing at least 4 regular cycles of the calibration signal (in all channels!) and select Calibration.

== Video ==

'''Default settings provided for section [Video]:'''

'''DVCFilePath=C:\DVC\DVPlay.exe''' holds the path to the digital video player

'''DVCCommandLineArguments=/S:3 /M:P /T:M'''  arguments to be passed to the digital video player

'''CursorPagingOffsetLeft=0.2  '''

'''CursorPagingOffsetRight=0.8'''

'''CursorMinDistToBorderBeforePaging=0.02'''

'''PageDisplayIfCursorIsBelowVideo=1'''

'''MappingRepetitionRateWithVideoInMS=100'''  gives the number of milliseconds between two maps if the mapping window is open while the video is running. If the graphics board encounters problems during the display, this value should be increased.

== Mapping ==

'''Default settings provided for section [Mapping]:'''

'''UseBitmapDrawing=Off'''

Set this to "On" if 3D maps show a strange pattern of black triangular shapes (this is frequently observed with modern Intel On-Board graphics controllers, and is a result of inadequate drivers for Open-GL).

'''Use3DVBlending=Auto'''

Set this to "Off" if the 3D view in the Montage Editor or the Source Analysis window does not show up properly (this may happen with some older graphics cards).

Set this to "On" if the 3D view in the Montage Editor or the Source Analysis window shows a ragged surface boundary.

'''MapSmoothing=0 '''

Set a non-zero value to specify a default map smoothing parameter (normally specified in ''Options/Mapping/Spline Interpolation Smoothing Constant'').

== Matlab ==

'''Default settings for the [Matlab] section:'''

'''Platform=32'''

'''Set Platform=64''' if you want to use the 64-bit version of Matlab

== Updates ==

This section is not normally required, but the variables here can be altered or defined to determine how BESA Research checks for dongle and program updates.

'''DaysBetweenUpdateChecks=7'''

Sets the number of days between automatic checks for updates. Set the value to 0 to check every time BESA Research is started. Set to -1 to turn off automatic update checks.

'''CheckNetworkDongle=Off'''

For the network administrator: If set to "On", BESA Research will check the dongle on the network for updates. Otherwise the state of the network dongle will be ignored.

'''LocalPath'''

For the network administrator. This can be set to a path on the local network to the BESA update files, so that users can obtain their updates locally. The path is given to the text file "'''UpdateVersions.txt'''" (e.g. ''LocalPath=\\transtec-sak\zarascratch\BESA\Updates\UpdateVersions.txt''), which contains further details for the program to obtain its updates. If you want to use this feature, please contact us at [mailto:support@besa.de support@besa.de].

The following variables are not required, because BESA Research has the paths hardwired:

'''FTP1 (also FTP2, FTP3)'''

ftp download server

'''Path1 (also Path2, Path3)'''

Path on the server to UpdateVersions.txt.

'''HaspPath1 (also HaspPath2, HaspPath3)'''

Path on the server to HASP (dongle) update files.

'''History'''

Path on the server to general history file

== Reader-Specific Settings ==

=== BrainLab ===

'''Default settings provided for section [BrainLab]:'''

'''BrainLabFormat=New''' this entry ensures that the newer BrainLab file format can be read by BESA Research.

=== Bio-Logic ===

'''FileSelect=Yes'''

If there are several Bio-Logic files in a data folder, the reader can check if the files have the same settings. There are three possible options:

* Open a dialog to ask if the files should be treated as a single data set, or as individual, separate files.

[[Image:ST Besa ini (2).jpg ‎]]

<div style="margin-left:0.953cm;margin-right:0cm;">in this case, use '''FileSelect=Yes''' (this is the default setting) Note that the choice made in the dialog will apply to the file(s) within a BESA Research session. For a given file and session, the dialog will only be opened once, even if the file is closed and reopened.</div>

* Always concatenate such files into a single data set. In this case use '''FileSelect=All'''
* Always open the files as single, separate files. In this case use '''FileSelect=Single'''

=== EDF+/BDF/Trackit ===

'''TriggerScan=On'''

Set '''TriggerScan=Off '''to prevent BESA Research from scanning the file for triggers. This is done separately for EDF+, BDF, and Trackit files in sections '''[EDF+], [BDF],''' and '''[Trackit]''' in the '''BESA.ini''' file.

=== EGI ===

The treatment of DIN events can be modified in the''' [EGI] '''section:

'''CombineDINevents'''<nowiki>=yes/no    (default is “yes”)</nowiki>

Set to “no” if you want to treat DIN events separately, and not generate combined values.

'''SeparateDINevents'''<nowiki>=yes/no    (default is “yes”)</nowiki>

Set to “no” if you don’t want to treat DIN events separately.

Thus, using the above two parameters, you can choose whether you want to treat DIN events as combined, separate, both, or completely ignored.

'''CombineDINeventsPrefix'''<nowiki>=dinComb</nowiki>

<div style="margin-left:0.953cm;margin-right:0cm;">This defines the text preceding the number when DIN events are combined. The default is “dinComb”.</div>

=== Harmonie ===

'''Default settings provided for section [Harmonie] (Stellate Harmonie systems):'''

'''SeizurePreEpoch=60''' length of the epoch preceding a seizure detection in s

'''SeizurePostEpoch=60''' length of the epoch following a seizure detection in s

'''PushButtonPreEpoch=60''' length of the epoch preceding a push button detection

'''PushButtonPostEpoch=60''' length of the epoch following a push button detection

When BESA Research encounters a seizure detection event or a push button detection event in a Stellate Harmonie file, it automatically sets an epoch around the event, which makes it convenient to view just those epochs for analysis. The length of the epochs preceding and following the events can be adjusted in the '''.ini''' file.

=== Neuroscan Keys ===

'''Note that there is a setting "NeuroScanDataNumberOfBits" in the [Defaults] section of BESA.ini that is used for distinguishing the data format of Neuroscan files (16 or 32-bit).'''

'''Default settings provided for section [NeuroScan Keys] (NeuroScan systems):'''

Event1=Movement Text corresponding to keyboard events 1 through 10

Event2=Blink

Event3=Talking

Event4=Cough

Event5=Muscle

Event6=Jaw

Event7=Sneeze

Event8=Swallow

Event9=Eye movement

Event10=Hiccup

=== NKT2100 ===

'''Default settings provided for section [NKT2100] (Nihon Kohden EEG 21xx systems):'''

'''TriggerScan=On'''   Set to "Off" to prevent a scan for trigger events.

'''Country=NotKanji''' set to NotKanji for non-Kanji characters else to Kanji

'''KanjiCharSize=16''' Kanji character size

'''KanjiPrinterCharSize=32''' Kanji printer character size

'''EEG_Sensitivity=50''' default sensitivity of Nihon Kohden EEG-2100 system

'''DC_Sensitivity=50''' default sensitivity of Nihon Kohden DAE-2100 system

'''QJ_Sensitivity=100''' default sensitivity of Nihon Kohden QJ-403 system

'''Mark_Sensitivity=100''' default sensitivity of EEG-2100 marker channels

These settings need to be changed only if the manufacturer has specified different gains for your system. Otherwise do not alter these settings.

=== Vangard ===

'''AlwaysOpenFileSelect=Yes'''

If "Yes" is selected, each time a Vangard file is opened, a dialog box will open, asking for a selection of the segment type to display.

If "No" is selected, the selection dialog is opened whenever a Vangard file is opened for the first time, or if the ''Channel and digitized head surface point information dialog box'' is opened (e.g. with '''ctrl-L''' or ''File/Head Surface Points and Sensors/Load Coordinate Files...'' ).

=== XLTEK ===

'''TriggerScan=Off '''Set to "On" to scan the data file for trigger events

'''MontageNo=2''' Set to 1 or 2. If two montages for the data file are defined, this variable determines whether the first or the second alternative should be used.

[[Category:Research Manual]]

{{BESAManualNav}}

The Initialization File: BESA.ini

2019-03-27T13:27:44Z

Jamie: /* Introduction */

{{BESAInfobox
|title = Module information
|module = BESA Research Basic or higher
|version = 6.1 or higher
}}

== Introduction ==

'''BESA.ini File'''

BESA Research uses settings provided in the initialization file '''BESA.ini''' whenever BESA Research is started or a new file is opened for the first time. The format of this file conforms with standard initialization files ('''<nowiki>*.ini</nowiki>''') of Windows. You may change the settings in '''BESA.ini''' using NOTEPAD.exe from the ACCESSORIES group, or other plain text editors to adapt BESA Research to '''your own everyday needs'''. The default settings provided in '''BESA.ini''' will be used by BESA Research whenever BESA Research or the launch program is started. It is advised that you make a backup copy of '''BESA.ini''' before you change the default settings.

'''Location of BESA.ini'''

You can place '''BESA.ini''' at three possible locations:

# '''Private''': each user on a PC should have his/her own private settings. This is normally in ''My Documents/BESA/Research_6_1''
# '''Public''': all users should use one setting, but they can edit '''BESA.ini''' to change the settings. This is normally in ''Public Documents/BESA/Research_6_1''
# '''Administrator''': the PC administrator determines the settings. This is normally in ''C:Program Files(x86)/BESA/Research_6_1''

The actual folder names depend on the operating system and the system language.

When BESA starts, it first looks for the '''administrator''' version of '''BESA.ini'''. If this is not found, it looks for the '''private''' version. If this is not found, it looks for the '''public''' version. If this is not found, internal default values are used.

'''There are 13 general sections, and several reader-specific sections:'''

[Defaults]                    General settings (filters, scaling, and various other settings)

[Folders]                     Folders used by BESA Research (Examples, Montages, Scripts, Settings,...)

[Electrodes]                Electrode renaming

[Patterns]                   Rename patterns in the '''Tags''' menu

[Artifacts]                   Settings for artifact correction

[KEYCONTROLS]      Function key definitions

[Search]                     Default parameters for search

[FFT]                           Frequency band definitions

[Printer]                      Printer control

[Calibration]              Calibration control

[Video]                       Digital video control

[Mapping]                  Mapping control

[Updates]                   Options for program updates

[Matlab]                      Settings for the Matlab interface

[fMRI]                   Settings for the fMRI arfifact removal

[Montages]                   A setting for a default source montage

'''Reader-specific settings'''

[BrainLab]

[Bio-Logic]

[EDF+] [BDF] [Trackit]

[EGI]

[Harmonie]

[NeuroScan Keys]

[NKT2100]

[Vangard]

[XLTEK]

== Defaults ==

'''Default settings provided for section [Defaults]:'''

'''DatabaseAllowLocalFiles=Yes''' (If set to "Yes", BESA Research will write filenames "'''datafilename.ftg'''" and "'''datafilename.fst"''' to the data folder, saving current file tag and display settings there. If set to "No", these files are only written to the database. If set to "Yes", you can copy these files along with the data to a new folder, and display settings and tags will be preserved.)

'''DataBuffering=Off''' (If set to "On", an internal buffer of length 180 s of data is kept to speed up paging). This can speed up paging, particularly when the data are in a network folder.

'''DisplayedTime=10''' displayed time window [s] on the screen

'''Montage=Org''' montage used when opening a new file

'''ScpScale=50''' scale of scalp channels in [mV]

'''PgrScale=500''' scale of polygraphic channels in [mV]

'''IcrScale=500''' scale of intracranial channels in [mV]

'''MegScale=500''' scale of MEG/marker channels in [fT]

'''BaselineCorrection=On''' baseline correction, do not switch off in AC systems

'''ClippingPercent= '''set from 100 to 200 if you want to clip artifacts in displayed EEG (not used if empty or 0)

'''LowFilter=''' low filter cutoff frequency [Hz] (variable filter)

'''TimeConstant=0.3''' time constant for low filter cutoff frequency [sec] (fixed forward filter, 0.3 sec is equivalent to 0.53 Hz)

'''HighFilter=70''' high filter cutoff frequency [Hz] (variable filter)

'''NotchFilter=50''' notch filter center frequency [Hz]

'''NotchFilterStatus=Off''' notch filter is off, set=On if you want to use as default

'''BandFilter=12''' band pass filter center frequency [Hz]

'''BandFilterStatus=Off''' band pass is off, set=On if you want to use as default

'''AdditionalChannelFile=''' defines the full path and name of an additional channels montage file, e.g. '''C:\Program Files\BESA\Research_x\Montages\AdditionalChannels\EKG.sel'''

'''ColoredWaveforms=On''' scalp waveforms are (not) colored according to region

'''WriteSegmentPath=''' defines default path for saving segments/averages. If blank, the path of the current data file is used.

'''ShowSubjectInfo=Off''' subject info will (not) be displayed.

The following optional parameters are not defined as default and can be set manually in''' BESA.ini''':

'''TextEditor="Notepad.exe"''' defines the path to your preferred text editor. This will be used when you press the '''Edit''' button the ''Load Coordinate Files dialog box''.

'''NeuroScanDataNumberOfBits=32''' defines the format of NeuroScan data files ('16' for 16-bit, '32' for 32-bit). If this variable is not specified, BESA uses a heuristic to (try to) decide which of the two data formats is used. This variable overrides the heuristic. If you want to specify the NeuroScan data format for specific files, create a file, named "16bit" or "32bit", and place it in the data folder.

'''ScaleAmplitudesForNNChannels=25''' Scale waveforms as if a fixed number of channels were displayed in the window (here: 25). A minimum of 10 channels can be used for the scaling. This parameter is superseded if the parameter "''ScaleAmplitudesFixedPixelHeight"'' is specified.

'''ScaleAmplitudesFixedPixelHeight=70''' Set the scale bar for amplitudes to a fixed pixel height (here: 70). If this parameter is set in the '''.ini''' file, it supersedes the parameter "''ScaleAmplitudesForNNChannels''".

'''Notes'''

Check the Menu descriptions for the various definitions of filters, montages etc. For montage preselection, use the labels as visible on the montage push-buttons.

The additional channels file should contain all polygraphic channels (e.g. EKG, EOG, respiratory) that you want to view regularly along with the scalp channels. The entry AdditionalChannelFile must specify the full path pointing to the location of additional channel files (recommended: ''Montages\AdditionalChannels''). If no drive is specified, the installation drive of BESA is used.

If BaselineCorrection is set to 'On', before displaying a screen of data, BESA subtracts for each channel the mean over its displayed time points. This optimizes viewing, because it ensures that the vertical position of each channel is not shifted upward or downward from the channel label at the left of the screen. There are some cases in which you will not want baseline correction, i.e. when the DC level in the data is already correctly defined. This is usually the case, for instance, when reading in files that have been processed by BESA. In this case, BaselineCorrection should be set to 'Off', because otherwise maps and source montage displays may be distorted.

== Folders ==

'''The [Folders] section defines where BESA Research places its files. In versions 5.1 and earlier, files were located in various subfolders of the program folder. This led to problems if the user did not have administrator rights, e.g. to create or write to a file. For compatibility with Windows 7 and higher versions, many folders are now located by default in locations where normal users can create and write files. If you wish, you can also specify paths in the [Folders] section to use the previous locations. The previous location is given for each variable.'''

These settings allow some flexibility that can be useful if you want to tune BESA Research for use by several users, or on a network. For instance, the Examples and Montages folders might be located on a network disk. For the current defaults, the database, Examples, Montages, and Scripts are set up for use by all users on the PC on which BESA Research is installed. The settings files ('''Besa.set''', '''Besa.cfg''', etc.) are located in private folders so that each user retains his or her own settings.

The '''default''' settings (i.e. settings that BESA Research uses if the entries are omitted in the '''.ini''' file) are shown for each variable definition.

The folder definitions can use '''placeholders''', labels enclosed by a % sign (e.g. %localapp%), to define paths that vary depending on the language version and on the Windows system. These are defined below.

'''The Variables'''

'''Database=%localapp%''' The path of the BESA Research database folder (used to be ''%progdir%System\DB'' in BESA versions up to 5.1.x). Unless the provided path ends with ''\DB'' or ''\Database'', BESA Research will automatically create a folder named ''Database'' in the provided path.

'''Settings=%privatprog%Settings''' The path of the BESA Research settings folder (used to be ''%progdir%System'' in BESA versions up to 5.1.x)

'''Montages=%publicprog%Montages''' The path of the BESA Research montages folder (used to be ''%progdir%Montages'' in BESA versions up to 5.1.x)

'''Scripts=%publicprog%Scripts''' The path of the BESA Research Scripts folder (used to be ''%progdir%Scripts'' in BESA versions up to 5.1.x)

'''Examples=%publicprog%Examples''' The path of the BESA Research Examples folder (used to be ''%progdir%Examples'' in BESA versions up to 5.1.x)

'''User=%privatprog%Settings''' The path for user defined settings (used to be ''%progdir%System\Userdirs'' in BESA versions up to 5.1.x)

'''Placeholders'''

The strings enclosed by percent signs (%) are placeholders for the following folders in English-language versions of Windows. Folder names differ depending on Windows version, and for other language settings. BESA Research will substitute the placeholders by the appropriate folder name for the system and the system language:

* '''Windows 7 and higher (English):'''

'''%localapp%''' = "''C:\Users\[user]\AppData\Local\BESA\Research_6_1''", where [user] is the logon name of the current user. This folder is directly accessible from the Desktop as "''Desktop\[user]\AppData\Local\BESA\Research_6_1''".

'''%publicprog%''' = "''C:\Users\Public\Public Documents\BESA\Research_6_1''". This folder is directly accessible from the Windows Explorer under "''Libraries\Documents\Public'' ''Documents\BESA\Research_6_1''".

'''%privateprog%''' = "''C:\Users\[user]\Documents\BESA\Research_6_1''", where [user] is the logon name of the current user. This folder is directly accessible from the Windows Explorer as "''Libraries\Documents\My'' ''Documents\Research_6_1''" or "''Desktop\[User]\My Documents\BESA\Research_6_1''.

'''%progdir%''' = the BESA Research root folder. In a default installation, this is "''C:\Program'' ''Files\BESA\Research_6_1''".

'''%besaroot%''' is the same as '''%progdir%'''

* '''Windows Vista (English'''):

'''%localapp% '''<nowiki>= "</nowiki>''C:\Users\[user]\AppData\Local\BESA\Research_6_1''", where [user] is the logon name of the current user. This folder is directly accessible from the Windows Explorer as "''Desktop\[user]\AppData\Local\BESA\Research_6_1''".

'''%publicprog%''' = "''C:\Users\Public\Public Documents\BESA\Research_6_1''". This folder is directly accessible from the Windows Explorer under "''Desktop\Public\Public Documents\BESA\Research_6_1''".

'''%privateprog%''' = "''C:\Users\[user]\Documents\BESA\Research_6_1''", where [user] is the logon name of the current user. This folder is directly accessible from the Windows Explorer as "''Desktop\[user]\Documents\BESA\Research_6_1''".

'''%progdir%''' = the BESA Research root folder. In a default installation, this is "''C:\Program'' ''Files\BESA\Research_6_1''".

'''%besaroot%''' is the same as '''%progdir%'''  

* '''Windows XP (English) (note: not supported by BESA Research 6.1 and higher):'''

'''%localapp% '''<nowiki>= "</nowiki>''C:\Documents and Settings\[user]\Local Settings\Application Data\BESA\Research_6_0''", where [user] is the logon name of the current user.

'''%publicprog%''' = "''C:\Documents and Settings\All Users\Documents\BESA\Research_6_0". ''This folder is directly accessible from the Windows Explorer under "''My Computer\Shared'' ''Documents\BESA\Research_6_0''".

'''%privateprog%''' = "''C:\Documents and Settings\[user]\My Documents\BESA\Research_6_0''", where [user] is the logon name of the current user. This folder is directly accessible from the Windows Explorer as "''My Documents\BESA\Research_6_0''".

'''%progdir%''' = the BESA Research root folder. In a default installation, this is "''C:\Program'' ''Files\BESA\Research_6_0''".

'''%besaroot%''' is the same as '''%progdir%  '''

* '''Windows 2000 (English) (note: not supported by BESA Research 6.1 and higher):'''

'''%localapp%''' = "''C:\Documents and Settings\[user]\Local Settings\Application Data\BESA\Research_6_0''", where [user] is the logon name of the current user.

'''%publicprog%''' = "''C:\Documents and Settings\All Users\Documents\BESA\Research_6_0''".

'''%privateprog%''' = "''C:\Documents and Settings\[user]\My Documents\BESA\Research_6_0''", where [user] is the logon name of the current user. This folder is directly accessible from the Windows Explorer '''as "'''''My Documents\BESA\Research_6_0'''''". '''

'''%progdir%''' = the BESA Research root folder. In a default installation, this is "''C:\Program'' ''Files\BESA\\Research_6_0''".

'''%besaroot%''' is the same as '''%progdir%'''

== Electrodes ==

'''This section allows for automatic relabeling of electrodes. For instance, the 10-20 label "T3" can be replaced by the 10-10 convention "T7".'''

'''Default settings provided for section [Electrodes]:'''

T7=T3 replace 10-10 label with old 10-20 convention

T8=T4 replace 10-10 label with old 10-20 convention

P7=T5 replace 10-10 label with old 10-20 convention

P8=T6 replace 10-10 label with old 10-20 convention

X1=ECG1 define X1 channel to be ECG1

X2=ECG2 define X2 channel to be ECG2

Other examples, depending on your electrode input box definition, could be:

PG1=LO1 define X3 as lateral orbital eye electrode left

PG2=LO2 bipolar LO1-LO2 defines horizontal EOG (additional channel)

X3=IO1 infraorbital, e.g. use with FP1 as additional channel for VEOG

X9=Rsp define X9 channel to be a respiratory channel

Relabeling of channel names (as stored in the EEG file header) is helpful to predefine your standard sequence of channels and to avoid the need for reading and/or editing a Channel Configuration file for every EEG file.

'''Note 1''': For polygraphic channels, or if your EKG has been recorded differentially, you should edit and define an ''Additional Channels Montage'' according to your recording channel configuration (e.g. Fp1-IO1=vertical EOG). The Additional Channels group permits to display these channels regularly below the scalp montages with individual scales.

'''Note 2''': EOG channels record both eye and scalp activity. In digital EEG systems, EOG electrodes should be labeled according to their position in the 10-10 system (see "''Electrode Conventions''"). This permits use of these electrodes for mapping and suppression of eye artifacts. The standard definitions above give an example of how to relabel extra channels (X1...X10, PG1, PG2) for the use of EOG, EKG and respiratory (Rsp) channels. Use an ''Additional Channels'' file to define horizontal and vertical EOG channels by using the appropriate electrodes in a bipolar montage (an example is provided in '''eog-ecg.mtg''' in ''Montages\AdditionalChannels''). Differentially recorded EKG and respiratory channel can be defined in the same file.

== Patterns ==

'''Default settings provided for section [Patterns]:'''

These settings define labels for each of the five patterns. The labels are shown* in the''' Tags''' menu,
* in the '''TAG push-button''' popup menu, and
* when displaying tag info clicking with the right mouse on a tag at the bottom of the EEG or on the event bar.

By default, no labels are defined. Define a label, e.g. for Pattern1 and Pattern2, as in the following example:

Pattern1=Spike

Pattern2=Sharp Wave

== Artifacts ==

'''Artifact default settings:'''

See the chapter "''Artifact Correction / Reference / Artifact settings in the BESA.ini file''" in the online help.

== Search ==

Default settings for pattern search.

'''Default Settings for the ''Search/Options ''Dialog box:'''

'''CorrelationThreshold''' = '''75%'''

'''AmplitudeThreshold = 100 µV'''

'''GradientThreshold = 25'''

'''Default Settings for the ''Search/Average/View'' (SAV) Dialog box:'''

'''PreCursor = -250 ms'''

'''PostCursor = 150 ms'''

'''HighPassFreq = 2 Hz'''

'''HighPassSlope = 12 dB/Octave'''

'''HighPassType = 0 (0 = zero phase, 1 = forward, 2 = backward'''

'''LowPassFreq = 35 Hz'''

'''LowPassSlope = 24 dB/Octave'''

'''LowPassType = 0 (0 = zero phase, 1 = forward, 2 = backward)'''

'''CorrelationThresholdNoMarked = 60%'''

Default correlation threshold if no channel labels are marked when the SAV Dialog is opened.

'''CorrelationThresholdOneMarked = 85%'''

Default correlation threshold if one channel label is marked when the SAV Dialog is opened.

'''CorrelationThresholdFourMarked = 65%'''

Default correlation threshold if between two channel labels are marked when the SAV Dialog is opened.

'''SelectedViewWindowWidthMultiplier = 300%'''

'''WriteAfterSearch = No'''

If set to "Yes", a File Save dialog will open, to allow to save the search average to a file (as with the SAW function).

'''WriteAfterSearchCheckBox = No'''

If set to "Yes", an additional checkbox "Write after search" is displayed at the bottom of the SAV Dialog, allowing to choose whether or not to write the search average after a search:

[[Image:ST Besa ini (1).gif ‎ ]]

'''PreserveDefaults = Yes'''

If set to "No", the SAV Dialog will open with the same boxes checked as the last time the dialog was opened during the current session.

If set to "Yes", the default frequency, buffer width, selected view after search, and default threshold are always checked when the dialog is opened.

== KeyControls ==

In the [KeyControls] section you can specify functions that can be allocated to '''function keys''' or to the ''Del'' key. Specify using the form:

'''Fn=function''' or

'''Del=function'''

where "''n''" is a number between 2 and 12 (F1 is reserved for Help). For example:

    F2 = Batch1

Possible functions are:

'''Setting or removing events:'''

'''Pattern''n''''', where ''n''<nowiki>=1-5: Sets the tag number </nowiki>''n'' at the cursor latency.

'''Epochfast:''' sets one boundary of an epoch at the cursor latency, but does not open the epoch text box to define a label.

'''Marker:'''  sets a marker at the cursor latency.

'''Comment:''' sets a comment at the cursor latency and opens the comment box to enter text.

'''Epoch:''' sets one boundary of an epoch at the cursor latency and opens the epoch text box to enter a label.

'''Artifact:''' sets one boundary of an artifact segment at the cursor latency.

'''Delete:'''  deletes a tag at the cursor latency

'''Batches and Montages:'''

'''Batch''n''''', where n=1-12: Runs a predefined batch file corresponding to the number ''n''.

<div style="margin-left:0.953cm;margin-right:0cm;">If a key has not yet been associated with a batch, pressing it will open a ''File Open Dialog'' to select a batch. The setting you have chosen will be retained across BESA Research sessions. Holding the '''<shift>''' key while pressing the '''function key''' will always open the dialog. Hold the''' <ctrl> '''key with the function key to open the associated batch in the batch edit dialog.</div>

'''Montage''n''''', where n=1-12: Sets a montage corresponding to the number'' n''.

<div style="margin-left:0.953cm;margin-right:0cm;">If a key has not yet been associated with a montage, pressing it will generate a message asking you to associate a montage as follows: Holding the '''<shift> '''key while pressing the '''function key''' will remove the current association, and substitute it with the current montage.</div>

The default settings after program installation are listed in the online help chapter ''Review / Reference / Controls / Mouse and Keyboard / Keyboard Controls''.

== FFT ==

'''Default settings provided for section [FFT]:'''

These settings define the setup in the Spectral Analysis section of the BESA Research program (FFT window, see the chapter "''Spectral Analysis / FFT''"). Up to 7 frequency bands may be defined. Five are defined by default.

'''FFTBand1=On''' FFT Bands 1-5 are defined

'''FFTBand2=On'''

'''FFTBand3=On'''

'''FFTBand4=On'''

'''FFTBand5=On'''

'''FFTBand6=Off''' FFT Bands 6-7 are not defined

'''FFTBand7=Off'''

'''FFTNameBand1=Delta''' Names of the defined bands

'''FFTNameBand2=Theta'''

'''FFTNameBand3=Alpha'''

'''FFTNameBand4=Beta'''

'''FFTNameBand5=Gamma'''

'''FFTColorBand1=RGB(0,0,0)'''  Default color of each band

'''FFTColorBand2=RGB(0,128,64)'''

'''FFTColorBand3=RGB(128,0,0)'''

'''FFTColorBand4=RGB(255,0,0)'''

'''FFTColorBand5=RGB(255,128,0)'''

'''FFTColorBand6=RGB(255,192,0)'''

'''FFTColorBand7=RGB(255,255,0)'''

'''FFTLowBand1=1''' Delta from 1-4 Hz

'''FFTHighBand1=4'''

'''FFTLowBand2=4''' Theta from 4-8 Hz

'''FFTHighBand2=8'''

'''FFTLowBand3=8''' Alpha from 8-14 Hz

'''FFTHighBand3=14'''

'''FFTLowBand4=14''' Beta from 14-30 Hz

'''FFTHighBand4=30'''

'''FFTLowBand5=30''' Gamma from 30-50 Hz

'''FFTHighBand5=50'''

These values are best set from within BESA Research, using the '''Options''' menu in the FFT window (see the chapter "''Spectral Analysis / FFT / FFT Options Menu''"). Current settings are stored after each session and retrieved in the next session.

== Printer ==

'''Default settings provided for section [Printer]:'''

'''PrinterMarginPercent=100''' controls size of printout

'''PrinterColors=256''' set to 1/2 for black&white, 0/256 for color printers

'''PrinterLineMode=1''' set to 2 for thicker lines and to save printer memory

'''PrinterMapResolution=1''' set to 2, 3, 4 to save printer memory and increase speed

== Calibration ==

'''Default settings provided for section [Calibration]:'''

'''AutoCalibration=Off''' On: automatic calibration of signals >= 4 cycles

'''MicrovoltCalibration=50''' peak voltage of calibration signal

If calibration is set to'' On'', the menu item ''Calibration ''will appear in the''' Process '''menu. Position your current screen at an epoch containing at least 4 regular cycles of the calibration signal (in all channels!) and select Calibration.

== Video ==

'''Default settings provided for section [Video]:'''

'''DVCFilePath=C:\DVC\DVPlay.exe''' holds the path to the digital video player

'''DVCCommandLineArguments=/S:3 /M:P /T:M'''  arguments to be passed to the digital video player

'''CursorPagingOffsetLeft=0.2  '''

'''CursorPagingOffsetRight=0.8'''

'''CursorMinDistToBorderBeforePaging=0.02'''

'''PageDisplayIfCursorIsBelowVideo=1'''

'''MappingRepetitionRateWithVideoInMS=100'''  gives the number of milliseconds between two maps if the mapping window is open while the video is running. If the graphics board encounters problems during the display, this value should be increased.

== Mapping ==

'''Default settings provided for section [Mapping]:'''

'''UseBitmapDrawing=Off'''

Set this to "On" if 3D maps show a strange pattern of black triangular shapes (this is frequently observed with modern Intel On-Board graphics controllers, and is a result of inadequate drivers for Open-GL).

'''Use3DVBlending=Auto'''

Set this to "Off" if the 3D view in the Montage Editor or the Source Analysis window does not show up properly (this may happen with some older graphics cards).

Set this to "On" if the 3D view in the Montage Editor or the Source Analysis window shows a ragged surface boundary.

'''MapSmoothing=0 '''

Set a non-zero value to specify a default map smoothing parameter (normally specified in ''Options/Mapping/Spline Interpolation Smoothing Constant'').

== Matlab ==

'''Default settings for the [Matlab] section:'''

'''Platform=32'''

'''Set Platform=64''' if you want to use the 64-bit version of Matlab

== Updates ==

This section is not normally required, but the variables here can be altered or defined to determine how BESA Research checks for dongle and program updates.

'''DaysBetweenUpdateChecks=7'''

Sets the number of days between automatic checks for updates. Set the value to 0 to check every time BESA Research is started. Set to -1 to turn off automatic update checks.

'''CheckNetworkDongle=Off'''

For the network administrator: If set to "On", BESA Research will check the dongle on the network for updates. Otherwise the state of the network dongle will be ignored.

'''LocalPath'''

For the network administrator. This can be set to a path on the local network to the BESA update files, so that users can obtain their updates locally. The path is given to the text file "'''UpdateVersions.txt'''" (e.g. ''LocalPath=\\transtec-sak\zarascratch\BESA\Updates\UpdateVersions.txt''), which contains further details for the program to obtain its updates. If you want to use this feature, please contact us at [mailto:support@besa.de support@besa.de].

The following variables are not required, because BESA Research has the paths hardwired:

'''FTP1 (also FTP2, FTP3)'''

ftp download server

'''Path1 (also Path2, Path3)'''

Path on the server to UpdateVersions.txt.

'''HaspPath1 (also HaspPath2, HaspPath3)'''

Path on the server to HASP (dongle) update files.

'''History'''

Path on the server to general history file

== Reader-Specific Settings ==

=== BrainLab ===

'''Default settings provided for section [BrainLab]:'''

'''BrainLabFormat=New''' this entry ensures that the newer BrainLab file format can be read by BESA Research.

=== Bio-Logic ===

'''FileSelect=Yes'''

If there are several Bio-Logic files in a data folder, the reader can check if the files have the same settings. There are three possible options:

* Open a dialog to ask if the files should be treated as a single data set, or as individual, separate files.

[[Image:ST Besa ini (2).jpg ‎]]

<div style="margin-left:0.953cm;margin-right:0cm;">in this case, use '''FileSelect=Yes''' (this is the default setting) Note that the choice made in the dialog will apply to the file(s) within a BESA Research session. For a given file and session, the dialog will only be opened once, even if the file is closed and reopened.</div>

* Always concatenate such files into a single data set. In this case use '''FileSelect=All'''
* Always open the files as single, separate files. In this case use '''FileSelect=Single'''

=== EDF+/BDF/Trackit ===

'''TriggerScan=On'''

Set '''TriggerScan=Off '''to prevent BESA Research from scanning the file for triggers. This is done separately for EDF+, BDF, and Trackit files in sections '''[EDF+], [BDF],''' and '''[Trackit]''' in the '''BESA.ini''' file.

=== EGI ===

The treatment of DIN events can be modified in the''' [EGI] '''section:

'''CombineDINevents'''<nowiki>=yes/no    (default is “yes”)</nowiki>

Set to “no” if you want to treat DIN events separately, and not generate combined values.

'''SeparateDINevents'''<nowiki>=yes/no    (default is “yes”)</nowiki>

Set to “no” if you don’t want to treat DIN events separately.

Thus, using the above two parameters, you can choose whether you want to treat DIN events as combined, separate, both, or completely ignored.

'''CombineDINeventsPrefix'''<nowiki>=dinComb</nowiki>

<div style="margin-left:0.953cm;margin-right:0cm;">This defines the text preceding the number when DIN events are combined. The default is “dinComb”.</div>

=== Harmonie ===

'''Default settings provided for section [Harmonie] (Stellate Harmonie systems):'''

'''SeizurePreEpoch=60''' length of the epoch preceding a seizure detection in s

'''SeizurePostEpoch=60''' length of the epoch following a seizure detection in s

'''PushButtonPreEpoch=60''' length of the epoch preceding a push button detection

'''PushButtonPostEpoch=60''' length of the epoch following a push button detection

When BESA Research encounters a seizure detection event or a push button detection event in a Stellate Harmonie file, it automatically sets an epoch around the event, which makes it convenient to view just those epochs for analysis. The length of the epochs preceding and following the events can be adjusted in the '''.ini''' file.

=== Neuroscan Keys ===

'''Note that there is a setting "NeuroScanDataNumberOfBits" in the [Defaults] section of BESA.ini that is used for distinguishing the data format of Neuroscan files (16 or 32-bit).'''

'''Default settings provided for section [NeuroScan Keys] (NeuroScan systems):'''

Event1=Movement Text corresponding to keyboard events 1 through 10

Event2=Blink

Event3=Talking

Event4=Cough

Event5=Muscle

Event6=Jaw

Event7=Sneeze

Event8=Swallow

Event9=Eye movement

Event10=Hiccup

=== NKT2100 ===

'''Default settings provided for section [NKT2100] (Nihon Kohden EEG 21xx systems):'''

'''TriggerScan=On'''   Set to "Off" to prevent a scan for trigger events.

'''Country=NotKanji''' set to NotKanji for non-Kanji characters else to Kanji

'''KanjiCharSize=16''' Kanji character size

'''KanjiPrinterCharSize=32''' Kanji printer character size

'''EEG_Sensitivity=50''' default sensitivity of Nihon Kohden EEG-2100 system

'''DC_Sensitivity=50''' default sensitivity of Nihon Kohden DAE-2100 system

'''QJ_Sensitivity=100''' default sensitivity of Nihon Kohden QJ-403 system

'''Mark_Sensitivity=100''' default sensitivity of EEG-2100 marker channels

These settings need to be changed only if the manufacturer has specified different gains for your system. Otherwise do not alter these settings.

=== Vangard ===

'''AlwaysOpenFileSelect=Yes'''

If "Yes" is selected, each time a Vangard file is opened, a dialog box will open, asking for a selection of the segment type to display.

If "No" is selected, the selection dialog is opened whenever a Vangard file is opened for the first time, or if the ''Channel and digitized head surface point information dialog box'' is opened (e.g. with '''ctrl-L''' or ''File/Head Surface Points and Sensors/Load Coordinate Files...'' ).

=== XLTEK ===

'''TriggerScan=Off '''Set to "On" to scan the data file for trigger events

'''MontageNo=2''' Set to 1 or 2. If two montages for the data file are defined, this variable determines whether the first or the second alternative should be used.

[[Category:Research Manual]]

{{BESAManualNav}}

The Initialization File: BESA.ini

2019-03-27T13:23:22Z

Jamie: /* Introduction */

{{BESAInfobox
|title = Module information
|module = BESA Research Basic or higher
|version = 6.1 or higher
}}

== Introduction ==

'''BESA.ini File'''

BESA Research uses settings provided in the initialization file '''BESA.ini''' whenever BESA Research is started or a new file is opened for the first time. The format of this file conforms with standard initialization files ('''<nowiki>*.ini</nowiki>''') of Windows. You may change the settings in '''BESA.ini''' using NOTEPAD.exe from the ACCESSORIES group, or other plain text editors to adapt BESA Research to '''your own everyday needs'''. The default settings provided in '''BESA.ini''' will be used by BESA Research whenever BESA Research or the launch program is started. It is advised that you make a backup copy of '''BESA.ini''' before you change the default settings.

'''Location of BESA.ini'''

You can place '''BESA.ini''' at three possible locations:

# '''Private''': each user on a PC should have his/her own private settings. This is normally in ''My Documents/BESA/Research_6_1''
# '''Public''': all users should use one setting, but they can edit '''BESA.ini''' to change the settings. This is normally in ''Public Documents/BESA/Research_6_1''
# '''Administrator''': the PC administrator determines the settings. This is normally in ''C:Program Files(x86)/BESA/Research_6_1''

The actual folder names depend on the operating system and the system language.

When BESA starts, it first looks for the '''administrator''' version of '''BESA.ini'''. If this is not found, it looks for the '''private''' version. If this is not found, it looks for the '''public''' version. If this is not found, internal default values are used.

'''There are 13 general sections, and several reader-specific sections:'''

[Defaults]                    General settings (filters, scaling, and various other settings)

[Folders]                     Folders used by BESA Research (Examples, Montages, Scripts, Settings,...)

[Electrodes]                Electrode renaming

[Patterns]                    Rename patterns in the '''Tags''' menu

[Artifacts]                   Settings for artifact correction

[KEYCONTROLS]      Function key definitions

[Search]                      Default parameters for search

[FFT]                           Frequency band definitions

[Printer]                      Printer control

[Calibration]              Calibration control

[Video]                       Digital video control

[Mapping]                  Mapping control

[Updates]                   Options for program updates

[Matlab]                      Settings for the Matlab interface

[fMRI]                   Settings for the fMRI arfifact removal

[Montages]                   A setting for a default source montage

'''Reader-specific settings'''

[BrainLab]

[Bio-Logic]

[EDF+] [BDF] [Trackit]

[EGI]

[Harmonie]

[NeuroScan Keys]

[NKT2100]

[Vangard]

[XLTEK]

== Defaults ==

'''Default settings provided for section [Defaults]:'''

'''DatabaseAllowLocalFiles=Yes''' (If set to "Yes", BESA Research will write filenames "'''datafilename.ftg'''" and "'''datafilename.fst"''' to the data folder, saving current file tag and display settings there. If set to "No", these files are only written to the database. If set to "Yes", you can copy these files along with the data to a new folder, and display settings and tags will be preserved.)

'''DataBuffering=Off''' (If set to "On", an internal buffer of length 180 s of data is kept to speed up paging). This can speed up paging, particularly when the data are in a network folder.

'''DisplayedTime=10''' displayed time window [s] on the screen

'''Montage=Org''' montage used when opening a new file

'''ScpScale=50''' scale of scalp channels in [mV]

'''PgrScale=500''' scale of polygraphic channels in [mV]

'''IcrScale=500''' scale of intracranial channels in [mV]

'''MegScale=500''' scale of MEG/marker channels in [fT]

'''BaselineCorrection=On''' baseline correction, do not switch off in AC systems

'''ClippingPercent= '''set from 100 to 200 if you want to clip artifacts in displayed EEG (not used if empty or 0)

'''LowFilter=''' low filter cutoff frequency [Hz] (variable filter)

'''TimeConstant=0.3''' time constant for low filter cutoff frequency [sec] (fixed forward filter, 0.3 sec is equivalent to 0.53 Hz)

'''HighFilter=70''' high filter cutoff frequency [Hz] (variable filter)

'''NotchFilter=50''' notch filter center frequency [Hz]

'''NotchFilterStatus=Off''' notch filter is off, set=On if you want to use as default

'''BandFilter=12''' band pass filter center frequency [Hz]

'''BandFilterStatus=Off''' band pass is off, set=On if you want to use as default

'''AdditionalChannelFile=''' defines the full path and name of an additional channels montage file, e.g. '''C:\Program Files\BESA\Research_x\Montages\AdditionalChannels\EKG.sel'''

'''ColoredWaveforms=On''' scalp waveforms are (not) colored according to region

'''WriteSegmentPath=''' defines default path for saving segments/averages. If blank, the path of the current data file is used.

'''ShowSubjectInfo=Off''' subject info will (not) be displayed.

The following optional parameters are not defined as default and can be set manually in''' BESA.ini''':

'''TextEditor="Notepad.exe"''' defines the path to your preferred text editor. This will be used when you press the '''Edit''' button the ''Load Coordinate Files dialog box''.

'''NeuroScanDataNumberOfBits=32''' defines the format of NeuroScan data files ('16' for 16-bit, '32' for 32-bit). If this variable is not specified, BESA uses a heuristic to (try to) decide which of the two data formats is used. This variable overrides the heuristic. If you want to specify the NeuroScan data format for specific files, create a file, named "16bit" or "32bit", and place it in the data folder.

'''ScaleAmplitudesForNNChannels=25''' Scale waveforms as if a fixed number of channels were displayed in the window (here: 25). A minimum of 10 channels can be used for the scaling. This parameter is superseded if the parameter "''ScaleAmplitudesFixedPixelHeight"'' is specified.

'''ScaleAmplitudesFixedPixelHeight=70''' Set the scale bar for amplitudes to a fixed pixel height (here: 70). If this parameter is set in the '''.ini''' file, it supersedes the parameter "''ScaleAmplitudesForNNChannels''".

'''Notes'''

Check the Menu descriptions for the various definitions of filters, montages etc. For montage preselection, use the labels as visible on the montage push-buttons.

The additional channels file should contain all polygraphic channels (e.g. EKG, EOG, respiratory) that you want to view regularly along with the scalp channels. The entry AdditionalChannelFile must specify the full path pointing to the location of additional channel files (recommended: ''Montages\AdditionalChannels''). If no drive is specified, the installation drive of BESA is used.

If BaselineCorrection is set to 'On', before displaying a screen of data, BESA subtracts for each channel the mean over its displayed time points. This optimizes viewing, because it ensures that the vertical position of each channel is not shifted upward or downward from the channel label at the left of the screen. There are some cases in which you will not want baseline correction, i.e. when the DC level in the data is already correctly defined. This is usually the case, for instance, when reading in files that have been processed by BESA. In this case, BaselineCorrection should be set to 'Off', because otherwise maps and source montage displays may be distorted.

== Folders ==

'''The [Folders] section defines where BESA Research places its files. In versions 5.1 and earlier, files were located in various subfolders of the program folder. This led to problems if the user did not have administrator rights, e.g. to create or write to a file. For compatibility with Windows 7 and higher versions, many folders are now located by default in locations where normal users can create and write files. If you wish, you can also specify paths in the [Folders] section to use the previous locations. The previous location is given for each variable.'''

These settings allow some flexibility that can be useful if you want to tune BESA Research for use by several users, or on a network. For instance, the Examples and Montages folders might be located on a network disk. For the current defaults, the database, Examples, Montages, and Scripts are set up for use by all users on the PC on which BESA Research is installed. The settings files ('''Besa.set''', '''Besa.cfg''', etc.) are located in private folders so that each user retains his or her own settings.

The '''default''' settings (i.e. settings that BESA Research uses if the entries are omitted in the '''.ini''' file) are shown for each variable definition.

The folder definitions can use '''placeholders''', labels enclosed by a % sign (e.g. %localapp%), to define paths that vary depending on the language version and on the Windows system. These are defined below.

'''The Variables'''

'''Database=%localapp%''' The path of the BESA Research database folder (used to be ''%progdir%System\DB'' in BESA versions up to 5.1.x). Unless the provided path ends with ''\DB'' or ''\Database'', BESA Research will automatically create a folder named ''Database'' in the provided path.

'''Settings=%privatprog%Settings''' The path of the BESA Research settings folder (used to be ''%progdir%System'' in BESA versions up to 5.1.x)

'''Montages=%publicprog%Montages''' The path of the BESA Research montages folder (used to be ''%progdir%Montages'' in BESA versions up to 5.1.x)

'''Scripts=%publicprog%Scripts''' The path of the BESA Research Scripts folder (used to be ''%progdir%Scripts'' in BESA versions up to 5.1.x)

'''Examples=%publicprog%Examples''' The path of the BESA Research Examples folder (used to be ''%progdir%Examples'' in BESA versions up to 5.1.x)

'''User=%privatprog%Settings''' The path for user defined settings (used to be ''%progdir%System\Userdirs'' in BESA versions up to 5.1.x)

'''Placeholders'''

The strings enclosed by percent signs (%) are placeholders for the following folders in English-language versions of Windows. Folder names differ depending on Windows version, and for other language settings. BESA Research will substitute the placeholders by the appropriate folder name for the system and the system language:

* '''Windows 7 and higher (English):'''

'''%localapp%''' = "''C:\Users\[user]\AppData\Local\BESA\Research_6_1''", where [user] is the logon name of the current user. This folder is directly accessible from the Desktop as "''Desktop\[user]\AppData\Local\BESA\Research_6_1''".

'''%publicprog%''' = "''C:\Users\Public\Public Documents\BESA\Research_6_1''". This folder is directly accessible from the Windows Explorer under "''Libraries\Documents\Public'' ''Documents\BESA\Research_6_1''".

'''%privateprog%''' = "''C:\Users\[user]\Documents\BESA\Research_6_1''", where [user] is the logon name of the current user. This folder is directly accessible from the Windows Explorer as "''Libraries\Documents\My'' ''Documents\Research_6_1''" or "''Desktop\[User]\My Documents\BESA\Research_6_1''.

'''%progdir%''' = the BESA Research root folder. In a default installation, this is "''C:\Program'' ''Files\BESA\Research_6_1''".

'''%besaroot%''' is the same as '''%progdir%'''

* '''Windows Vista (English'''):

'''%localapp% '''<nowiki>= "</nowiki>''C:\Users\[user]\AppData\Local\BESA\Research_6_1''", where [user] is the logon name of the current user. This folder is directly accessible from the Windows Explorer as "''Desktop\[user]\AppData\Local\BESA\Research_6_1''".

'''%publicprog%''' = "''C:\Users\Public\Public Documents\BESA\Research_6_1''". This folder is directly accessible from the Windows Explorer under "''Desktop\Public\Public Documents\BESA\Research_6_1''".

'''%privateprog%''' = "''C:\Users\[user]\Documents\BESA\Research_6_1''", where [user] is the logon name of the current user. This folder is directly accessible from the Windows Explorer as "''Desktop\[user]\Documents\BESA\Research_6_1''".

'''%progdir%''' = the BESA Research root folder. In a default installation, this is "''C:\Program'' ''Files\BESA\Research_6_1''".

'''%besaroot%''' is the same as '''%progdir%'''  

* '''Windows XP (English) (note: not supported by BESA Research 6.1 and higher):'''

'''%localapp% '''<nowiki>= "</nowiki>''C:\Documents and Settings\[user]\Local Settings\Application Data\BESA\Research_6_0''", where [user] is the logon name of the current user.

'''%publicprog%''' = "''C:\Documents and Settings\All Users\Documents\BESA\Research_6_0". ''This folder is directly accessible from the Windows Explorer under "''My Computer\Shared'' ''Documents\BESA\Research_6_0''".

'''%privateprog%''' = "''C:\Documents and Settings\[user]\My Documents\BESA\Research_6_0''", where [user] is the logon name of the current user. This folder is directly accessible from the Windows Explorer as "''My Documents\BESA\Research_6_0''".

'''%progdir%''' = the BESA Research root folder. In a default installation, this is "''C:\Program'' ''Files\BESA\Research_6_0''".

'''%besaroot%''' is the same as '''%progdir%  '''

* '''Windows 2000 (English) (note: not supported by BESA Research 6.1 and higher):'''

'''%localapp%''' = "''C:\Documents and Settings\[user]\Local Settings\Application Data\BESA\Research_6_0''", where [user] is the logon name of the current user.

'''%publicprog%''' = "''C:\Documents and Settings\All Users\Documents\BESA\Research_6_0''".

'''%privateprog%''' = "''C:\Documents and Settings\[user]\My Documents\BESA\Research_6_0''", where [user] is the logon name of the current user. This folder is directly accessible from the Windows Explorer '''as "'''''My Documents\BESA\Research_6_0'''''". '''

'''%progdir%''' = the BESA Research root folder. In a default installation, this is "''C:\Program'' ''Files\BESA\\Research_6_0''".

'''%besaroot%''' is the same as '''%progdir%'''

== Electrodes ==

'''This section allows for automatic relabeling of electrodes. For instance, the 10-20 label "T3" can be replaced by the 10-10 convention "T7".'''

'''Default settings provided for section [Electrodes]:'''

T7=T3 replace 10-10 label with old 10-20 convention

T8=T4 replace 10-10 label with old 10-20 convention

P7=T5 replace 10-10 label with old 10-20 convention

P8=T6 replace 10-10 label with old 10-20 convention

X1=ECG1 define X1 channel to be ECG1

X2=ECG2 define X2 channel to be ECG2

Other examples, depending on your electrode input box definition, could be:

PG1=LO1 define X3 as lateral orbital eye electrode left

PG2=LO2 bipolar LO1-LO2 defines horizontal EOG (additional channel)

X3=IO1 infraorbital, e.g. use with FP1 as additional channel for VEOG

X9=Rsp define X9 channel to be a respiratory channel

Relabeling of channel names (as stored in the EEG file header) is helpful to predefine your standard sequence of channels and to avoid the need for reading and/or editing a Channel Configuration file for every EEG file.

'''Note 1''': For polygraphic channels, or if your EKG has been recorded differentially, you should edit and define an ''Additional Channels Montage'' according to your recording channel configuration (e.g. Fp1-IO1=vertical EOG). The Additional Channels group permits to display these channels regularly below the scalp montages with individual scales.

'''Note 2''': EOG channels record both eye and scalp activity. In digital EEG systems, EOG electrodes should be labeled according to their position in the 10-10 system (see "''Electrode Conventions''"). This permits use of these electrodes for mapping and suppression of eye artifacts. The standard definitions above give an example of how to relabel extra channels (X1...X10, PG1, PG2) for the use of EOG, EKG and respiratory (Rsp) channels. Use an ''Additional Channels'' file to define horizontal and vertical EOG channels by using the appropriate electrodes in a bipolar montage (an example is provided in '''eog-ecg.mtg''' in ''Montages\AdditionalChannels''). Differentially recorded EKG and respiratory channel can be defined in the same file.

== Patterns ==

'''Default settings provided for section [Patterns]:'''

These settings define labels for each of the five patterns. The labels are shown* in the''' Tags''' menu,
* in the '''TAG push-button''' popup menu, and
* when displaying tag info clicking with the right mouse on a tag at the bottom of the EEG or on the event bar.

By default, no labels are defined. Define a label, e.g. for Pattern1 and Pattern2, as in the following example:

Pattern1=Spike

Pattern2=Sharp Wave

== Artifacts ==

'''Artifact default settings:'''

See the chapter "''Artifact Correction / Reference / Artifact settings in the BESA.ini file''" in the online help.

== Search ==

Default settings for pattern search.

'''Default Settings for the ''Search/Options ''Dialog box:'''

'''CorrelationThreshold''' = '''75%'''

'''AmplitudeThreshold = 100 µV'''

'''GradientThreshold = 25'''

'''Default Settings for the ''Search/Average/View'' (SAV) Dialog box:'''

'''PreCursor = -250 ms'''

'''PostCursor = 150 ms'''

'''HighPassFreq = 2 Hz'''

'''HighPassSlope = 12 dB/Octave'''

'''HighPassType = 0 (0 = zero phase, 1 = forward, 2 = backward'''

'''LowPassFreq = 35 Hz'''

'''LowPassSlope = 24 dB/Octave'''

'''LowPassType = 0 (0 = zero phase, 1 = forward, 2 = backward)'''

'''CorrelationThresholdNoMarked = 60%'''

Default correlation threshold if no channel labels are marked when the SAV Dialog is opened.

'''CorrelationThresholdOneMarked = 85%'''

Default correlation threshold if one channel label is marked when the SAV Dialog is opened.

'''CorrelationThresholdFourMarked = 65%'''

Default correlation threshold if between two channel labels are marked when the SAV Dialog is opened.

'''SelectedViewWindowWidthMultiplier = 300%'''

'''WriteAfterSearch = No'''

If set to "Yes", a File Save dialog will open, to allow to save the search average to a file (as with the SAW function).

'''WriteAfterSearchCheckBox = No'''

If set to "Yes", an additional checkbox "Write after search" is displayed at the bottom of the SAV Dialog, allowing to choose whether or not to write the search average after a search:

[[Image:ST Besa ini (1).gif ‎ ]]

'''PreserveDefaults = Yes'''

If set to "No", the SAV Dialog will open with the same boxes checked as the last time the dialog was opened during the current session.

If set to "Yes", the default frequency, buffer width, selected view after search, and default threshold are always checked when the dialog is opened.

== KeyControls ==

In the [KeyControls] section you can specify functions that can be allocated to '''function keys''' or to the ''Del'' key. Specify using the form:

'''Fn=function''' or

'''Del=function'''

where "''n''" is a number between 2 and 12 (F1 is reserved for Help). For example:

    F2 = Batch1

Possible functions are:

'''Setting or removing events:'''

'''Pattern''n''''', where ''n''<nowiki>=1-5: Sets the tag number </nowiki>''n'' at the cursor latency.

'''Epochfast:''' sets one boundary of an epoch at the cursor latency, but does not open the epoch text box to define a label.

'''Marker:'''  sets a marker at the cursor latency.

'''Comment:''' sets a comment at the cursor latency and opens the comment box to enter text.

'''Epoch:''' sets one boundary of an epoch at the cursor latency and opens the epoch text box to enter a label.

'''Artifact:''' sets one boundary of an artifact segment at the cursor latency.

'''Delete:'''  deletes a tag at the cursor latency

'''Batches and Montages:'''

'''Batch''n''''', where n=1-12: Runs a predefined batch file corresponding to the number ''n''.

<div style="margin-left:0.953cm;margin-right:0cm;">If a key has not yet been associated with a batch, pressing it will open a ''File Open Dialog'' to select a batch. The setting you have chosen will be retained across BESA Research sessions. Holding the '''<shift>''' key while pressing the '''function key''' will always open the dialog. Hold the''' <ctrl> '''key with the function key to open the associated batch in the batch edit dialog.</div>

'''Montage''n''''', where n=1-12: Sets a montage corresponding to the number'' n''.

<div style="margin-left:0.953cm;margin-right:0cm;">If a key has not yet been associated with a montage, pressing it will generate a message asking you to associate a montage as follows: Holding the '''<shift> '''key while pressing the '''function key''' will remove the current association, and substitute it with the current montage.</div>

The default settings after program installation are listed in the online help chapter ''Review / Reference / Controls / Mouse and Keyboard / Keyboard Controls''.

== FFT ==

'''Default settings provided for section [FFT]:'''

These settings define the setup in the Spectral Analysis section of the BESA Research program (FFT window, see the chapter "''Spectral Analysis / FFT''"). Up to 7 frequency bands may be defined. Five are defined by default.

'''FFTBand1=On''' FFT Bands 1-5 are defined

'''FFTBand2=On'''

'''FFTBand3=On'''

'''FFTBand4=On'''

'''FFTBand5=On'''

'''FFTBand6=Off''' FFT Bands 6-7 are not defined

'''FFTBand7=Off'''

'''FFTNameBand1=Delta''' Names of the defined bands

'''FFTNameBand2=Theta'''

'''FFTNameBand3=Alpha'''

'''FFTNameBand4=Beta'''

'''FFTNameBand5=Gamma'''

'''FFTColorBand1=RGB(0,0,0)'''  Default color of each band

'''FFTColorBand2=RGB(0,128,64)'''

'''FFTColorBand3=RGB(128,0,0)'''

'''FFTColorBand4=RGB(255,0,0)'''

'''FFTColorBand5=RGB(255,128,0)'''

'''FFTColorBand6=RGB(255,192,0)'''

'''FFTColorBand7=RGB(255,255,0)'''

'''FFTLowBand1=1''' Delta from 1-4 Hz

'''FFTHighBand1=4'''

'''FFTLowBand2=4''' Theta from 4-8 Hz

'''FFTHighBand2=8'''

'''FFTLowBand3=8''' Alpha from 8-14 Hz

'''FFTHighBand3=14'''

'''FFTLowBand4=14''' Beta from 14-30 Hz

'''FFTHighBand4=30'''

'''FFTLowBand5=30''' Gamma from 30-50 Hz

'''FFTHighBand5=50'''

These values are best set from within BESA Research, using the '''Options''' menu in the FFT window (see the chapter "''Spectral Analysis / FFT / FFT Options Menu''"). Current settings are stored after each session and retrieved in the next session.

== Printer ==

'''Default settings provided for section [Printer]:'''

'''PrinterMarginPercent=100''' controls size of printout

'''PrinterColors=256''' set to 1/2 for black&white, 0/256 for color printers

'''PrinterLineMode=1''' set to 2 for thicker lines and to save printer memory

'''PrinterMapResolution=1''' set to 2, 3, 4 to save printer memory and increase speed

== Calibration ==

'''Default settings provided for section [Calibration]:'''

'''AutoCalibration=Off''' On: automatic calibration of signals >= 4 cycles

'''MicrovoltCalibration=50''' peak voltage of calibration signal

If calibration is set to'' On'', the menu item ''Calibration ''will appear in the''' Process '''menu. Position your current screen at an epoch containing at least 4 regular cycles of the calibration signal (in all channels!) and select Calibration.

== Video ==

'''Default settings provided for section [Video]:'''

'''DVCFilePath=C:\DVC\DVPlay.exe''' holds the path to the digital video player

'''DVCCommandLineArguments=/S:3 /M:P /T:M'''  arguments to be passed to the digital video player

'''CursorPagingOffsetLeft=0.2  '''

'''CursorPagingOffsetRight=0.8'''

'''CursorMinDistToBorderBeforePaging=0.02'''

'''PageDisplayIfCursorIsBelowVideo=1'''

'''MappingRepetitionRateWithVideoInMS=100'''  gives the number of milliseconds between two maps if the mapping window is open while the video is running. If the graphics board encounters problems during the display, this value should be increased.

== Mapping ==

'''Default settings provided for section [Mapping]:'''

'''UseBitmapDrawing=Off'''

Set this to "On" if 3D maps show a strange pattern of black triangular shapes (this is frequently observed with modern Intel On-Board graphics controllers, and is a result of inadequate drivers for Open-GL).

'''Use3DVBlending=Auto'''

Set this to "Off" if the 3D view in the Montage Editor or the Source Analysis window does not show up properly (this may happen with some older graphics cards).

Set this to "On" if the 3D view in the Montage Editor or the Source Analysis window shows a ragged surface boundary.

'''MapSmoothing=0 '''

Set a non-zero value to specify a default map smoothing parameter (normally specified in ''Options/Mapping/Spline Interpolation Smoothing Constant'').

== Matlab ==

'''Default settings for the [Matlab] section:'''

'''Platform=32'''

'''Set Platform=64''' if you want to use the 64-bit version of Matlab

== Updates ==

This section is not normally required, but the variables here can be altered or defined to determine how BESA Research checks for dongle and program updates.

'''DaysBetweenUpdateChecks=7'''

Sets the number of days between automatic checks for updates. Set the value to 0 to check every time BESA Research is started. Set to -1 to turn off automatic update checks.

'''CheckNetworkDongle=Off'''

For the network administrator: If set to "On", BESA Research will check the dongle on the network for updates. Otherwise the state of the network dongle will be ignored.

'''LocalPath'''

For the network administrator. This can be set to a path on the local network to the BESA update files, so that users can obtain their updates locally. The path is given to the text file "'''UpdateVersions.txt'''" (e.g. ''LocalPath=\\transtec-sak\zarascratch\BESA\Updates\UpdateVersions.txt''), which contains further details for the program to obtain its updates. If you want to use this feature, please contact us at [mailto:support@besa.de support@besa.de].

The following variables are not required, because BESA Research has the paths hardwired:

'''FTP1 (also FTP2, FTP3)'''

ftp download server

'''Path1 (also Path2, Path3)'''

Path on the server to UpdateVersions.txt.

'''HaspPath1 (also HaspPath2, HaspPath3)'''

Path on the server to HASP (dongle) update files.

'''History'''

Path on the server to general history file

== Reader-Specific Settings ==

=== BrainLab ===

'''Default settings provided for section [BrainLab]:'''

'''BrainLabFormat=New''' this entry ensures that the newer BrainLab file format can be read by BESA Research.

=== Bio-Logic ===

'''FileSelect=Yes'''

If there are several Bio-Logic files in a data folder, the reader can check if the files have the same settings. There are three possible options:

* Open a dialog to ask if the files should be treated as a single data set, or as individual, separate files.

[[Image:ST Besa ini (2).jpg ‎]]

<div style="margin-left:0.953cm;margin-right:0cm;">in this case, use '''FileSelect=Yes''' (this is the default setting) Note that the choice made in the dialog will apply to the file(s) within a BESA Research session. For a given file and session, the dialog will only be opened once, even if the file is closed and reopened.</div>

* Always concatenate such files into a single data set. In this case use '''FileSelect=All'''
* Always open the files as single, separate files. In this case use '''FileSelect=Single'''

=== EDF+/BDF/Trackit ===

'''TriggerScan=On'''

Set '''TriggerScan=Off '''to prevent BESA Research from scanning the file for triggers. This is done separately for EDF+, BDF, and Trackit files in sections '''[EDF+], [BDF],''' and '''[Trackit]''' in the '''BESA.ini''' file.

=== EGI ===

The treatment of DIN events can be modified in the''' [EGI] '''section:

'''CombineDINevents'''<nowiki>=yes/no    (default is “yes”)</nowiki>

Set to “no” if you want to treat DIN events separately, and not generate combined values.

'''SeparateDINevents'''<nowiki>=yes/no    (default is “yes”)</nowiki>

Set to “no” if you don’t want to treat DIN events separately.

Thus, using the above two parameters, you can choose whether you want to treat DIN events as combined, separate, both, or completely ignored.

'''CombineDINeventsPrefix'''<nowiki>=dinComb</nowiki>

<div style="margin-left:0.953cm;margin-right:0cm;">This defines the text preceding the number when DIN events are combined. The default is “dinComb”.</div>

=== Harmonie ===

'''Default settings provided for section [Harmonie] (Stellate Harmonie systems):'''

'''SeizurePreEpoch=60''' length of the epoch preceding a seizure detection in s

'''SeizurePostEpoch=60''' length of the epoch following a seizure detection in s

'''PushButtonPreEpoch=60''' length of the epoch preceding a push button detection

'''PushButtonPostEpoch=60''' length of the epoch following a push button detection

When BESA Research encounters a seizure detection event or a push button detection event in a Stellate Harmonie file, it automatically sets an epoch around the event, which makes it convenient to view just those epochs for analysis. The length of the epochs preceding and following the events can be adjusted in the '''.ini''' file.

=== Neuroscan Keys ===

'''Note that there is a setting "NeuroScanDataNumberOfBits" in the [Defaults] section of BESA.ini that is used for distinguishing the data format of Neuroscan files (16 or 32-bit).'''

'''Default settings provided for section [NeuroScan Keys] (NeuroScan systems):'''

Event1=Movement Text corresponding to keyboard events 1 through 10

Event2=Blink

Event3=Talking

Event4=Cough

Event5=Muscle

Event6=Jaw

Event7=Sneeze

Event8=Swallow

Event9=Eye movement

Event10=Hiccup

=== NKT2100 ===

'''Default settings provided for section [NKT2100] (Nihon Kohden EEG 21xx systems):'''

'''TriggerScan=On'''   Set to "Off" to prevent a scan for trigger events.

'''Country=NotKanji''' set to NotKanji for non-Kanji characters else to Kanji

'''KanjiCharSize=16''' Kanji character size

'''KanjiPrinterCharSize=32''' Kanji printer character size

'''EEG_Sensitivity=50''' default sensitivity of Nihon Kohden EEG-2100 system

'''DC_Sensitivity=50''' default sensitivity of Nihon Kohden DAE-2100 system

'''QJ_Sensitivity=100''' default sensitivity of Nihon Kohden QJ-403 system

'''Mark_Sensitivity=100''' default sensitivity of EEG-2100 marker channels

These settings need to be changed only if the manufacturer has specified different gains for your system. Otherwise do not alter these settings.

=== Vangard ===

'''AlwaysOpenFileSelect=Yes'''

If "Yes" is selected, each time a Vangard file is opened, a dialog box will open, asking for a selection of the segment type to display.

If "No" is selected, the selection dialog is opened whenever a Vangard file is opened for the first time, or if the ''Channel and digitized head surface point information dialog box'' is opened (e.g. with '''ctrl-L''' or ''File/Head Surface Points and Sensors/Load Coordinate Files...'' ).

=== XLTEK ===

'''TriggerScan=Off '''Set to "On" to scan the data file for trigger events

'''MontageNo=2''' Set to 1 or 2. If two montages for the data file are defined, this variable determines whether the first or the second alternative should be used.

[[Category:Research Manual]]

{{BESAManualNav}}

MATLAB Interface

2019-03-27T13:07:45Z

Jamie: /* Configuration */

{{BESAInfobox
|title = Module information
|module = BESA Research Basic or higher
|version = 6.1 or higher
}}

= MATLAB Interface =

== Introduction ==

BESA Research has menu items ''"Send to MATLAB..."'' at various locations that allow to send data as structures to Matlab. After sending the data, BESA Research starts a Matlab script that can be used to start further data analysis on the data structure. These scripts, located in the ''Scripts\Matlab'' folder in the BESA Research installation, can be edited by the user to perform further data analysis in Matlab. For example, if "''Send to MATLAB''" is selected in the ''File Export Dialog'', a data structure "''besa_channels''" will be created. After filling the structure, the script "''besa_action_channels.m''" will be started.

All the Matlab export functions are batchable. Thus, a complete data analysis can be performed, in which BESA Research does the preprocessing, and passes the data on to Matlab for a statistical analysis of the results.

An example for the application of the MATLAB interface is demonstrated in the BESA Research Tutorial on Batch Scripts, Multiple Subjects & Conditions, MATLAB-Interface. You can download this tutorial from our website at www.besa.de/downloads/training-material/tutorials/.

Some MATLAB scripts that can be used in conjunction with the BESA Research MATLAB interface are also available on our website at www.besa.de/downloads/matlab/. You are invited to send your own scripts for data analysis or to submit any questions or feedback here: www.besa.de/support/support-page/.

'''Important! Please follow the instructions in the “''Installation” ''chapter! Then read the “''How the interface'' ''works” ''section to get started.'''

== Configuration ==

In order for the BESA-Matlab interface to work, please follow the instructions below. If you start BESA Research, and the file menu does not display the "''Send to MATLAB''" item, the interface is not installed correctly!

'''1'''. '''Matlab must be installed.'''

For step 2 (required for MATLAB versions 2009b and over), we need to know whether the 32-bit or 64-bit version of Matlab is installed. We also need to know the path to the Matlab installation (e.g. ''c:\Program'' ''Files\MATLAB\2009b\)''.

'''2'''. '''PATH environment variable:'''

For versions 2009b and over, make sure that the path to the Win32 or Win64 folder in the Matlab installation to the PATH environment variable is defined:

* The path for the 64-bit version for Matlab 2009b is typically ''c:\Program'' ''Files\MATLAB\2009b\bin\win64''. For the 32-bit version, the path is typically ''c:\Program Files\MATLAB\2009b\bin\win32''.
* Open the "System Properties" Dialog by holding down the '''Windows''' key and pressing the '''Pause '''button. In XP, the dialog is opened directly. In Vista and Window 7, the key combination opens the System Display. Click on the link "Change Settings".

[[Image:Matlab (1) .gif]]

* Select the "Advanced" tab.

[[Image:Matlab (2) .gif]]

* Press the "'''Environment Variables'''" button.

[[Image:Matlab (3) .gif]]

* Under "System variables" click on the "Path" variable and press "'''Edit'''". In the resulting dialog, enter a semicolon (;) at the end of the path string, and add the path after the semicolon.

[[Image:Matlab (4) .gif]]

* Press "'''OK'''" to close and save the path variable. Press "'''OK'''" to close the "System Properties" Dialog.

'''3. Additional configuration''' (only required after a change of your MATLAB configuration after installation of BESA Research):

During the installation process of BESA Research, the program "''SetupBesaMatlabInterface.exe''" in the BESA Research root folder was executed. Run this program again when your MATLAB configuration has changed, e.g. after updating your MATLAB version.

In the dropdown list, select the Matlab version that you are using.

This program does two operations:

1. it copies the appropriate interface Dll to the BESA Research root folder and renames it to "'''BesaMatlab.dll'''" (32-bit version) or "'''BesaMatlab64.dll'''" (64-bit version), and

2. if you are using a 64-bit version it creates an entry in '''BESA.ini''' as follows:

[Matlab]

Platform=64

'''4. Testing:'''

Start BESA Research and check if ''Send to MATLAB ''is displayed in the''' File '''menu. If it is, the interface is set up correctly. (Note that the item will be grayed if no file is open in BESA Research.)

Test the interface: open a data file, mark a short (e.g. 1 s) time range, and select ''File / Send to Matlab'' to open the ''Export Dialog'':

[[Image:Matlab1.png]]

The Matlab window should open, and BESA Research will display a progress bar:

[[Image:Matlab (6) .gif]]

After the window closes, open the Matlab window, and type "'''<code>workspace</code>'''" to open the workspace window, or "'''<code>desktop</code>'''" to open the standard Matlab desktop.

Examine the "'''<code>besa_channels</code>'''" variable, which contains the data for the marked data segment.

[[Image:Matlab (7) .gif]]

'''Troubleshooting if the interface is not working after the above steps'''

If the ''File / Send to MATLAB''... menu item is not shown, this means that either the path (step 2 above) is not defined properly, or that the interface Dll '''BesaMatlab.dll''' or '''BesaMatlab64.dll''' is not compatible with the currently installed version of Matlab.

If the path is correct, then please contact our support team here: [http://besa.de/contact/support/form.php http://besa.de/contact/support/form.php], including the following information:
* Which Matlab version are you using?
* Specify also if you are using the 32-bit or 64-bit version.

== How the interface works ==

'''The interface'''

The interface uses libraries supplied by Matlab. Their descriptions can be found in Matlab Help under the keywords "Engine Library". The Matlab libraries are incorporated into the interface Dll ('''BesaMatlab.dll''' or '''BesaMatlab64.dll''') that provides the interface between BESA Research and Matlab. As newer versions of Matlab are released, it may be necessary to generate new versions of the dll to match the new library versions.

'''Matlab automation window'''

On the first call to one of the Matlab routines, the Matlab Automation Window is opened. This is not the same as the window that is normally opened when Matlab is started directly in Windows (the window can also be opened by typing "Matlab /automation" from the command line). From the Automation Window one can run normal Matlab scripts. It is also possible to type "'''<code>desktop</code>'''" in the Automation Window to open the standard Matlab desktop. All variables that have been sent from BESA Research are then visible there.

'''BESA Research "Send to MATLAB" commands and scripts'''

Send to MATLAB commands generate data structures that differ depending on the type of data that are sent. After each export the corresponding script is executed. They are available at the following locations in BESA Research:
* From the Main program window ('''File''' Menu), as part of the ''Export Dialog''. Structure name ''besa_channels''. Script name ''besa_action_channels.m''.
* From the FFT analysis ('''File''' Menu). Structure name ''besa_fft''. Script name ''besa_action_fft.m''.
* From Combine Conditions (''Run Scripts Tab''), in the export of peaks and mean amplitudes. Structure name ''besa_peak''. Script name ''besa_action_peak.m''.
* From Source Analysis ('''File''' Menu), for exporting source waveforms (''besa_sourcewaveforms''), source models (''besa_sourcemodel''), data, residual and model waveforms (''besa_sa_channels''), and 3D images (''besa_image''). Script names ''besa_action_sourcewaveforms.m'', ''besa_action_sourcemodel.m'', ''besa_action_sa_channels.m'', and ''besa_action_image.m''.
* From Time-Frequency/Coherence Analysis ('''File''' Menu). Structure names ''besa_tfc'', and ''besa_tfc_trials'' (for single-trial time-frequency data). Script names ''besa_action_tfc.m'' and ''besa_action_tfc_trials.m''.

Some additional scripts are used for specific data types. For example, when exporting raw data, two scripts, ''besa_helper_channels_event.m'' and ''besa_helper_channels_continuousdata.m'' are used to collect events from each data block and to combine the exported data blocks into a single matrix.

'''Command script path'''

When the commands are executed, BESA Research automatically executes an "addpath" command in Matlab to add the ''Scripts\MATLAB'' folder (in Windows 7 typically ''C:\Users\Public\Public'' ''Documents\BESA\Research_6_0\Scripts\MATLAB'') and its first-level subfolders to the Matlab search path.

'''Units'''

Unless otherwise stated, distances are in meters, times are in seconds, and the head-frame (fiducial-based) coordinate system is used.

[[Category:Research Manual]]

{{BESAManualNav}}

File:Matlab1.png

2019-03-27T13:07:02Z

Jamie:

MATLAB Interface

2019-03-27T13:03:06Z

Jamie: /* Introduction */

{{BESAInfobox
|title = Module information
|module = BESA Research Basic or higher
|version = 6.1 or higher
}}

= MATLAB Interface =

== Introduction ==

BESA Research has menu items ''"Send to MATLAB..."'' at various locations that allow to send data as structures to Matlab. After sending the data, BESA Research starts a Matlab script that can be used to start further data analysis on the data structure. These scripts, located in the ''Scripts\Matlab'' folder in the BESA Research installation, can be edited by the user to perform further data analysis in Matlab. For example, if "''Send to MATLAB''" is selected in the ''File Export Dialog'', a data structure "''besa_channels''" will be created. After filling the structure, the script "''besa_action_channels.m''" will be started.

All the Matlab export functions are batchable. Thus, a complete data analysis can be performed, in which BESA Research does the preprocessing, and passes the data on to Matlab for a statistical analysis of the results.

An example for the application of the MATLAB interface is demonstrated in the BESA Research Tutorial on Batch Scripts, Multiple Subjects & Conditions, MATLAB-Interface. You can download this tutorial from our website at www.besa.de/downloads/training-material/tutorials/.

Some MATLAB scripts that can be used in conjunction with the BESA Research MATLAB interface are also available on our website at www.besa.de/downloads/matlab/. You are invited to send your own scripts for data analysis or to submit any questions or feedback here: www.besa.de/support/support-page/.

'''Important! Please follow the instructions in the “''Installation” ''chapter! Then read the “''How the interface'' ''works” ''section to get started.'''

== Configuration ==

In order for the BESA-Matlab interface to work, please follow the instructions below. If you start BESA Research, and the file menu does not display the "''Send to MATLAB''" item, the interface is not installed correctly!

'''1'''. '''Matlab must be installed.'''

For step 2 (required for MATLAB versions 2009b and over), we need to know whether the 32-bit or 64-bit version of Matlab is installed. We also need to know the path to the Matlab installation (e.g. ''c:\Program'' ''Files\MATLAB\2009b\)''.

'''2'''. '''PATH environment variable:'''

For versions 2009b and over, make sure that the path to the Win32 or Win64 folder in the Matlab installation to the PATH environment variable is defined:

* The path for the 64-bit version for Matlab 2009b is typically ''c:\Program'' ''Files\MATLAB\2009b\bin\win64''. For the 32-bit version, the path is typically ''c:\Program Files\MATLAB\2009b\bin\win32''.
* Open the "System Properties" Dialog by holding down the '''Windows''' key and pressing the '''Pause '''button. In XP, the dialog is opened directly. In Vista and Window 7, the key combination opens the System Display. Click on the link "Change Settings".

[[Image:Matlab (1) .gif]]

* Select the "Advanced" tab.

[[Image:Matlab (2) .gif]]

* Press the "'''Environment Variables'''" button.

[[Image:Matlab (3) .gif]]

* Under "System variables" click on the "Path" variable and press "'''Edit'''". In the resulting dialog, enter a semicolon (;) at the end of the path string, and add the path after the semicolon.

[[Image:Matlab (4) .gif]]

* Press "'''OK'''" to close and save the path variable. Press "'''OK'''" to close the "System Properties" Dialog.

'''3. Additional configuration''' (only required after a change of your MATLAB configuration after installation of BESA Research):

During the installation process of BESA Research, the program "''SetupBesaMatlabInterface.exe''" in the BESA Research root folder was executed. Run this program again when your MATLAB configuration has changed, e.g. after updating your MATLAB version.

In the dropdown list, select the Matlab version that you are using.

This program does two operations:

1. it copies the appropriate interface Dll to the BESA Research root folder and renames it to "'''BesaMatlab.dll'''" (32-bit version) or "'''BesaMatlab64.dll'''" (64-bit version), and

2. if you are using a 64-bit version it creates an entry in '''BESA.ini''' as follows:

[Matlab]

Platform=64

'''4. Testing:'''

Start BESA Research and check if ''Send to MATLAB ''is displayed in the''' File '''menu. If it is, the interface is set up correctly. (Note that the item will be grayed if no file is open in BESA Research.)

Test the interface: open a data file, mark a short (e.g. 1 s) time range, and select ''File / Send to Matlab'' to open the ''Export Dialog'':

[[Image:Matlab (5) .gif]]

The Matlab window should open, and BESA Research will display a progress bar:

[[Image:Matlab (6) .gif]]

After the window closes, open the Matlab window, and type "'''<code>workspace</code>'''" to open the workspace window, or "'''<code>desktop</code>'''" to open the standard Matlab desktop.

Examine the "'''<code>besa_channels</code>'''" variable, which contains the data for the marked data segment.

[[Image:Matlab (7) .gif]]

'''Troubleshooting if the interface is not working after the above steps'''

If the ''File / Send to MATLAB''... menu item is not shown, this means that either the path (step 2 above) is not defined properly, or that the interface Dll '''BesaMatlab.dll''' or '''BesaMatlab64.dll''' is not compatible with the currently installed version of Matlab.

If the path is correct, then please contact our support team here: [http://besa.de/contact/support/form.php http://besa.de/contact/support/form.php], including the following information:
* Which Matlab version are you using?
* Specify also if you are using the 32-bit or 64-bit version.

== How the interface works ==

'''The interface'''

The interface uses libraries supplied by Matlab. Their descriptions can be found in Matlab Help under the keywords "Engine Library". The Matlab libraries are incorporated into the interface Dll ('''BesaMatlab.dll''' or '''BesaMatlab64.dll''') that provides the interface between BESA Research and Matlab. As newer versions of Matlab are released, it may be necessary to generate new versions of the dll to match the new library versions.

'''Matlab automation window'''

On the first call to one of the Matlab routines, the Matlab Automation Window is opened. This is not the same as the window that is normally opened when Matlab is started directly in Windows (the window can also be opened by typing "Matlab /automation" from the command line). From the Automation Window one can run normal Matlab scripts. It is also possible to type "'''<code>desktop</code>'''" in the Automation Window to open the standard Matlab desktop. All variables that have been sent from BESA Research are then visible there.

'''BESA Research "Send to MATLAB" commands and scripts'''

Send to MATLAB commands generate data structures that differ depending on the type of data that are sent. After each export the corresponding script is executed. They are available at the following locations in BESA Research:
* From the Main program window ('''File''' Menu), as part of the ''Export Dialog''. Structure name ''besa_channels''. Script name ''besa_action_channels.m''.
* From the FFT analysis ('''File''' Menu). Structure name ''besa_fft''. Script name ''besa_action_fft.m''.
* From Combine Conditions (''Run Scripts Tab''), in the export of peaks and mean amplitudes. Structure name ''besa_peak''. Script name ''besa_action_peak.m''.
* From Source Analysis ('''File''' Menu), for exporting source waveforms (''besa_sourcewaveforms''), source models (''besa_sourcemodel''), data, residual and model waveforms (''besa_sa_channels''), and 3D images (''besa_image''). Script names ''besa_action_sourcewaveforms.m'', ''besa_action_sourcemodel.m'', ''besa_action_sa_channels.m'', and ''besa_action_image.m''.
* From Time-Frequency/Coherence Analysis ('''File''' Menu). Structure names ''besa_tfc'', and ''besa_tfc_trials'' (for single-trial time-frequency data). Script names ''besa_action_tfc.m'' and ''besa_action_tfc_trials.m''.

Some additional scripts are used for specific data types. For example, when exporting raw data, two scripts, ''besa_helper_channels_event.m'' and ''besa_helper_channels_continuousdata.m'' are used to collect events from each data block and to combine the exported data blocks into a single matrix.

'''Command script path'''

When the commands are executed, BESA Research automatically executes an "addpath" command in Matlab to add the ''Scripts\MATLAB'' folder (in Windows 7 typically ''C:\Users\Public\Public'' ''Documents\BESA\Research_6_0\Scripts\MATLAB'') and its first-level subfolders to the Matlab search path.

'''Units'''

Unless otherwise stated, distances are in meters, times are in seconds, and the head-frame (fiducial-based) coordinate system is used.

[[Category:Research Manual]]

{{BESAManualNav}}

Export

2019-03-27T12:59:49Z

Jamie: /* Export Dialog */

{{BESAInfobox
|title = Module information
|module = BESA Research Basic or higher
|version = 6.1 or higher
}}

== Exporting files from BESA ==

Data can be exported from BESA Research in the following formats:
* BESA's own binary format (compressed or uncompressed)
* ASCII multiplexed
* ASCII vectorized (short files only)
* EDF+
* simple floating point matrix (e.g. for exporting data to Matlab)
* Send the data directly to Matlab

You can export
* The entire data set or between markers
* The currently marked segment
* Epochs around triggers
* Standard deviations from binary average files ('''*.fsg''')

Export is allowed to various montages:
* filtered or unfiltered data
* original data
* current montage (including artifact correction if applied)
* standard 81-electrode montage.

On export, you can choose to change the sampling rate.

If exporting to BESA's binary format, you can optionally append the data to a preexisting data set, if sampling rates and the number of channels match. Therefore, please use the Combine Conditions module.

Export is started either
* select File / Export...
* press the '''WrS '''button.
* In both cases, you are taken to the ''Export Dialog''.
* for Send to Matlab only: select File / Send To MATLAB... This also opens the Export Dialog, but only the '''Send To Matlab radio''' button is enabled as target format in the dialog.

== Export Dialog ==

[[Image:Export1.png]]

The dialog is started when you select'' File / Export...'' or press the '''WrS''' button or select '''Write Segment''' in the right click context menu when a segment has been highlighted.

The dialog is divided into four sections. Please read the following chapters for more details:
* ''Data to export''. Describes which data are to be exported.
* ''Montage and Filters.'' Which montage is to be exported, and whether or not filters are used.
* ''Target data formats''. Specify the format of the exported data.
* ''Resampling.'' Specify a new sampling rate in the exported data.

== Type of data to export ==

[[Image:Export (2).gif ]]

The types of data to export are:
* '''Continuous data'''. The whole data set or the data between markers are exported.
* '''Marked segment.''' If a segment of data is highlighted, this radio button is enabled. Select Marked segment to export just this segment.
* '''Epochs around triggers.''' Export data segments around triggers. If this item is selected, the two buttons '''Interval'''... and '''Triggers'''... are enabled. They allow to select the interval (cf ''Edit / Default'' ''Block Epoch''...), and choose among the available triggers (see ''Edit / Trigger Values''...). Note that the default block epoch values are persistent across BESA Research sessions. The trigger selection is not persistent!
* '''Standard Deviations (from fsg file only).''' If the average file was generated using the BESA Research ERP module, standard deviations are saved in the file. Check this item to export these values to an ASCII file.

'''Between markers.''' If there are markers in the file, and '''Marked segment''' is not selected, selecting '''Between markers''' will result in the export of data between markers relative to the current position in the file (as defined by the middle of the current display), either:
* if there is no previous marker, from the beginning of the file to the next marker, or
* from the previous to the next marker, or
* if there is no next marker, from the previous marker to the end of the file.

== Montages and Filters ==

[[Image:Export (3).gif ]]

The data can be exported either

* '''Original data.''' The data are exported using the original montage

* '''Current montage.''' The currently selected montage is exported. If extra channels, e.g. selected channels or artifact waveforms are displayed, these are exported as well. Notes:
** When 'Current Montage' is selected, no auxiliary files are exported. When re-importing the data into BESA Research, all channels will be defined as polygraphic.
** If the current data is artifact-corrected, the artifact-corrected data will be exported when 'Current Montage' is selected.

* '''Standard 81 electrode locations.''' EEG data are interpolated to a set of 81 electrodes on a standard head (average over 24 mainly Caucasian heads).

* Export can be performed either with or without the currently selected filters. Press the '''Filters'''... button to change the current filter settings (see also ''Filters / Edit Filter Settings''...).

== Target Data Formats ==

[[Image:Export (4).gif ]]

The following target formats are available:

* '''BESA binary''': Data are saved with the extension "'''.foc'''" or "'''.fsg'''". You can select whether to export with no compression (recommended for averages), or compressed (recommended for raw data). Note that compression can result in loss of resolution in averaged data. See ''Data Compression.''

* '''ASCII multiplexed''': Data are normally saved as text with the extension "'''.mul'''". See ''ASCII multiplexed format'' for a description of the data format. If the type of data to export is '''Epochs''' '''around triggers''', one file is exported for each trigger, and the file extension is a number, starting with ".000", and continuing ".001", ".002", etc.

* '''ASCII vectorized''': Data are normally saved as text with the extension "'''.avr'''". See ''ASCII Multiplexed format ''for a description of the data format. If the type of data to export is '''Epochs around triggers''', one file is exported for each trigger, and the file extension is a number, starting with ".000", and continuing ".001", ".002", etc. The data are not average referenced before saving. They will only be average referenced if the data are exported using an average referenced '''Current montage'''. You are only allowed to export small segments in vectorized format. If you have selected '''Continuous data''', this item will be disabled if the data are longer than 20 s in duration.

* '''European Data Format (EDF+)''': Data are saved with the extension "'''.edf'''". Export of '''Epochs around triggers''' to EDF+ is currently not possible.

* '''Simple binary matrix''': Data are written to a floating point binary matrix with the extension "'''.dat'''". The matrix has the dimension no of samples x no of channels. In addition, a header file with the extension "'''.generic'''" is also written. The header file is a text file contains information about the number of channels, sampling rate, and number of samples. These follow the specifications of the Generic File Format that can also be read by BESA Research if the Generic Reader is installed. This data format can be useful as a means of transferring data to other programs (e.g. '''MATLAB''') in a relatively compact form. If the type of data to export is '''Epochs around triggers''', the epochs are concatenated in the same target file. In this case, the header file contains a line specifying the number of epochs (cf. ''Generic File Format''). The number of samples in each epoch is the total number of samples, divided by the number of epochs.

* '''Send To MATLAB''': The data are exported directly to MATLAB into the struct variable <code>besa_channels</code>. For more information on the data transfer from BESA Research to MATLAB, please refer to the Help chapter [[MATLAB_Interface | MATLAB interface]].

== Resampling ==

[[Image:Export (5).gif ]]

Check '''Resample data''' to change the sampling rate of the target data. The edit box is enabled, and you specify a sampling rate.

Data are resampled using splines. Thus, the new sampling rate is not limited to fractions or multiples of the original rate.

Note that if '''Resample data''' is not checked, the sampling rate of the source data is displayed.

'''Resampling and aliasing'''. If you want to reduce the sampling rate it is important to avoid aliasing! It is recommended that a low-pass filter with a boundary frequency of not more than 1/3 of the original sampling rate is used. When you set a new sampling rate, BESA Research checks the current filter settings. If export without filters is selected, or if the current low-pass filter is set to a value that is higher than 1/3 of the sampling rate, BESA Research sets the filter, and opens a message box with a warning:

[[Image:Export (6).gif ]]

You may adjust the filters by pressing the''' Filter''' button, e.g. if the original data were already recorded with a sufficiently low low-pass filter setting, so that additional filtering is unnecessary.

== Data Compression ==

When exporting to BESA binary format, you can compress the data to save space. Here we describe properties and pitfalls of the compression algorithm.

'''How compression works'''

The compression algorithm works on two principals:
* '''Data resolution can often be reduced without losing data quality.''' For instance, a data resolution of 0.1 µV or higher is unnecessary for viewing normal EEG -- 0.5 µV or 1 µV steps are sufficient. Similarly for event-related potentials: the raw data only require a resolution of 0.5 µV or 1 µV to achieve a much higher resolution after averaging.
* '''Differences between successive data samples''' on a signal are generally much smaller than '''the absolute values of the data'''. Thus, one start value, and then a series of subsequent differences can be stored in a much smaller space than an equivalent series of absolute values. A consequence of this principle is that smoothed signals (with high frequencies removed) can be compressed into a smaller space than signals with a lot of high frequency noise.

'''Compression parameter'''

The parameter you need to choose is the data resolution, or step size. Steps smaller than this size will no longer be represented in the compressed data. The BESA Research Export Module allows the following steps for the compression of EEG signals:

0.1 µV, 0.2 µV, 0.5 µV, 1 µV

For raw EEG data, we recommend using a step size of 0.5 µV.

'''Different compression parameters for different data types (pitfalls!)'''

As described above, the step sizes make sense for EEG signals. For other types of data, other step sizes make more sense. In addition, a polygraphic signal can have the same order of signal magnitude as the EEG (e.g. an EOG or EKG signal), but it might have a completely different scale, e.g. a voice signal, recorded in mV or V. To help accommodate different orders of signal magnitude, BESA Research applies the following rules:
* '''MEG data:''' Step sizes (in units of fT) are 20 x the step size in µV. Thus, a step size of 0.5 µV will lead to a step size of 10 fT for MEG data.
* '''Polygraphic and ICR data''': The step size depends on the current amplitude scaling factor in BESA Research. A multiplication factor is used that is the current scaling factor, divided by 100. Thus, if the scale is set to 1 V, the factor is 10 mV. If you have chosen an EEG step size of 0.5 µV, the resulting step size will be 10 x 0.5 = 5 mV.

A pitfall in compression is that if the current amplitude scaling for polygraphic or ICR data does not display the signal sensibly, compression may lead to complete loss of the signal. Note that this only applies to polygraphic and ICR channel types.

* '''Averages:''' We recommend that averaged ERPs are not compressed. Since the signals are generally much smaller than the raw data, compression will lead to unacceptable loss of data resolution.

[[Category:Research Manual]]

{{BESAManualNav}}

File:Export1.png

2019-03-27T12:59:23Z

Jamie:

Export

2019-03-27T12:57:36Z

Jamie: /* Exporting files from BESA */

{{BESAInfobox
|title = Module information
|module = BESA Research Basic or higher
|version = 6.1 or higher
}}

== Exporting files from BESA ==

Data can be exported from BESA Research in the following formats:
* BESA's own binary format (compressed or uncompressed)
* ASCII multiplexed
* ASCII vectorized (short files only)
* EDF+
* simple floating point matrix (e.g. for exporting data to Matlab)
* Send the data directly to Matlab

You can export
* The entire data set or between markers
* The currently marked segment
* Epochs around triggers
* Standard deviations from binary average files ('''*.fsg''')

Export is allowed to various montages:
* filtered or unfiltered data
* original data
* current montage (including artifact correction if applied)
* standard 81-electrode montage.

On export, you can choose to change the sampling rate.

If exporting to BESA's binary format, you can optionally append the data to a preexisting data set, if sampling rates and the number of channels match. Therefore, please use the Combine Conditions module.

Export is started either
* select File / Export...
* press the '''WrS '''button.
* In both cases, you are taken to the ''Export Dialog''.
* for Send to Matlab only: select File / Send To MATLAB... This also opens the Export Dialog, but only the '''Send To Matlab radio''' button is enabled as target format in the dialog.

== Export Dialog ==

[[Image:Export (1).gif ]]

The dialog is started when you select'' File / Export...'' or press the '''WrS''' button or select '''Write Segment''' in the right click context menu when a segment has been highlighted.

The dialog is divided into four sections. Please read the following chapters for more details:
* ''Data to export''. Describes which data are to be exported.
* ''Montage and Filters.'' Which montage is to be exported, and whether or not filters are used.
* ''Target data formats''. Specify the format of the exported data.
* ''Resampling.'' Specify a new sampling rate in the exported data.

== Type of data to export ==

[[Image:Export (2).gif ]]

The types of data to export are:
* '''Continuous data'''. The whole data set or the data between markers are exported.
* '''Marked segment.''' If a segment of data is highlighted, this radio button is enabled. Select Marked segment to export just this segment.
* '''Epochs around triggers.''' Export data segments around triggers. If this item is selected, the two buttons '''Interval'''... and '''Triggers'''... are enabled. They allow to select the interval (cf ''Edit / Default'' ''Block Epoch''...), and choose among the available triggers (see ''Edit / Trigger Values''...). Note that the default block epoch values are persistent across BESA Research sessions. The trigger selection is not persistent!
* '''Standard Deviations (from fsg file only).''' If the average file was generated using the BESA Research ERP module, standard deviations are saved in the file. Check this item to export these values to an ASCII file.

'''Between markers.''' If there are markers in the file, and '''Marked segment''' is not selected, selecting '''Between markers''' will result in the export of data between markers relative to the current position in the file (as defined by the middle of the current display), either:
* if there is no previous marker, from the beginning of the file to the next marker, or
* from the previous to the next marker, or
* if there is no next marker, from the previous marker to the end of the file.

== Montages and Filters ==

[[Image:Export (3).gif ]]

The data can be exported either

* '''Original data.''' The data are exported using the original montage

* '''Current montage.''' The currently selected montage is exported. If extra channels, e.g. selected channels or artifact waveforms are displayed, these are exported as well. Notes:
** When 'Current Montage' is selected, no auxiliary files are exported. When re-importing the data into BESA Research, all channels will be defined as polygraphic.
** If the current data is artifact-corrected, the artifact-corrected data will be exported when 'Current Montage' is selected.

* '''Standard 81 electrode locations.''' EEG data are interpolated to a set of 81 electrodes on a standard head (average over 24 mainly Caucasian heads).

* Export can be performed either with or without the currently selected filters. Press the '''Filters'''... button to change the current filter settings (see also ''Filters / Edit Filter Settings''...).

== Target Data Formats ==

[[Image:Export (4).gif ]]

The following target formats are available:

* '''BESA binary''': Data are saved with the extension "'''.foc'''" or "'''.fsg'''". You can select whether to export with no compression (recommended for averages), or compressed (recommended for raw data). Note that compression can result in loss of resolution in averaged data. See ''Data Compression.''

* '''ASCII multiplexed''': Data are normally saved as text with the extension "'''.mul'''". See ''ASCII multiplexed format'' for a description of the data format. If the type of data to export is '''Epochs''' '''around triggers''', one file is exported for each trigger, and the file extension is a number, starting with ".000", and continuing ".001", ".002", etc.

* '''ASCII vectorized''': Data are normally saved as text with the extension "'''.avr'''". See ''ASCII Multiplexed format ''for a description of the data format. If the type of data to export is '''Epochs around triggers''', one file is exported for each trigger, and the file extension is a number, starting with ".000", and continuing ".001", ".002", etc. The data are not average referenced before saving. They will only be average referenced if the data are exported using an average referenced '''Current montage'''. You are only allowed to export small segments in vectorized format. If you have selected '''Continuous data''', this item will be disabled if the data are longer than 20 s in duration.

* '''European Data Format (EDF+)''': Data are saved with the extension "'''.edf'''". Export of '''Epochs around triggers''' to EDF+ is currently not possible.

* '''Simple binary matrix''': Data are written to a floating point binary matrix with the extension "'''.dat'''". The matrix has the dimension no of samples x no of channels. In addition, a header file with the extension "'''.generic'''" is also written. The header file is a text file contains information about the number of channels, sampling rate, and number of samples. These follow the specifications of the Generic File Format that can also be read by BESA Research if the Generic Reader is installed. This data format can be useful as a means of transferring data to other programs (e.g. '''MATLAB''') in a relatively compact form. If the type of data to export is '''Epochs around triggers''', the epochs are concatenated in the same target file. In this case, the header file contains a line specifying the number of epochs (cf. ''Generic File Format''). The number of samples in each epoch is the total number of samples, divided by the number of epochs.

* '''Send To MATLAB''': The data are exported directly to MATLAB into the struct variable <code>besa_channels</code>. For more information on the data transfer from BESA Research to MATLAB, please refer to the Help chapter [[MATLAB_Interface | MATLAB interface]].

== Resampling ==

[[Image:Export (5).gif ]]

Check '''Resample data''' to change the sampling rate of the target data. The edit box is enabled, and you specify a sampling rate.

Data are resampled using splines. Thus, the new sampling rate is not limited to fractions or multiples of the original rate.

Note that if '''Resample data''' is not checked, the sampling rate of the source data is displayed.

'''Resampling and aliasing'''. If you want to reduce the sampling rate it is important to avoid aliasing! It is recommended that a low-pass filter with a boundary frequency of not more than 1/3 of the original sampling rate is used. When you set a new sampling rate, BESA Research checks the current filter settings. If export without filters is selected, or if the current low-pass filter is set to a value that is higher than 1/3 of the sampling rate, BESA Research sets the filter, and opens a message box with a warning:

[[Image:Export (6).gif ]]

You may adjust the filters by pressing the''' Filter''' button, e.g. if the original data were already recorded with a sufficiently low low-pass filter setting, so that additional filtering is unnecessary.

== Data Compression ==

When exporting to BESA binary format, you can compress the data to save space. Here we describe properties and pitfalls of the compression algorithm.

'''How compression works'''

The compression algorithm works on two principals:
* '''Data resolution can often be reduced without losing data quality.''' For instance, a data resolution of 0.1 µV or higher is unnecessary for viewing normal EEG -- 0.5 µV or 1 µV steps are sufficient. Similarly for event-related potentials: the raw data only require a resolution of 0.5 µV or 1 µV to achieve a much higher resolution after averaging.
* '''Differences between successive data samples''' on a signal are generally much smaller than '''the absolute values of the data'''. Thus, one start value, and then a series of subsequent differences can be stored in a much smaller space than an equivalent series of absolute values. A consequence of this principle is that smoothed signals (with high frequencies removed) can be compressed into a smaller space than signals with a lot of high frequency noise.

'''Compression parameter'''

The parameter you need to choose is the data resolution, or step size. Steps smaller than this size will no longer be represented in the compressed data. The BESA Research Export Module allows the following steps for the compression of EEG signals:

0.1 µV, 0.2 µV, 0.5 µV, 1 µV

For raw EEG data, we recommend using a step size of 0.5 µV.

'''Different compression parameters for different data types (pitfalls!)'''

As described above, the step sizes make sense for EEG signals. For other types of data, other step sizes make more sense. In addition, a polygraphic signal can have the same order of signal magnitude as the EEG (e.g. an EOG or EKG signal), but it might have a completely different scale, e.g. a voice signal, recorded in mV or V. To help accommodate different orders of signal magnitude, BESA Research applies the following rules:
* '''MEG data:''' Step sizes (in units of fT) are 20 x the step size in µV. Thus, a step size of 0.5 µV will lead to a step size of 10 fT for MEG data.
* '''Polygraphic and ICR data''': The step size depends on the current amplitude scaling factor in BESA Research. A multiplication factor is used that is the current scaling factor, divided by 100. Thus, if the scale is set to 1 V, the factor is 10 mV. If you have chosen an EEG step size of 0.5 µV, the resulting step size will be 10 x 0.5 = 5 mV.

A pitfall in compression is that if the current amplitude scaling for polygraphic or ICR data does not display the signal sensibly, compression may lead to complete loss of the signal. Note that this only applies to polygraphic and ICR channel types.

* '''Averages:''' We recommend that averaged ERPs are not compressed. Since the signals are generally much smaller than the raw data, compression will lead to unacceptable loss of data resolution.

[[Category:Research Manual]]

{{BESAManualNav}}

Integration with MRI and fMRI

2019-03-27T12:54:15Z

Jamie: /* How to Generate a Brain Surface Mesh */

{{BESAInfobox
|title = Module information
|module = BESA Research Basic or higher and BESA MRI
|version = 6.1 or higher
}}



== Introduction ==

Both for developing and evaluating dipole source models of EEG or MEG activity, it is useful to have access to structural MRI or fMRI data.

The BESA MRI software allows to preprocess structural MRI data so that the individual anatomical information contained in the MRI can be utilized in BESA Research. BESA MRI makes it possible ...
* ... to align the EEG and MEG sensors with the structural MRI data.
* ... to read and display the aligned, individual Talairach structural MRIs directly in the BESA Research Source Analysis module. In this way, source analysis results can be presented on top of the aligned MRIs, which allows us to evaluate the anatomical regions to which the reconstructed sources may correspond.
* ... to use an individual, realistically shaped FEM head model for source analysis in BESA Research. FEM head models take into account the individual volume conduction properties of the subject's head derived from the structural MRI data. This allows for more accurate source analysis (Yvert 1997, Lanfer 2012).

To offer an easy integration with fMRI data we have, in collaboration with Rainer Goebel, optimized the interface between BESA Research and BrainVoyagerQX.

With these tools, we can ...
* ... use fMRI BOLD regions or MRI structures to initialize dipole models.
* ... visualize dipoles from BESA Research models together with the structural MRI in BrainVoyager in order to evaluate the regions to which the dipoles may correspond.
* ... combine the localization advantages of (f)MRI with the high temporal resolution of EEG and MEG, for instance by using (f)MRI to place the sources, and the source waveforms of BESA Research to provide feedback about the time course of the source activity.
* ... overlay source analysis results obtained in BESA Research with fMRI data.

'''Note:''' For simpler coregistration, we recommend to use BrainVoyagerQX rather than the older BrainVoyager, but BESA Research will work with both program versions.

The chapters below describe the steps necessary to integrate the MRI and fMRI data with BESA Research. Detailed instructions on (f)MRI import and processing in Brain Voyager is provided by the '''BrainVoyager Getting Started Guide''' that can be downloaded from the Brain Innovation website (https://www.brainvoyager.com/downloads/downloads.html).

'''Aligning Coordinate Systems'''

* For a given BESA data set, the electrode and other head surface points need to be aligned to the MRI coordinates.
* The basic steps necessary to align the EEG electrode locations, the MEG sensors and the MRI are described in Section “[[Integration_with_MRI_and_fMRI#Setting_Up_Coregistration_Using_BrainVoyager|How Coregistration is done]]”.
* Detailed instructions on how to align EEG / MEG and MRI data using BESA MRI can be found in the coregistration quick guide which is available on the BESA homepage ((http://www.besa.de/downloads/quick-guides/).
* Detailed instructions on how to align EEG / MEG and MRI data using BrainVoyager are described in Section “[[Integration_with_MRI_and_fMRI#Setting_Up_Coregistration_Using_BrainVoyager|How To set up Coregistration between BESA and BrainVoyager]]”.
* In BESA Research, all necessary settings with regard to the alignment are made in the [[Integration_with_MRI_and_fMRI#The_Coregistration_Dialog|Coregistration Dialog]].
* Requirements with respect to the MRI data for a good coregistration can be found in Section “''MRI Requirements for Good Coregistration”.''
* Requirements with respect to EEG and MEG data for a good coregistration can be found in Section “''EEG/MEG Data Requirements for Good Coregistration”.''

'''Generating an individual, realistically shaped FEM head model'''

* The generation of a FEM head model that can be used in BESA Research is done in BESA MRI as an additional step following the EEG / MEG to MRI coregistration.
* Detailed instructions on how to generate the FEM head model can be found in the coregistration quick guide which is available on the BESA homepage (http://www.besa.de/downloads/quick-guides/).

'''Co-locating dipoles and MRI locations'''

* After aligning the EEG / MEG and the MRI data it is possible to co-locate dipoles and MRI locations. This means, it is possible to visualize the dipoles and to specify the dipole parameters in the MRI coordinate system.
* “[[Integration_with_MRI_and_fMRI#Co-locating_Sources_and_MRI_in_the_BESA_Research_Source_Module|How to Co-locate sources and MRI in the BESA Research Source Module]]" describes how in the BESA Research Source Analysis module dipoles can directly be visualized in the space of the individual MRI.
* “[[Integration_with_MRI_and_fMRI#Send_a_Dipole_from_BESA_Research_to_BrainVoyager|How to Send a Dipole from BESA Research to BrainVoyager]]” describes how to send a source model from BESA Research to BrainVoyager for further inspection.
* “[[Integration_with_MRI_and_fMRI#Define_a_Dipole_in_BESA_Research_at_a_Location_Defined_in_the_MRI|How to Define a Dipole in BESA Research at a Location Defined in the MRI]]” describes how to insert a dipole at a location defined in the MRI in BrainVoyager.

'''References'''

Lanfer, B., I. Paul-Jordanov, M. Scherg, and C. H. Wolters. “Influence of Interior Cerebrospinal Fluid Compartments on EEG Source Analysis.” In Proceedings BMT 2012, Vol. 57. Jena: De Gruyter, 2012. doi:10.1515/bmt-2012-4020.

Yvert, B., O. Bertrand, M. Thévenet, J. F. Echallier, and J. Pernier. “A Systematic Evaluation of the Spherical Model Accuracy in EEG Dipole Localization.” Electroencephalography and Clinical Neurophysiology 102, no. 5 (May 1997): 452–59. doi:16/S0921-884X(97)96611-X.

== How Coregistration is done ==

This section outlines the basic steps to coregister the EEG / MEG data to an individual MRI. These steps are necessary to load an individual MRI into BESA Research.

'''What happens:'''

* EEG / MEG sensor locations and the MRI data are defined in different coordinate systems. Setting up coregistration is the process of aligning the two coordinate systems.
* BESA Research uses the ''Coregistration Dialog'' to coordinate the alignment procedure.
* Alignment is done with the ''AC-PC-transformed MRI''.
* BESA Research displays the ''Talairach-transformed MRI'' in the source analysis module.
* A coregistration file (with the extension "'''.sfh'''") is used to mediate between BESA Research and BESA MRI (or BrainVoyagerQX):
* BESA Research writes the coregistration file which contains the coordinates of head surface points (fiducials, electrodes, other digitized surface points).
* The coordinates are read into BESA MRI (or BrainVoyager), and aligned with the AC-PC-transformed MRI. The alignment information is then appended to the ''coregistration file''. The names of the AC-PC MRI ('''<nowiki>*.vmr</nowiki>''') and the surface mesh ('''<nowiki>*.srf</nowiki>'''), and, if available, the Talairach transformation, are also appended.
* BESA Research reads the coregistration file and appends the name of the Talairach-transformed MRI and head surface. If a brain surface has been created, this is also appended.
* Subsequently, BESA Research reads the coregistration file automatically when loading the data file.
* In the BESA Research source module, the individual MRI is displayed instead of the standard MRI. Talairach coordinates of dipoles are the "real" Talairach coordinates as defined, e.g., in BrainVoyager.

'''The steps you have to take (once for each data set):'''

* From the BESA Research ''Coregistration Dialog'', write a coregistration file. Switch to BESA MRI (or BrainVoyagerQX).
* If BESA MRI is used follow the steps in the coregistration quickguide which is available on the BESA homepage (http://www.besa.de/downloads/quick-guides/).
* If BrainVoyager is used follow the steps in Section “''How to set up coregistration between BESA and BrainVoyager”.''
* Back in BESA Research, reload the altered '''coregistration file'''. When using BESA MRI the file names of the generated surface and volume data files will be automatically filled in. When using BrainVoyager file names are only filled in automatically when the files are named according to the file naming conventions. Otherwise, file names have to be set manually.
* The coregistration file is now associated with the data file in the BESA Research database and will be used automatically the next time the file is opened in BESA Research. If the database entry is cleared, and the data are reloaded, you must make sure the coregistration file is also loaded (either using the ''Coregistration Dialog'' or the ''Channel and digitized head surface point information Dialog'').

== Alignment of BESA and MRICoordinate Systems ==

=== The Coregistration Dialog ===

The dialog is opened either from the ''Channel and digitized head surface point information'' ('''Ctrl-L''') ''dialog ''by pressing the '''Edit/Coreg''' button, or from the main menu ("'''File/MRI Coregistration...'''").

'''Note:''' If the coregistration dialog is invoked from an EEG data set in which no digitized electrode coordinates are available (i.e. standard electrode positions located on a sphere are assumed), BESA Research presents a warning message, saying that for MRI coregistration realistic electrode coordinates produce better results. BESA Research has a list of such realistic standard coordinates (i.e. located on a pre-defined standard head surface) for various electrodes available in file '''Default.sfp''', which is located in the Standard Electrode folder. If all electrodes in the dataset are listed in this file, a dialog window suggests to apply this file to the current data set, i.e. to switch from standard sphere coordinates to the standard realistic electrode coordinates in file '''Default.sfp'''. If the suggestion is accepted, '''default.sfp''' is assigned to the dataset (see Channel and digitized head surface point information ('''Ctrl-L''') dialog).

'''The Dialog:'''

[[Image:MRI Integration (1).gif ‎]]

* Press the '''Select MRI prog''' button to select your preferred MRI program. The current choice is between ''BESA MRI.exe'' and ''BrainVoyagerQX.exe''. The path to the MRI program is saved (in ''System\BESA.set'') and will be remembered by BESA Research. The top right hand button (now showing '''BESA MRI''') shows the current selection.
* Press the '''BESA MRI''' button to start the process of aligning the BESA Research and MRI coordinate systems. If no coregistration ('''<nowiki>*.sfh</nowiki>''') file is defined in the dialog (empty ''Surface coregistration file edit box''), BESA Research will first prompt for a file name. We recommend saving this file to the folder where the MRIs are kept. The MRI program will then be started. When you return to the ''Coregistration Dialog'', BESA Research checks if the ''Coregistration File'' has changed. If so, the dialog is updated with the new information.
* Press the top '''Browse... '''button to select a preexisting ''Coregistration File''.
* The entries in the edit boxes below show the files that will be used in the BESA Research Source Analysis module when the individual MRI is loaded. When using BESA MRI the file names will be automatically filled in. If you are using BrainVoagerQX and you are following our (and the BrainVoyagerQX) recommended naming conventions for files, and the files exist, then the names will be filled in automatically after you have completed the alignment procedure in BrainVoyagerQX. Otherwise you may have to browse for the files.
* Below the edit boxes the FEM field states whether all necessary information for the individual FEM head model were found in the coregistration file. If the field says ''Individual FEM for EEG'' ''defined!'' then all necessary data was found and the individual FEM EEG head model can be used in the BESA Research Source Analysis module. A similar message indicates whether the FEM MEG head model is available.
* Note that the MRI and the surfaces are Talairach-transformed! Alignment between BESA Research and the individual MRI is done with the MRI transformed to the AC-PC coordinate system, but the BESA Research Source Analysis module uses the Talairach-transformed image data and surfaces.

<div style="color:#ff0000;"></div>

=== Setting Up Coregistration Using BrainVoyager ===

It is assumed that you know how to load an MRI as a 3D data set into BrainVoyagerQX, and how to clean the image so that regions outside the head are black. We also assume knowledge of how to create AC-PC-aligned and Talairach-transformed MRIs.

Perform the following steps:

* BESA Research. Start the ''Coregistration Dialog''. Export the Coregistration File (head surface points) from your data by pressing the '''BrainVoyagerQX''' button in the dialog. Save the file to the directory where your MRI is located. BrainVoyagerQX is started.
* BrainVoyagerQX. Load the MRI corresponding to the EEG/MEG data. For optimal performance, the MRI should be cleaned so that regions outside the head are black. Prepare an AC-PC-transformed MRI and a Talairach MRI. For each, generate a surface mesh. Save these files following our recommended naming conventions (see chapter “[[Integration_with_MRI_and_fMRI#MRI_file_Name_Conventions|MRI File Name Conventions]]”). Save the Talairach coordinate file ('''<nowiki>*.tal</nowiki>'''). If these steps have already been performed, load the ACPC MRI and load the ACPC mesh. If you want to generate a brain surface mesh, see chapter “[[Integration_with_MRI_and_fMRI#How_to_Generate_a_Brain_Surface_Mesh|How to Generate a Brain Surface Mesh]]”.
* BrainVoyagerQX. Load the Coregistration File (''EEG-MEG BESA/Load Surface Points''). The points will be displayed, but they are not aligned to the head:

[[Image:MRI Integration (2).gif ‎]]

* BrainVoyagerQX. Define fiducial points on the head surface. Right click on the 3D head display and select the ''Fiducials Dialog'' in the drop-down menu:

[[Image:MRI Integration (3).gif ‎]] [[Image:MRI Integration (4).gif ‎]]

* BrainVoyagerQX. Rotate the head (by holding the '''Shift '''button down and clicking and dragging with the mouse) so that the Nasion is clearly visible. Move the mouse to the Nasion, and press '''Ctrl+Left Click'''. The coordinates of the Nasion are inserted into the dialog. Repeat for the left preauricular point, and then for the right preauricular point.

[[Image:MRI Integration (5).gif ‎]]

Note: if you have defined your fiducials differently in your BESA Research data (e.g. ear holes), click on the corresponding points in the MRI. If you have additional head surface points (step 8), accuracy in pinpointing the fiducials is not critical.

* BrainVoyagerQX. In the Fiducials Dialog, press the '''Fit fiducials''' button. The head surface points are now more or less aligned to the head.

[[Image:MRI Integration (6).gif ‎]]

* BrainVoyagerQX. Now select '''''EEG-MEG BESA/Fit Surface Points...'''''

[[Image:MRI Integration (7).gif ‎]]

If you do not see the right half of the dialog, press the '''Advanced >>''' button.

* Specify the distances of the digitization points from the skin. In the illustration above, the digitization points for electrodes are estimated to be 8 mm from the surface of the head. For the purpose of accurate alignment, the distance of digitization points from skin section of the dialog needs to be filled in correctly. We recommend that "Restrain solution around fiducials" is checked, and a reasonable limit (here 3 mm) of the restraint is defined. Then press '''OK'''.

[[Image:MRI Integration (8).gif ‎]]

BrainVoyager fits the points to the head, stretching x, y, and z coordinates to obtain a better fit than before.

Note: The fit performed during this step accounts for scaling inequalities between the x, y, and z axes in the MRI. Coregistration gains in accuracy over the use of fiducials alone a) because more head surface points are used, and b) because the scaling inequalities are accounted for.

* Alignment is now completed. If you only want to display the structural MRI in the BESA Source Module, you can return to the BESA Coregistration Dialog.
* BESA Research. When you switch back to the Coregistration Dialog, BESA Research will try to fill in the names of the Talairach MRI and surface meshes. If the names are not filled in, use the '''Browse...''' buttons to select the MRI and surface meshes. Press '''OK''' to save the Coregistration File. Alignment is completed!

The alignment steps need only be performed once for a given MRI and EEG/MEG data set. Otherwise, after starting BrainVoyager, just load the MRI, the surface mesh, and the surface points (see “[[Integration_with_MRI_and_fMRI#Coregistration_with_BrainVoyager_after_Alignment_has_been_Done |How to Set Up Coregistration with BrainVoyager after Alignment has been Done]]”). Now the following actions are possible: see chapters

* [[Integration_with_MRI_and_fMRI#Co-locating_Sources_and_MRI_in_the_BESA_Research_Source_Module|How to Co-Locate Sources and MRI in the BESA Research Source Module]]
* [[Integration_with_MRI_and_fMRI#Send_a_Dipole_from_BESA_Research_to_BrainVoyager|How to Send a Dipole from BESA Research to BrainVoyager]]
* [[Integration_with_MRI_and_fMRI#Define_a_Dipole_in_BESA_Research_at_a_Location_Defined_in_the_MRI|How to Define a Dipole in BESA Research at a Location Defined in the MRI]]

=== MRI file Name Conventions ===

If you follow the naming conventions for file names as described here, BESA Research detects the file names it requires, and the ''Coregistration Dialog'' is filled in automatically.

Please note that BESA MRI automatically uses these naming conventions for the generated files.

* '''The AC-PC MRI file name''' should end with "'''_ACPC.vmr'''", and the corresponding surface mesh name should end with "'''_ACPC.srf'''". After alignment, BrainVoyagerQX writes these names to the Coregistration File.
* '''The Talairach MRI file name '''should end with "'''_TAL.vmr'''", and the corresponding surface mesh name should end with "'''_TAL.srf'''". If defined, the brain surface mesh should end with "'''_TAL_WM.srf'''" ('''WM''' = '''w'''hite '''m'''atter).
* '''How BESA Research finds the Talairach files.''' When BESA Research rereads the Coregistration File after alignment of the coordinate systems, it finds the ACPC file names and defines the corresponding TAL file names. If these files exist, the names are entered into the Coregistration Dialog. For instance, if the Coregistration File contains the name "'''MRI''' '''PB_ACPC.vmr'''", BESA Research will look for the files "'''MRI_PB_TAL.vmr'''", "'''MRI_PB_TAL.srf'''", and "'''MRI_PB_TAL_WM.srf'''". If these files exist, they are entered into the dialog.
* '''Older BrainVoyager version.''' If you use BrainVoyager.exe to align coordinate systems, the file names are not saved with the Coregistration File. In this case, browse for the Talairach or the ACPC MRI from the Coregistration Dialog. BESA Research will use the rules as described above to insert the correct file names into the dialog.
* '''Missing Talairach coordinates.''' If, after aligning coordinate systems, the Talairach coordinates are missing from the Coregistration File (you forgot to load the Talairach coordinates in BrainVoyagerQX, or you used BrainVoyager.exe), BESA Research will look for a file ending with "'''_ACPC.tal'''", and read the coordinates from this file. You can also browse for a '''<nowiki>*.tal</nowiki>''' file in the Coregistration Dialog. For instance, if the MRI file is named "'''MRI_PB_ACPC.vmr'''" or "'''MR_''' '''PB_TAL.vmr'''", BESA Research will look for "'''MRI_PB_ACPC.tal'''" to find the Talairach coordinates.
* '''File names in the Coregistration File are saved relative to the Coregistration File location, if they are in the same folder.''' If the MRIs are in the same folder as the Coregistration File they will be recorded as ".\filename" (e.g. "'''.\MRI PB_tal.vmr'''"). This means that you can copy the Coregistration File together with the MRIs and meshes to a different folder, and BESA Research will be able to locate the files when the Coregistration File is opened. If the MRIs are saved in a different folder from the Coregistration File, the absolute paths are saved in the file. If the files are moved to new locations, you will have to restart the Coregistration Dialog and redefine the file locations.

=== How to Generate a Brain Surface Mesh ===

BESA Research is able to compute surface images, such as (Cortical LORETA, Cortical CLARA, Minimum Norm) using an individual cortex surface as the source space. A suitable cortex surface for this purpose can be effortlessly created using BESA MRI. Alternatively, BrainVoyager can be used for the creation of the brain surface mesh.

'''BESA MRI'''
* The brain surface generation is performed as one work step of the BESA MRI segmentation workflow.
* The cortex surface reconstruction is done using a robust and accurate automatic segmentation procedure.
* Details on how to generate the brain surface mesh in BESA MRI can be found in the coregistration quickguide which is available on the BESA homepage (http://www.besa.de/downloads/quick-guides/).

'''BrainVoyager'''
* BrainVoyagerQX provides a semiautomatic procedure to generate meshes for the brain surface of the Talairach MRI. Please refer to the BrainVoyager Help to find out how to do this.
* The result of the BrainVoyager procedure is two meshes, one for the left and one for the right hemisphere.
* BESA Research requires a single mesh. Therefore, load first one mesh (''Meshes/Load Mesh..''.), and append the other mesh (''Meshes/Add Mesh...''). Merge these two meshes (''Meshes/Merge'' ''meshes in surface window'') and then save the result (''Meshes/Save Mesh...''). If possible, use the recommended name conventions for the resulting file (file name ends in "'''_TAL_WM.srf"). '''For instance, if the Talairach MRI is named "'''MRI PB_TAL.vmr'''", name the brain surface mesh "'''MRI PB_TAL_WM.srf'''".
* See also the '''BrainVoyager Getting Started Guide''' that can be downloaded from the Brain Innovation website (http://brainvoyager.com/Downloads.html).

== Co-locating Dipoles and MRI Locations ==

=== Co-locating Sources and MRI in the BESA Research Source Module ===

If the alignment procedure using BESA MRI (or BrainVoyager) has been completed then you can load the individual structural MRI in the Source Module by pressing ''''A'''' or using a mouse right click and selecting '''''Display MRI'''''.

Sources in the current model are then overlayed onto the individual MRI.

A double-click at any location in the MRI will define a new source at the corresponding location in the BESA Research head model.

[[Image:MRI Integration (9).gif ‎]]

=== Coregistration with BrainVoyager after Alignment has been Done ===

Alignment between BESA Research and BrainVoyager is only required once for a given BESA Research data set and the corresponding MRI. At a later time, if you want to Co-locate sources between BESA Research and BrainVoyager, perform the following steps in BrainVoyager:
* Load the MRI.
* Load the head surface mesh (''Meshes/Load Mesh..''.).
* Load the Coregistration File (''EEG-MEG BESA/Load Surface Points..''.).

BrainVoyager is now ready for Co-location.

=== Send a Dipole from BESA Research to BrainVoyager ===

First, start BrainVoyager(QX). This can be done from the BESA Research Source Module by pressing the '''BrainVoyager '''button. Note that in the Source Module, the ''Options / Preferences / BrainVoyager'' tab allows to define the path to BrainVoyager.

In BrainVoyager, [[Integration_with_MRI_and_fMRI#Coregistration_with_BrainVoyager_after_Alignment_has_been_Done|set up coregistration]].

In the BESA Research Source Module, highlight the dipole of interest.

In the BESA Research Source Module, click on the '''BrainVoyager''' button.

Program control will automatically switch to BrainVoyager. The head will be cut at the section corresponding to the dipole of interest.

[[Image:MRI Integration (10).gif‎|200px]]

Note that all dipoles in the current model are sent to BrainVoyager. The highlighted dipole (here, the red dipole) determines the plane at which the head will be cut.

Note that the dipoles are visible in both the surface module and in the 2D view:

[[Image:MRI Integration (11).gif|400px]]

=== Define a Dipole in BESA Research at a Location Defined in the MRI ===

First set up coregistration (see chapter ''“[[Integration_with_MRI_and_fMRI#Coregistration_with_BrainVoyager_after_Alignment_has_been_Done|Coregistration with BrainVoyager after Alignment has been Done]]”'').

In the BrainVoyager 2D MRI view, place the mouse over the point at which you would like to define a dipole. Right click at this point. If this point lies within an fRMI cluster, BrainVoyager will automatically determine its center and use it as a seeding point instead. Press '''Send Seed Point To BESA....'''

[[Image:MRI Integration (12).gif ‎]]

The following Dialog is opened:

[[Image:MRI Integration (13).gif ‎]]

Press '''Send to BESA'''.

The BESA Source Analysis window appears. The new dipole or regional source (depending on the setting in the ‘Options’ dialog in the Source Analysis window is now displayed at the corresponding location. If a dipole is seeded, BESA automatically fits its orientation. For further adjustment of the model, you may need to refit the orientation, e.g. at a certain time range, or in the presence of other sources.

Detailed instructions on (f)MRI import and processing in Brain Voyager is provided by the '''BrainVoyager Getting Started Guide''' that can be downloaded from the Brain Innovation website ([http://brainvoyager.com/Downloads.html http://brainvoyager.com/Downloads.html]).

== Reference ==

=== The Coregistration File (*.sfh) ===

This file is used to mediate between BESA Research and BESA MRI (or BrainVoyager(QX)). When it is first written by BESA Research, it contains a list of the digitized head surface points (fiducials, electrodes, other digitized points), e.g.

<source lang="dos">
NrOfPoints: 68
Fid_Nz 0.00000 103.10000 0.00000 3 255 128 255
Fid_T9 -78.40000 0.00000 0.00000 3 255 128 255
Fid_T10 73.00000 0.00000 0.00000 3 255 128 255
Ele_E1 -28.70000 23.90000 122.30000 3 255 0 0
Ele_E2 -80.40000 19.80000 75.90000 3 255 0 0
Ele_E3 -84.00000 37.90000 9.00000 3 255 0 0
Ele_E4 -17.60000 92.90000 89.10000 3 255 0 0

...

Ele_E63 -6.80000 -104.00000 54.40000 3 255 0 0
Ele_E64 -42.80000 -46.90000 115.60000 3 255 0 0
Ele_Cz' -2.10000 2.20000 131.10000 3 255 0 0
</source>

Each line contains a label, the coordinates in the Head Coordinate system, and parameters specifying the size and color of the sensor or head surface point as displayed in BESA MRI (or BrainVoyager).

After aligning the coordinate systems, BESA MRI (or BrainVoyagerQX) appends lines defining the transformation between the BESA Research and the MRI coordinate systems:

<pre>
# Trans-data(in BV-coords): 3 translation, 3 rotation (in grad), 3 scale
37.435 15.811 2.820 0.025 1.938 8.779 1.009 0.973 0.977
Fiducials:
41.7873 148.0180 128.0844
154.7772 169.4783 204.1080
147.0154 168.9746 54.1266
Midpoint (in BV-coords):
128.0000 128.0000 128.0000
Volume: C:\BESA\Examples\ERP P300-Auditory\MRI_PB_acpc.vmr
Surface: C:\BESA\Examples\ERP P300-Auditory\MRI_PB_acpc.srf
AC: 128 128 128
PC: 154 128 128
AP: 58 128 128
PP: 241 129 130
SP: 154 50 128
IP: 128 172 128
RP: 128 128 60
LP: 165 128 198
</pre>

Note: Older versions of BrainVoyager.exe do not append the lines starting with "Volume". In addition, the Talairach coordinates (starting at "AC: ...") are not appended if they were not loaded in BrainVoyagerQX.

Finally, when the Coregistration Dialog in BESA Research has found the Talairach MRI and surface meshes, and you press the OK button, BESA Research appends the additional file names:

<pre>
TalVolume: C:\BESA\Examples\ERP P300-Auditory\MRI_PB_tal.vmr
TalSurface: C:\BESA\Examples\ERP P300-Auditory\MRI_PB_tal.srf
TalBrainSurface: C:\BESA\Examples\ERP P300-Auditory\MRI_PB_tal_wm.srf
</pre>

BESA MRI already inserts the correct file names into the coregistration file when doing the coregistration. When also an EEG or MEG FEM head model is generated then additional lines are appended to the coregistration file containing the file names of the generated FEM data files.

=== MRI Requirements for Good Coregistration ===

We recommend a high quality T1-weighted anatomical image with 1 mm³ voxels (e.g. 256 x 256 saggital scan with 1 mm spacing).

In order to define the surface mesh, a clear contrast between the head surface and the outside of the head (T1-weighting) is required. Noise and measurement artifacts can influence the representation of the scalp surface. When doing the coregistration in BrainVoyager improvements in noisy images often can be achieved by cleaning up the image after first reading it using the tools provided by BrainVoyager.

For coregistration with head surface points, it is useful to include the whole head in the image, including nose and ears. If surface points on the nose are included with the EEG/MEG data set, these points help to stabilize the fit of head surface points to the surface mesh.

=== EEG/MEG Data Requirements for Good Coregistration ===

We recommend several (30 or more) digitized head surface points in addition to the fiducials, including points on the nose (nose tip and sides). These points may include electrodes. In the case of electrodes, it is important to measure the distance from the scalp to the digitization point, i.e. the electrode thickness.

[[Category:Research Manual]]

{{BESAManualNav}}

Integration with MRI and fMRI

2019-03-27T12:51:50Z

Jamie: /* How Coregistration is done */

{{BESAInfobox
|title = Module information
|module = BESA Research Basic or higher and BESA MRI
|version = 6.1 or higher
}}



== Introduction ==

Both for developing and evaluating dipole source models of EEG or MEG activity, it is useful to have access to structural MRI or fMRI data.

The BESA MRI software allows to preprocess structural MRI data so that the individual anatomical information contained in the MRI can be utilized in BESA Research. BESA MRI makes it possible ...
* ... to align the EEG and MEG sensors with the structural MRI data.
* ... to read and display the aligned, individual Talairach structural MRIs directly in the BESA Research Source Analysis module. In this way, source analysis results can be presented on top of the aligned MRIs, which allows us to evaluate the anatomical regions to which the reconstructed sources may correspond.
* ... to use an individual, realistically shaped FEM head model for source analysis in BESA Research. FEM head models take into account the individual volume conduction properties of the subject's head derived from the structural MRI data. This allows for more accurate source analysis (Yvert 1997, Lanfer 2012).

To offer an easy integration with fMRI data we have, in collaboration with Rainer Goebel, optimized the interface between BESA Research and BrainVoyagerQX.

With these tools, we can ...
* ... use fMRI BOLD regions or MRI structures to initialize dipole models.
* ... visualize dipoles from BESA Research models together with the structural MRI in BrainVoyager in order to evaluate the regions to which the dipoles may correspond.
* ... combine the localization advantages of (f)MRI with the high temporal resolution of EEG and MEG, for instance by using (f)MRI to place the sources, and the source waveforms of BESA Research to provide feedback about the time course of the source activity.
* ... overlay source analysis results obtained in BESA Research with fMRI data.

'''Note:''' For simpler coregistration, we recommend to use BrainVoyagerQX rather than the older BrainVoyager, but BESA Research will work with both program versions.

The chapters below describe the steps necessary to integrate the MRI and fMRI data with BESA Research. Detailed instructions on (f)MRI import and processing in Brain Voyager is provided by the '''BrainVoyager Getting Started Guide''' that can be downloaded from the Brain Innovation website (https://www.brainvoyager.com/downloads/downloads.html).

'''Aligning Coordinate Systems'''

* For a given BESA data set, the electrode and other head surface points need to be aligned to the MRI coordinates.
* The basic steps necessary to align the EEG electrode locations, the MEG sensors and the MRI are described in Section “[[Integration_with_MRI_and_fMRI#Setting_Up_Coregistration_Using_BrainVoyager|How Coregistration is done]]”.
* Detailed instructions on how to align EEG / MEG and MRI data using BESA MRI can be found in the coregistration quick guide which is available on the BESA homepage ((http://www.besa.de/downloads/quick-guides/).
* Detailed instructions on how to align EEG / MEG and MRI data using BrainVoyager are described in Section “[[Integration_with_MRI_and_fMRI#Setting_Up_Coregistration_Using_BrainVoyager|How To set up Coregistration between BESA and BrainVoyager]]”.
* In BESA Research, all necessary settings with regard to the alignment are made in the [[Integration_with_MRI_and_fMRI#The_Coregistration_Dialog|Coregistration Dialog]].
* Requirements with respect to the MRI data for a good coregistration can be found in Section “''MRI Requirements for Good Coregistration”.''
* Requirements with respect to EEG and MEG data for a good coregistration can be found in Section “''EEG/MEG Data Requirements for Good Coregistration”.''

'''Generating an individual, realistically shaped FEM head model'''

* The generation of a FEM head model that can be used in BESA Research is done in BESA MRI as an additional step following the EEG / MEG to MRI coregistration.
* Detailed instructions on how to generate the FEM head model can be found in the coregistration quick guide which is available on the BESA homepage (http://www.besa.de/downloads/quick-guides/).

'''Co-locating dipoles and MRI locations'''

* After aligning the EEG / MEG and the MRI data it is possible to co-locate dipoles and MRI locations. This means, it is possible to visualize the dipoles and to specify the dipole parameters in the MRI coordinate system.
* “[[Integration_with_MRI_and_fMRI#Co-locating_Sources_and_MRI_in_the_BESA_Research_Source_Module|How to Co-locate sources and MRI in the BESA Research Source Module]]" describes how in the BESA Research Source Analysis module dipoles can directly be visualized in the space of the individual MRI.
* “[[Integration_with_MRI_and_fMRI#Send_a_Dipole_from_BESA_Research_to_BrainVoyager|How to Send a Dipole from BESA Research to BrainVoyager]]” describes how to send a source model from BESA Research to BrainVoyager for further inspection.
* “[[Integration_with_MRI_and_fMRI#Define_a_Dipole_in_BESA_Research_at_a_Location_Defined_in_the_MRI|How to Define a Dipole in BESA Research at a Location Defined in the MRI]]” describes how to insert a dipole at a location defined in the MRI in BrainVoyager.

'''References'''

Lanfer, B., I. Paul-Jordanov, M. Scherg, and C. H. Wolters. “Influence of Interior Cerebrospinal Fluid Compartments on EEG Source Analysis.” In Proceedings BMT 2012, Vol. 57. Jena: De Gruyter, 2012. doi:10.1515/bmt-2012-4020.

Yvert, B., O. Bertrand, M. Thévenet, J. F. Echallier, and J. Pernier. “A Systematic Evaluation of the Spherical Model Accuracy in EEG Dipole Localization.” Electroencephalography and Clinical Neurophysiology 102, no. 5 (May 1997): 452–59. doi:16/S0921-884X(97)96611-X.

== How Coregistration is done ==

This section outlines the basic steps to coregister the EEG / MEG data to an individual MRI. These steps are necessary to load an individual MRI into BESA Research.

'''What happens:'''

* EEG / MEG sensor locations and the MRI data are defined in different coordinate systems. Setting up coregistration is the process of aligning the two coordinate systems.
* BESA Research uses the ''Coregistration Dialog'' to coordinate the alignment procedure.
* Alignment is done with the ''AC-PC-transformed MRI''.
* BESA Research displays the ''Talairach-transformed MRI'' in the source analysis module.
* A coregistration file (with the extension "'''.sfh'''") is used to mediate between BESA Research and BESA MRI (or BrainVoyagerQX):
* BESA Research writes the coregistration file which contains the coordinates of head surface points (fiducials, electrodes, other digitized surface points).
* The coordinates are read into BESA MRI (or BrainVoyager), and aligned with the AC-PC-transformed MRI. The alignment information is then appended to the ''coregistration file''. The names of the AC-PC MRI ('''<nowiki>*.vmr</nowiki>''') and the surface mesh ('''<nowiki>*.srf</nowiki>'''), and, if available, the Talairach transformation, are also appended.
* BESA Research reads the coregistration file and appends the name of the Talairach-transformed MRI and head surface. If a brain surface has been created, this is also appended.
* Subsequently, BESA Research reads the coregistration file automatically when loading the data file.
* In the BESA Research source module, the individual MRI is displayed instead of the standard MRI. Talairach coordinates of dipoles are the "real" Talairach coordinates as defined, e.g., in BrainVoyager.

'''The steps you have to take (once for each data set):'''

* From the BESA Research ''Coregistration Dialog'', write a coregistration file. Switch to BESA MRI (or BrainVoyagerQX).
* If BESA MRI is used follow the steps in the coregistration quickguide which is available on the BESA homepage (http://www.besa.de/downloads/quick-guides/).
* If BrainVoyager is used follow the steps in Section “''How to set up coregistration between BESA and BrainVoyager”.''
* Back in BESA Research, reload the altered '''coregistration file'''. When using BESA MRI the file names of the generated surface and volume data files will be automatically filled in. When using BrainVoyager file names are only filled in automatically when the files are named according to the file naming conventions. Otherwise, file names have to be set manually.
* The coregistration file is now associated with the data file in the BESA Research database and will be used automatically the next time the file is opened in BESA Research. If the database entry is cleared, and the data are reloaded, you must make sure the coregistration file is also loaded (either using the ''Coregistration Dialog'' or the ''Channel and digitized head surface point information Dialog'').

== Alignment of BESA and MRICoordinate Systems ==

=== The Coregistration Dialog ===

The dialog is opened either from the ''Channel and digitized head surface point information'' ('''Ctrl-L''') ''dialog ''by pressing the '''Edit/Coreg''' button, or from the main menu ("'''File/MRI Coregistration...'''").

'''Note:''' If the coregistration dialog is invoked from an EEG data set in which no digitized electrode coordinates are available (i.e. standard electrode positions located on a sphere are assumed), BESA Research presents a warning message, saying that for MRI coregistration realistic electrode coordinates produce better results. BESA Research has a list of such realistic standard coordinates (i.e. located on a pre-defined standard head surface) for various electrodes available in file '''Default.sfp''', which is located in the Standard Electrode folder. If all electrodes in the dataset are listed in this file, a dialog window suggests to apply this file to the current data set, i.e. to switch from standard sphere coordinates to the standard realistic electrode coordinates in file '''Default.sfp'''. If the suggestion is accepted, '''default.sfp''' is assigned to the dataset (see Channel and digitized head surface point information ('''Ctrl-L''') dialog).

'''The Dialog:'''

[[Image:MRI Integration (1).gif ‎]]

* Press the '''Select MRI prog''' button to select your preferred MRI program. The current choice is between ''BESA MRI.exe'' and ''BrainVoyagerQX.exe''. The path to the MRI program is saved (in ''System\BESA.set'') and will be remembered by BESA Research. The top right hand button (now showing '''BESA MRI''') shows the current selection.
* Press the '''BESA MRI''' button to start the process of aligning the BESA Research and MRI coordinate systems. If no coregistration ('''<nowiki>*.sfh</nowiki>''') file is defined in the dialog (empty ''Surface coregistration file edit box''), BESA Research will first prompt for a file name. We recommend saving this file to the folder where the MRIs are kept. The MRI program will then be started. When you return to the ''Coregistration Dialog'', BESA Research checks if the ''Coregistration File'' has changed. If so, the dialog is updated with the new information.
* Press the top '''Browse... '''button to select a preexisting ''Coregistration File''.
* The entries in the edit boxes below show the files that will be used in the BESA Research Source Analysis module when the individual MRI is loaded. When using BESA MRI the file names will be automatically filled in. If you are using BrainVoagerQX and you are following our (and the BrainVoyagerQX) recommended naming conventions for files, and the files exist, then the names will be filled in automatically after you have completed the alignment procedure in BrainVoyagerQX. Otherwise you may have to browse for the files.
* Below the edit boxes the FEM field states whether all necessary information for the individual FEM head model were found in the coregistration file. If the field says ''Individual FEM for EEG'' ''defined!'' then all necessary data was found and the individual FEM EEG head model can be used in the BESA Research Source Analysis module. A similar message indicates whether the FEM MEG head model is available.
* Note that the MRI and the surfaces are Talairach-transformed! Alignment between BESA Research and the individual MRI is done with the MRI transformed to the AC-PC coordinate system, but the BESA Research Source Analysis module uses the Talairach-transformed image data and surfaces.

<div style="color:#ff0000;"></div>

=== Setting Up Coregistration Using BrainVoyager ===

It is assumed that you know how to load an MRI as a 3D data set into BrainVoyagerQX, and how to clean the image so that regions outside the head are black. We also assume knowledge of how to create AC-PC-aligned and Talairach-transformed MRIs.

Perform the following steps:

* BESA Research. Start the ''Coregistration Dialog''. Export the Coregistration File (head surface points) from your data by pressing the '''BrainVoyagerQX''' button in the dialog. Save the file to the directory where your MRI is located. BrainVoyagerQX is started.
* BrainVoyagerQX. Load the MRI corresponding to the EEG/MEG data. For optimal performance, the MRI should be cleaned so that regions outside the head are black. Prepare an AC-PC-transformed MRI and a Talairach MRI. For each, generate a surface mesh. Save these files following our recommended naming conventions (see chapter “[[Integration_with_MRI_and_fMRI#MRI_file_Name_Conventions|MRI File Name Conventions]]”). Save the Talairach coordinate file ('''<nowiki>*.tal</nowiki>'''). If these steps have already been performed, load the ACPC MRI and load the ACPC mesh. If you want to generate a brain surface mesh, see chapter “[[Integration_with_MRI_and_fMRI#How_to_Generate_a_Brain_Surface_Mesh|How to Generate a Brain Surface Mesh]]”.
* BrainVoyagerQX. Load the Coregistration File (''EEG-MEG BESA/Load Surface Points''). The points will be displayed, but they are not aligned to the head:

[[Image:MRI Integration (2).gif ‎]]

* BrainVoyagerQX. Define fiducial points on the head surface. Right click on the 3D head display and select the ''Fiducials Dialog'' in the drop-down menu:

[[Image:MRI Integration (3).gif ‎]] [[Image:MRI Integration (4).gif ‎]]

* BrainVoyagerQX. Rotate the head (by holding the '''Shift '''button down and clicking and dragging with the mouse) so that the Nasion is clearly visible. Move the mouse to the Nasion, and press '''Ctrl+Left Click'''. The coordinates of the Nasion are inserted into the dialog. Repeat for the left preauricular point, and then for the right preauricular point.

[[Image:MRI Integration (5).gif ‎]]

Note: if you have defined your fiducials differently in your BESA Research data (e.g. ear holes), click on the corresponding points in the MRI. If you have additional head surface points (step 8), accuracy in pinpointing the fiducials is not critical.

* BrainVoyagerQX. In the Fiducials Dialog, press the '''Fit fiducials''' button. The head surface points are now more or less aligned to the head.

[[Image:MRI Integration (6).gif ‎]]

* BrainVoyagerQX. Now select '''''EEG-MEG BESA/Fit Surface Points...'''''

[[Image:MRI Integration (7).gif ‎]]

If you do not see the right half of the dialog, press the '''Advanced >>''' button.

* Specify the distances of the digitization points from the skin. In the illustration above, the digitization points for electrodes are estimated to be 8 mm from the surface of the head. For the purpose of accurate alignment, the distance of digitization points from skin section of the dialog needs to be filled in correctly. We recommend that "Restrain solution around fiducials" is checked, and a reasonable limit (here 3 mm) of the restraint is defined. Then press '''OK'''.

[[Image:MRI Integration (8).gif ‎]]

BrainVoyager fits the points to the head, stretching x, y, and z coordinates to obtain a better fit than before.

Note: The fit performed during this step accounts for scaling inequalities between the x, y, and z axes in the MRI. Coregistration gains in accuracy over the use of fiducials alone a) because more head surface points are used, and b) because the scaling inequalities are accounted for.

* Alignment is now completed. If you only want to display the structural MRI in the BESA Source Module, you can return to the BESA Coregistration Dialog.
* BESA Research. When you switch back to the Coregistration Dialog, BESA Research will try to fill in the names of the Talairach MRI and surface meshes. If the names are not filled in, use the '''Browse...''' buttons to select the MRI and surface meshes. Press '''OK''' to save the Coregistration File. Alignment is completed!

The alignment steps need only be performed once for a given MRI and EEG/MEG data set. Otherwise, after starting BrainVoyager, just load the MRI, the surface mesh, and the surface points (see “[[Integration_with_MRI_and_fMRI#Coregistration_with_BrainVoyager_after_Alignment_has_been_Done |How to Set Up Coregistration with BrainVoyager after Alignment has been Done]]”). Now the following actions are possible: see chapters

* [[Integration_with_MRI_and_fMRI#Co-locating_Sources_and_MRI_in_the_BESA_Research_Source_Module|How to Co-Locate Sources and MRI in the BESA Research Source Module]]
* [[Integration_with_MRI_and_fMRI#Send_a_Dipole_from_BESA_Research_to_BrainVoyager|How to Send a Dipole from BESA Research to BrainVoyager]]
* [[Integration_with_MRI_and_fMRI#Define_a_Dipole_in_BESA_Research_at_a_Location_Defined_in_the_MRI|How to Define a Dipole in BESA Research at a Location Defined in the MRI]]

=== MRI file Name Conventions ===

If you follow the naming conventions for file names as described here, BESA Research detects the file names it requires, and the ''Coregistration Dialog'' is filled in automatically.

Please note that BESA MRI automatically uses these naming conventions for the generated files.

* '''The AC-PC MRI file name''' should end with "'''_ACPC.vmr'''", and the corresponding surface mesh name should end with "'''_ACPC.srf'''". After alignment, BrainVoyagerQX writes these names to the Coregistration File.
* '''The Talairach MRI file name '''should end with "'''_TAL.vmr'''", and the corresponding surface mesh name should end with "'''_TAL.srf'''". If defined, the brain surface mesh should end with "'''_TAL_WM.srf'''" ('''WM''' = '''w'''hite '''m'''atter).
* '''How BESA Research finds the Talairach files.''' When BESA Research rereads the Coregistration File after alignment of the coordinate systems, it finds the ACPC file names and defines the corresponding TAL file names. If these files exist, the names are entered into the Coregistration Dialog. For instance, if the Coregistration File contains the name "'''MRI''' '''PB_ACPC.vmr'''", BESA Research will look for the files "'''MRI_PB_TAL.vmr'''", "'''MRI_PB_TAL.srf'''", and "'''MRI_PB_TAL_WM.srf'''". If these files exist, they are entered into the dialog.
* '''Older BrainVoyager version.''' If you use BrainVoyager.exe to align coordinate systems, the file names are not saved with the Coregistration File. In this case, browse for the Talairach or the ACPC MRI from the Coregistration Dialog. BESA Research will use the rules as described above to insert the correct file names into the dialog.
* '''Missing Talairach coordinates.''' If, after aligning coordinate systems, the Talairach coordinates are missing from the Coregistration File (you forgot to load the Talairach coordinates in BrainVoyagerQX, or you used BrainVoyager.exe), BESA Research will look for a file ending with "'''_ACPC.tal'''", and read the coordinates from this file. You can also browse for a '''<nowiki>*.tal</nowiki>''' file in the Coregistration Dialog. For instance, if the MRI file is named "'''MRI_PB_ACPC.vmr'''" or "'''MR_''' '''PB_TAL.vmr'''", BESA Research will look for "'''MRI_PB_ACPC.tal'''" to find the Talairach coordinates.
* '''File names in the Coregistration File are saved relative to the Coregistration File location, if they are in the same folder.''' If the MRIs are in the same folder as the Coregistration File they will be recorded as ".\filename" (e.g. "'''.\MRI PB_tal.vmr'''"). This means that you can copy the Coregistration File together with the MRIs and meshes to a different folder, and BESA Research will be able to locate the files when the Coregistration File is opened. If the MRIs are saved in a different folder from the Coregistration File, the absolute paths are saved in the file. If the files are moved to new locations, you will have to restart the Coregistration Dialog and redefine the file locations.

=== How to Generate a Brain Surface Mesh ===

BESA Research is able to compute surface images, such as (Cortical LORETA, Cortical CLARA, Minimum Norm) using an individual cortex surface as the source space. A suitable cortex surface for this purpose can be effortlessly created using BESA MRI. Alternatively, BrainVoyager can be used for the creation of the brain surface mesh.

'''BESA MRI'''
* The brain surface generation is performed as one work step of the BESA MRI segmentation workflow.
* The cortex surface reconstruction is done using a robust and accurate automatic segmentation procedure.
* Details on how to generate the brain surface mesh in BESA MRI can be found in the coregistration quickguide which is available on the BESA homepage (http://www.besa.de/tutorials/quickguides/).

'''BrainVoyager'''
* BrainVoyagerQX provides a semiautomatic procedure to generate meshes for the brain surface of the Talairach MRI. Please refer to the BrainVoyager Help to find out how to do this.
* The result of the BrainVoyager procedure is two meshes, one for the left and one for the right hemisphere.
* BESA Research requires a single mesh. Therefore, load first one mesh (''Meshes/Load Mesh..''.), and append the other mesh (''Meshes/Add Mesh...''). Merge these two meshes (''Meshes/Merge'' ''meshes in surface window'') and then save the result (''Meshes/Save Mesh...''). If possible, use the recommended name conventions for the resulting file (file name ends in "'''_TAL_WM.srf"). '''For instance, if the Talairach MRI is named "'''MRI PB_TAL.vmr'''", name the brain surface mesh "'''MRI PB_TAL_WM.srf'''".
* See also the '''BrainVoyager Getting Started Guide''' that can be downloaded from the Brain Innovation website (http://brainvoyager.com/Downloads.html).

== Co-locating Dipoles and MRI Locations ==

=== Co-locating Sources and MRI in the BESA Research Source Module ===

If the alignment procedure using BESA MRI (or BrainVoyager) has been completed then you can load the individual structural MRI in the Source Module by pressing ''''A'''' or using a mouse right click and selecting '''''Display MRI'''''.

Sources in the current model are then overlayed onto the individual MRI.

A double-click at any location in the MRI will define a new source at the corresponding location in the BESA Research head model.

[[Image:MRI Integration (9).gif ‎]]

=== Coregistration with BrainVoyager after Alignment has been Done ===

Alignment between BESA Research and BrainVoyager is only required once for a given BESA Research data set and the corresponding MRI. At a later time, if you want to Co-locate sources between BESA Research and BrainVoyager, perform the following steps in BrainVoyager:
* Load the MRI.
* Load the head surface mesh (''Meshes/Load Mesh..''.).
* Load the Coregistration File (''EEG-MEG BESA/Load Surface Points..''.).

BrainVoyager is now ready for Co-location.

=== Send a Dipole from BESA Research to BrainVoyager ===

First, start BrainVoyager(QX). This can be done from the BESA Research Source Module by pressing the '''BrainVoyager '''button. Note that in the Source Module, the ''Options / Preferences / BrainVoyager'' tab allows to define the path to BrainVoyager.

In BrainVoyager, [[Integration_with_MRI_and_fMRI#Coregistration_with_BrainVoyager_after_Alignment_has_been_Done|set up coregistration]].

In the BESA Research Source Module, highlight the dipole of interest.

In the BESA Research Source Module, click on the '''BrainVoyager''' button.

Program control will automatically switch to BrainVoyager. The head will be cut at the section corresponding to the dipole of interest.

[[Image:MRI Integration (10).gif‎|200px]]

Note that all dipoles in the current model are sent to BrainVoyager. The highlighted dipole (here, the red dipole) determines the plane at which the head will be cut.

Note that the dipoles are visible in both the surface module and in the 2D view:

[[Image:MRI Integration (11).gif|400px]]

=== Define a Dipole in BESA Research at a Location Defined in the MRI ===

First set up coregistration (see chapter ''“[[Integration_with_MRI_and_fMRI#Coregistration_with_BrainVoyager_after_Alignment_has_been_Done|Coregistration with BrainVoyager after Alignment has been Done]]”'').

In the BrainVoyager 2D MRI view, place the mouse over the point at which you would like to define a dipole. Right click at this point. If this point lies within an fRMI cluster, BrainVoyager will automatically determine its center and use it as a seeding point instead. Press '''Send Seed Point To BESA....'''

[[Image:MRI Integration (12).gif ‎]]

The following Dialog is opened:

[[Image:MRI Integration (13).gif ‎]]

Press '''Send to BESA'''.

The BESA Source Analysis window appears. The new dipole or regional source (depending on the setting in the ‘Options’ dialog in the Source Analysis window is now displayed at the corresponding location. If a dipole is seeded, BESA automatically fits its orientation. For further adjustment of the model, you may need to refit the orientation, e.g. at a certain time range, or in the presence of other sources.

Detailed instructions on (f)MRI import and processing in Brain Voyager is provided by the '''BrainVoyager Getting Started Guide''' that can be downloaded from the Brain Innovation website ([http://brainvoyager.com/Downloads.html http://brainvoyager.com/Downloads.html]).

== Reference ==

=== The Coregistration File (*.sfh) ===

This file is used to mediate between BESA Research and BESA MRI (or BrainVoyager(QX)). When it is first written by BESA Research, it contains a list of the digitized head surface points (fiducials, electrodes, other digitized points), e.g.

<source lang="dos">
NrOfPoints: 68
Fid_Nz 0.00000 103.10000 0.00000 3 255 128 255
Fid_T9 -78.40000 0.00000 0.00000 3 255 128 255
Fid_T10 73.00000 0.00000 0.00000 3 255 128 255
Ele_E1 -28.70000 23.90000 122.30000 3 255 0 0
Ele_E2 -80.40000 19.80000 75.90000 3 255 0 0
Ele_E3 -84.00000 37.90000 9.00000 3 255 0 0
Ele_E4 -17.60000 92.90000 89.10000 3 255 0 0

...

Ele_E63 -6.80000 -104.00000 54.40000 3 255 0 0
Ele_E64 -42.80000 -46.90000 115.60000 3 255 0 0
Ele_Cz' -2.10000 2.20000 131.10000 3 255 0 0
</source>

Each line contains a label, the coordinates in the Head Coordinate system, and parameters specifying the size and color of the sensor or head surface point as displayed in BESA MRI (or BrainVoyager).

After aligning the coordinate systems, BESA MRI (or BrainVoyagerQX) appends lines defining the transformation between the BESA Research and the MRI coordinate systems:

<pre>
# Trans-data(in BV-coords): 3 translation, 3 rotation (in grad), 3 scale
37.435 15.811 2.820 0.025 1.938 8.779 1.009 0.973 0.977
Fiducials:
41.7873 148.0180 128.0844
154.7772 169.4783 204.1080
147.0154 168.9746 54.1266
Midpoint (in BV-coords):
128.0000 128.0000 128.0000
Volume: C:\BESA\Examples\ERP P300-Auditory\MRI_PB_acpc.vmr
Surface: C:\BESA\Examples\ERP P300-Auditory\MRI_PB_acpc.srf
AC: 128 128 128
PC: 154 128 128
AP: 58 128 128
PP: 241 129 130
SP: 154 50 128
IP: 128 172 128
RP: 128 128 60
LP: 165 128 198
</pre>

Note: Older versions of BrainVoyager.exe do not append the lines starting with "Volume". In addition, the Talairach coordinates (starting at "AC: ...") are not appended if they were not loaded in BrainVoyagerQX.

Finally, when the Coregistration Dialog in BESA Research has found the Talairach MRI and surface meshes, and you press the OK button, BESA Research appends the additional file names:

<pre>
TalVolume: C:\BESA\Examples\ERP P300-Auditory\MRI_PB_tal.vmr
TalSurface: C:\BESA\Examples\ERP P300-Auditory\MRI_PB_tal.srf
TalBrainSurface: C:\BESA\Examples\ERP P300-Auditory\MRI_PB_tal_wm.srf
</pre>

BESA MRI already inserts the correct file names into the coregistration file when doing the coregistration. When also an EEG or MEG FEM head model is generated then additional lines are appended to the coregistration file containing the file names of the generated FEM data files.

=== MRI Requirements for Good Coregistration ===

We recommend a high quality T1-weighted anatomical image with 1 mm³ voxels (e.g. 256 x 256 saggital scan with 1 mm spacing).

In order to define the surface mesh, a clear contrast between the head surface and the outside of the head (T1-weighting) is required. Noise and measurement artifacts can influence the representation of the scalp surface. When doing the coregistration in BrainVoyager improvements in noisy images often can be achieved by cleaning up the image after first reading it using the tools provided by BrainVoyager.

For coregistration with head surface points, it is useful to include the whole head in the image, including nose and ears. If surface points on the nose are included with the EEG/MEG data set, these points help to stabilize the fit of head surface points to the surface mesh.

=== EEG/MEG Data Requirements for Good Coregistration ===

We recommend several (30 or more) digitized head surface points in addition to the fiducials, including points on the nose (nose tip and sides). These points may include electrodes. In the case of electrodes, it is important to measure the distance from the scalp to the digitization point, i.e. the electrode thickness.

[[Category:Research Manual]]

{{BESAManualNav}}

Integration with MRI and fMRI

2019-03-27T12:51:13Z

Jamie: /* Introduction */

{{BESAInfobox
|title = Module information
|module = BESA Research Basic or higher and BESA MRI
|version = 6.1 or higher
}}



== Introduction ==

Both for developing and evaluating dipole source models of EEG or MEG activity, it is useful to have access to structural MRI or fMRI data.

The BESA MRI software allows to preprocess structural MRI data so that the individual anatomical information contained in the MRI can be utilized in BESA Research. BESA MRI makes it possible ...
* ... to align the EEG and MEG sensors with the structural MRI data.
* ... to read and display the aligned, individual Talairach structural MRIs directly in the BESA Research Source Analysis module. In this way, source analysis results can be presented on top of the aligned MRIs, which allows us to evaluate the anatomical regions to which the reconstructed sources may correspond.
* ... to use an individual, realistically shaped FEM head model for source analysis in BESA Research. FEM head models take into account the individual volume conduction properties of the subject's head derived from the structural MRI data. This allows for more accurate source analysis (Yvert 1997, Lanfer 2012).

To offer an easy integration with fMRI data we have, in collaboration with Rainer Goebel, optimized the interface between BESA Research and BrainVoyagerQX.

With these tools, we can ...
* ... use fMRI BOLD regions or MRI structures to initialize dipole models.
* ... visualize dipoles from BESA Research models together with the structural MRI in BrainVoyager in order to evaluate the regions to which the dipoles may correspond.
* ... combine the localization advantages of (f)MRI with the high temporal resolution of EEG and MEG, for instance by using (f)MRI to place the sources, and the source waveforms of BESA Research to provide feedback about the time course of the source activity.
* ... overlay source analysis results obtained in BESA Research with fMRI data.

'''Note:''' For simpler coregistration, we recommend to use BrainVoyagerQX rather than the older BrainVoyager, but BESA Research will work with both program versions.

The chapters below describe the steps necessary to integrate the MRI and fMRI data with BESA Research. Detailed instructions on (f)MRI import and processing in Brain Voyager is provided by the '''BrainVoyager Getting Started Guide''' that can be downloaded from the Brain Innovation website (https://www.brainvoyager.com/downloads/downloads.html).

'''Aligning Coordinate Systems'''

* For a given BESA data set, the electrode and other head surface points need to be aligned to the MRI coordinates.
* The basic steps necessary to align the EEG electrode locations, the MEG sensors and the MRI are described in Section “[[Integration_with_MRI_and_fMRI#Setting_Up_Coregistration_Using_BrainVoyager|How Coregistration is done]]”.
* Detailed instructions on how to align EEG / MEG and MRI data using BESA MRI can be found in the coregistration quick guide which is available on the BESA homepage ((http://www.besa.de/downloads/quick-guides/).
* Detailed instructions on how to align EEG / MEG and MRI data using BrainVoyager are described in Section “[[Integration_with_MRI_and_fMRI#Setting_Up_Coregistration_Using_BrainVoyager|How To set up Coregistration between BESA and BrainVoyager]]”.
* In BESA Research, all necessary settings with regard to the alignment are made in the [[Integration_with_MRI_and_fMRI#The_Coregistration_Dialog|Coregistration Dialog]].
* Requirements with respect to the MRI data for a good coregistration can be found in Section “''MRI Requirements for Good Coregistration”.''
* Requirements with respect to EEG and MEG data for a good coregistration can be found in Section “''EEG/MEG Data Requirements for Good Coregistration”.''

'''Generating an individual, realistically shaped FEM head model'''

* The generation of a FEM head model that can be used in BESA Research is done in BESA MRI as an additional step following the EEG / MEG to MRI coregistration.
* Detailed instructions on how to generate the FEM head model can be found in the coregistration quick guide which is available on the BESA homepage (http://www.besa.de/downloads/quick-guides/).

'''Co-locating dipoles and MRI locations'''

* After aligning the EEG / MEG and the MRI data it is possible to co-locate dipoles and MRI locations. This means, it is possible to visualize the dipoles and to specify the dipole parameters in the MRI coordinate system.
* “[[Integration_with_MRI_and_fMRI#Co-locating_Sources_and_MRI_in_the_BESA_Research_Source_Module|How to Co-locate sources and MRI in the BESA Research Source Module]]" describes how in the BESA Research Source Analysis module dipoles can directly be visualized in the space of the individual MRI.
* “[[Integration_with_MRI_and_fMRI#Send_a_Dipole_from_BESA_Research_to_BrainVoyager|How to Send a Dipole from BESA Research to BrainVoyager]]” describes how to send a source model from BESA Research to BrainVoyager for further inspection.
* “[[Integration_with_MRI_and_fMRI#Define_a_Dipole_in_BESA_Research_at_a_Location_Defined_in_the_MRI|How to Define a Dipole in BESA Research at a Location Defined in the MRI]]” describes how to insert a dipole at a location defined in the MRI in BrainVoyager.

'''References'''

Lanfer, B., I. Paul-Jordanov, M. Scherg, and C. H. Wolters. “Influence of Interior Cerebrospinal Fluid Compartments on EEG Source Analysis.” In Proceedings BMT 2012, Vol. 57. Jena: De Gruyter, 2012. doi:10.1515/bmt-2012-4020.

Yvert, B., O. Bertrand, M. Thévenet, J. F. Echallier, and J. Pernier. “A Systematic Evaluation of the Spherical Model Accuracy in EEG Dipole Localization.” Electroencephalography and Clinical Neurophysiology 102, no. 5 (May 1997): 452–59. doi:16/S0921-884X(97)96611-X.

== How Coregistration is done ==

This section outlines the basic steps to coregister the EEG / MEG data to an individual MRI. These steps are necessary to load an individual MRI into BESA Research.

'''What happens:'''

* EEG / MEG sensor locations and the MRI data are defined in different coordinate systems. Setting up coregistration is the process of aligning the two coordinate systems.
* BESA Research uses the ''Coregistration Dialog'' to coordinate the alignment procedure.
* Alignment is done with the ''AC-PC-transformed MRI''.
* BESA Research displays the ''Talairach-transformed MRI'' in the source analysis module.
* A coregistration file (with the extension "'''.sfh'''") is used to mediate between BESA Research and BESA MRI (or BrainVoyagerQX):
* BESA Research writes the coregistration file which contains the coordinates of head surface points (fiducials, electrodes, other digitized surface points).
* The coordinates are read into BESA MRI (or BrainVoyager), and aligned with the AC-PC-transformed MRI. The alignment information is then appended to the ''coregistration file''. The names of the AC-PC MRI ('''<nowiki>*.vmr</nowiki>''') and the surface mesh ('''<nowiki>*.srf</nowiki>'''), and, if available, the Talairach transformation, are also appended.
* BESA Research reads the coregistration file and appends the name of the Talairach-transformed MRI and head surface. If a brain surface has been created, this is also appended.
* Subsequently, BESA Research reads the coregistration file automatically when loading the data file.
* In the BESA Research source module, the individual MRI is displayed instead of the standard MRI. Talairach coordinates of dipoles are the "real" Talairach coordinates as defined, e.g., in BrainVoyager.

'''The steps you have to take (once for each data set):'''

* From the BESA Research ''Coregistration Dialog'', write a coregistration file. Switch to BESA MRI (or BrainVoyagerQX).
* If BESA MRI is used follow the steps in the coregistration quickguide which is available on the BESA homepage (http://www.besa.de/tutorials/quickguides/).
* If BrainVoyager is used follow the steps in Section “''How to set up coregistration between BESA and BrainVoyager”.''
* Back in BESA Research, reload the altered '''coregistration file'''. When using BESA MRI the file names of the generated surface and volume data files will be automatically filled in. When using BrainVoyager file names are only filled in automatically when the files are named according to the file naming conventions. Otherwise, file names have to be set manually.
* The coregistration file is now associated with the data file in the BESA Research database and will be used automatically the next time the file is opened in BESA Research. If the database entry is cleared, and the data are reloaded, you must make sure the coregistration file is also loaded (either using the ''Coregistration Dialog'' or the ''Channel and digitized head surface point information Dialog'').

== Alignment of BESA and MRICoordinate Systems ==

=== The Coregistration Dialog ===

The dialog is opened either from the ''Channel and digitized head surface point information'' ('''Ctrl-L''') ''dialog ''by pressing the '''Edit/Coreg''' button, or from the main menu ("'''File/MRI Coregistration...'''").

'''Note:''' If the coregistration dialog is invoked from an EEG data set in which no digitized electrode coordinates are available (i.e. standard electrode positions located on a sphere are assumed), BESA Research presents a warning message, saying that for MRI coregistration realistic electrode coordinates produce better results. BESA Research has a list of such realistic standard coordinates (i.e. located on a pre-defined standard head surface) for various electrodes available in file '''Default.sfp''', which is located in the Standard Electrode folder. If all electrodes in the dataset are listed in this file, a dialog window suggests to apply this file to the current data set, i.e. to switch from standard sphere coordinates to the standard realistic electrode coordinates in file '''Default.sfp'''. If the suggestion is accepted, '''default.sfp''' is assigned to the dataset (see Channel and digitized head surface point information ('''Ctrl-L''') dialog).

'''The Dialog:'''

[[Image:MRI Integration (1).gif ‎]]

* Press the '''Select MRI prog''' button to select your preferred MRI program. The current choice is between ''BESA MRI.exe'' and ''BrainVoyagerQX.exe''. The path to the MRI program is saved (in ''System\BESA.set'') and will be remembered by BESA Research. The top right hand button (now showing '''BESA MRI''') shows the current selection.
* Press the '''BESA MRI''' button to start the process of aligning the BESA Research and MRI coordinate systems. If no coregistration ('''<nowiki>*.sfh</nowiki>''') file is defined in the dialog (empty ''Surface coregistration file edit box''), BESA Research will first prompt for a file name. We recommend saving this file to the folder where the MRIs are kept. The MRI program will then be started. When you return to the ''Coregistration Dialog'', BESA Research checks if the ''Coregistration File'' has changed. If so, the dialog is updated with the new information.
* Press the top '''Browse... '''button to select a preexisting ''Coregistration File''.
* The entries in the edit boxes below show the files that will be used in the BESA Research Source Analysis module when the individual MRI is loaded. When using BESA MRI the file names will be automatically filled in. If you are using BrainVoagerQX and you are following our (and the BrainVoyagerQX) recommended naming conventions for files, and the files exist, then the names will be filled in automatically after you have completed the alignment procedure in BrainVoyagerQX. Otherwise you may have to browse for the files.
* Below the edit boxes the FEM field states whether all necessary information for the individual FEM head model were found in the coregistration file. If the field says ''Individual FEM for EEG'' ''defined!'' then all necessary data was found and the individual FEM EEG head model can be used in the BESA Research Source Analysis module. A similar message indicates whether the FEM MEG head model is available.
* Note that the MRI and the surfaces are Talairach-transformed! Alignment between BESA Research and the individual MRI is done with the MRI transformed to the AC-PC coordinate system, but the BESA Research Source Analysis module uses the Talairach-transformed image data and surfaces.

<div style="color:#ff0000;"></div>

=== Setting Up Coregistration Using BrainVoyager ===

It is assumed that you know how to load an MRI as a 3D data set into BrainVoyagerQX, and how to clean the image so that regions outside the head are black. We also assume knowledge of how to create AC-PC-aligned and Talairach-transformed MRIs.

Perform the following steps:

* BESA Research. Start the ''Coregistration Dialog''. Export the Coregistration File (head surface points) from your data by pressing the '''BrainVoyagerQX''' button in the dialog. Save the file to the directory where your MRI is located. BrainVoyagerQX is started.
* BrainVoyagerQX. Load the MRI corresponding to the EEG/MEG data. For optimal performance, the MRI should be cleaned so that regions outside the head are black. Prepare an AC-PC-transformed MRI and a Talairach MRI. For each, generate a surface mesh. Save these files following our recommended naming conventions (see chapter “[[Integration_with_MRI_and_fMRI#MRI_file_Name_Conventions|MRI File Name Conventions]]”). Save the Talairach coordinate file ('''<nowiki>*.tal</nowiki>'''). If these steps have already been performed, load the ACPC MRI and load the ACPC mesh. If you want to generate a brain surface mesh, see chapter “[[Integration_with_MRI_and_fMRI#How_to_Generate_a_Brain_Surface_Mesh|How to Generate a Brain Surface Mesh]]”.
* BrainVoyagerQX. Load the Coregistration File (''EEG-MEG BESA/Load Surface Points''). The points will be displayed, but they are not aligned to the head:

[[Image:MRI Integration (2).gif ‎]]

* BrainVoyagerQX. Define fiducial points on the head surface. Right click on the 3D head display and select the ''Fiducials Dialog'' in the drop-down menu:

[[Image:MRI Integration (3).gif ‎]] [[Image:MRI Integration (4).gif ‎]]

* BrainVoyagerQX. Rotate the head (by holding the '''Shift '''button down and clicking and dragging with the mouse) so that the Nasion is clearly visible. Move the mouse to the Nasion, and press '''Ctrl+Left Click'''. The coordinates of the Nasion are inserted into the dialog. Repeat for the left preauricular point, and then for the right preauricular point.

[[Image:MRI Integration (5).gif ‎]]

Note: if you have defined your fiducials differently in your BESA Research data (e.g. ear holes), click on the corresponding points in the MRI. If you have additional head surface points (step 8), accuracy in pinpointing the fiducials is not critical.

* BrainVoyagerQX. In the Fiducials Dialog, press the '''Fit fiducials''' button. The head surface points are now more or less aligned to the head.

[[Image:MRI Integration (6).gif ‎]]

* BrainVoyagerQX. Now select '''''EEG-MEG BESA/Fit Surface Points...'''''

[[Image:MRI Integration (7).gif ‎]]

If you do not see the right half of the dialog, press the '''Advanced >>''' button.

* Specify the distances of the digitization points from the skin. In the illustration above, the digitization points for electrodes are estimated to be 8 mm from the surface of the head. For the purpose of accurate alignment, the distance of digitization points from skin section of the dialog needs to be filled in correctly. We recommend that "Restrain solution around fiducials" is checked, and a reasonable limit (here 3 mm) of the restraint is defined. Then press '''OK'''.

[[Image:MRI Integration (8).gif ‎]]

BrainVoyager fits the points to the head, stretching x, y, and z coordinates to obtain a better fit than before.

Note: The fit performed during this step accounts for scaling inequalities between the x, y, and z axes in the MRI. Coregistration gains in accuracy over the use of fiducials alone a) because more head surface points are used, and b) because the scaling inequalities are accounted for.

* Alignment is now completed. If you only want to display the structural MRI in the BESA Source Module, you can return to the BESA Coregistration Dialog.
* BESA Research. When you switch back to the Coregistration Dialog, BESA Research will try to fill in the names of the Talairach MRI and surface meshes. If the names are not filled in, use the '''Browse...''' buttons to select the MRI and surface meshes. Press '''OK''' to save the Coregistration File. Alignment is completed!

The alignment steps need only be performed once for a given MRI and EEG/MEG data set. Otherwise, after starting BrainVoyager, just load the MRI, the surface mesh, and the surface points (see “[[Integration_with_MRI_and_fMRI#Coregistration_with_BrainVoyager_after_Alignment_has_been_Done |How to Set Up Coregistration with BrainVoyager after Alignment has been Done]]”). Now the following actions are possible: see chapters

* [[Integration_with_MRI_and_fMRI#Co-locating_Sources_and_MRI_in_the_BESA_Research_Source_Module|How to Co-Locate Sources and MRI in the BESA Research Source Module]]
* [[Integration_with_MRI_and_fMRI#Send_a_Dipole_from_BESA_Research_to_BrainVoyager|How to Send a Dipole from BESA Research to BrainVoyager]]
* [[Integration_with_MRI_and_fMRI#Define_a_Dipole_in_BESA_Research_at_a_Location_Defined_in_the_MRI|How to Define a Dipole in BESA Research at a Location Defined in the MRI]]

=== MRI file Name Conventions ===

If you follow the naming conventions for file names as described here, BESA Research detects the file names it requires, and the ''Coregistration Dialog'' is filled in automatically.

Please note that BESA MRI automatically uses these naming conventions for the generated files.

* '''The AC-PC MRI file name''' should end with "'''_ACPC.vmr'''", and the corresponding surface mesh name should end with "'''_ACPC.srf'''". After alignment, BrainVoyagerQX writes these names to the Coregistration File.
* '''The Talairach MRI file name '''should end with "'''_TAL.vmr'''", and the corresponding surface mesh name should end with "'''_TAL.srf'''". If defined, the brain surface mesh should end with "'''_TAL_WM.srf'''" ('''WM''' = '''w'''hite '''m'''atter).
* '''How BESA Research finds the Talairach files.''' When BESA Research rereads the Coregistration File after alignment of the coordinate systems, it finds the ACPC file names and defines the corresponding TAL file names. If these files exist, the names are entered into the Coregistration Dialog. For instance, if the Coregistration File contains the name "'''MRI''' '''PB_ACPC.vmr'''", BESA Research will look for the files "'''MRI_PB_TAL.vmr'''", "'''MRI_PB_TAL.srf'''", and "'''MRI_PB_TAL_WM.srf'''". If these files exist, they are entered into the dialog.
* '''Older BrainVoyager version.''' If you use BrainVoyager.exe to align coordinate systems, the file names are not saved with the Coregistration File. In this case, browse for the Talairach or the ACPC MRI from the Coregistration Dialog. BESA Research will use the rules as described above to insert the correct file names into the dialog.
* '''Missing Talairach coordinates.''' If, after aligning coordinate systems, the Talairach coordinates are missing from the Coregistration File (you forgot to load the Talairach coordinates in BrainVoyagerQX, or you used BrainVoyager.exe), BESA Research will look for a file ending with "'''_ACPC.tal'''", and read the coordinates from this file. You can also browse for a '''<nowiki>*.tal</nowiki>''' file in the Coregistration Dialog. For instance, if the MRI file is named "'''MRI_PB_ACPC.vmr'''" or "'''MR_''' '''PB_TAL.vmr'''", BESA Research will look for "'''MRI_PB_ACPC.tal'''" to find the Talairach coordinates.
* '''File names in the Coregistration File are saved relative to the Coregistration File location, if they are in the same folder.''' If the MRIs are in the same folder as the Coregistration File they will be recorded as ".\filename" (e.g. "'''.\MRI PB_tal.vmr'''"). This means that you can copy the Coregistration File together with the MRIs and meshes to a different folder, and BESA Research will be able to locate the files when the Coregistration File is opened. If the MRIs are saved in a different folder from the Coregistration File, the absolute paths are saved in the file. If the files are moved to new locations, you will have to restart the Coregistration Dialog and redefine the file locations.

=== How to Generate a Brain Surface Mesh ===

BESA Research is able to compute surface images, such as (Cortical LORETA, Cortical CLARA, Minimum Norm) using an individual cortex surface as the source space. A suitable cortex surface for this purpose can be effortlessly created using BESA MRI. Alternatively, BrainVoyager can be used for the creation of the brain surface mesh.

'''BESA MRI'''
* The brain surface generation is performed as one work step of the BESA MRI segmentation workflow.
* The cortex surface reconstruction is done using a robust and accurate automatic segmentation procedure.
* Details on how to generate the brain surface mesh in BESA MRI can be found in the coregistration quickguide which is available on the BESA homepage (http://www.besa.de/tutorials/quickguides/).

'''BrainVoyager'''
* BrainVoyagerQX provides a semiautomatic procedure to generate meshes for the brain surface of the Talairach MRI. Please refer to the BrainVoyager Help to find out how to do this.
* The result of the BrainVoyager procedure is two meshes, one for the left and one for the right hemisphere.
* BESA Research requires a single mesh. Therefore, load first one mesh (''Meshes/Load Mesh..''.), and append the other mesh (''Meshes/Add Mesh...''). Merge these two meshes (''Meshes/Merge'' ''meshes in surface window'') and then save the result (''Meshes/Save Mesh...''). If possible, use the recommended name conventions for the resulting file (file name ends in "'''_TAL_WM.srf"). '''For instance, if the Talairach MRI is named "'''MRI PB_TAL.vmr'''", name the brain surface mesh "'''MRI PB_TAL_WM.srf'''".
* See also the '''BrainVoyager Getting Started Guide''' that can be downloaded from the Brain Innovation website (http://brainvoyager.com/Downloads.html).

== Co-locating Dipoles and MRI Locations ==

=== Co-locating Sources and MRI in the BESA Research Source Module ===

If the alignment procedure using BESA MRI (or BrainVoyager) has been completed then you can load the individual structural MRI in the Source Module by pressing ''''A'''' or using a mouse right click and selecting '''''Display MRI'''''.

Sources in the current model are then overlayed onto the individual MRI.

A double-click at any location in the MRI will define a new source at the corresponding location in the BESA Research head model.

[[Image:MRI Integration (9).gif ‎]]

=== Coregistration with BrainVoyager after Alignment has been Done ===

Alignment between BESA Research and BrainVoyager is only required once for a given BESA Research data set and the corresponding MRI. At a later time, if you want to Co-locate sources between BESA Research and BrainVoyager, perform the following steps in BrainVoyager:
* Load the MRI.
* Load the head surface mesh (''Meshes/Load Mesh..''.).
* Load the Coregistration File (''EEG-MEG BESA/Load Surface Points..''.).

BrainVoyager is now ready for Co-location.

=== Send a Dipole from BESA Research to BrainVoyager ===

First, start BrainVoyager(QX). This can be done from the BESA Research Source Module by pressing the '''BrainVoyager '''button. Note that in the Source Module, the ''Options / Preferences / BrainVoyager'' tab allows to define the path to BrainVoyager.

In BrainVoyager, [[Integration_with_MRI_and_fMRI#Coregistration_with_BrainVoyager_after_Alignment_has_been_Done|set up coregistration]].

In the BESA Research Source Module, highlight the dipole of interest.

In the BESA Research Source Module, click on the '''BrainVoyager''' button.

Program control will automatically switch to BrainVoyager. The head will be cut at the section corresponding to the dipole of interest.

[[Image:MRI Integration (10).gif‎|200px]]

Note that all dipoles in the current model are sent to BrainVoyager. The highlighted dipole (here, the red dipole) determines the plane at which the head will be cut.

Note that the dipoles are visible in both the surface module and in the 2D view:

[[Image:MRI Integration (11).gif|400px]]

=== Define a Dipole in BESA Research at a Location Defined in the MRI ===

First set up coregistration (see chapter ''“[[Integration_with_MRI_and_fMRI#Coregistration_with_BrainVoyager_after_Alignment_has_been_Done|Coregistration with BrainVoyager after Alignment has been Done]]”'').

In the BrainVoyager 2D MRI view, place the mouse over the point at which you would like to define a dipole. Right click at this point. If this point lies within an fRMI cluster, BrainVoyager will automatically determine its center and use it as a seeding point instead. Press '''Send Seed Point To BESA....'''

[[Image:MRI Integration (12).gif ‎]]

The following Dialog is opened:

[[Image:MRI Integration (13).gif ‎]]

Press '''Send to BESA'''.

The BESA Source Analysis window appears. The new dipole or regional source (depending on the setting in the ‘Options’ dialog in the Source Analysis window is now displayed at the corresponding location. If a dipole is seeded, BESA automatically fits its orientation. For further adjustment of the model, you may need to refit the orientation, e.g. at a certain time range, or in the presence of other sources.

Detailed instructions on (f)MRI import and processing in Brain Voyager is provided by the '''BrainVoyager Getting Started Guide''' that can be downloaded from the Brain Innovation website ([http://brainvoyager.com/Downloads.html http://brainvoyager.com/Downloads.html]).

== Reference ==

=== The Coregistration File (*.sfh) ===

This file is used to mediate between BESA Research and BESA MRI (or BrainVoyager(QX)). When it is first written by BESA Research, it contains a list of the digitized head surface points (fiducials, electrodes, other digitized points), e.g.

<source lang="dos">
NrOfPoints: 68
Fid_Nz 0.00000 103.10000 0.00000 3 255 128 255
Fid_T9 -78.40000 0.00000 0.00000 3 255 128 255
Fid_T10 73.00000 0.00000 0.00000 3 255 128 255
Ele_E1 -28.70000 23.90000 122.30000 3 255 0 0
Ele_E2 -80.40000 19.80000 75.90000 3 255 0 0
Ele_E3 -84.00000 37.90000 9.00000 3 255 0 0
Ele_E4 -17.60000 92.90000 89.10000 3 255 0 0

...

Ele_E63 -6.80000 -104.00000 54.40000 3 255 0 0
Ele_E64 -42.80000 -46.90000 115.60000 3 255 0 0
Ele_Cz' -2.10000 2.20000 131.10000 3 255 0 0
</source>

Each line contains a label, the coordinates in the Head Coordinate system, and parameters specifying the size and color of the sensor or head surface point as displayed in BESA MRI (or BrainVoyager).

After aligning the coordinate systems, BESA MRI (or BrainVoyagerQX) appends lines defining the transformation between the BESA Research and the MRI coordinate systems:

<pre>
# Trans-data(in BV-coords): 3 translation, 3 rotation (in grad), 3 scale
37.435 15.811 2.820 0.025 1.938 8.779 1.009 0.973 0.977
Fiducials:
41.7873 148.0180 128.0844
154.7772 169.4783 204.1080
147.0154 168.9746 54.1266
Midpoint (in BV-coords):
128.0000 128.0000 128.0000
Volume: C:\BESA\Examples\ERP P300-Auditory\MRI_PB_acpc.vmr
Surface: C:\BESA\Examples\ERP P300-Auditory\MRI_PB_acpc.srf
AC: 128 128 128
PC: 154 128 128
AP: 58 128 128
PP: 241 129 130
SP: 154 50 128
IP: 128 172 128
RP: 128 128 60
LP: 165 128 198
</pre>

Note: Older versions of BrainVoyager.exe do not append the lines starting with "Volume". In addition, the Talairach coordinates (starting at "AC: ...") are not appended if they were not loaded in BrainVoyagerQX.

Finally, when the Coregistration Dialog in BESA Research has found the Talairach MRI and surface meshes, and you press the OK button, BESA Research appends the additional file names:

<pre>
TalVolume: C:\BESA\Examples\ERP P300-Auditory\MRI_PB_tal.vmr
TalSurface: C:\BESA\Examples\ERP P300-Auditory\MRI_PB_tal.srf
TalBrainSurface: C:\BESA\Examples\ERP P300-Auditory\MRI_PB_tal_wm.srf
</pre>

BESA MRI already inserts the correct file names into the coregistration file when doing the coregistration. When also an EEG or MEG FEM head model is generated then additional lines are appended to the coregistration file containing the file names of the generated FEM data files.

=== MRI Requirements for Good Coregistration ===

We recommend a high quality T1-weighted anatomical image with 1 mm³ voxels (e.g. 256 x 256 saggital scan with 1 mm spacing).

In order to define the surface mesh, a clear contrast between the head surface and the outside of the head (T1-weighting) is required. Noise and measurement artifacts can influence the representation of the scalp surface. When doing the coregistration in BrainVoyager improvements in noisy images often can be achieved by cleaning up the image after first reading it using the tools provided by BrainVoyager.

For coregistration with head surface points, it is useful to include the whole head in the image, including nose and ears. If surface points on the nose are included with the EEG/MEG data set, these points help to stabilize the fit of head surface points to the surface mesh.

=== EEG/MEG Data Requirements for Good Coregistration ===

We recommend several (30 or more) digitized head surface points in addition to the fiducials, including points on the nose (nose tip and sides). These points may include electrodes. In the case of electrodes, it is important to measure the distance from the scalp to the digitization point, i.e. the electrode thickness.

[[Category:Research Manual]]

{{BESAManualNav}}

Source Analysis 3D Imaging

2019-03-27T12:47:21Z

Jamie: /* Cortical LORETA */

{{BESAInfobox
|title = Module information
|module = BESA Research Standard or higher
|version = 6.1 or higher
}}


== Overview ==

BESA Research features a set of new functions that provide 3D images that are displayed superimposed to the individual subject's anatomy. This chapter introduces these different images and describe their properties and applications.

The 3D images can be divided into three categories:

'''Volume images:'''

* '''The Multiple Source Beamformer (MSBF)''' is a tool for imaging brain activity. It is applied in the time-domain or time-frequency domain. The beamformer technique in time-frequency domain can image not only evoked, but also induced activity, which is not visible in time-domain averages of the data.
* '''Dynamic Imaging of Coherent Sources (DICS)''' can find coherence between any two pairs of voxels in the brain or between an external source and brain voxels. DICS requires time-frequency-transformed data and can find coherence for evoked and induced activity.

The following imaging methods provide an image of brain activity based on a distributed multiple source model:
* '''CLARA''' is an iterative application of LORETA images, focusing the obtained 3D image in each iteration step.
* '''LAURA '''uses a spatial weighting function that has the form of a local autoregressive function.
* '''LORETA''' has the 3D Laplacian operator implemented as spatial weighting prior.
* '''sLORETA''' is an unweighted minimum norm that is standardized by the resolution matrix.
* '''swLORETA '''is equivalent to sLORETA, except for an additional depth weighting.
* '''SSLOFO '''is an iterative application of standardized minimum norm images with consecutive shrinkage of the source space.
* A '''User-defined volume image''' allows to experiment with the different imaging techniques. It is possible to specify user-defined parameters for the family of distributed source images to create a new imaging technique.
* Bayesian source imaging: '''SESAME''' uses a semi-automated Bayesian approach to estimate the number of dipoles along with their parameters.

'''Surface image:'''

* The '''Surface Minimum Norm Image'''. If no individual MRI is available, the minimum norm image is displayed on a standard brain surface and computed for standard source locations. If available, an individual brain surface is used to construct the distributed source model and to image the brain activity.
* '''Cortical LORETA'''. Unlike classical LORETA, cortical LORETA is not computed in a 3D volume, but on the cortical surface.
* '''Cortical CLARA'''. Unlike classical CLARA, cortical CLARA is not computed in a 3D volume, but on the cortical surface.

'''Discrete model probing:'''

These images do not visualize source activity. Rather, they visualize properties of the currently applied discrete source model:
* The '''Multiple Source Probe Scan (MSPS)''' is a tool for the validation of a discrete multiple source model.
* The '''Source Sensitivity image''' displays the sensitivity of a selected source in the current discrete source model and is therefore data independent.

== Multiple Source Beamformer (MSBF) in the Time-frequency Domain ==

 
'''Short mathematical introduction'''

The BESA beamformer is a modified version of the linearly constrained minimum variance vector beamformer in the time-frequency domain as described in [https://dx.doi.org/10.1073/pnas.98.2.694 Gross et al., "Dynamic imaging of coherent sources: Studying neural interactions in the human brain", PNAS 98, 694-699, 2001]. It allows to image evoked and induced oscillatory activity in a user-defined time-frequency range, where time is taken relative to a triggered event.

The computation is based on a transformation of each channel's single trial data from the time domain into the time-frequency domain. This transformation is performed by the BESA Research Source Coherence module and leads to the complex spectral density Si (f,t), where i is the channel index and f and t denote frequency and time, respectively. Complex cross spectral density matrices C are computed for each trial:

<math>\mathrm{C}_{ij}\left( f,t \right) = \mathrm{S}_{i}\left( f,t \right) \cdot \mathrm{S}_{j}^{*}\left( f,t \right)</math>


The output power P of the beamformer for a specific brain region at location r is then computed by the following equation:

<math>\mathrm{P}\left( r \right) = \operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{-1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{-1}</math>


Here, Cr-1 is the inverse of the SVD-regularized average of Cij(f,t) over trials and the time-frequency range of interest; L is the leadfield matrix of the model containing a regional source at target location r and, optionally, additional sources whose interference with the target source is to be minimized; tr'[] is the trace of the [3×3] (MEG:[2×2]) submatrix of the bracketed expression that corresponds to the source at target location r.

In BESA Research, the output power P(r) is normalized with the output power in a reference time-frequency interval Pref(r). A value q ist defined as follows:

<math> \mathrm{q}\left( r \right) =
\begin{cases}
\sqrt{\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}(r)}} - 1 = \sqrt{\frac{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{\text{ref},r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}} - 1, & \text{for }\mathrm{P}(r) \geq \mathrm{P}_{\text{ref}}(r) \\

1 - \sqrt{\frac{\mathrm{P}_{\text{ref}}\left( r \right)}{\mathrm{P}\left( r \right)}} = 1 - \sqrt{\frac{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{\text{ref},r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}}, & \text{for }\mathrm{P}(r) < \mathrm{P}_{\text{ref}}(r)
\end{cases} </math>


Pref can be computed either from the corresponding frequency range in the baseline of the same condition (i.e. the beamformer images event-related power increase or decrease) or from the corresponding time-frequency range in a control condition (i.e. the beamformer images differences between two conditions). The beamformer image is constructed from values q(r) computed for all locations on a grid specified in the '''General Settings tab'''. For MEG data, the innermost grid points within a sphere of approx. 12% of the head diameter are assigned interpolated rather than calculated values).
q-values are shown in %, where where q[%] = q*100. Alternatively to the definition above, q can also be displayed in units of dB:

<math>\mathrm{q}\left\lbrack \text{dB} \right\rbrack = 10 \cdot \log_{10}\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}</math>


A beamformer operator is designed to pass signals from the brain region of interest r without attenuation, while minimizing interference from activity in all other brain regions. Traditional single-source beamformers are known to mislocalize sources if several brain regions have highly correlated activity. Therefore, the BESA beamformer extends the traditional single-source beamformer in order to implicitly suppress activity from possibly correlated brain regions. This is achieved by using a multiple source beamformer calculation that contains not only the leadfields of the source at the location of interest r, but also those of possibly interfering sources. As a default, BESA Research uses a bilateral beamformer, where specifically contributions from the homologue source in the opposite hemisphere are taken into account (the matrix L thus being of dimension N×6 for EEG and N×4 for MEG, respectively, where N is the number of sensors). This allows for imaging of highly correlated bilateral activity in the two hemispheres that commonly occurs during processing of external stimuli.

In addition, the beamformer computation can take into account possibly correlated sources at arbitrary locations that are specified in the current solution. This is achieved by adding their leadfield vectors to the matrix L in the equation above.

'''Applying the Beamformer'''

This chapter illustrates the usage of the BESA beamformer. The displayed figures are generated using the file ''''Examples/Learn-by-Simulations/AC-Coherence/AC-Osc20.foc'''' (see BESA Tutorial 6: "''Time-frequency analysis and Source coherence''").

'''Starting the beamformer from the time-frequency window'''

The BESA beamformer is applied in the time-frequency domain and therefore requires the Source Coherence module to be enabled. The time-frequency beamformer is especially useful to image in- or decrease of induced oscillatory activity. Induced activity cannot be observed in the averaged data, but shows up as enhanced averaged power in the TSE (Temporal-Spectral Evolution) plot. For instructions on how to initiate a beamformer computation in the time-frequency window, please refer to Chapter '''[[Source_Coherence_How_to...#How_to_Start_the_Beamformer_from_the_Time-Frequency_Window|How to Create Beamformer Images]]'''.

After the beamformer computation has been initiated in the time-frequency window, the source analysis window opens with an enlarged 3D image of the q-value computed with a '''bilateral beamformer'''. The result is superimposed onto the MR image assigned to the data set (individual or standard).

[[Image:SA 3Dimaging (5).gif]]

''Beamformer image after starting the computation in the Time-Frequency window. A bilateral pair of sources in the auditory cortex accounts for the highly correlated oscillatory induced activity. Only the bilateral beamformer manages to separate these activities; a traditional single-source beamformer would merge the two sources into one image maximum in the head center instead.''

'''Multiple source beamformer in the Source Analysis window'''

The 3D imaging display is part of the source analysis window. If you press the '''Restore''' button at the right end of the title bar of the 3D window, the window appears at the bottom right of the source analysis window. In the channel box, the averaged (evoked) data of the selected condition is shown. When a control condition was selected, its average is appended to the average of the target condition.

[[Image:SA 3Dimaging (6).gif]]

''Source Analysis window with beamformer image. The two sources have been added using the '''''Switch to''''' '''''Maximum''''' and '''''Add Source '''''toolbar buttons (see below). Source waveforms are computed from the displayed averaged data. Therefore, they do not represent the activity displayed in the beamformer image, which in this simulation example is induced (i.e. not phase-locked to the trigger)!''

When starting the beamformer from the time-frequency window, a bilateral beamformer scan is performed. In the source analysis window, the beamformer computation can be repeated taking into account possibly correlated sources that are specified in the current solution. Interfering activities generated by all sources in the current solution that are in the 'On' state are specifically suppressed ('''they enter the matrix L in the beamformer calculation''', see Chapter ''Short mathematical description'' above). The computation can be started from the '''Image''' menu or from the '''Image selector button''' dropdown menu. The '''Image''' menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window.

[[Image:SA 3Dimaging (7).gif]]

''Multiple source beamformer image calculated in the presence of a source in the left hemisphere. A '''single''' source scan has been performed. The source set in the current solution accounts for the left-hemispheric q-maximum in the data. Accordingly, the beamformer scan reveals only the as yet unmodeled additional activity in the right hemisphere (note the radiological convention in the 3D image display).''

The beamformer scan can be performed with a '''single''' or a '''bilateral''' source scan. The default scan type depends on the current solution:
* When the beamformer is started from the Time-Frequency window, the Source Analysis window opens with a new solution and a '''bilateral''' beamformer scan is performed.
* When the beamformer is started within the Source Analysis window, the default is
** a scan with a '''single''' source in addition to the sources in the current solution, if at least one source is active.
** a '''bilateral''' scan if no source in the current solution is active.

The default scan type is the multiple source beamformer. The non-default scan type can be enforced using the corresponding ''Volume Image / Beamformer'' entry in the '''Image''' menu.

'''Inserting Sources out of the Beamformer Image'''

The beamformer image can be used to add sources to the current solution. A simple double-click anywhere in the 2D- or 3D-view will generate a non-oriented regional source at the corresponding location. However, a better and easier way to create sources at image maxima and minima is to use the toolbar buttons '''Switch to Maximum''' [[Image:SA 3Dimaging (8).gif]] and '''Add Source''' [[Image:SA 3Dimaging (9).gif]].

Use the '''Switch to Maximum''' button to place the red crosshair of the 3D window onto a local image maximum or minimum. Hitting the '''Add Source''' button creates a regional source at the location of the crosshair and therefore ensures the exact placement of the source at the image extremum. Moreover, the '''Add Source''' button generates an oriented regional source. BESA Research automatically estimates the source orientation that contributes most to the power in the target time-frequency interval (or the reference time-frequency interval, if its power is larger than that in the target interval). The accuracy of this orientation estimate depends largely on the noise content of the data. The smaller the signal-to-noise ratio of the data, the lower is the accuracy of the orientation estimate. '''This feature allows to use the beamformer as a tool to create a source montage for source coherence analysis, where it is of advantage to work with oriented sources'''.

'''Notes:'''

* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image '''menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the''' Image''' menu.
* For scaling options, use the [[Image:SA 3Dimaging (10).gif]] and [[Image:SA 3Dimaging (11).gif]] '''Image Scale toolbar''' buttons.
* Parameters used for the beamformer calculations can be set in the '''Standard Volumes''' of the ''Image Settings dialog box.''

== Dynamic Imaging of Coherent Sources (DICS) ==

 
'''Short mathematical introduction'''

Dynamic Imaging of Coherent Sources (DICS) is a sophisticated method for imaging cortico-cortical coherence in the brain, or coherence between an external reference (e.g. EMG channel) and cortical structures. DICS can be applied to localize evoked as well as induced coherent cortical activity in a user-defined time-frequency range.

DICS was implemented in BESA closely following [https://dx.doi.org/10.1073/pnas.98.2.694 Gross et al., "Dynamic imaging of coherent sources: Studying neural interactions in the human brain", PNAS 98, 694-699, 2001].

The computation is based on a transformation of each channel's single trial data from the time domain into the frequency domain. This transformation is performed by the BESA Research Coherence module and results in the complex spectral density matrix that is used for constructing the spatial filter similar to beamforming.

DICS computation yields a 3-D image, each voxel being assigned a coherence value. Coherence values can be described as a neural activity index and do not have a unit. The neural activity index contrasts coherence in a target time-frequency bin with coherence of the same time-frequency bin in a baseline.

'''DICS for cortico-cortical coherence is computed as follows:'''

Let L(r) be the leadfield in voxel r in the brain and C the complex cross-spectral density matrix. The spatial filter W(r) for the voxel r in the head is defined as follows:

<math>W\left( r \right) = \left\lbrack L^{T}\left( r \right) \cdot C^{- 1} \cdot L\left( r \right) \right\rbrack^{- 1} \cdot L^{T}(r) \cdot C^{- 1}</math>


The cross-spectrum between two locations (voxels) r1 and r2 in the head are calculated with the following equation:

<math>C_{s}\left( r_{1},r_{2} \right) = W\left( r_{1} \right) \cdot C \cdot W^{*T}\left( r_{2} \right),</math>


where <nowiki>*T</nowiki> means the transposed complex conjugate of a matrix. The cross-spectral density can then be calculated from the cross spectrum as follows:

<math>c_{s}\left( r_{1},r_{2} \right) = \lambda_{1}\left\{ C_{s}\left( r_{1},r_{2} \right) \right\},</math>


where λ1{} indicates the largest singular value of the cross spectrum. Once the cross spectral density is estimated, the connectivity¹(CON) between the two brain regions r1 and r2 are calculated as follows:

<math>\text{CON}\left( r_{1},r_{2} \right) = \frac{c_{s}^{\text{sig}}\left( r_{1},r_{2} \right) - c_{s}^{\text{bl}}(r_{1},r_{2})}{c_{s}^{\text{sig}}\left( r_{1},r_{2} \right) + c_{s}^{\text{bl}}(r_{1},r_{2})},</math>


where cssig is the cross-spectral density for the signal of interest between the two brain regions r1 and r2, and csbl is the corresponding cross spectral density for the baseline or the control condition, respectively. In the case DICS is computed with a cortical reference, r1 is the reference region (voxel) and remains constant while r2 scans all the grid points within the brain sequentially. In that way, the connectivity between the reference brain region and all other brain regions is estimated. The value of CON(r1, r2) falls in the interval [-1 1]. If the cross-spectral density for the baseline is 0 the connectivity value will be 1. If the cross-spectral density for the signal is 0 the connectivity value will be -1.

¹ Here, the term connectivity is used rather than coherence, as strictly speaking the coherence equation is defined slightly differently. For simplicity reasons the rest of the tutorial uses the term coherence.

'''DICS for cortico-muscular coherence is computed as follows:'''

When using an external reference, the equation for coherence calculation is slightly different compared to the equation for cortico-cortical coherence. First of all, the cross-spectral density matrix is not only computed for the MEG/EEG channels, but the external reference channel is added. This resulting matrix is Call. In this case, the cross-spectral density between the reference signal and all other MEG/EEG

channels is called cref. It is only one column of Call. Hence, the cross-spectrum in voxel r is calculated with the following equation:

<math>C_{s}\left( r \right) = W\left( r \right) \cdot c_{\text{ref}}</math>


and the corresponding cross-spectral density is calculated as the sum of squares of Cs:

<math>c_{s}\left( r \right) = \sum_{i = 1}^{n}{C_{s}\left( r \right)_{i}^{2}},</math>


where n is 2 for MEG and 3 for EEG. This equation can also be described as the squared Euclidean norm of the cross-spectrum:

<math>c_{s}\left( r \right) = \left\| C_{s} \right\|^{2},</math>


The power in voxel r is calculated as in the cortico-cortical case:

<math>p\left( r \right) = \lambda_{1}\left\{ C_{s}(r,r) \right\}.</math>


At last, coherence between the external reference and cortical activity is calculated with the equation:

<math>\text{CON}\left( r \right) = \frac{c_{s}(r)}{p\left( r \right) \cdot C_{\text{all}}(k,k)},</math>


where Call(k, k) is the (k,k)-th diagonal element of the matrix Call.

DICS is particularly useful, if coherence is to be calculated without an a-priory source model (in contrast to source coherence based on pre-defined source montages). However, the recommended analysis strategy for DICS is to use a brain source as a starting point for coherence calculation that is known to contribute to the EEG/MEG signal of interest. For example, one might first run a beamformer on the time-frequency range of interest and use the voxel with the strongest oscillatory activity as a starting point for DICS. The resulting coherence image will again lead to several maxima (ordered by magnitude), which in turn can serve as starting points for DICS calculation. This way, it is possible to detect even weak sources that show coherent activity in the given time-frequency range.

The other significant application for DICS is estimating coherence between an external source and voxels in the brain. For example, an external source can be muscle activity recoded by an electrode placed over the according peripheral region. This way, the direct relationship between muscle activity and brain activation can be measured.

'''Starting DICS computation from the Time-Frequency Window'''

DICS is particularly useful, if coherence in a user-defined time-frequency bin (evoked or induced) is to be calculated between any two brain regions or between an external reference and the brain. DICS runs only on time-frequency decomposed data, so time-frequency analysis needs to be run before starting DICS computation.

To start the DICS computation, left-drag a window over a selected time-frequency bin in the Time-Frequency Window. Right-click and select “Image”. A dialogue will open (see fig. 1) prompting you to specify time and frequency settings as well as the baseline period. It is recommended to use a baseline period of equal length as the data period of interest. Make sure to select “DICS” in the top row and press “'''Go'''”.

[[Image:SA 3Dimaging (21).gif|450px|thumb|c|none|Fig. 1: Time and frequency settings for DICS and MSBF]]

Next, a window will appear allowing you to specify the reference source for coherence calculation (see fig. 2). It is possible to select a channel (e.g. EMG) or a brain source. If a brain source is chosen and no source analysis was computed beforehand, the option “Use current cross-hair position” must be chosen. In case discrete source analysis was computed previously, the selected source can be chosen as the reference for DICS. Please note that DICS can be re-computed with any cross-hair or source position at a later stage.

[[Image:SA 3Dimaging (1).jpg|400px|thumb|c|none|Fig. 2: Possible options for choosing the reference]]

Confirming with “'''OK'''” will start computation of coherence between the selected channel/voxel and all other brain voxels. In case DICS is computed for a reference source in the brain, it can be advantageous to run a beamforming analysis in the selected time-frequency window first and use one of the beamforming maxima as reference for DICS. Fig. 3 shows an example for DICS calculation.

[[Image:SA 3Dimaging (22).gif|500px|thumb|c|none|Fig. 3: Coherence between left-hemispheric auditory areas and the selected voxel in the right auditory cortex.]]

Coherence values range between -1 and 1. If coherence in the signal is much larger than coherence in the baseline (control condition) then the DICS value is going to approach 1. Contrary, if coherence in the baseline is much larger than coherence in the signal, then the DICS value is going to approach -1. At last, if coherence in the signal is equal to coherence in the baseline, then the DICS value is 0.

In case DICS is to be re-computed with a different reference, simply mark the desired reference position by placing the cross-hair in the anatomical view and select “DICS” in the middle panel of the source analysis window (see Fig. 4). In case an external reference is to be selected, click on “DICS” in the middle panel to bring up the DICS dialogue (see. Fig. 2) and select the desired channel. Please note that DICS computation will only be available after running time-frequency analysis.

[[Image:SA 3Dimaging (23).gif|700px|thumb|c|none|Fig. 4: Integration of DICS in the Source Analysis window]]

== Multiple Source Beamformer (MSBF) in the Time Domain ==
''(requires Besa Research 7.0 or higher)''

===Short mathematical introduction===

Beamforming approach can be also applied in the time domain data. This approach was introduced as linearly constrained minimum variance (LCMV) beamformer (Van Veen et al., 1997). It allows to image evoked activity in a user-defined time range, where time is taken relative to a triggered event, and to estimate source waveforms using the calculated spatial weight at locations of interest. For an implementation of the beamformer in the time domain, data covariance matrices are required, while complex cross spectral density matrices are used for the beamformer approaches in the time-frequency domain as described in the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section.

The bilateral beamformer introduced in the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section is also implemented for the time-domain beamformer to take into account contributions from the homologue source in the opposite. This allows for imaging of highly correlated bilateral activity in the two hemispheres that commonly occurs during processing of external stimuli. In addition, the beamformer computation can take into account possibly correlated sources at arbitrary locations.
The beamformer spatial weight W(r) for the voxel r in the brain is defined as follows (Van Veen et al., 1997):

[[File:MSBF1.png]]

where '''C-1''' is the inversed regularized average of covariance matrix over trials, '''L''' is the leadfield matrix of the model containing a regional source at target location r and optionally
additional sources whose interference with the target source is to be minimized. The beamformer spatial weight '''W'''(r) can be applied to the measured data to estimate source
waveform at a location r (beamformer virtual sensor):

[[File:MSBF2.png]]

where '''S'''(r,t) represents the estimated source waveform and '''M'''(t) represents measured EEG or MEG signals.
The output power P of the beamformer for a specific brain region at location r is computed by the following equation:

[[File:MSBF3.png]]

where tr’[ ] is the trace of the [3×3] (MEG: [2×2]) submatrix of the bracketed expression that corresponds to the source at target location r.
Beamformer can suppress noise sources that are correlated across sensors. However, uncorrelated noise will be amplified in a spatially non-uniform manner, with increasing
distortion with increasing distance from the sensors (Van Veen et al., 1997; Sekihara et al., 2001). For this reason, estimated source power should be normalized by a noise power.
In BESA Research, the output power P(r) is normalized with the output power in a baseline interval or with the output power of a uncorrelated noise: P(r) / Pref (r).
The time-domain beamformer image is constructed from values q(r) computed for all locations on a grid specified in the '''General Settings''' tab. A value q(r) is defined as described in
the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section with data covariance matrices instead of cross-spectral density matrices.

===Applying the Beamformer===

This chapter illustrates the usage of the BESA beamformer in the time domain. The displayed figures are generated using the file ‘Examples/ERP-Auditory-Intensity/S1.cnt’.

'''Starting the time-domain beamformer from the Average tab of the Paradigm dialog box'''

The time-domain beamformer is needed data covariance matrices and therefore requires the ERP module to be enabled. After the beamformer computation has been initiated in the
'''Average tab of the Paradigm dialog box''', the source analysis window opens with an enlarged 3D image of the q-value computed with a bilateral beamformer. The result is
superimposed onto the MR image assigned to the data set (individual or standard).

[[File:MSBF44.png]]

''Beamformer image for auditory evoked data after starting the computation in the '''Average tab of the Paradigm dialog box'''. The bilateral beamformer manages to separate the
activities in auditory areas, while a traditional single-source beamformer would merge the two sources into one image maximum in the head center instead.''

'''Multiple-source beamformer in the Source Analysis window'''

The 3D imaging display is part of the source analysis window. In the Channel box, the averaged (evoked) data of the selected condition is shown. Selected covariance intervals in
the ERP module can be checked in the Channel box. The red, gray, and blue rectangles indicate signal, baseline, and common interval, respectively.

[[File:MSBF55.png]]

''Source Analysis window with beamformer image. The two beamformer virtual sensors have been added using the Switch to Maximum and Add Source toolbar buttons (see below).
Source waveforms are computed using the beamformer spatial weights and the displayed averaged data (the noise normalized weights (5% noise) option was used to compute the
beamformer image).''

When starting the beamformer from the '''Average tab of the Paradigm dialog box''', the bilateral beamformer scan is performed. In the source analysis window, the beamformer computation can be repeated taking into account possibly correlated sources that are specified in the current solution. Interfering activities generated by all sources in the current solution that are in the 'On' state are specifically suppressed (they enter the leadfield matrix L in the beamformer calculation). The computation can be started from the '''Image''' menu or from the Image selector button [[File:MSBF_Button.png|22px|Image: 22 pixels]] dropdown menu. The Image menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window.

[[File:MSBF66.png]]

''Multiple-source beamformer image calculated in the presence of a source in the left hemisphere. A single-source scan has been performed instead of a bilateral beamforemr. The
source set in the current solution accounts for the left-hemispheric q-maximum in the data. Accordingly, the beamformer scan reveals only the as yet unmodeled additional activity in
the right hemisphere (note the radiological convention in the 3D image display). The source waveform of the beamformer virtual sensor in the left hemisphere is not shown since the
location (blue square in the figure) is not considered for the multiple-source beamformer.''

The beamformer scan can be performed with a single or a bilateral source scan. The default scan type depends on the current solution:
When the beamformer is started from the '''Average tab of the Paradigm dialog box''' the Source Analysis window opens with a new solution and a bilateral beamformer scan is
performed.
When the beamformer is started within the Source Analysis window, the default is:

* a scan with a single source in addition to the sources in the current solution, if at least one source is active.
* a bilateral scan if no source in the current solution is active.
* a scan with a single source when scalar-type beamformer is selected in the '''beamformer option dialog box'''.

The default scan type is the multiple source beamformer. The non-default scan type can be enforced using the corresponding Volume Image / Beamformer entry in the Image main
menu or in the beamformer option dialog box (only for the time-domain beamformer).

===Inserting Sources as Beamformer Virtual Sensor out of the Beamformer Image===

This is similar to the inserting sources out of the beamformer image in Multiple Source Beamformer (MSBF) in the Time-frequency Domain section.
The beamformer image can be used to add beamformer virtual sensors to the current solution. A simple double-click anywhere in the 3D view (not in the 2D view) will generate a
source at the corresponding location. A better and easier way to create sources at image maxima and minima is to use the toolbar buttons '''Switch to Maximum''' and '''Add Source'''

This feature allows to use the beamformer as a tool to create a source montage for '''source coherence''' analysis. A source montage file (*.mtg) for beamformer virtual sensors can
be saved using File \ Save Source Montage As… entry.

The time-domain beamformer image can be also used to add regional or dipole sources to the current solution. Press '''N''' key when there is no source in the current source array or
there is more than one beamformer virtual sensor. To create a new source array for beamformer virtual sensor, press '''N''' key when there is more than one regional or dipole source in
the current source array.

===Notes===

* You can hide or re-display the last computed image by selecting ''Hide Image'' entry in the '''Image''' menu.
* The current image can be exported to ASCII, ANALYZE, or BrainVoyager (vmp) format from the '''Image''' menu.
* For scaling options, use the and Image Scale toolbar buttons.
* Parameters used for the beamformer calculations can be set in the '''Standard Volume tab of the Image Settings dialog box'''.
* Note that Model, Residual, Order, and Residual variance are not shown for the beamformer virtual sensor type sources.

===References===

* Sekihara, K., Nagarajan, S. S., Poeppel, D., Marantz, A., & Miyashita, Y. (2001). Reconstructing spatio-temporal activities of neural sources using an MEG vector beamformer technique. IEEE Transactions on Biomedical Engineering, 48(7), 760–771.

* Van Veen, B. D., Van Drongelen, W., Yuchtman, M., & Suzuki, A. (1997). Localization of brain electrical activity via linearly constrained minimum variance spatial filtering. IEEE Transactions on Biomedical Engineering, 44(9), 867–880

== CLARA ==

CLARA ('Classical LORETA Analysis Recursively Applied') is an iterative application of weighted LORETA images with a reduced source space in each iteration.

In an initialization step, a LORETA image is calculated. Then in each iteration the following steps are performed:

# The obtained image is spatially smoothed (this step is left out in the first iteration).
# All grid points with amplitudes below a threshold of 1% of the maximum activity are set to zero, thus being effectively eliminated from the source space in the following step.
# The resulting image defines a spatial weighting term (for each voxel the corresponding image amplitude).
# A LORETA image is computed with an additional spatial weighting term for each voxel as computed in step 3. By the default settings in BESA Research, the regularization values used in the iteration steps are slightly higher than that of the initialization LORETA image.

The procedure stops after 2 iterations, and the image computed in the last iteration is displayed. Please note that you can change all parameters by creating a user-defined volume image.

The advantage of CLARA over non-focusing distributed imaging methods is visualized by the figure below. Both images are computed from the N100 response in an auditory oddball experiment (file '''Oddball.fsg''' in subfolder ''fMRI+EEG-RT-Experiment'' of the ''Examples'' folder). The CLARA image is much more focal than the sLORETA image, making it easier to determine the location of the image maxima.

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (24).gif|thumb|350px|sLORETA image]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (25).gif|thumb|350px|CLARA image]] </li>
</ul></div>

'''Notes:'''

* Starting CLARA: CLARA can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter ''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]'' for important information on regularization of distributed inverses.

== LAURA ==

LAURA (Local Auto Regressive Average) belongs to the distributed inverse method of the family of weighted minimum norm methods ([https://doi.org/10.1023/A:1012944913650 Grave de Peralta Menendeza et al., "Noninvasive Localization of Electromagnetic Epileptic Activity. I. Method Descriptions and Simulations", BrainTopography 14(2), 131-137, 2001]). LAURA uses a spatial weighting function that includes depth weighting and that term has the form of a local autoregressive function.

The source activity is estimated by applying the general formula for a weighted minimum norm:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T}\left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings.''

In LAURA, V contains both a depth weighting term W and a representation of a local autoregressive function A. V is computed as:

<math>\mathrm{V} = \left( \mathrm{U}^{T} \cdot \mathrm{U} \right)^{-1}</math>


Where

<math>\mathrm{U} = \left( \mathrm{W} \cdot \mathrm{A} \right) \otimes \mathrm{I}_{3}</math>


Here, <math>\otimes</math> denotes the Kronecker product. I3 is the [3×3] identity matrix. W is an [s×s] diagonal matrix (with s the number of source locations on the grid), where each diagonal element is the inverse of the maximum singular value of the corresponding regional source's leadfields. The formula for the diagonal components Aii and the off-diagonal components Aik are as follows:

<math>\mathrm{A}_{ii} = \frac{26}{\mathrm{N}_{i}}\sum_{k \subset V_{i}}^{}\frac{1}{\mathrm{d}_{ik}^{2}}</math>


<math>
\mathrm{A}_{ik} =
\begin{cases}
- 1/\operatorname{dist}\left( i,k \right)^{2}, & \text{if } k \subset V_{i} \\
0, & \text{otherwise}
\end{cases}
</math>


Here, Vi is the vicinity around grid point i that includes the 26 direct neighbors.

The LAURA image in BESA Research displays the norm of the 3 components of S at each location r. Using the menu function ''Image / Export Image As... ''you have the option to save this norm of S or alternatively all components separately to disk.

'''Notes:'''

* '''Grid spacing:''' Due to memory limitations, LAURA images require a grid spacing of 7 mm or more.
* '''Computation time:''' Computation speed during the first LAURA image calculation depends on the grid spacing (computation is faster with larger grid spacing). After the first computation of a LAURA image, a '''*.laura''' file is stored in the data folder, containing intermediate results of the LAURA inverse. This file is used during all subsequent LAURA image computations. Thereby, the time needed to obtain the image is substantially reduced.
* '''MEG:''' In the case of MEG data, an additional constraint is implemented in the LAURA algorithm that prevents solutions from containing radial source currents (compare Pascual-Marqui, ISBET Newsletter 1995, 22-29). In MEG, an additional source space regularization is necessary in the inverse matrix operation required compute V
* '''Starting LAURA:''' LAURA can be started from the''' Image''' menu or from the '''Image Selection''' button.
* '''Regularization:''' Please refer to Chapter'' “Regularization of distributed volume images” ''for important information on regularization of distributed inverses.

== LORETA ==

LORETA ("Low Resolution Electromagnetic Tomography") is a distributed inverse method of the family of ''weighted minimum norm'' methods. LORETA was suggested by R.D. Pascual-Marqui (International Journal of Psychophysiology. 1994, 18:49-65). LORETA is characterized by a smoothness constraint, represented by a discrete 3D Laplacian.

The source activity is estimated by applying the general formula for a weighted minimum norm:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T}\left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings.''

In LORETA, V contains both a depth weighting term and a representation of the 3D Laplacian matrix. V is computed as:

<math>\mathrm{V} = \left( \mathrm{U}^{T} \cdot \mathrm{U} \right)^{- 1}</math>


where

<math>\mathrm{U} = \left( \mathrm{W} \cdot \mathrm{A} \right) \otimes \mathrm{I}_{3}</math>


Here, <math>\otimes</math> denotes the Kronecker product. I3 is the [3x3] identity matrix. W is an [sxs] diagonal matrix (with s the number of source locations on the grid), where each diagonal element is the inverse of the maximum singular value of the corresponding regional source's leadfields. A contains the 3D Laplacian and is computed as

<math>\mathrm{A} = \mathrm{Y} - \mathrm{I}_{s}</math>


with Is the [sxs] identity matrix, where s is the number of sources (= three times the number of grid points) and

<math>\mathrm{Y} = \frac{1}{2}\left\{ \mathrm{I}_{s} + \left\lbrack \operatorname{diag}\left( \mathrm{Z} \cdot \left\lbrack 111 \ldots 1 \right\rbrack^{T} \right) \right\rbrack^{- 1} \right\} \cdot \mathrm{Z}</math>


where

<math>
\mathrm{Z}_{ik} =
\begin{cases}
1/6, & \text{if } \operatorname{dist}\left( i,k \right) = 1 \text{ grid point} \\
0, & \text{otherwise}
\end{cases}
</math>


The LORETA image in BESA Research displays the norm of the 3 components of S at each location r. Using the menu function ''Image / Export Image As... ''you have the option to save this norm of S or alternatively all components separately to disk.

'''Notes:'''
* '''Grid spacing:''' Due to memory limitations, LORETA images require a grid spacing of 5 mm or more.
* '''Computation time:''' Computation speed during the first LORETA image calculation depends on the grid spacing (computation is faster with larger grid spacing). After the first computation of a LORETA image, a '''<nowiki>*.loreta</nowiki>''' file is stored in the data folder, containing intermediate results of the LORETA inverse. This file is used during all subsequent LORETA image computations. Thereby, the time needed to obtain the image is substantially reduced.
* '''MEG''': In the case of MEG data, an additional constraint is implemented in the LORETA algorithm that prevents solutions from containing radial source currents (Pascual-Marqui, ISBET Newsletter 1995, 22-29). In MEG, an additional source space regularization is necessary in the inverse matrix operation required compute V.
* '''Starting LORETA:''' LORETA can be started from the''' Image''' menu or from the '''Image Selection '''button.
* '''Regularization:''' Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed source models.

== sLORETA ==

This distributed inverse method consists of a ''standardized, unweighted minimum norm''. The method was originally suggested by R.D. Pascual-Marqui (Methods & Findings in Experimental & Clinical Pharmacology 2002, 24D:5-12) Starting point is an unweighted minimum norm computation:

<math>\mathrm{S}_{\text{MN}}\left( t \right) = \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings''.

This minimum norm estimate is now standardized to produce the sLORETA activity at a certain brain location r:

<math>\mathrm{S}_{\text{sLORETA}, r} = \mathrm{R}_{rr}^{-1/2} \cdot \mathrm{S}_{\text{MN},r}</math>


SsMN,r is the [3x1] (MEG: [2x1]) minimum norm estimate of the 3 (MEG: 2) dipoles at location r. Rrr is the [3x3] (MEG: [2x2]) diagonal block of the resolution matrix R that corresponds to the source components at the target location r. The resolution matrix is defined as:

<math>\mathrm{R} = \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{L}^{T} + \lambda \cdot \mathrm{I} \right)^{-1} \cdot \mathrm{L}</math>


The sLORETA image in BESA Research displays the norm of SsLORETA, r at each location r. Using the menu function ''Image / Export Image As...'' you have the option to save this norm of SsLORETA, r or alternatively all components separately to disk.

'''Notes:'''

* sLORETA can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== swLORETA ==

This distributed inverse method is a ''standardized, depth-weighted minimum norm'' (E. Palmero-Soler et al 2007 Phys. Med. Biol. 52 1783-1800). It differs from sLORETA only by an additional depth weighting.

Starting point is a depth-weighted minimum norm computation:

<math>\mathrm{S}_{\text{MN}}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings''.

V is the diagonal depth weighting matrix. For s grid locations, V is of dimension [3s x 3s] (MEG: [2s x 2s]). Each diagonal element of V is the inverse of the first singular value of the leadfield of the corresponding regional source. Hence, the first 3 (MEG: 2) diagonal elements equal the inverse of the largest eigenvalue of the leadfield matrix of regional source 1, and so on.

This minimum norm estimate is now standardized to produce the swLORETA activity at a certain brain location r:

<math>\mathrm{S}_{\text{swLORETA},r} = \mathrm{R}_{rr}^{-1/2} \cdot \mathrm{S}_{\text{MN},r}</math>


SsMN,r is the [3x1] (MEG: [2x1]) depth-weighted minimum norm estimate of the regional source at location r. Rrr is the [3x3] (MEG: [2x2]) diagonal block of the resolution matrix R that corresponds to the source components at the target location r. The resolution matrix is defined as:

<math>\mathrm{R} = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} + \lambda \cdot \mathrm{I} \right)^{-1} \cdot \mathrm{L}</math>


The swLORETA image in BESA Research displays the norm of SswLORETA, r at each location r. Using the menu function ''Image / Export Image As...'' you have the option to save this norm of SswLORETA, r or alternatively all components separately to disk.

'''Notes:'''

* sLORETA can be started from the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== sSLOFO ==

SSLOFO (standardized shrinking LORETA-FOCUSS) is an iterative application of weighted distributed source images with a reduced source space in each iteration ([https://dx.doi.org/10.1109/TBME.2005.855720 Liu et al., "Standardized shrinking LORETA-FOCUSS (SSLOFO): a new algorithm for spatio-temporal EEG source reconstruction", IEEE Transactions on Biomedical Engineering 52(10), 1681-1691, 2005]).

In an initialization step, an [[#sLORETA | sLORETA]] image is calculated. Then in each iteration the following steps are performed:

# A weighted minimum norm solution is computed according to the formula <math display="inline">\mathrm{S} = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}</math> . Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D is the data at the time point under consideration. V is a diagonal spatial weighting matrix that is computed in the previous iteration step. In the first iteration, the elements of V contain the magnitudes of the initially computed LORETA image.
# Standardization of this weighted minimum norm image is performed with the resolution matrix as in [[#sLORETA | sLORETA]].
# The obtained standardized weighted minimum norm image is being smoothed to get Ssmooth.
# All voxels with amplitudes below a threshold of 1% of the maximum activity get a weight of zero in the next iteration step, thus being effectively eliminated from the source space in the next iteration step.
# For all other voxels, compute the elements of the spatial weighting matrix V to be used in the next iteration as follows: <math display="inline">\mathrm{V}_{ii,\text{next iteration}} = \frac{1}{\left\| \mathrm{L}_{i} \right\|} \cdot \mathrm{S}_{ii,\text{smooth}} \cdot \mathrm{V}_{ii,\text{current iteration}}</math>



The procedure stops after 3 iterations. Please note that you can change all parameters by creating a [[#User-Defined Volume Image | user-defined volume image]].

'''Notes:'''
* '''Starting sSLOFO''': sSLOFO can be started from the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter ''[[#Regularization of distributed volume images | Regularization of distributed volume images]]'' for important information on regularization of distributed inverses.

== User-Defined Volume Image ==

In addition to the predefined 3D imaging methods in BESA Research, it is possible to create user-defined imaging methods based on the general formula for distributed inverses:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. Custom-defined parameters are:* The spatial weighting matrix V: This may include depth weighting, image weighting, or cross-voxel weighting with a 3D Laplacian (as in LORETA) or an autoregressive function (as in LAURA).

* Regularization: The term in parentheses is generally regularized. Note that regularization has a strong effect on the obtained results. Please refer to chapter “''Regularization of Distributed Volume Images” ''for more information.
* Standardization: Optionally, the result of the distributed inverse can be standardized with the resolution matrix (as in sLORETA).
* Iterations: Inverse computations can be applied iteratively. Each iteration is weighted with the image obtained in the previous iteration.

All parameters for the user-defined volume image are specified in the User-Defined Volume Tab of the Image Settings dialog box. Please refer to chapter “''User-Defined Volume Tab”'' for details.

'''Notes:'''
* Starting the user-defined volume image: the image calculation can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== Regularization of distributed volume images ==

Distributed source images require the inversion of a term of the form L V LT. This term is generally regularized before its inversion. In BESA Research, selection can be made between two different regularization approaches (parameters are defined in the ''Image Settings dialog box''):

* '''Tikhonov regularization''': In Tikhonov regularization, the term L V LT is inverted as (L V LT +λ I)-1. Here, l is the regularization constant, and I is the identity matrix.
* One way of determining the optimum regularization constant is by minimizing the ''generalized cross'' ''validation error'' (CVE).
* Alternatively, the regularization constant can be specified manually as a percentage of the trace of the matrix L V LT.
* '''TSVD''': In the truncated singular value decomposition (TSVD) approach, an SVD decomposition of L V LT is computed as  L V LT = U S UT, where the diagonal matrix S contains the singular values. All singular values smaller than the specified percentage of the maximum singular values are set to zero. The inverse is computed as U S-1 UT, where the diagonal elements of S-1 are the inverse of the corresponding non-zero diagonal elements of S.

Regularization has a critical effect on the obtained distributed source images. The results may differ completely with different choices of the regularization parameter (see examples below). Therefore, it is important to evaluate the generated image critically with respect to the regularization constant, and to keep in mind the uncertainties resulting from this fact when interpreting the results. The default setting in BESA Research is a TSVD regularization with a 0.03% threshold. However, this value might need to be adjusted to the specific data set at hand.

The following example illustrates the influence of the regularization parameter on the obtained images. The data used here is condition '''St-Cor of dataset Examples \ TFC-Error-Related-Negativity \ Correct+Error.fsg''' at 176 ms following the visual stimulus. Discrete dipole analysis reveals the main activity in the left and right lateral visual cortex at this latency.

[[Image:SA 3Dimaging (42).gif]]

''Discrete source model at 176 ms: Main activity in the left and right lateral visual cortex, no visual midline activity.''

LORETA images computed at this latency depend critically on the choice of the regularization constant. The following 3D images are created with TSVD regularization with SVD cutoffs of 0.1%, 0.005%, and 0.0001%, respectively. The volume grid size was 9 mm. The example demonstrates the dramatic effect of regularization and demonstrates the typical tradeoff between too strong regularization (leading to too smeared 3D images that tend to show blurred maxima) and too small regularization (resulting in too superficial 3D images with multiple maxima).

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (43).gif|thumb|350px|'''SVD cutoff 0.1%''': Regularization too strong. No separation between sources, mislocalization towards the middle of the brain.]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (44).gif|thumb|350px|'''SVD cutoff 0.005%''': Appropriate regularization. Separation of the bilateral activities. Location in agreement with the discrete multiple source model.]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (45).gif|thumb|350px|'''SVD cutoff 0.0001%''': Too small regularization. Mislocalization, too superficial 3D image. ]] </li>
</ul></div>

The automatic determination of the regularization constant using the CVE approach does not necessarily result in the optimum regularization parameter either. In this example, the unscaled CVE approach rather resembles the TSVD image with a cutoff of 0.0001%, i.e. regularization is too small. Therefore, it is advisable to compare different settings of the regularization parameter and make the final choice based on the above-mentioned considerations.

== Cortical LORETA ==

Cortical LORETA is principally the same technique as LORETA, however, Cortical LORETA is not computed in a 3D volume, but on the cortical surface.

The cortical reconstruction in BESA Research fed from BESA MRI is a closed 2D surface with no boundaries and a very close approximation of the actual cortical form. It consists of an irregular triangulated grid.

The Laplace operator that is used for identifying a smooth solution in a three-dimensional space is exchanged with a Laplace operator that runs on the two-dimensional cortical surface.

There is a wide variety of 2D Laplace operators with different characteristics. The general form of the discrete Laplace operator is

<math>\Delta f\left( p_{i} \right) = \frac{1}{d_{i}}\sum_{j \in N(i)}^{}{w_{ij}\left\lbrack f\left( p_{i} \right) - f\left( p_{j} \right) \right\rbrack},</math>


where '''pi''' is the '''i-th''' node of the triangular mesh, '''f(pi) '''is the value of a function f defined on the cortical mesh at the node '''pi''', '''wij''' is the weight for the connection between the nodes '''pi''' and '''pj''' and '''di''' is a normalization factor for the '''i-th''' row of the operator. Furthermore, '''N(i)''' is the set of indices corresponding to the direct (also called "1-ring") neighbors of '''pi'''.

BESA offers the choice of three Laplace operators with slightly different characteristics.

* '''Unweighted Graph Laplacian''': This is the simplest operator. It takes into account only the adjacency of the nodes and not the geometry of the mesh:

<math>
w_{ij} =
\begin{cases}
1, & \text{if } p_{i} \text{ and } p_{j} \text{ are connected by an edge} \\
0, & \text{otherwise}
\end{cases}
</math>

<math>d_{i} = 1</math>


[[Image:SA 3Dimaging (4).jpg |450px]]

* '''Weighted Graph Laplacian:''' This operator is similar to the unweighted graph Laplacian but with different weights for the different connections. The connections between nearby nodes get larger weights than the connections between farther nodes:

<math>w_{ij} = \frac{1}{\operatorname{dist}\left( p_{i},p_{j} \right)}</math>

<math>d_{i} = \sum_{j \in N(i)}^{} {\operatorname{dist}\left(p_{i}, p_{j} \right)}</math>


where '''dist''' ('''pi''' , '''pj''') is the distance between the nodes '''pi '''and '''pj'''.

[[Image:SA 3Dimaging (6).jpg|450px]]

* '''Geometric Laplacian with mixed area weights''': This operator takes into account the angles in the corresponding triangles into account as well as the area around the nodes in order to determine the connection weights:

<math>w_{ij} = \frac{\cot\left( \alpha_{ij} \right) + \cot\left( \beta_{ij} \right)}{2}</math>

<math>d_{i} = A_{\text{mixed}}</math>


where '''αij''' and '''βij''' denote the two angles opposite to the edge ('''i , j''') and '''Amixed '''is either the Voronoi area, or 1/2 of the triangle area or 1/4 of the triangle area depending on the type of the triangle.

[[Image:SA 3Dimaging (8).jpg|450px]]

'''Regularization and other parameters:'''

[[Image:CorticalLOR.png‎]]

* '''SVD cutoff''': The regularization for the inverse operator as a percent of the largest singular value.
* '''Depth weighting''': Turn depth weighting on or off.
* '''Laplacian type''': Selection of Laplacian operators (see above).

'''Notes:'''
* '''Starting Cortical LORETA''': Cortical LORETA can be started from the sub-menu '''Surface Image''' of the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]''” for important information on regularization of distributed inverses.

== Cortical CLARA ==

Cortical CLARA is principally the same technique as CLARA, but Cortical CLARA is not computed in a 3D volume, but on the cortical surface. Instead of using a LORETA image as the basis for the iterative application, cortical CLARA uses cortical LORETA.

'''Regularization and other parameters:'''

[[Image:SA 3Dimaging (47).gif]]

* '''SVD cutoff''': The regularization for the inverse operator as a percent of the largest singular value.
* '''Depth weighting''': Turn depth weighting on or off.
* '''Laplacian type''': Selection of Laplacian operators (see Cortical LORETA).
* '''No of iterations''': Number of iterations for CLARA. The more iterations are used, the sparser becomes the solution.
* '''Automatic''': The algorithm tries to determine the number of iterations automatically. The goodness of fit (GOF) is calculated after every iteration and if there is a big jump in the GOF then the algorithm will stop. If no jumps appear during the calculations then CLARA iterates until the specified number of iterations is reached.
* '''Regularize iterations''': If one wants to use different regularization for the CLARA iterations than the value specified as "SVD cutoff", this option should be selected.
* '''Amount to clip from img (%)''': Cortical CLARA uses the solution from the previous iteration as an additional weighting matrix for the current iteration. That weighting matrix is constructed by cutting the "low" activity from the solution. This number specifies how much of the activity should be cut from the previous solution in order to construct the weighting matrix. This value is given as a percentage of the maximal activity. Default value is 10%.

'''Notes:'''

* '''Starting Cortical CLARA:''' Cortical CLARA can be started from the sub-menu '''Surface Image''' of the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]''” for important information on regularization of distributed inverses.

== Cortex Inflation ==

The inflated cortex is a smoothened version of the individual cortical surface with minimal metric distortions (Fischl, B. et al. (1999). Cortical Surface-Based Analysis: II: Inflation, Flattening, and a Surface-Based Coordinate System. ''NeuroImage'', 9(2), 195–207). Gyri and sulci are smoothened out. The original distances between each point on the cortex and its neighbors are, however, mostly preserved.

[[Image:SA 3Dimaging (48).gif]]

''Cortical LORETA map overlaid on top of the inflated cortical surface.''

A lighter gray color overlaid on top of the surface image indicates the location of a gyrus of the individual cortex surface, while a darker gray color indicates the location of a sulcus. The inflated cortical surface can be computed in '''BESA MRI 2.0'''. For more details please refer to the BESA MRI 2.0 help.

== Surface Minimum Norm Image ==

'''Introduction'''

The minimum norm approach is a common method to estimate a distributed electrical current image in the brain at each time sample (Hämäläinen & Ilmoniemi 1984). The source activities of a large number of regional sources are computed. The sources are evenly distributed using 1500 standard locations 10% and 30% below the smoothed standard brain surface (when using the standard MRI) or using between 3000-4000 locations on the individual brain surface defined by the gray-white-matter boundary.

Since the number of sources is much larger than the number of sensors in a minimum norm solution, the inverse problem is highly underdetermined and must be stabilized by a mathematical constraint, the minimum norm. Out of the many current distributions that can account for the recorded sensor data, the solution with the minimum L2 norm, i.e. the minimum total power of the current distribution is displayed in BESA Research.

First, the forward solution (leadfield matrix L) of all sources is calculated in the current head model. Then, the source activities S(t) of all source components are computed from the data matrix D(t) using an inverse regularized by the estimated noise covariance matrix:

<math>\mathrm{S}\left( t \right) = \mathrm{R} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{R} \cdot \mathrm{L}^{T} + \mathrm{C}_N \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed regional source model, CN denotes the noise correlation matrix in sensor space, and R is a weighting matrix in source space. R and CN can be designed in different ways in order to optimize the minimum norm result. The total activity of each regional source is computed as the root mean square of the source activities S(t) of its 3 (MEG:2) components. This total source activity is transformed to a color-coded image of the brain surface. (When the standard brain is used, two sources are assigned to each surface location, located 10% and 30% below the surface, respectively. The color that is displayed on the standard brain surface is the larger of the two corresponding source activities.)

'''Weighting options'''

The minimum norm current imaging techniques of BESA Research provide different weighting strategies. Two weighting approaches are available: Depth weighting and spatio-temporal approaches.
* '''Depth weighting:''' Without depth weighting, deep sources appear very smeared in a minimum-norm reconstruction. With depth weighting, both deep and superficial sources produce a similar, more focal result. If this weighting method is selected, the leadfield of each regional source is scaled with the largest singular value of the SVD (singular value decomposition) of the source's leadfield.
* '''Spatio-temporal weighting''': Spatio-temporal weighting tries to assign large weight to sources that are assumed to be more likely to contribute to the recorded data.
** '''Subspace correlation after single source scan''': This method divides the signal into a signal and a noise subspace. The correlation of the leadfield of a regional source i with the signal subspace (pi) is computed to find out if the source location contributes to the measured data. The weighting matrix R becomes a diagonal matrix. Each of the three (MEG: 2) components of a regional source get the same weighting value pi2. This approach is based on the signal subspace correlation measure introduced by J.C. Mosher, R. M. Leahy (Recursive MUSIC: A Framework for EEG and MEG Source Localization, IEEE Trans. On Biomed. Eng. Vol. 45, No. 11, November 1998)
** '''Dale & Sereno 1993:''' In the approach of Dale and Sereno (J Cogn Neurosci, 1993, 5: 162-176) a signal subspace needs not be defined. The correlation pi of the leadfield of regional source i with the inverse of the data covariance matrix is computed along with the largest singular value λmax of the data covariance matrix. The weighting matrix R is a diagonal matrix with weights: [[Image:SA 3Dimaging (50).gif]]. Each of the three (MEG: 2) components of a regional source receives the same weighting value.

'''Noise regularization'''

Two methods to estimate the channel noise correlation matrix CN are provided by the program:
* '''Use baseline:''' Select this option to estimate the noise from the user-definable baseline. The signal is computed from the data at non-baseline latencies.
* '''Use 15% lowest values:''' The baseline activity is computed from the data at those 15% of all displayed latencies that have the lowest global field power. The signal is computed from all displayed latencies.

In each case, the activity (noise or signal, respectively) is defined as root-mean-square across all respective latencies for each channel.

The noise covariance matrix CN is constructed as a diagonal matrix. The entries in the main diagonal are proportional to the noise activity of the individual channels (if selected) or are all equally proportional to the average noise activity over all channels. The noise covariance matrix CN is then scaled such that the ratio of the Frobenius norms of the weighted leadfield projector matrix (LRLT) and the noise covariance matrix CN equals the Signal-to-Noise ratio. This scaling can be multiplied by an additional factor (default=1) to sharpen (<1) or smoothen (>1) the minimum norm image.

'''Applying the Minimum Norm Image'''

The minimum-norm algorithm is started via the ''Surface minimum norm image dialog box'', which is opened from the''' Image''' menu, or by typing the shortcut '''Ctrl-M''': Please refer to Chapter ''“Surface'' ''Minimum Norm Tab”'' for more details.

As opposed to the other 3D images available from the '''Image '''menu, the surface minimum norm image is not computed on a volumetric grid, but rather for locations on the brain surface. Accordingly, the results of the minimum norm image are displayed superimposed to the brain surface mesh rather than to the volumetric MR image.

The figure below shows a minimum norm image computed from the file '''Examples\Epilepsy\Spikes\Spikes-Child4_EEG+MEG_averaged.fsg'''. The EEG spike peak was imaged using the individual brain surface of the subject. A baseline from -300 to -70 ms was used. Minimum norm was computed with depth weighting, Spatio-temporal weighting according to Dale & Sereno 1993 and individual noise weighting with a noise scale factor of 0.01. The minimum norm image reveals the location of the spike generator in the close vicinity of the frontal left-hemispheric lesion in this subject.

[[Image:SA 3Dimaging (51).gif]]

== Multiple Source Probe Scan (MSPS) ==

 
'''Introduction'''

The MSPS function provides a tool for the validation of a given solution. It is based on the following theoretical consideration: If the recorded EEG/MEG data has been modeled adequately, i.e. all active brain regions are represented by a source in the current solution, then any additional probe source added to the solution will not show any activity apart from noise. The only exception occurs if this probe source is placed in close vicinity to one of the sources in the current solution. In that case, the solution's source and the probe source will share the activity of the corresponding brain area. The MSPS applies these considerations by scanning the brain on a pre-defined grid with a regional probe added to the current solution. Grid extent and density can be specified in the Image settings. The power P of the probe source at location r in the signal interval is compared with the power of the probe source in a reference interval, defining a value q:

<math>\mathrm{q}\left( r \right) = \sqrt{\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}} - 1</math>


MSPS can be computed on time domain or time-frequency domain data:
* In the time domain, q(r) is computed from the source waveform of the probe source. Here, P(r) is the mean power of the probe source at location r in the marked latency range, and Pref(r) is the mean probe source power in the user-definable baseline interval.
* In the time-frequency domain, an MSPS image can be computed from the complex cross spectral density matrices. By applying the inverse operator for a source configuration consisting of the current solution and the probe source, the power of the probe source can be computed for the target interval [P(r)] and the reference time-frequency interval [Pref(r)]. In the resulting MSPS image, q-values are shown in %, where q[%] = q*100.

The inverse operator used to determine the probe source power uses different regularization constants for the probe source and the sources in the current solution. The regularization constant of the sources in the current solution can be specified in the Image settings (default 4%). The regularization constant of the probe source is internally set to 0%.

Alternatively to the definition above, q can also be displayed in units of dB:

<math>\mathrm{q}\left\lbrack \text{dB} \right\rbrack = 10 \cdot \log_{10}\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}</math>


Values of q smaller than zero are not shown in the MSPS image.

According to the considerations above, an MSPS of a correct source model should optimally yield image maxima around the sources in the current solution only. If the MSPS image is blurred or shows maxima at locations different from the modeled sources, this indicates a non-sufficient or incorrect solution.

'''Applying the MSPS'''

This chapter illustrates the application of the Multiple Source Probe Scan. The figures are generated with data from file '''Examples/Epilepsy/Spikes/Rolandic-Spike-Child.fsg''' (-300 : +200 ms, filtered from 3 Hz [forward] to 40 Hz [zero-phase]).

'''Time domain versus time-frequency domain MSPS'''

The multiple source probe scan can be computed in the time domain or the time-frequency domain. The latter is possible only when time-frequency domain data is available for the current condition, i.e. if the condition has been created by starting a multiple source beamformer (MSBF) computation from the source coherence window. In this case, evoking the MSPS calculation from the '''Imaging '''button or from the '''Image''' menu will bring up the following dialog window that allows to choose between time- or time-frequency MSPS. If only time domain data is available, this dialog window will not appear and MSPS will be computed in the time domain.

[[Image:SA 3Dimaging (53).gif]]

For a time-frequency domain MSPS, the target and the reference time-frequency interval have been specified already in the Time-Frequency window (see Chapter "''How To Create Beamformer Images''"). For a time-domain MSPS, the target and the reference epoch have to be specified in the Source Analysis window as described below.

'''Time domain MSPS'''

The time-domain MSPS image displays the ratio of the power of a regional probe source in the signal and the baseline interval. The currently set baseline is indicated by a horizontal line in the upper left corner of the channel box.

[[Image:SA 3Dimaging (54).gif|thumb|c|none|330px|The black horizontal bar in the upper part of the channel box (here circled in red) indicates the baseline interval.]]

By default, BESA Research defines the pre-stimulus interval of the current data segment as baseline. The baseline should represent a latency range in which no event-related activity is present in the data. There are several possibilities to modify the baseline interval: by clicking on the horizontal line with the left mouse button or by using the corresponding entry in the '''Condition '''menu or '''Fit Interval''' popup menu.

Mark an interval to define the target epoch, i.e. the time-interval for which the current solution is to be tested. Start the MSPS by selecting it from the '''Image selection '''button or from the '''Image''' menu to start the probe source scan. The''' Image '''menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window. The 3D window opens and displays the scan result.

<div><ul>
<li style="display: inline-block;"> [[Image:SA 3Dimaging (55).gif|thumb|c|none|650px|This figure shows the MSPS image applied on the three left-hemispheric sources in the solution ''''Rolandic-Spike-Child-RS2.bsa''''. The baseline is set from -300ms to -50 ms. The right-hemispheric sources have been switched off. The fit interval is set to the latency range of large overall activity in the data (-43 ms : 117 ms). A realistic FEM model appropriate for the subject's age (12 years, conductivity ratios (cr) 50) is applied. The MSPS image does not show maxima at the modeled source locations and rather shows a spread q-value distribution.]] </li>

<li style="display: inline-block;"> [[Image:SA 3Dimaging (56).gif|thumb|c|none|650px|The MSPS image for the same latency range when the right-hemispheric sources have been included. The MSPS image appears more focal and shows maxima around the modeled brain regions. This indicates the substantial improvement of the solution by adding the right-hemispheric sources that model the propagation of the epileptic spike from the left to the right hemisphere (note the radiological side convention in the 3D window).]] </li>
</ul></div>

'''Time-Resolved MSPS'''

If the MSPS has been computed on time domain data, the image can be shown separately for each latency in the selected interval. After the MSPS has been computed for the marked epoch, double-click anywhere within this epoch to display the ratio of the probe source magnitude at the selected latency and the mean probe source magnitude in the baseline. Scanning the latency range by moving the cursor (e.g. with the left and right arrow cursor keys) provides a time-resolved MSPS image.

Time-resolved MSPS images are not available if the MSPS has been computed on data in the time-frequency domain.

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (57).gif|thumb|450px|MSPS image of the spike peak activity at 0ms. The activity mainly occurs in the left hemisphere. This fact is illustrated by the source waveforms and confirmed in the MSPS image, which shows a focal maximum around the location of the red sources.]] </li>

<li style="display: inline-block;"> [[File:SA 3Dimaging (58).gif|thumb|450px|Around +27 ms, the spike has propagated to the right hemisphere. This becomes evident from the waveforms of the blue sources, which show a significant latency lag with respect to the first three sources, and from the MSPS image, which shows the maximum around blue sources at this latency.]] </li>
</ul></div>



'''Notes:'''

* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image''' menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the''' Image''' menu.
* For scaling options, please refer to the '''scaling buttons''' popup menu .
* Parameters used for the MSPS calculations can be set in the ''General Settings tab'' of the ''Image Settings dialog box.''

== Source Sensitivity ==

'''Introduction'''

The 'Source sensitivity' function displays the sensitivity of the selected source in the current source model to activity in other brain regions. Sensitivity is defined as the fraction of power at the scanned brain location that is mapped onto the selected source.

To compute the source sensitivity, unit brain activity is modeled at different locations (probe source) throughout the brain. To this data, the current source model is applied to compute the source waveforms SCM of all modeled sources:

<math>\mathrm{S}_{\text{CM}} = \mathrm{L}_{\text{CM}}^{-1} \cdot \mathrm{L}_{\text{PS}}</math>


Here LCM-1 is the regularized inverse operator for the current model, and LPS is the leadfield of the regional probe source (dimension [Nx3] for EEG and [Nx2] for MEG, respectively, where N is the number of sensors). The source amplitude SSS of the selected source in the model is a 3x3 (MEG: 2x2) sub-matrix of SCM (if the selected source is a regional source) or a 1x3-matrix (MEG: 1x2) (if the selected source is a dipole). The root mean square of the singular values of SCM is defined as the source sensitivity.

The 3D source sensitivity image displays this value for all locations on a grid specified under '''Image/Settings'''. Grid density can be specified in the Image Settings.

'''Applying the Source Sensitivity Image'''

The Source Sensitivity image is evoked from the '''Image''' menu or by pressing the corresponding hot key (default: '''V''').

This function is enabled only when a solution with an active selected source is present in the Source Analysis window. The source sensitivity image then displays the sensitivity of the selected source to activity in other brain regions.

[[Image:SA 3Dimaging (59).gif]]

''Source Sensitivity image for the selected frontal source (green) in model ''''''High_Intensity_3RS.bsa'''''' in folder 'Examples/ERP_Auditory_Intensity'. The data displayed is the '100dB' condition in file ''''''All_Subjects_cc.fsg''''''. The selected source is sensitive to activity in the frontal brain region (yellow/white), while it is not influenced by activity in the vicinity of the left and right auditory cortex areas, which are modeled by the red and blue source in the model (transparent/gray).''

'''Notes:'''

* The sensitivity image is independent of the recorded sensor signals. It only depends on the current source model, the sensor configuration, the head model, and the regularization constant.
* If the regularization constant is set to zero, each source has a sensitivity of 100% to activity around its own location. With increasing regularization, the spatial filter becomes less focused, and the sensitivity of a source to activity at its location decreases.
* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image''' menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the '''Image''' menu.

{{BESAManualNav}}

File:CorticalLOR.png

2019-03-27T12:46:37Z

Jamie:

Source Analysis 3D Imaging

2019-03-27T12:42:51Z

Jamie: /* swLORETA */

{{BESAInfobox
|title = Module information
|module = BESA Research Standard or higher
|version = 6.1 or higher
}}


== Overview ==

BESA Research features a set of new functions that provide 3D images that are displayed superimposed to the individual subject's anatomy. This chapter introduces these different images and describe their properties and applications.

The 3D images can be divided into three categories:

'''Volume images:'''

* '''The Multiple Source Beamformer (MSBF)''' is a tool for imaging brain activity. It is applied in the time-domain or time-frequency domain. The beamformer technique in time-frequency domain can image not only evoked, but also induced activity, which is not visible in time-domain averages of the data.
* '''Dynamic Imaging of Coherent Sources (DICS)''' can find coherence between any two pairs of voxels in the brain or between an external source and brain voxels. DICS requires time-frequency-transformed data and can find coherence for evoked and induced activity.

The following imaging methods provide an image of brain activity based on a distributed multiple source model:
* '''CLARA''' is an iterative application of LORETA images, focusing the obtained 3D image in each iteration step.
* '''LAURA '''uses a spatial weighting function that has the form of a local autoregressive function.
* '''LORETA''' has the 3D Laplacian operator implemented as spatial weighting prior.
* '''sLORETA''' is an unweighted minimum norm that is standardized by the resolution matrix.
* '''swLORETA '''is equivalent to sLORETA, except for an additional depth weighting.
* '''SSLOFO '''is an iterative application of standardized minimum norm images with consecutive shrinkage of the source space.
* A '''User-defined volume image''' allows to experiment with the different imaging techniques. It is possible to specify user-defined parameters for the family of distributed source images to create a new imaging technique.
* Bayesian source imaging: '''SESAME''' uses a semi-automated Bayesian approach to estimate the number of dipoles along with their parameters.

'''Surface image:'''

* The '''Surface Minimum Norm Image'''. If no individual MRI is available, the minimum norm image is displayed on a standard brain surface and computed for standard source locations. If available, an individual brain surface is used to construct the distributed source model and to image the brain activity.
* '''Cortical LORETA'''. Unlike classical LORETA, cortical LORETA is not computed in a 3D volume, but on the cortical surface.
* '''Cortical CLARA'''. Unlike classical CLARA, cortical CLARA is not computed in a 3D volume, but on the cortical surface.

'''Discrete model probing:'''

These images do not visualize source activity. Rather, they visualize properties of the currently applied discrete source model:
* The '''Multiple Source Probe Scan (MSPS)''' is a tool for the validation of a discrete multiple source model.
* The '''Source Sensitivity image''' displays the sensitivity of a selected source in the current discrete source model and is therefore data independent.

== Multiple Source Beamformer (MSBF) in the Time-frequency Domain ==

 
'''Short mathematical introduction'''

The BESA beamformer is a modified version of the linearly constrained minimum variance vector beamformer in the time-frequency domain as described in [https://dx.doi.org/10.1073/pnas.98.2.694 Gross et al., "Dynamic imaging of coherent sources: Studying neural interactions in the human brain", PNAS 98, 694-699, 2001]. It allows to image evoked and induced oscillatory activity in a user-defined time-frequency range, where time is taken relative to a triggered event.

The computation is based on a transformation of each channel's single trial data from the time domain into the time-frequency domain. This transformation is performed by the BESA Research Source Coherence module and leads to the complex spectral density Si (f,t), where i is the channel index and f and t denote frequency and time, respectively. Complex cross spectral density matrices C are computed for each trial:

<math>\mathrm{C}_{ij}\left( f,t \right) = \mathrm{S}_{i}\left( f,t \right) \cdot \mathrm{S}_{j}^{*}\left( f,t \right)</math>


The output power P of the beamformer for a specific brain region at location r is then computed by the following equation:

<math>\mathrm{P}\left( r \right) = \operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{-1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{-1}</math>


Here, Cr-1 is the inverse of the SVD-regularized average of Cij(f,t) over trials and the time-frequency range of interest; L is the leadfield matrix of the model containing a regional source at target location r and, optionally, additional sources whose interference with the target source is to be minimized; tr'[] is the trace of the [3×3] (MEG:[2×2]) submatrix of the bracketed expression that corresponds to the source at target location r.

In BESA Research, the output power P(r) is normalized with the output power in a reference time-frequency interval Pref(r). A value q ist defined as follows:

<math> \mathrm{q}\left( r \right) =
\begin{cases}
\sqrt{\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}(r)}} - 1 = \sqrt{\frac{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{\text{ref},r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}} - 1, & \text{for }\mathrm{P}(r) \geq \mathrm{P}_{\text{ref}}(r) \\

1 - \sqrt{\frac{\mathrm{P}_{\text{ref}}\left( r \right)}{\mathrm{P}\left( r \right)}} = 1 - \sqrt{\frac{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{\text{ref},r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}}, & \text{for }\mathrm{P}(r) < \mathrm{P}_{\text{ref}}(r)
\end{cases} </math>


Pref can be computed either from the corresponding frequency range in the baseline of the same condition (i.e. the beamformer images event-related power increase or decrease) or from the corresponding time-frequency range in a control condition (i.e. the beamformer images differences between two conditions). The beamformer image is constructed from values q(r) computed for all locations on a grid specified in the '''General Settings tab'''. For MEG data, the innermost grid points within a sphere of approx. 12% of the head diameter are assigned interpolated rather than calculated values).
q-values are shown in %, where where q[%] = q*100. Alternatively to the definition above, q can also be displayed in units of dB:

<math>\mathrm{q}\left\lbrack \text{dB} \right\rbrack = 10 \cdot \log_{10}\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}</math>


A beamformer operator is designed to pass signals from the brain region of interest r without attenuation, while minimizing interference from activity in all other brain regions. Traditional single-source beamformers are known to mislocalize sources if several brain regions have highly correlated activity. Therefore, the BESA beamformer extends the traditional single-source beamformer in order to implicitly suppress activity from possibly correlated brain regions. This is achieved by using a multiple source beamformer calculation that contains not only the leadfields of the source at the location of interest r, but also those of possibly interfering sources. As a default, BESA Research uses a bilateral beamformer, where specifically contributions from the homologue source in the opposite hemisphere are taken into account (the matrix L thus being of dimension N×6 for EEG and N×4 for MEG, respectively, where N is the number of sensors). This allows for imaging of highly correlated bilateral activity in the two hemispheres that commonly occurs during processing of external stimuli.

In addition, the beamformer computation can take into account possibly correlated sources at arbitrary locations that are specified in the current solution. This is achieved by adding their leadfield vectors to the matrix L in the equation above.

'''Applying the Beamformer'''

This chapter illustrates the usage of the BESA beamformer. The displayed figures are generated using the file ''''Examples/Learn-by-Simulations/AC-Coherence/AC-Osc20.foc'''' (see BESA Tutorial 6: "''Time-frequency analysis and Source coherence''").

'''Starting the beamformer from the time-frequency window'''

The BESA beamformer is applied in the time-frequency domain and therefore requires the Source Coherence module to be enabled. The time-frequency beamformer is especially useful to image in- or decrease of induced oscillatory activity. Induced activity cannot be observed in the averaged data, but shows up as enhanced averaged power in the TSE (Temporal-Spectral Evolution) plot. For instructions on how to initiate a beamformer computation in the time-frequency window, please refer to Chapter '''[[Source_Coherence_How_to...#How_to_Start_the_Beamformer_from_the_Time-Frequency_Window|How to Create Beamformer Images]]'''.

After the beamformer computation has been initiated in the time-frequency window, the source analysis window opens with an enlarged 3D image of the q-value computed with a '''bilateral beamformer'''. The result is superimposed onto the MR image assigned to the data set (individual or standard).

[[Image:SA 3Dimaging (5).gif]]

''Beamformer image after starting the computation in the Time-Frequency window. A bilateral pair of sources in the auditory cortex accounts for the highly correlated oscillatory induced activity. Only the bilateral beamformer manages to separate these activities; a traditional single-source beamformer would merge the two sources into one image maximum in the head center instead.''

'''Multiple source beamformer in the Source Analysis window'''

The 3D imaging display is part of the source analysis window. If you press the '''Restore''' button at the right end of the title bar of the 3D window, the window appears at the bottom right of the source analysis window. In the channel box, the averaged (evoked) data of the selected condition is shown. When a control condition was selected, its average is appended to the average of the target condition.

[[Image:SA 3Dimaging (6).gif]]

''Source Analysis window with beamformer image. The two sources have been added using the '''''Switch to''''' '''''Maximum''''' and '''''Add Source '''''toolbar buttons (see below). Source waveforms are computed from the displayed averaged data. Therefore, they do not represent the activity displayed in the beamformer image, which in this simulation example is induced (i.e. not phase-locked to the trigger)!''

When starting the beamformer from the time-frequency window, a bilateral beamformer scan is performed. In the source analysis window, the beamformer computation can be repeated taking into account possibly correlated sources that are specified in the current solution. Interfering activities generated by all sources in the current solution that are in the 'On' state are specifically suppressed ('''they enter the matrix L in the beamformer calculation''', see Chapter ''Short mathematical description'' above). The computation can be started from the '''Image''' menu or from the '''Image selector button''' dropdown menu. The '''Image''' menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window.

[[Image:SA 3Dimaging (7).gif]]

''Multiple source beamformer image calculated in the presence of a source in the left hemisphere. A '''single''' source scan has been performed. The source set in the current solution accounts for the left-hemispheric q-maximum in the data. Accordingly, the beamformer scan reveals only the as yet unmodeled additional activity in the right hemisphere (note the radiological convention in the 3D image display).''

The beamformer scan can be performed with a '''single''' or a '''bilateral''' source scan. The default scan type depends on the current solution:
* When the beamformer is started from the Time-Frequency window, the Source Analysis window opens with a new solution and a '''bilateral''' beamformer scan is performed.
* When the beamformer is started within the Source Analysis window, the default is
** a scan with a '''single''' source in addition to the sources in the current solution, if at least one source is active.
** a '''bilateral''' scan if no source in the current solution is active.

The default scan type is the multiple source beamformer. The non-default scan type can be enforced using the corresponding ''Volume Image / Beamformer'' entry in the '''Image''' menu.

'''Inserting Sources out of the Beamformer Image'''

The beamformer image can be used to add sources to the current solution. A simple double-click anywhere in the 2D- or 3D-view will generate a non-oriented regional source at the corresponding location. However, a better and easier way to create sources at image maxima and minima is to use the toolbar buttons '''Switch to Maximum''' [[Image:SA 3Dimaging (8).gif]] and '''Add Source''' [[Image:SA 3Dimaging (9).gif]].

Use the '''Switch to Maximum''' button to place the red crosshair of the 3D window onto a local image maximum or minimum. Hitting the '''Add Source''' button creates a regional source at the location of the crosshair and therefore ensures the exact placement of the source at the image extremum. Moreover, the '''Add Source''' button generates an oriented regional source. BESA Research automatically estimates the source orientation that contributes most to the power in the target time-frequency interval (or the reference time-frequency interval, if its power is larger than that in the target interval). The accuracy of this orientation estimate depends largely on the noise content of the data. The smaller the signal-to-noise ratio of the data, the lower is the accuracy of the orientation estimate. '''This feature allows to use the beamformer as a tool to create a source montage for source coherence analysis, where it is of advantage to work with oriented sources'''.

'''Notes:'''

* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image '''menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the''' Image''' menu.
* For scaling options, use the [[Image:SA 3Dimaging (10).gif]] and [[Image:SA 3Dimaging (11).gif]] '''Image Scale toolbar''' buttons.
* Parameters used for the beamformer calculations can be set in the '''Standard Volumes''' of the ''Image Settings dialog box.''

== Dynamic Imaging of Coherent Sources (DICS) ==

 
'''Short mathematical introduction'''

Dynamic Imaging of Coherent Sources (DICS) is a sophisticated method for imaging cortico-cortical coherence in the brain, or coherence between an external reference (e.g. EMG channel) and cortical structures. DICS can be applied to localize evoked as well as induced coherent cortical activity in a user-defined time-frequency range.

DICS was implemented in BESA closely following [https://dx.doi.org/10.1073/pnas.98.2.694 Gross et al., "Dynamic imaging of coherent sources: Studying neural interactions in the human brain", PNAS 98, 694-699, 2001].

The computation is based on a transformation of each channel's single trial data from the time domain into the frequency domain. This transformation is performed by the BESA Research Coherence module and results in the complex spectral density matrix that is used for constructing the spatial filter similar to beamforming.

DICS computation yields a 3-D image, each voxel being assigned a coherence value. Coherence values can be described as a neural activity index and do not have a unit. The neural activity index contrasts coherence in a target time-frequency bin with coherence of the same time-frequency bin in a baseline.

'''DICS for cortico-cortical coherence is computed as follows:'''

Let L(r) be the leadfield in voxel r in the brain and C the complex cross-spectral density matrix. The spatial filter W(r) for the voxel r in the head is defined as follows:

<math>W\left( r \right) = \left\lbrack L^{T}\left( r \right) \cdot C^{- 1} \cdot L\left( r \right) \right\rbrack^{- 1} \cdot L^{T}(r) \cdot C^{- 1}</math>


The cross-spectrum between two locations (voxels) r1 and r2 in the head are calculated with the following equation:

<math>C_{s}\left( r_{1},r_{2} \right) = W\left( r_{1} \right) \cdot C \cdot W^{*T}\left( r_{2} \right),</math>


where <nowiki>*T</nowiki> means the transposed complex conjugate of a matrix. The cross-spectral density can then be calculated from the cross spectrum as follows:

<math>c_{s}\left( r_{1},r_{2} \right) = \lambda_{1}\left\{ C_{s}\left( r_{1},r_{2} \right) \right\},</math>


where λ1{} indicates the largest singular value of the cross spectrum. Once the cross spectral density is estimated, the connectivity¹(CON) between the two brain regions r1 and r2 are calculated as follows:

<math>\text{CON}\left( r_{1},r_{2} \right) = \frac{c_{s}^{\text{sig}}\left( r_{1},r_{2} \right) - c_{s}^{\text{bl}}(r_{1},r_{2})}{c_{s}^{\text{sig}}\left( r_{1},r_{2} \right) + c_{s}^{\text{bl}}(r_{1},r_{2})},</math>


where cssig is the cross-spectral density for the signal of interest between the two brain regions r1 and r2, and csbl is the corresponding cross spectral density for the baseline or the control condition, respectively. In the case DICS is computed with a cortical reference, r1 is the reference region (voxel) and remains constant while r2 scans all the grid points within the brain sequentially. In that way, the connectivity between the reference brain region and all other brain regions is estimated. The value of CON(r1, r2) falls in the interval [-1 1]. If the cross-spectral density for the baseline is 0 the connectivity value will be 1. If the cross-spectral density for the signal is 0 the connectivity value will be -1.

¹ Here, the term connectivity is used rather than coherence, as strictly speaking the coherence equation is defined slightly differently. For simplicity reasons the rest of the tutorial uses the term coherence.

'''DICS for cortico-muscular coherence is computed as follows:'''

When using an external reference, the equation for coherence calculation is slightly different compared to the equation for cortico-cortical coherence. First of all, the cross-spectral density matrix is not only computed for the MEG/EEG channels, but the external reference channel is added. This resulting matrix is Call. In this case, the cross-spectral density between the reference signal and all other MEG/EEG

channels is called cref. It is only one column of Call. Hence, the cross-spectrum in voxel r is calculated with the following equation:

<math>C_{s}\left( r \right) = W\left( r \right) \cdot c_{\text{ref}}</math>


and the corresponding cross-spectral density is calculated as the sum of squares of Cs:

<math>c_{s}\left( r \right) = \sum_{i = 1}^{n}{C_{s}\left( r \right)_{i}^{2}},</math>


where n is 2 for MEG and 3 for EEG. This equation can also be described as the squared Euclidean norm of the cross-spectrum:

<math>c_{s}\left( r \right) = \left\| C_{s} \right\|^{2},</math>


The power in voxel r is calculated as in the cortico-cortical case:

<math>p\left( r \right) = \lambda_{1}\left\{ C_{s}(r,r) \right\}.</math>


At last, coherence between the external reference and cortical activity is calculated with the equation:

<math>\text{CON}\left( r \right) = \frac{c_{s}(r)}{p\left( r \right) \cdot C_{\text{all}}(k,k)},</math>


where Call(k, k) is the (k,k)-th diagonal element of the matrix Call.

DICS is particularly useful, if coherence is to be calculated without an a-priory source model (in contrast to source coherence based on pre-defined source montages). However, the recommended analysis strategy for DICS is to use a brain source as a starting point for coherence calculation that is known to contribute to the EEG/MEG signal of interest. For example, one might first run a beamformer on the time-frequency range of interest and use the voxel with the strongest oscillatory activity as a starting point for DICS. The resulting coherence image will again lead to several maxima (ordered by magnitude), which in turn can serve as starting points for DICS calculation. This way, it is possible to detect even weak sources that show coherent activity in the given time-frequency range.

The other significant application for DICS is estimating coherence between an external source and voxels in the brain. For example, an external source can be muscle activity recoded by an electrode placed over the according peripheral region. This way, the direct relationship between muscle activity and brain activation can be measured.

'''Starting DICS computation from the Time-Frequency Window'''

DICS is particularly useful, if coherence in a user-defined time-frequency bin (evoked or induced) is to be calculated between any two brain regions or between an external reference and the brain. DICS runs only on time-frequency decomposed data, so time-frequency analysis needs to be run before starting DICS computation.

To start the DICS computation, left-drag a window over a selected time-frequency bin in the Time-Frequency Window. Right-click and select “Image”. A dialogue will open (see fig. 1) prompting you to specify time and frequency settings as well as the baseline period. It is recommended to use a baseline period of equal length as the data period of interest. Make sure to select “DICS” in the top row and press “'''Go'''”.

[[Image:SA 3Dimaging (21).gif|450px|thumb|c|none|Fig. 1: Time and frequency settings for DICS and MSBF]]

Next, a window will appear allowing you to specify the reference source for coherence calculation (see fig. 2). It is possible to select a channel (e.g. EMG) or a brain source. If a brain source is chosen and no source analysis was computed beforehand, the option “Use current cross-hair position” must be chosen. In case discrete source analysis was computed previously, the selected source can be chosen as the reference for DICS. Please note that DICS can be re-computed with any cross-hair or source position at a later stage.

[[Image:SA 3Dimaging (1).jpg|400px|thumb|c|none|Fig. 2: Possible options for choosing the reference]]

Confirming with “'''OK'''” will start computation of coherence between the selected channel/voxel and all other brain voxels. In case DICS is computed for a reference source in the brain, it can be advantageous to run a beamforming analysis in the selected time-frequency window first and use one of the beamforming maxima as reference for DICS. Fig. 3 shows an example for DICS calculation.

[[Image:SA 3Dimaging (22).gif|500px|thumb|c|none|Fig. 3: Coherence between left-hemispheric auditory areas and the selected voxel in the right auditory cortex.]]

Coherence values range between -1 and 1. If coherence in the signal is much larger than coherence in the baseline (control condition) then the DICS value is going to approach 1. Contrary, if coherence in the baseline is much larger than coherence in the signal, then the DICS value is going to approach -1. At last, if coherence in the signal is equal to coherence in the baseline, then the DICS value is 0.

In case DICS is to be re-computed with a different reference, simply mark the desired reference position by placing the cross-hair in the anatomical view and select “DICS” in the middle panel of the source analysis window (see Fig. 4). In case an external reference is to be selected, click on “DICS” in the middle panel to bring up the DICS dialogue (see. Fig. 2) and select the desired channel. Please note that DICS computation will only be available after running time-frequency analysis.

[[Image:SA 3Dimaging (23).gif|700px|thumb|c|none|Fig. 4: Integration of DICS in the Source Analysis window]]

== Multiple Source Beamformer (MSBF) in the Time Domain ==
''(requires Besa Research 7.0 or higher)''

===Short mathematical introduction===

Beamforming approach can be also applied in the time domain data. This approach was introduced as linearly constrained minimum variance (LCMV) beamformer (Van Veen et al., 1997). It allows to image evoked activity in a user-defined time range, where time is taken relative to a triggered event, and to estimate source waveforms using the calculated spatial weight at locations of interest. For an implementation of the beamformer in the time domain, data covariance matrices are required, while complex cross spectral density matrices are used for the beamformer approaches in the time-frequency domain as described in the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section.

The bilateral beamformer introduced in the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section is also implemented for the time-domain beamformer to take into account contributions from the homologue source in the opposite. This allows for imaging of highly correlated bilateral activity in the two hemispheres that commonly occurs during processing of external stimuli. In addition, the beamformer computation can take into account possibly correlated sources at arbitrary locations.
The beamformer spatial weight W(r) for the voxel r in the brain is defined as follows (Van Veen et al., 1997):

[[File:MSBF1.png]]

where '''C-1''' is the inversed regularized average of covariance matrix over trials, '''L''' is the leadfield matrix of the model containing a regional source at target location r and optionally
additional sources whose interference with the target source is to be minimized. The beamformer spatial weight '''W'''(r) can be applied to the measured data to estimate source
waveform at a location r (beamformer virtual sensor):

[[File:MSBF2.png]]

where '''S'''(r,t) represents the estimated source waveform and '''M'''(t) represents measured EEG or MEG signals.
The output power P of the beamformer for a specific brain region at location r is computed by the following equation:

[[File:MSBF3.png]]

where tr’[ ] is the trace of the [3×3] (MEG: [2×2]) submatrix of the bracketed expression that corresponds to the source at target location r.
Beamformer can suppress noise sources that are correlated across sensors. However, uncorrelated noise will be amplified in a spatially non-uniform manner, with increasing
distortion with increasing distance from the sensors (Van Veen et al., 1997; Sekihara et al., 2001). For this reason, estimated source power should be normalized by a noise power.
In BESA Research, the output power P(r) is normalized with the output power in a baseline interval or with the output power of a uncorrelated noise: P(r) / Pref (r).
The time-domain beamformer image is constructed from values q(r) computed for all locations on a grid specified in the '''General Settings''' tab. A value q(r) is defined as described in
the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section with data covariance matrices instead of cross-spectral density matrices.

===Applying the Beamformer===

This chapter illustrates the usage of the BESA beamformer in the time domain. The displayed figures are generated using the file ‘Examples/ERP-Auditory-Intensity/S1.cnt’.

'''Starting the time-domain beamformer from the Average tab of the Paradigm dialog box'''

The time-domain beamformer is needed data covariance matrices and therefore requires the ERP module to be enabled. After the beamformer computation has been initiated in the
'''Average tab of the Paradigm dialog box''', the source analysis window opens with an enlarged 3D image of the q-value computed with a bilateral beamformer. The result is
superimposed onto the MR image assigned to the data set (individual or standard).

[[File:MSBF44.png]]

''Beamformer image for auditory evoked data after starting the computation in the '''Average tab of the Paradigm dialog box'''. The bilateral beamformer manages to separate the
activities in auditory areas, while a traditional single-source beamformer would merge the two sources into one image maximum in the head center instead.''

'''Multiple-source beamformer in the Source Analysis window'''

The 3D imaging display is part of the source analysis window. In the Channel box, the averaged (evoked) data of the selected condition is shown. Selected covariance intervals in
the ERP module can be checked in the Channel box. The red, gray, and blue rectangles indicate signal, baseline, and common interval, respectively.

[[File:MSBF55.png]]

''Source Analysis window with beamformer image. The two beamformer virtual sensors have been added using the Switch to Maximum and Add Source toolbar buttons (see below).
Source waveforms are computed using the beamformer spatial weights and the displayed averaged data (the noise normalized weights (5% noise) option was used to compute the
beamformer image).''

When starting the beamformer from the '''Average tab of the Paradigm dialog box''', the bilateral beamformer scan is performed. In the source analysis window, the beamformer computation can be repeated taking into account possibly correlated sources that are specified in the current solution. Interfering activities generated by all sources in the current solution that are in the 'On' state are specifically suppressed (they enter the leadfield matrix L in the beamformer calculation). The computation can be started from the '''Image''' menu or from the Image selector button [[File:MSBF_Button.png|22px|Image: 22 pixels]] dropdown menu. The Image menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window.

[[File:MSBF66.png]]

''Multiple-source beamformer image calculated in the presence of a source in the left hemisphere. A single-source scan has been performed instead of a bilateral beamforemr. The
source set in the current solution accounts for the left-hemispheric q-maximum in the data. Accordingly, the beamformer scan reveals only the as yet unmodeled additional activity in
the right hemisphere (note the radiological convention in the 3D image display). The source waveform of the beamformer virtual sensor in the left hemisphere is not shown since the
location (blue square in the figure) is not considered for the multiple-source beamformer.''

The beamformer scan can be performed with a single or a bilateral source scan. The default scan type depends on the current solution:
When the beamformer is started from the '''Average tab of the Paradigm dialog box''' the Source Analysis window opens with a new solution and a bilateral beamformer scan is
performed.
When the beamformer is started within the Source Analysis window, the default is:

* a scan with a single source in addition to the sources in the current solution, if at least one source is active.
* a bilateral scan if no source in the current solution is active.
* a scan with a single source when scalar-type beamformer is selected in the '''beamformer option dialog box'''.

The default scan type is the multiple source beamformer. The non-default scan type can be enforced using the corresponding Volume Image / Beamformer entry in the Image main
menu or in the beamformer option dialog box (only for the time-domain beamformer).

===Inserting Sources as Beamformer Virtual Sensor out of the Beamformer Image===

This is similar to the inserting sources out of the beamformer image in Multiple Source Beamformer (MSBF) in the Time-frequency Domain section.
The beamformer image can be used to add beamformer virtual sensors to the current solution. A simple double-click anywhere in the 3D view (not in the 2D view) will generate a
source at the corresponding location. A better and easier way to create sources at image maxima and minima is to use the toolbar buttons '''Switch to Maximum''' and '''Add Source'''

This feature allows to use the beamformer as a tool to create a source montage for '''source coherence''' analysis. A source montage file (*.mtg) for beamformer virtual sensors can
be saved using File \ Save Source Montage As… entry.

The time-domain beamformer image can be also used to add regional or dipole sources to the current solution. Press '''N''' key when there is no source in the current source array or
there is more than one beamformer virtual sensor. To create a new source array for beamformer virtual sensor, press '''N''' key when there is more than one regional or dipole source in
the current source array.

===Notes===

* You can hide or re-display the last computed image by selecting ''Hide Image'' entry in the '''Image''' menu.
* The current image can be exported to ASCII, ANALYZE, or BrainVoyager (vmp) format from the '''Image''' menu.
* For scaling options, use the and Image Scale toolbar buttons.
* Parameters used for the beamformer calculations can be set in the '''Standard Volume tab of the Image Settings dialog box'''.
* Note that Model, Residual, Order, and Residual variance are not shown for the beamformer virtual sensor type sources.

===References===

* Sekihara, K., Nagarajan, S. S., Poeppel, D., Marantz, A., & Miyashita, Y. (2001). Reconstructing spatio-temporal activities of neural sources using an MEG vector beamformer technique. IEEE Transactions on Biomedical Engineering, 48(7), 760–771.

* Van Veen, B. D., Van Drongelen, W., Yuchtman, M., & Suzuki, A. (1997). Localization of brain electrical activity via linearly constrained minimum variance spatial filtering. IEEE Transactions on Biomedical Engineering, 44(9), 867–880

== CLARA ==

CLARA ('Classical LORETA Analysis Recursively Applied') is an iterative application of weighted LORETA images with a reduced source space in each iteration.

In an initialization step, a LORETA image is calculated. Then in each iteration the following steps are performed:

# The obtained image is spatially smoothed (this step is left out in the first iteration).
# All grid points with amplitudes below a threshold of 1% of the maximum activity are set to zero, thus being effectively eliminated from the source space in the following step.
# The resulting image defines a spatial weighting term (for each voxel the corresponding image amplitude).
# A LORETA image is computed with an additional spatial weighting term for each voxel as computed in step 3. By the default settings in BESA Research, the regularization values used in the iteration steps are slightly higher than that of the initialization LORETA image.

The procedure stops after 2 iterations, and the image computed in the last iteration is displayed. Please note that you can change all parameters by creating a user-defined volume image.

The advantage of CLARA over non-focusing distributed imaging methods is visualized by the figure below. Both images are computed from the N100 response in an auditory oddball experiment (file '''Oddball.fsg''' in subfolder ''fMRI+EEG-RT-Experiment'' of the ''Examples'' folder). The CLARA image is much more focal than the sLORETA image, making it easier to determine the location of the image maxima.

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (24).gif|thumb|350px|sLORETA image]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (25).gif|thumb|350px|CLARA image]] </li>
</ul></div>

'''Notes:'''

* Starting CLARA: CLARA can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter ''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]'' for important information on regularization of distributed inverses.

== LAURA ==

LAURA (Local Auto Regressive Average) belongs to the distributed inverse method of the family of weighted minimum norm methods ([https://doi.org/10.1023/A:1012944913650 Grave de Peralta Menendeza et al., "Noninvasive Localization of Electromagnetic Epileptic Activity. I. Method Descriptions and Simulations", BrainTopography 14(2), 131-137, 2001]). LAURA uses a spatial weighting function that includes depth weighting and that term has the form of a local autoregressive function.

The source activity is estimated by applying the general formula for a weighted minimum norm:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T}\left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings.''

In LAURA, V contains both a depth weighting term W and a representation of a local autoregressive function A. V is computed as:

<math>\mathrm{V} = \left( \mathrm{U}^{T} \cdot \mathrm{U} \right)^{-1}</math>


Where

<math>\mathrm{U} = \left( \mathrm{W} \cdot \mathrm{A} \right) \otimes \mathrm{I}_{3}</math>


Here, <math>\otimes</math> denotes the Kronecker product. I3 is the [3×3] identity matrix. W is an [s×s] diagonal matrix (with s the number of source locations on the grid), where each diagonal element is the inverse of the maximum singular value of the corresponding regional source's leadfields. The formula for the diagonal components Aii and the off-diagonal components Aik are as follows:

<math>\mathrm{A}_{ii} = \frac{26}{\mathrm{N}_{i}}\sum_{k \subset V_{i}}^{}\frac{1}{\mathrm{d}_{ik}^{2}}</math>


<math>
\mathrm{A}_{ik} =
\begin{cases}
- 1/\operatorname{dist}\left( i,k \right)^{2}, & \text{if } k \subset V_{i} \\
0, & \text{otherwise}
\end{cases}
</math>


Here, Vi is the vicinity around grid point i that includes the 26 direct neighbors.

The LAURA image in BESA Research displays the norm of the 3 components of S at each location r. Using the menu function ''Image / Export Image As... ''you have the option to save this norm of S or alternatively all components separately to disk.

'''Notes:'''

* '''Grid spacing:''' Due to memory limitations, LAURA images require a grid spacing of 7 mm or more.
* '''Computation time:''' Computation speed during the first LAURA image calculation depends on the grid spacing (computation is faster with larger grid spacing). After the first computation of a LAURA image, a '''*.laura''' file is stored in the data folder, containing intermediate results of the LAURA inverse. This file is used during all subsequent LAURA image computations. Thereby, the time needed to obtain the image is substantially reduced.
* '''MEG:''' In the case of MEG data, an additional constraint is implemented in the LAURA algorithm that prevents solutions from containing radial source currents (compare Pascual-Marqui, ISBET Newsletter 1995, 22-29). In MEG, an additional source space regularization is necessary in the inverse matrix operation required compute V
* '''Starting LAURA:''' LAURA can be started from the''' Image''' menu or from the '''Image Selection''' button.
* '''Regularization:''' Please refer to Chapter'' “Regularization of distributed volume images” ''for important information on regularization of distributed inverses.

== LORETA ==

LORETA ("Low Resolution Electromagnetic Tomography") is a distributed inverse method of the family of ''weighted minimum norm'' methods. LORETA was suggested by R.D. Pascual-Marqui (International Journal of Psychophysiology. 1994, 18:49-65). LORETA is characterized by a smoothness constraint, represented by a discrete 3D Laplacian.

The source activity is estimated by applying the general formula for a weighted minimum norm:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T}\left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings.''

In LORETA, V contains both a depth weighting term and a representation of the 3D Laplacian matrix. V is computed as:

<math>\mathrm{V} = \left( \mathrm{U}^{T} \cdot \mathrm{U} \right)^{- 1}</math>


where

<math>\mathrm{U} = \left( \mathrm{W} \cdot \mathrm{A} \right) \otimes \mathrm{I}_{3}</math>


Here, <math>\otimes</math> denotes the Kronecker product. I3 is the [3x3] identity matrix. W is an [sxs] diagonal matrix (with s the number of source locations on the grid), where each diagonal element is the inverse of the maximum singular value of the corresponding regional source's leadfields. A contains the 3D Laplacian and is computed as

<math>\mathrm{A} = \mathrm{Y} - \mathrm{I}_{s}</math>


with Is the [sxs] identity matrix, where s is the number of sources (= three times the number of grid points) and

<math>\mathrm{Y} = \frac{1}{2}\left\{ \mathrm{I}_{s} + \left\lbrack \operatorname{diag}\left( \mathrm{Z} \cdot \left\lbrack 111 \ldots 1 \right\rbrack^{T} \right) \right\rbrack^{- 1} \right\} \cdot \mathrm{Z}</math>


where

<math>
\mathrm{Z}_{ik} =
\begin{cases}
1/6, & \text{if } \operatorname{dist}\left( i,k \right) = 1 \text{ grid point} \\
0, & \text{otherwise}
\end{cases}
</math>


The LORETA image in BESA Research displays the norm of the 3 components of S at each location r. Using the menu function ''Image / Export Image As... ''you have the option to save this norm of S or alternatively all components separately to disk.

'''Notes:'''
* '''Grid spacing:''' Due to memory limitations, LORETA images require a grid spacing of 5 mm or more.
* '''Computation time:''' Computation speed during the first LORETA image calculation depends on the grid spacing (computation is faster with larger grid spacing). After the first computation of a LORETA image, a '''<nowiki>*.loreta</nowiki>''' file is stored in the data folder, containing intermediate results of the LORETA inverse. This file is used during all subsequent LORETA image computations. Thereby, the time needed to obtain the image is substantially reduced.
* '''MEG''': In the case of MEG data, an additional constraint is implemented in the LORETA algorithm that prevents solutions from containing radial source currents (Pascual-Marqui, ISBET Newsletter 1995, 22-29). In MEG, an additional source space regularization is necessary in the inverse matrix operation required compute V.
* '''Starting LORETA:''' LORETA can be started from the''' Image''' menu or from the '''Image Selection '''button.
* '''Regularization:''' Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed source models.

== sLORETA ==

This distributed inverse method consists of a ''standardized, unweighted minimum norm''. The method was originally suggested by R.D. Pascual-Marqui (Methods & Findings in Experimental & Clinical Pharmacology 2002, 24D:5-12) Starting point is an unweighted minimum norm computation:

<math>\mathrm{S}_{\text{MN}}\left( t \right) = \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings''.

This minimum norm estimate is now standardized to produce the sLORETA activity at a certain brain location r:

<math>\mathrm{S}_{\text{sLORETA}, r} = \mathrm{R}_{rr}^{-1/2} \cdot \mathrm{S}_{\text{MN},r}</math>


SsMN,r is the [3x1] (MEG: [2x1]) minimum norm estimate of the 3 (MEG: 2) dipoles at location r. Rrr is the [3x3] (MEG: [2x2]) diagonal block of the resolution matrix R that corresponds to the source components at the target location r. The resolution matrix is defined as:

<math>\mathrm{R} = \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{L}^{T} + \lambda \cdot \mathrm{I} \right)^{-1} \cdot \mathrm{L}</math>


The sLORETA image in BESA Research displays the norm of SsLORETA, r at each location r. Using the menu function ''Image / Export Image As...'' you have the option to save this norm of SsLORETA, r or alternatively all components separately to disk.

'''Notes:'''

* sLORETA can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== swLORETA ==

This distributed inverse method is a ''standardized, depth-weighted minimum norm'' (E. Palmero-Soler et al 2007 Phys. Med. Biol. 52 1783-1800). It differs from sLORETA only by an additional depth weighting.

Starting point is a depth-weighted minimum norm computation:

<math>\mathrm{S}_{\text{MN}}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings''.

V is the diagonal depth weighting matrix. For s grid locations, V is of dimension [3s x 3s] (MEG: [2s x 2s]). Each diagonal element of V is the inverse of the first singular value of the leadfield of the corresponding regional source. Hence, the first 3 (MEG: 2) diagonal elements equal the inverse of the largest eigenvalue of the leadfield matrix of regional source 1, and so on.

This minimum norm estimate is now standardized to produce the swLORETA activity at a certain brain location r:

<math>\mathrm{S}_{\text{swLORETA},r} = \mathrm{R}_{rr}^{-1/2} \cdot \mathrm{S}_{\text{MN},r}</math>


SsMN,r is the [3x1] (MEG: [2x1]) depth-weighted minimum norm estimate of the regional source at location r. Rrr is the [3x3] (MEG: [2x2]) diagonal block of the resolution matrix R that corresponds to the source components at the target location r. The resolution matrix is defined as:

<math>\mathrm{R} = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} + \lambda \cdot \mathrm{I} \right)^{-1} \cdot \mathrm{L}</math>


The swLORETA image in BESA Research displays the norm of SswLORETA, r at each location r. Using the menu function ''Image / Export Image As...'' you have the option to save this norm of SswLORETA, r or alternatively all components separately to disk.

'''Notes:'''

* sLORETA can be started from the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== sSLOFO ==

SSLOFO (standardized shrinking LORETA-FOCUSS) is an iterative application of weighted distributed source images with a reduced source space in each iteration ([https://dx.doi.org/10.1109/TBME.2005.855720 Liu et al., "Standardized shrinking LORETA-FOCUSS (SSLOFO): a new algorithm for spatio-temporal EEG source reconstruction", IEEE Transactions on Biomedical Engineering 52(10), 1681-1691, 2005]).

In an initialization step, an [[#sLORETA | sLORETA]] image is calculated. Then in each iteration the following steps are performed:

# A weighted minimum norm solution is computed according to the formula <math display="inline">\mathrm{S} = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}</math> . Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D is the data at the time point under consideration. V is a diagonal spatial weighting matrix that is computed in the previous iteration step. In the first iteration, the elements of V contain the magnitudes of the initially computed LORETA image.
# Standardization of this weighted minimum norm image is performed with the resolution matrix as in [[#sLORETA | sLORETA]].
# The obtained standardized weighted minimum norm image is being smoothed to get Ssmooth.
# All voxels with amplitudes below a threshold of 1% of the maximum activity get a weight of zero in the next iteration step, thus being effectively eliminated from the source space in the next iteration step.
# For all other voxels, compute the elements of the spatial weighting matrix V to be used in the next iteration as follows: <math display="inline">\mathrm{V}_{ii,\text{next iteration}} = \frac{1}{\left\| \mathrm{L}_{i} \right\|} \cdot \mathrm{S}_{ii,\text{smooth}} \cdot \mathrm{V}_{ii,\text{current iteration}}</math>



The procedure stops after 3 iterations. Please note that you can change all parameters by creating a [[#User-Defined Volume Image | user-defined volume image]].

'''Notes:'''
* '''Starting sSLOFO''': sSLOFO can be started from the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter ''[[#Regularization of distributed volume images | Regularization of distributed volume images]]'' for important information on regularization of distributed inverses.

== User-Defined Volume Image ==

In addition to the predefined 3D imaging methods in BESA Research, it is possible to create user-defined imaging methods based on the general formula for distributed inverses:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. Custom-defined parameters are:* The spatial weighting matrix V: This may include depth weighting, image weighting, or cross-voxel weighting with a 3D Laplacian (as in LORETA) or an autoregressive function (as in LAURA).

* Regularization: The term in parentheses is generally regularized. Note that regularization has a strong effect on the obtained results. Please refer to chapter “''Regularization of Distributed Volume Images” ''for more information.
* Standardization: Optionally, the result of the distributed inverse can be standardized with the resolution matrix (as in sLORETA).
* Iterations: Inverse computations can be applied iteratively. Each iteration is weighted with the image obtained in the previous iteration.

All parameters for the user-defined volume image are specified in the User-Defined Volume Tab of the Image Settings dialog box. Please refer to chapter “''User-Defined Volume Tab”'' for details.

'''Notes:'''
* Starting the user-defined volume image: the image calculation can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== Regularization of distributed volume images ==

Distributed source images require the inversion of a term of the form L V LT. This term is generally regularized before its inversion. In BESA Research, selection can be made between two different regularization approaches (parameters are defined in the ''Image Settings dialog box''):

* '''Tikhonov regularization''': In Tikhonov regularization, the term L V LT is inverted as (L V LT +λ I)-1. Here, l is the regularization constant, and I is the identity matrix.
* One way of determining the optimum regularization constant is by minimizing the ''generalized cross'' ''validation error'' (CVE).
* Alternatively, the regularization constant can be specified manually as a percentage of the trace of the matrix L V LT.
* '''TSVD''': In the truncated singular value decomposition (TSVD) approach, an SVD decomposition of L V LT is computed as  L V LT = U S UT, where the diagonal matrix S contains the singular values. All singular values smaller than the specified percentage of the maximum singular values are set to zero. The inverse is computed as U S-1 UT, where the diagonal elements of S-1 are the inverse of the corresponding non-zero diagonal elements of S.

Regularization has a critical effect on the obtained distributed source images. The results may differ completely with different choices of the regularization parameter (see examples below). Therefore, it is important to evaluate the generated image critically with respect to the regularization constant, and to keep in mind the uncertainties resulting from this fact when interpreting the results. The default setting in BESA Research is a TSVD regularization with a 0.03% threshold. However, this value might need to be adjusted to the specific data set at hand.

The following example illustrates the influence of the regularization parameter on the obtained images. The data used here is condition '''St-Cor of dataset Examples \ TFC-Error-Related-Negativity \ Correct+Error.fsg''' at 176 ms following the visual stimulus. Discrete dipole analysis reveals the main activity in the left and right lateral visual cortex at this latency.

[[Image:SA 3Dimaging (42).gif]]

''Discrete source model at 176 ms: Main activity in the left and right lateral visual cortex, no visual midline activity.''

LORETA images computed at this latency depend critically on the choice of the regularization constant. The following 3D images are created with TSVD regularization with SVD cutoffs of 0.1%, 0.005%, and 0.0001%, respectively. The volume grid size was 9 mm. The example demonstrates the dramatic effect of regularization and demonstrates the typical tradeoff between too strong regularization (leading to too smeared 3D images that tend to show blurred maxima) and too small regularization (resulting in too superficial 3D images with multiple maxima).

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (43).gif|thumb|350px|'''SVD cutoff 0.1%''': Regularization too strong. No separation between sources, mislocalization towards the middle of the brain.]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (44).gif|thumb|350px|'''SVD cutoff 0.005%''': Appropriate regularization. Separation of the bilateral activities. Location in agreement with the discrete multiple source model.]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (45).gif|thumb|350px|'''SVD cutoff 0.0001%''': Too small regularization. Mislocalization, too superficial 3D image. ]] </li>
</ul></div>

The automatic determination of the regularization constant using the CVE approach does not necessarily result in the optimum regularization parameter either. In this example, the unscaled CVE approach rather resembles the TSVD image with a cutoff of 0.0001%, i.e. regularization is too small. Therefore, it is advisable to compare different settings of the regularization parameter and make the final choice based on the above-mentioned considerations.

== Cortical LORETA ==

Cortical LORETA is principally the same technique as LORETA, however, Cortical LORETA is not computed in a 3D volume, but on the cortical surface.

The cortical reconstruction in BESA Research fed from BESA MRI is a closed 2D surface with no boundaries and a very close approximation of the actual cortical form. It consists of an irregular triangulated grid.

The Laplace operator that is used for identifying a smooth solution in a three-dimensional space is exchanged with a Laplace operator that runs on the two-dimensional cortical surface.

There is a wide variety of 2D Laplace operators with different characteristics. The general form of the discrete Laplace operator is

<math>\Delta f\left( p_{i} \right) = \frac{1}{d_{i}}\sum_{j \in N(i)}^{}{w_{ij}\left\lbrack f\left( p_{i} \right) - f\left( p_{j} \right) \right\rbrack},</math>


where '''pi''' is the '''i-th''' node of the triangular mesh, '''f(pi) '''is the value of a function f defined on the cortical mesh at the node '''pi''', '''wij''' is the weight for the connection between the nodes '''pi''' and '''pj''' and '''di''' is a normalization factor for the '''i-th''' row of the operator. Furthermore, '''N(i)''' is the set of indices corresponding to the direct (also called "1-ring") neighbors of '''pi'''.

BESA offers the choice of three Laplace operators with slightly different characteristics.

* '''Unweighted Graph Laplacian''': This is the simplest operator. It takes into account only the adjacency of the nodes and not the geometry of the mesh:

<math>
w_{ij} =
\begin{cases}
1, & \text{if } p_{i} \text{ and } p_{j} \text{ are connected by an edge} \\
0, & \text{otherwise}
\end{cases}
</math>

<math>d_{i} = 1</math>


[[Image:SA 3Dimaging (4).jpg |450px]]

* '''Weighted Graph Laplacian:''' This operator is similar to the unweighted graph Laplacian but with different weights for the different connections. The connections between nearby nodes get larger weights than the connections between farther nodes:

<math>w_{ij} = \frac{1}{\operatorname{dist}\left( p_{i},p_{j} \right)}</math>

<math>d_{i} = \sum_{j \in N(i)}^{} {\operatorname{dist}\left(p_{i}, p_{j} \right)}</math>


where '''dist''' ('''pi''' , '''pj''') is the distance between the nodes '''pi '''and '''pj'''.

[[Image:SA 3Dimaging (6).jpg|450px]]

* '''Geometric Laplacian with mixed area weights''': This operator takes into account the angles in the corresponding triangles into account as well as the area around the nodes in order to determine the connection weights:

<math>w_{ij} = \frac{\cot\left( \alpha_{ij} \right) + \cot\left( \beta_{ij} \right)}{2}</math>

<math>d_{i} = A_{\text{mixed}}</math>


where '''αij''' and '''βij''' denote the two angles opposite to the edge ('''i , j''') and '''Amixed '''is either the Voronoi area, or 1/2 of the triangle area or 1/4 of the triangle area depending on the type of the triangle.

[[Image:SA 3Dimaging (8).jpg|450px]]

'''Regularization and other parameters:'''

[[Image:SA 3Dimaging (46).gif ‎]]

* '''SVD cutoff''': The regularization for the inverse operator as a percent of the largest singular value.
* '''Depth weighting''': Turn depth weighting on or off.
* '''Laplacian type''': Selection of Laplacian operators (see above).

'''Notes:'''
* '''Starting Cortical LORETA''': Cortical LORETA can be started from the sub-menu '''Surface Image''' of the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]''” for important information on regularization of distributed inverses.

== Cortical CLARA ==

Cortical CLARA is principally the same technique as CLARA, but Cortical CLARA is not computed in a 3D volume, but on the cortical surface. Instead of using a LORETA image as the basis for the iterative application, cortical CLARA uses cortical LORETA.

'''Regularization and other parameters:'''

[[Image:SA 3Dimaging (47).gif]]

* '''SVD cutoff''': The regularization for the inverse operator as a percent of the largest singular value.
* '''Depth weighting''': Turn depth weighting on or off.
* '''Laplacian type''': Selection of Laplacian operators (see Cortical LORETA).
* '''No of iterations''': Number of iterations for CLARA. The more iterations are used, the sparser becomes the solution.
* '''Automatic''': The algorithm tries to determine the number of iterations automatically. The goodness of fit (GOF) is calculated after every iteration and if there is a big jump in the GOF then the algorithm will stop. If no jumps appear during the calculations then CLARA iterates until the specified number of iterations is reached.
* '''Regularize iterations''': If one wants to use different regularization for the CLARA iterations than the value specified as "SVD cutoff", this option should be selected.
* '''Amount to clip from img (%)''': Cortical CLARA uses the solution from the previous iteration as an additional weighting matrix for the current iteration. That weighting matrix is constructed by cutting the "low" activity from the solution. This number specifies how much of the activity should be cut from the previous solution in order to construct the weighting matrix. This value is given as a percentage of the maximal activity. Default value is 10%.

'''Notes:'''

* '''Starting Cortical CLARA:''' Cortical CLARA can be started from the sub-menu '''Surface Image''' of the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]''” for important information on regularization of distributed inverses.

== Cortex Inflation ==

The inflated cortex is a smoothened version of the individual cortical surface with minimal metric distortions (Fischl, B. et al. (1999). Cortical Surface-Based Analysis: II: Inflation, Flattening, and a Surface-Based Coordinate System. ''NeuroImage'', 9(2), 195–207). Gyri and sulci are smoothened out. The original distances between each point on the cortex and its neighbors are, however, mostly preserved.

[[Image:SA 3Dimaging (48).gif]]

''Cortical LORETA map overlaid on top of the inflated cortical surface.''

A lighter gray color overlaid on top of the surface image indicates the location of a gyrus of the individual cortex surface, while a darker gray color indicates the location of a sulcus. The inflated cortical surface can be computed in '''BESA MRI 2.0'''. For more details please refer to the BESA MRI 2.0 help.

== Surface Minimum Norm Image ==

'''Introduction'''

The minimum norm approach is a common method to estimate a distributed electrical current image in the brain at each time sample (Hämäläinen & Ilmoniemi 1984). The source activities of a large number of regional sources are computed. The sources are evenly distributed using 1500 standard locations 10% and 30% below the smoothed standard brain surface (when using the standard MRI) or using between 3000-4000 locations on the individual brain surface defined by the gray-white-matter boundary.

Since the number of sources is much larger than the number of sensors in a minimum norm solution, the inverse problem is highly underdetermined and must be stabilized by a mathematical constraint, the minimum norm. Out of the many current distributions that can account for the recorded sensor data, the solution with the minimum L2 norm, i.e. the minimum total power of the current distribution is displayed in BESA Research.

First, the forward solution (leadfield matrix L) of all sources is calculated in the current head model. Then, the source activities S(t) of all source components are computed from the data matrix D(t) using an inverse regularized by the estimated noise covariance matrix:

<math>\mathrm{S}\left( t \right) = \mathrm{R} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{R} \cdot \mathrm{L}^{T} + \mathrm{C}_N \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed regional source model, CN denotes the noise correlation matrix in sensor space, and R is a weighting matrix in source space. R and CN can be designed in different ways in order to optimize the minimum norm result. The total activity of each regional source is computed as the root mean square of the source activities S(t) of its 3 (MEG:2) components. This total source activity is transformed to a color-coded image of the brain surface. (When the standard brain is used, two sources are assigned to each surface location, located 10% and 30% below the surface, respectively. The color that is displayed on the standard brain surface is the larger of the two corresponding source activities.)

'''Weighting options'''

The minimum norm current imaging techniques of BESA Research provide different weighting strategies. Two weighting approaches are available: Depth weighting and spatio-temporal approaches.
* '''Depth weighting:''' Without depth weighting, deep sources appear very smeared in a minimum-norm reconstruction. With depth weighting, both deep and superficial sources produce a similar, more focal result. If this weighting method is selected, the leadfield of each regional source is scaled with the largest singular value of the SVD (singular value decomposition) of the source's leadfield.
* '''Spatio-temporal weighting''': Spatio-temporal weighting tries to assign large weight to sources that are assumed to be more likely to contribute to the recorded data.
** '''Subspace correlation after single source scan''': This method divides the signal into a signal and a noise subspace. The correlation of the leadfield of a regional source i with the signal subspace (pi) is computed to find out if the source location contributes to the measured data. The weighting matrix R becomes a diagonal matrix. Each of the three (MEG: 2) components of a regional source get the same weighting value pi2. This approach is based on the signal subspace correlation measure introduced by J.C. Mosher, R. M. Leahy (Recursive MUSIC: A Framework for EEG and MEG Source Localization, IEEE Trans. On Biomed. Eng. Vol. 45, No. 11, November 1998)
** '''Dale & Sereno 1993:''' In the approach of Dale and Sereno (J Cogn Neurosci, 1993, 5: 162-176) a signal subspace needs not be defined. The correlation pi of the leadfield of regional source i with the inverse of the data covariance matrix is computed along with the largest singular value λmax of the data covariance matrix. The weighting matrix R is a diagonal matrix with weights: [[Image:SA 3Dimaging (50).gif]]. Each of the three (MEG: 2) components of a regional source receives the same weighting value.

'''Noise regularization'''

Two methods to estimate the channel noise correlation matrix CN are provided by the program:
* '''Use baseline:''' Select this option to estimate the noise from the user-definable baseline. The signal is computed from the data at non-baseline latencies.
* '''Use 15% lowest values:''' The baseline activity is computed from the data at those 15% of all displayed latencies that have the lowest global field power. The signal is computed from all displayed latencies.

In each case, the activity (noise or signal, respectively) is defined as root-mean-square across all respective latencies for each channel.

The noise covariance matrix CN is constructed as a diagonal matrix. The entries in the main diagonal are proportional to the noise activity of the individual channels (if selected) or are all equally proportional to the average noise activity over all channels. The noise covariance matrix CN is then scaled such that the ratio of the Frobenius norms of the weighted leadfield projector matrix (LRLT) and the noise covariance matrix CN equals the Signal-to-Noise ratio. This scaling can be multiplied by an additional factor (default=1) to sharpen (<1) or smoothen (>1) the minimum norm image.

'''Applying the Minimum Norm Image'''

The minimum-norm algorithm is started via the ''Surface minimum norm image dialog box'', which is opened from the''' Image''' menu, or by typing the shortcut '''Ctrl-M''': Please refer to Chapter ''“Surface'' ''Minimum Norm Tab”'' for more details.

As opposed to the other 3D images available from the '''Image '''menu, the surface minimum norm image is not computed on a volumetric grid, but rather for locations on the brain surface. Accordingly, the results of the minimum norm image are displayed superimposed to the brain surface mesh rather than to the volumetric MR image.

The figure below shows a minimum norm image computed from the file '''Examples\Epilepsy\Spikes\Spikes-Child4_EEG+MEG_averaged.fsg'''. The EEG spike peak was imaged using the individual brain surface of the subject. A baseline from -300 to -70 ms was used. Minimum norm was computed with depth weighting, Spatio-temporal weighting according to Dale & Sereno 1993 and individual noise weighting with a noise scale factor of 0.01. The minimum norm image reveals the location of the spike generator in the close vicinity of the frontal left-hemispheric lesion in this subject.

[[Image:SA 3Dimaging (51).gif]]

== Multiple Source Probe Scan (MSPS) ==

 
'''Introduction'''

The MSPS function provides a tool for the validation of a given solution. It is based on the following theoretical consideration: If the recorded EEG/MEG data has been modeled adequately, i.e. all active brain regions are represented by a source in the current solution, then any additional probe source added to the solution will not show any activity apart from noise. The only exception occurs if this probe source is placed in close vicinity to one of the sources in the current solution. In that case, the solution's source and the probe source will share the activity of the corresponding brain area. The MSPS applies these considerations by scanning the brain on a pre-defined grid with a regional probe added to the current solution. Grid extent and density can be specified in the Image settings. The power P of the probe source at location r in the signal interval is compared with the power of the probe source in a reference interval, defining a value q:

<math>\mathrm{q}\left( r \right) = \sqrt{\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}} - 1</math>


MSPS can be computed on time domain or time-frequency domain data:
* In the time domain, q(r) is computed from the source waveform of the probe source. Here, P(r) is the mean power of the probe source at location r in the marked latency range, and Pref(r) is the mean probe source power in the user-definable baseline interval.
* In the time-frequency domain, an MSPS image can be computed from the complex cross spectral density matrices. By applying the inverse operator for a source configuration consisting of the current solution and the probe source, the power of the probe source can be computed for the target interval [P(r)] and the reference time-frequency interval [Pref(r)]. In the resulting MSPS image, q-values are shown in %, where q[%] = q*100.

The inverse operator used to determine the probe source power uses different regularization constants for the probe source and the sources in the current solution. The regularization constant of the sources in the current solution can be specified in the Image settings (default 4%). The regularization constant of the probe source is internally set to 0%.

Alternatively to the definition above, q can also be displayed in units of dB:

<math>\mathrm{q}\left\lbrack \text{dB} \right\rbrack = 10 \cdot \log_{10}\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}</math>


Values of q smaller than zero are not shown in the MSPS image.

According to the considerations above, an MSPS of a correct source model should optimally yield image maxima around the sources in the current solution only. If the MSPS image is blurred or shows maxima at locations different from the modeled sources, this indicates a non-sufficient or incorrect solution.

'''Applying the MSPS'''

This chapter illustrates the application of the Multiple Source Probe Scan. The figures are generated with data from file '''Examples/Epilepsy/Spikes/Rolandic-Spike-Child.fsg''' (-300 : +200 ms, filtered from 3 Hz [forward] to 40 Hz [zero-phase]).

'''Time domain versus time-frequency domain MSPS'''

The multiple source probe scan can be computed in the time domain or the time-frequency domain. The latter is possible only when time-frequency domain data is available for the current condition, i.e. if the condition has been created by starting a multiple source beamformer (MSBF) computation from the source coherence window. In this case, evoking the MSPS calculation from the '''Imaging '''button or from the '''Image''' menu will bring up the following dialog window that allows to choose between time- or time-frequency MSPS. If only time domain data is available, this dialog window will not appear and MSPS will be computed in the time domain.

[[Image:SA 3Dimaging (53).gif]]

For a time-frequency domain MSPS, the target and the reference time-frequency interval have been specified already in the Time-Frequency window (see Chapter "''How To Create Beamformer Images''"). For a time-domain MSPS, the target and the reference epoch have to be specified in the Source Analysis window as described below.

'''Time domain MSPS'''

The time-domain MSPS image displays the ratio of the power of a regional probe source in the signal and the baseline interval. The currently set baseline is indicated by a horizontal line in the upper left corner of the channel box.

[[Image:SA 3Dimaging (54).gif|thumb|c|none|330px|The black horizontal bar in the upper part of the channel box (here circled in red) indicates the baseline interval.]]

By default, BESA Research defines the pre-stimulus interval of the current data segment as baseline. The baseline should represent a latency range in which no event-related activity is present in the data. There are several possibilities to modify the baseline interval: by clicking on the horizontal line with the left mouse button or by using the corresponding entry in the '''Condition '''menu or '''Fit Interval''' popup menu.

Mark an interval to define the target epoch, i.e. the time-interval for which the current solution is to be tested. Start the MSPS by selecting it from the '''Image selection '''button or from the '''Image''' menu to start the probe source scan. The''' Image '''menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window. The 3D window opens and displays the scan result.

<div><ul>
<li style="display: inline-block;"> [[Image:SA 3Dimaging (55).gif|thumb|c|none|650px|This figure shows the MSPS image applied on the three left-hemispheric sources in the solution ''''Rolandic-Spike-Child-RS2.bsa''''. The baseline is set from -300ms to -50 ms. The right-hemispheric sources have been switched off. The fit interval is set to the latency range of large overall activity in the data (-43 ms : 117 ms). A realistic FEM model appropriate for the subject's age (12 years, conductivity ratios (cr) 50) is applied. The MSPS image does not show maxima at the modeled source locations and rather shows a spread q-value distribution.]] </li>

<li style="display: inline-block;"> [[Image:SA 3Dimaging (56).gif|thumb|c|none|650px|The MSPS image for the same latency range when the right-hemispheric sources have been included. The MSPS image appears more focal and shows maxima around the modeled brain regions. This indicates the substantial improvement of the solution by adding the right-hemispheric sources that model the propagation of the epileptic spike from the left to the right hemisphere (note the radiological side convention in the 3D window).]] </li>
</ul></div>

'''Time-Resolved MSPS'''

If the MSPS has been computed on time domain data, the image can be shown separately for each latency in the selected interval. After the MSPS has been computed for the marked epoch, double-click anywhere within this epoch to display the ratio of the probe source magnitude at the selected latency and the mean probe source magnitude in the baseline. Scanning the latency range by moving the cursor (e.g. with the left and right arrow cursor keys) provides a time-resolved MSPS image.

Time-resolved MSPS images are not available if the MSPS has been computed on data in the time-frequency domain.

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (57).gif|thumb|450px|MSPS image of the spike peak activity at 0ms. The activity mainly occurs in the left hemisphere. This fact is illustrated by the source waveforms and confirmed in the MSPS image, which shows a focal maximum around the location of the red sources.]] </li>

<li style="display: inline-block;"> [[File:SA 3Dimaging (58).gif|thumb|450px|Around +27 ms, the spike has propagated to the right hemisphere. This becomes evident from the waveforms of the blue sources, which show a significant latency lag with respect to the first three sources, and from the MSPS image, which shows the maximum around blue sources at this latency.]] </li>
</ul></div>



'''Notes:'''

* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image''' menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the''' Image''' menu.
* For scaling options, please refer to the '''scaling buttons''' popup menu .
* Parameters used for the MSPS calculations can be set in the ''General Settings tab'' of the ''Image Settings dialog box.''

== Source Sensitivity ==

'''Introduction'''

The 'Source sensitivity' function displays the sensitivity of the selected source in the current source model to activity in other brain regions. Sensitivity is defined as the fraction of power at the scanned brain location that is mapped onto the selected source.

To compute the source sensitivity, unit brain activity is modeled at different locations (probe source) throughout the brain. To this data, the current source model is applied to compute the source waveforms SCM of all modeled sources:

<math>\mathrm{S}_{\text{CM}} = \mathrm{L}_{\text{CM}}^{-1} \cdot \mathrm{L}_{\text{PS}}</math>


Here LCM-1 is the regularized inverse operator for the current model, and LPS is the leadfield of the regional probe source (dimension [Nx3] for EEG and [Nx2] for MEG, respectively, where N is the number of sensors). The source amplitude SSS of the selected source in the model is a 3x3 (MEG: 2x2) sub-matrix of SCM (if the selected source is a regional source) or a 1x3-matrix (MEG: 1x2) (if the selected source is a dipole). The root mean square of the singular values of SCM is defined as the source sensitivity.

The 3D source sensitivity image displays this value for all locations on a grid specified under '''Image/Settings'''. Grid density can be specified in the Image Settings.

'''Applying the Source Sensitivity Image'''

The Source Sensitivity image is evoked from the '''Image''' menu or by pressing the corresponding hot key (default: '''V''').

This function is enabled only when a solution with an active selected source is present in the Source Analysis window. The source sensitivity image then displays the sensitivity of the selected source to activity in other brain regions.

[[Image:SA 3Dimaging (59).gif]]

''Source Sensitivity image for the selected frontal source (green) in model ''''''High_Intensity_3RS.bsa'''''' in folder 'Examples/ERP_Auditory_Intensity'. The data displayed is the '100dB' condition in file ''''''All_Subjects_cc.fsg''''''. The selected source is sensitive to activity in the frontal brain region (yellow/white), while it is not influenced by activity in the vicinity of the left and right auditory cortex areas, which are modeled by the red and blue source in the model (transparent/gray).''

'''Notes:'''

* The sensitivity image is independent of the recorded sensor signals. It only depends on the current source model, the sensor configuration, the head model, and the regularization constant.
* If the regularization constant is set to zero, each source has a sensitivity of 100% to activity around its own location. With increasing regularization, the spatial filter becomes less focused, and the sensitivity of a source to activity at its location decreases.
* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image''' menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the '''Image''' menu.

{{BESAManualNav}}

Source Analysis 3D Imaging

2019-03-27T12:41:28Z

Jamie: /* swLORETA */

{{BESAInfobox
|title = Module information
|module = BESA Research Standard or higher
|version = 6.1 or higher
}}


== Overview ==

BESA Research features a set of new functions that provide 3D images that are displayed superimposed to the individual subject's anatomy. This chapter introduces these different images and describe their properties and applications.

The 3D images can be divided into three categories:

'''Volume images:'''

* '''The Multiple Source Beamformer (MSBF)''' is a tool for imaging brain activity. It is applied in the time-domain or time-frequency domain. The beamformer technique in time-frequency domain can image not only evoked, but also induced activity, which is not visible in time-domain averages of the data.
* '''Dynamic Imaging of Coherent Sources (DICS)''' can find coherence between any two pairs of voxels in the brain or between an external source and brain voxels. DICS requires time-frequency-transformed data and can find coherence for evoked and induced activity.

The following imaging methods provide an image of brain activity based on a distributed multiple source model:
* '''CLARA''' is an iterative application of LORETA images, focusing the obtained 3D image in each iteration step.
* '''LAURA '''uses a spatial weighting function that has the form of a local autoregressive function.
* '''LORETA''' has the 3D Laplacian operator implemented as spatial weighting prior.
* '''sLORETA''' is an unweighted minimum norm that is standardized by the resolution matrix.
* '''swLORETA '''is equivalent to sLORETA, except for an additional depth weighting.
* '''SSLOFO '''is an iterative application of standardized minimum norm images with consecutive shrinkage of the source space.
* A '''User-defined volume image''' allows to experiment with the different imaging techniques. It is possible to specify user-defined parameters for the family of distributed source images to create a new imaging technique.
* Bayesian source imaging: '''SESAME''' uses a semi-automated Bayesian approach to estimate the number of dipoles along with their parameters.

'''Surface image:'''

* The '''Surface Minimum Norm Image'''. If no individual MRI is available, the minimum norm image is displayed on a standard brain surface and computed for standard source locations. If available, an individual brain surface is used to construct the distributed source model and to image the brain activity.
* '''Cortical LORETA'''. Unlike classical LORETA, cortical LORETA is not computed in a 3D volume, but on the cortical surface.
* '''Cortical CLARA'''. Unlike classical CLARA, cortical CLARA is not computed in a 3D volume, but on the cortical surface.

'''Discrete model probing:'''

These images do not visualize source activity. Rather, they visualize properties of the currently applied discrete source model:
* The '''Multiple Source Probe Scan (MSPS)''' is a tool for the validation of a discrete multiple source model.
* The '''Source Sensitivity image''' displays the sensitivity of a selected source in the current discrete source model and is therefore data independent.

== Multiple Source Beamformer (MSBF) in the Time-frequency Domain ==

 
'''Short mathematical introduction'''

The BESA beamformer is a modified version of the linearly constrained minimum variance vector beamformer in the time-frequency domain as described in [https://dx.doi.org/10.1073/pnas.98.2.694 Gross et al., "Dynamic imaging of coherent sources: Studying neural interactions in the human brain", PNAS 98, 694-699, 2001]. It allows to image evoked and induced oscillatory activity in a user-defined time-frequency range, where time is taken relative to a triggered event.

The computation is based on a transformation of each channel's single trial data from the time domain into the time-frequency domain. This transformation is performed by the BESA Research Source Coherence module and leads to the complex spectral density Si (f,t), where i is the channel index and f and t denote frequency and time, respectively. Complex cross spectral density matrices C are computed for each trial:

<math>\mathrm{C}_{ij}\left( f,t \right) = \mathrm{S}_{i}\left( f,t \right) \cdot \mathrm{S}_{j}^{*}\left( f,t \right)</math>


The output power P of the beamformer for a specific brain region at location r is then computed by the following equation:

<math>\mathrm{P}\left( r \right) = \operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{-1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{-1}</math>


Here, Cr-1 is the inverse of the SVD-regularized average of Cij(f,t) over trials and the time-frequency range of interest; L is the leadfield matrix of the model containing a regional source at target location r and, optionally, additional sources whose interference with the target source is to be minimized; tr'[] is the trace of the [3×3] (MEG:[2×2]) submatrix of the bracketed expression that corresponds to the source at target location r.

In BESA Research, the output power P(r) is normalized with the output power in a reference time-frequency interval Pref(r). A value q ist defined as follows:

<math> \mathrm{q}\left( r \right) =
\begin{cases}
\sqrt{\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}(r)}} - 1 = \sqrt{\frac{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{\text{ref},r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}} - 1, & \text{for }\mathrm{P}(r) \geq \mathrm{P}_{\text{ref}}(r) \\

1 - \sqrt{\frac{\mathrm{P}_{\text{ref}}\left( r \right)}{\mathrm{P}\left( r \right)}} = 1 - \sqrt{\frac{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{\text{ref},r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}}, & \text{for }\mathrm{P}(r) < \mathrm{P}_{\text{ref}}(r)
\end{cases} </math>


Pref can be computed either from the corresponding frequency range in the baseline of the same condition (i.e. the beamformer images event-related power increase or decrease) or from the corresponding time-frequency range in a control condition (i.e. the beamformer images differences between two conditions). The beamformer image is constructed from values q(r) computed for all locations on a grid specified in the '''General Settings tab'''. For MEG data, the innermost grid points within a sphere of approx. 12% of the head diameter are assigned interpolated rather than calculated values).
q-values are shown in %, where where q[%] = q*100. Alternatively to the definition above, q can also be displayed in units of dB:

<math>\mathrm{q}\left\lbrack \text{dB} \right\rbrack = 10 \cdot \log_{10}\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}</math>


A beamformer operator is designed to pass signals from the brain region of interest r without attenuation, while minimizing interference from activity in all other brain regions. Traditional single-source beamformers are known to mislocalize sources if several brain regions have highly correlated activity. Therefore, the BESA beamformer extends the traditional single-source beamformer in order to implicitly suppress activity from possibly correlated brain regions. This is achieved by using a multiple source beamformer calculation that contains not only the leadfields of the source at the location of interest r, but also those of possibly interfering sources. As a default, BESA Research uses a bilateral beamformer, where specifically contributions from the homologue source in the opposite hemisphere are taken into account (the matrix L thus being of dimension N×6 for EEG and N×4 for MEG, respectively, where N is the number of sensors). This allows for imaging of highly correlated bilateral activity in the two hemispheres that commonly occurs during processing of external stimuli.

In addition, the beamformer computation can take into account possibly correlated sources at arbitrary locations that are specified in the current solution. This is achieved by adding their leadfield vectors to the matrix L in the equation above.

'''Applying the Beamformer'''

This chapter illustrates the usage of the BESA beamformer. The displayed figures are generated using the file ''''Examples/Learn-by-Simulations/AC-Coherence/AC-Osc20.foc'''' (see BESA Tutorial 6: "''Time-frequency analysis and Source coherence''").

'''Starting the beamformer from the time-frequency window'''

The BESA beamformer is applied in the time-frequency domain and therefore requires the Source Coherence module to be enabled. The time-frequency beamformer is especially useful to image in- or decrease of induced oscillatory activity. Induced activity cannot be observed in the averaged data, but shows up as enhanced averaged power in the TSE (Temporal-Spectral Evolution) plot. For instructions on how to initiate a beamformer computation in the time-frequency window, please refer to Chapter '''[[Source_Coherence_How_to...#How_to_Start_the_Beamformer_from_the_Time-Frequency_Window|How to Create Beamformer Images]]'''.

After the beamformer computation has been initiated in the time-frequency window, the source analysis window opens with an enlarged 3D image of the q-value computed with a '''bilateral beamformer'''. The result is superimposed onto the MR image assigned to the data set (individual or standard).

[[Image:SA 3Dimaging (5).gif]]

''Beamformer image after starting the computation in the Time-Frequency window. A bilateral pair of sources in the auditory cortex accounts for the highly correlated oscillatory induced activity. Only the bilateral beamformer manages to separate these activities; a traditional single-source beamformer would merge the two sources into one image maximum in the head center instead.''

'''Multiple source beamformer in the Source Analysis window'''

The 3D imaging display is part of the source analysis window. If you press the '''Restore''' button at the right end of the title bar of the 3D window, the window appears at the bottom right of the source analysis window. In the channel box, the averaged (evoked) data of the selected condition is shown. When a control condition was selected, its average is appended to the average of the target condition.

[[Image:SA 3Dimaging (6).gif]]

''Source Analysis window with beamformer image. The two sources have been added using the '''''Switch to''''' '''''Maximum''''' and '''''Add Source '''''toolbar buttons (see below). Source waveforms are computed from the displayed averaged data. Therefore, they do not represent the activity displayed in the beamformer image, which in this simulation example is induced (i.e. not phase-locked to the trigger)!''

When starting the beamformer from the time-frequency window, a bilateral beamformer scan is performed. In the source analysis window, the beamformer computation can be repeated taking into account possibly correlated sources that are specified in the current solution. Interfering activities generated by all sources in the current solution that are in the 'On' state are specifically suppressed ('''they enter the matrix L in the beamformer calculation''', see Chapter ''Short mathematical description'' above). The computation can be started from the '''Image''' menu or from the '''Image selector button''' dropdown menu. The '''Image''' menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window.

[[Image:SA 3Dimaging (7).gif]]

''Multiple source beamformer image calculated in the presence of a source in the left hemisphere. A '''single''' source scan has been performed. The source set in the current solution accounts for the left-hemispheric q-maximum in the data. Accordingly, the beamformer scan reveals only the as yet unmodeled additional activity in the right hemisphere (note the radiological convention in the 3D image display).''

The beamformer scan can be performed with a '''single''' or a '''bilateral''' source scan. The default scan type depends on the current solution:
* When the beamformer is started from the Time-Frequency window, the Source Analysis window opens with a new solution and a '''bilateral''' beamformer scan is performed.
* When the beamformer is started within the Source Analysis window, the default is
** a scan with a '''single''' source in addition to the sources in the current solution, if at least one source is active.
** a '''bilateral''' scan if no source in the current solution is active.

The default scan type is the multiple source beamformer. The non-default scan type can be enforced using the corresponding ''Volume Image / Beamformer'' entry in the '''Image''' menu.

'''Inserting Sources out of the Beamformer Image'''

The beamformer image can be used to add sources to the current solution. A simple double-click anywhere in the 2D- or 3D-view will generate a non-oriented regional source at the corresponding location. However, a better and easier way to create sources at image maxima and minima is to use the toolbar buttons '''Switch to Maximum''' [[Image:SA 3Dimaging (8).gif]] and '''Add Source''' [[Image:SA 3Dimaging (9).gif]].

Use the '''Switch to Maximum''' button to place the red crosshair of the 3D window onto a local image maximum or minimum. Hitting the '''Add Source''' button creates a regional source at the location of the crosshair and therefore ensures the exact placement of the source at the image extremum. Moreover, the '''Add Source''' button generates an oriented regional source. BESA Research automatically estimates the source orientation that contributes most to the power in the target time-frequency interval (or the reference time-frequency interval, if its power is larger than that in the target interval). The accuracy of this orientation estimate depends largely on the noise content of the data. The smaller the signal-to-noise ratio of the data, the lower is the accuracy of the orientation estimate. '''This feature allows to use the beamformer as a tool to create a source montage for source coherence analysis, where it is of advantage to work with oriented sources'''.

'''Notes:'''

* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image '''menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the''' Image''' menu.
* For scaling options, use the [[Image:SA 3Dimaging (10).gif]] and [[Image:SA 3Dimaging (11).gif]] '''Image Scale toolbar''' buttons.
* Parameters used for the beamformer calculations can be set in the '''Standard Volumes''' of the ''Image Settings dialog box.''

== Dynamic Imaging of Coherent Sources (DICS) ==

 
'''Short mathematical introduction'''

Dynamic Imaging of Coherent Sources (DICS) is a sophisticated method for imaging cortico-cortical coherence in the brain, or coherence between an external reference (e.g. EMG channel) and cortical structures. DICS can be applied to localize evoked as well as induced coherent cortical activity in a user-defined time-frequency range.

DICS was implemented in BESA closely following [https://dx.doi.org/10.1073/pnas.98.2.694 Gross et al., "Dynamic imaging of coherent sources: Studying neural interactions in the human brain", PNAS 98, 694-699, 2001].

The computation is based on a transformation of each channel's single trial data from the time domain into the frequency domain. This transformation is performed by the BESA Research Coherence module and results in the complex spectral density matrix that is used for constructing the spatial filter similar to beamforming.

DICS computation yields a 3-D image, each voxel being assigned a coherence value. Coherence values can be described as a neural activity index and do not have a unit. The neural activity index contrasts coherence in a target time-frequency bin with coherence of the same time-frequency bin in a baseline.

'''DICS for cortico-cortical coherence is computed as follows:'''

Let L(r) be the leadfield in voxel r in the brain and C the complex cross-spectral density matrix. The spatial filter W(r) for the voxel r in the head is defined as follows:

<math>W\left( r \right) = \left\lbrack L^{T}\left( r \right) \cdot C^{- 1} \cdot L\left( r \right) \right\rbrack^{- 1} \cdot L^{T}(r) \cdot C^{- 1}</math>


The cross-spectrum between two locations (voxels) r1 and r2 in the head are calculated with the following equation:

<math>C_{s}\left( r_{1},r_{2} \right) = W\left( r_{1} \right) \cdot C \cdot W^{*T}\left( r_{2} \right),</math>


where <nowiki>*T</nowiki> means the transposed complex conjugate of a matrix. The cross-spectral density can then be calculated from the cross spectrum as follows:

<math>c_{s}\left( r_{1},r_{2} \right) = \lambda_{1}\left\{ C_{s}\left( r_{1},r_{2} \right) \right\},</math>


where λ1{} indicates the largest singular value of the cross spectrum. Once the cross spectral density is estimated, the connectivity¹(CON) between the two brain regions r1 and r2 are calculated as follows:

<math>\text{CON}\left( r_{1},r_{2} \right) = \frac{c_{s}^{\text{sig}}\left( r_{1},r_{2} \right) - c_{s}^{\text{bl}}(r_{1},r_{2})}{c_{s}^{\text{sig}}\left( r_{1},r_{2} \right) + c_{s}^{\text{bl}}(r_{1},r_{2})},</math>


where cssig is the cross-spectral density for the signal of interest between the two brain regions r1 and r2, and csbl is the corresponding cross spectral density for the baseline or the control condition, respectively. In the case DICS is computed with a cortical reference, r1 is the reference region (voxel) and remains constant while r2 scans all the grid points within the brain sequentially. In that way, the connectivity between the reference brain region and all other brain regions is estimated. The value of CON(r1, r2) falls in the interval [-1 1]. If the cross-spectral density for the baseline is 0 the connectivity value will be 1. If the cross-spectral density for the signal is 0 the connectivity value will be -1.

¹ Here, the term connectivity is used rather than coherence, as strictly speaking the coherence equation is defined slightly differently. For simplicity reasons the rest of the tutorial uses the term coherence.

'''DICS for cortico-muscular coherence is computed as follows:'''

When using an external reference, the equation for coherence calculation is slightly different compared to the equation for cortico-cortical coherence. First of all, the cross-spectral density matrix is not only computed for the MEG/EEG channels, but the external reference channel is added. This resulting matrix is Call. In this case, the cross-spectral density between the reference signal and all other MEG/EEG

channels is called cref. It is only one column of Call. Hence, the cross-spectrum in voxel r is calculated with the following equation:

<math>C_{s}\left( r \right) = W\left( r \right) \cdot c_{\text{ref}}</math>


and the corresponding cross-spectral density is calculated as the sum of squares of Cs:

<math>c_{s}\left( r \right) = \sum_{i = 1}^{n}{C_{s}\left( r \right)_{i}^{2}},</math>


where n is 2 for MEG and 3 for EEG. This equation can also be described as the squared Euclidean norm of the cross-spectrum:

<math>c_{s}\left( r \right) = \left\| C_{s} \right\|^{2},</math>


The power in voxel r is calculated as in the cortico-cortical case:

<math>p\left( r \right) = \lambda_{1}\left\{ C_{s}(r,r) \right\}.</math>


At last, coherence between the external reference and cortical activity is calculated with the equation:

<math>\text{CON}\left( r \right) = \frac{c_{s}(r)}{p\left( r \right) \cdot C_{\text{all}}(k,k)},</math>


where Call(k, k) is the (k,k)-th diagonal element of the matrix Call.

DICS is particularly useful, if coherence is to be calculated without an a-priory source model (in contrast to source coherence based on pre-defined source montages). However, the recommended analysis strategy for DICS is to use a brain source as a starting point for coherence calculation that is known to contribute to the EEG/MEG signal of interest. For example, one might first run a beamformer on the time-frequency range of interest and use the voxel with the strongest oscillatory activity as a starting point for DICS. The resulting coherence image will again lead to several maxima (ordered by magnitude), which in turn can serve as starting points for DICS calculation. This way, it is possible to detect even weak sources that show coherent activity in the given time-frequency range.

The other significant application for DICS is estimating coherence between an external source and voxels in the brain. For example, an external source can be muscle activity recoded by an electrode placed over the according peripheral region. This way, the direct relationship between muscle activity and brain activation can be measured.

'''Starting DICS computation from the Time-Frequency Window'''

DICS is particularly useful, if coherence in a user-defined time-frequency bin (evoked or induced) is to be calculated between any two brain regions or between an external reference and the brain. DICS runs only on time-frequency decomposed data, so time-frequency analysis needs to be run before starting DICS computation.

To start the DICS computation, left-drag a window over a selected time-frequency bin in the Time-Frequency Window. Right-click and select “Image”. A dialogue will open (see fig. 1) prompting you to specify time and frequency settings as well as the baseline period. It is recommended to use a baseline period of equal length as the data period of interest. Make sure to select “DICS” in the top row and press “'''Go'''”.

[[Image:SA 3Dimaging (21).gif|450px|thumb|c|none|Fig. 1: Time and frequency settings for DICS and MSBF]]

Next, a window will appear allowing you to specify the reference source for coherence calculation (see fig. 2). It is possible to select a channel (e.g. EMG) or a brain source. If a brain source is chosen and no source analysis was computed beforehand, the option “Use current cross-hair position” must be chosen. In case discrete source analysis was computed previously, the selected source can be chosen as the reference for DICS. Please note that DICS can be re-computed with any cross-hair or source position at a later stage.

[[Image:SA 3Dimaging (1).jpg|400px|thumb|c|none|Fig. 2: Possible options for choosing the reference]]

Confirming with “'''OK'''” will start computation of coherence between the selected channel/voxel and all other brain voxels. In case DICS is computed for a reference source in the brain, it can be advantageous to run a beamforming analysis in the selected time-frequency window first and use one of the beamforming maxima as reference for DICS. Fig. 3 shows an example for DICS calculation.

[[Image:SA 3Dimaging (22).gif|500px|thumb|c|none|Fig. 3: Coherence between left-hemispheric auditory areas and the selected voxel in the right auditory cortex.]]

Coherence values range between -1 and 1. If coherence in the signal is much larger than coherence in the baseline (control condition) then the DICS value is going to approach 1. Contrary, if coherence in the baseline is much larger than coherence in the signal, then the DICS value is going to approach -1. At last, if coherence in the signal is equal to coherence in the baseline, then the DICS value is 0.

In case DICS is to be re-computed with a different reference, simply mark the desired reference position by placing the cross-hair in the anatomical view and select “DICS” in the middle panel of the source analysis window (see Fig. 4). In case an external reference is to be selected, click on “DICS” in the middle panel to bring up the DICS dialogue (see. Fig. 2) and select the desired channel. Please note that DICS computation will only be available after running time-frequency analysis.

[[Image:SA 3Dimaging (23).gif|700px|thumb|c|none|Fig. 4: Integration of DICS in the Source Analysis window]]

== Multiple Source Beamformer (MSBF) in the Time Domain ==
''(requires Besa Research 7.0 or higher)''

===Short mathematical introduction===

Beamforming approach can be also applied in the time domain data. This approach was introduced as linearly constrained minimum variance (LCMV) beamformer (Van Veen et al., 1997). It allows to image evoked activity in a user-defined time range, where time is taken relative to a triggered event, and to estimate source waveforms using the calculated spatial weight at locations of interest. For an implementation of the beamformer in the time domain, data covariance matrices are required, while complex cross spectral density matrices are used for the beamformer approaches in the time-frequency domain as described in the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section.

The bilateral beamformer introduced in the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section is also implemented for the time-domain beamformer to take into account contributions from the homologue source in the opposite. This allows for imaging of highly correlated bilateral activity in the two hemispheres that commonly occurs during processing of external stimuli. In addition, the beamformer computation can take into account possibly correlated sources at arbitrary locations.
The beamformer spatial weight W(r) for the voxel r in the brain is defined as follows (Van Veen et al., 1997):

[[File:MSBF1.png]]

where '''C-1''' is the inversed regularized average of covariance matrix over trials, '''L''' is the leadfield matrix of the model containing a regional source at target location r and optionally
additional sources whose interference with the target source is to be minimized. The beamformer spatial weight '''W'''(r) can be applied to the measured data to estimate source
waveform at a location r (beamformer virtual sensor):

[[File:MSBF2.png]]

where '''S'''(r,t) represents the estimated source waveform and '''M'''(t) represents measured EEG or MEG signals.
The output power P of the beamformer for a specific brain region at location r is computed by the following equation:

[[File:MSBF3.png]]

where tr’[ ] is the trace of the [3×3] (MEG: [2×2]) submatrix of the bracketed expression that corresponds to the source at target location r.
Beamformer can suppress noise sources that are correlated across sensors. However, uncorrelated noise will be amplified in a spatially non-uniform manner, with increasing
distortion with increasing distance from the sensors (Van Veen et al., 1997; Sekihara et al., 2001). For this reason, estimated source power should be normalized by a noise power.
In BESA Research, the output power P(r) is normalized with the output power in a baseline interval or with the output power of a uncorrelated noise: P(r) / Pref (r).
The time-domain beamformer image is constructed from values q(r) computed for all locations on a grid specified in the '''General Settings''' tab. A value q(r) is defined as described in
the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section with data covariance matrices instead of cross-spectral density matrices.

===Applying the Beamformer===

This chapter illustrates the usage of the BESA beamformer in the time domain. The displayed figures are generated using the file ‘Examples/ERP-Auditory-Intensity/S1.cnt’.

'''Starting the time-domain beamformer from the Average tab of the Paradigm dialog box'''

The time-domain beamformer is needed data covariance matrices and therefore requires the ERP module to be enabled. After the beamformer computation has been initiated in the
'''Average tab of the Paradigm dialog box''', the source analysis window opens with an enlarged 3D image of the q-value computed with a bilateral beamformer. The result is
superimposed onto the MR image assigned to the data set (individual or standard).

[[File:MSBF44.png]]

''Beamformer image for auditory evoked data after starting the computation in the '''Average tab of the Paradigm dialog box'''. The bilateral beamformer manages to separate the
activities in auditory areas, while a traditional single-source beamformer would merge the two sources into one image maximum in the head center instead.''

'''Multiple-source beamformer in the Source Analysis window'''

The 3D imaging display is part of the source analysis window. In the Channel box, the averaged (evoked) data of the selected condition is shown. Selected covariance intervals in
the ERP module can be checked in the Channel box. The red, gray, and blue rectangles indicate signal, baseline, and common interval, respectively.

[[File:MSBF55.png]]

''Source Analysis window with beamformer image. The two beamformer virtual sensors have been added using the Switch to Maximum and Add Source toolbar buttons (see below).
Source waveforms are computed using the beamformer spatial weights and the displayed averaged data (the noise normalized weights (5% noise) option was used to compute the
beamformer image).''

When starting the beamformer from the '''Average tab of the Paradigm dialog box''', the bilateral beamformer scan is performed. In the source analysis window, the beamformer computation can be repeated taking into account possibly correlated sources that are specified in the current solution. Interfering activities generated by all sources in the current solution that are in the 'On' state are specifically suppressed (they enter the leadfield matrix L in the beamformer calculation). The computation can be started from the '''Image''' menu or from the Image selector button [[File:MSBF_Button.png|22px|Image: 22 pixels]] dropdown menu. The Image menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window.

[[File:MSBF66.png]]

''Multiple-source beamformer image calculated in the presence of a source in the left hemisphere. A single-source scan has been performed instead of a bilateral beamforemr. The
source set in the current solution accounts for the left-hemispheric q-maximum in the data. Accordingly, the beamformer scan reveals only the as yet unmodeled additional activity in
the right hemisphere (note the radiological convention in the 3D image display). The source waveform of the beamformer virtual sensor in the left hemisphere is not shown since the
location (blue square in the figure) is not considered for the multiple-source beamformer.''

The beamformer scan can be performed with a single or a bilateral source scan. The default scan type depends on the current solution:
When the beamformer is started from the '''Average tab of the Paradigm dialog box''' the Source Analysis window opens with a new solution and a bilateral beamformer scan is
performed.
When the beamformer is started within the Source Analysis window, the default is:

* a scan with a single source in addition to the sources in the current solution, if at least one source is active.
* a bilateral scan if no source in the current solution is active.
* a scan with a single source when scalar-type beamformer is selected in the '''beamformer option dialog box'''.

The default scan type is the multiple source beamformer. The non-default scan type can be enforced using the corresponding Volume Image / Beamformer entry in the Image main
menu or in the beamformer option dialog box (only for the time-domain beamformer).

===Inserting Sources as Beamformer Virtual Sensor out of the Beamformer Image===

This is similar to the inserting sources out of the beamformer image in Multiple Source Beamformer (MSBF) in the Time-frequency Domain section.
The beamformer image can be used to add beamformer virtual sensors to the current solution. A simple double-click anywhere in the 3D view (not in the 2D view) will generate a
source at the corresponding location. A better and easier way to create sources at image maxima and minima is to use the toolbar buttons '''Switch to Maximum''' and '''Add Source'''

This feature allows to use the beamformer as a tool to create a source montage for '''source coherence''' analysis. A source montage file (*.mtg) for beamformer virtual sensors can
be saved using File \ Save Source Montage As… entry.

The time-domain beamformer image can be also used to add regional or dipole sources to the current solution. Press '''N''' key when there is no source in the current source array or
there is more than one beamformer virtual sensor. To create a new source array for beamformer virtual sensor, press '''N''' key when there is more than one regional or dipole source in
the current source array.

===Notes===

* You can hide or re-display the last computed image by selecting ''Hide Image'' entry in the '''Image''' menu.
* The current image can be exported to ASCII, ANALYZE, or BrainVoyager (vmp) format from the '''Image''' menu.
* For scaling options, use the and Image Scale toolbar buttons.
* Parameters used for the beamformer calculations can be set in the '''Standard Volume tab of the Image Settings dialog box'''.
* Note that Model, Residual, Order, and Residual variance are not shown for the beamformer virtual sensor type sources.

===References===

* Sekihara, K., Nagarajan, S. S., Poeppel, D., Marantz, A., & Miyashita, Y. (2001). Reconstructing spatio-temporal activities of neural sources using an MEG vector beamformer technique. IEEE Transactions on Biomedical Engineering, 48(7), 760–771.

* Van Veen, B. D., Van Drongelen, W., Yuchtman, M., & Suzuki, A. (1997). Localization of brain electrical activity via linearly constrained minimum variance spatial filtering. IEEE Transactions on Biomedical Engineering, 44(9), 867–880

== CLARA ==

CLARA ('Classical LORETA Analysis Recursively Applied') is an iterative application of weighted LORETA images with a reduced source space in each iteration.

In an initialization step, a LORETA image is calculated. Then in each iteration the following steps are performed:

# The obtained image is spatially smoothed (this step is left out in the first iteration).
# All grid points with amplitudes below a threshold of 1% of the maximum activity are set to zero, thus being effectively eliminated from the source space in the following step.
# The resulting image defines a spatial weighting term (for each voxel the corresponding image amplitude).
# A LORETA image is computed with an additional spatial weighting term for each voxel as computed in step 3. By the default settings in BESA Research, the regularization values used in the iteration steps are slightly higher than that of the initialization LORETA image.

The procedure stops after 2 iterations, and the image computed in the last iteration is displayed. Please note that you can change all parameters by creating a user-defined volume image.

The advantage of CLARA over non-focusing distributed imaging methods is visualized by the figure below. Both images are computed from the N100 response in an auditory oddball experiment (file '''Oddball.fsg''' in subfolder ''fMRI+EEG-RT-Experiment'' of the ''Examples'' folder). The CLARA image is much more focal than the sLORETA image, making it easier to determine the location of the image maxima.

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (24).gif|thumb|350px|sLORETA image]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (25).gif|thumb|350px|CLARA image]] </li>
</ul></div>

'''Notes:'''

* Starting CLARA: CLARA can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter ''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]'' for important information on regularization of distributed inverses.

== LAURA ==

LAURA (Local Auto Regressive Average) belongs to the distributed inverse method of the family of weighted minimum norm methods ([https://doi.org/10.1023/A:1012944913650 Grave de Peralta Menendeza et al., "Noninvasive Localization of Electromagnetic Epileptic Activity. I. Method Descriptions and Simulations", BrainTopography 14(2), 131-137, 2001]). LAURA uses a spatial weighting function that includes depth weighting and that term has the form of a local autoregressive function.

The source activity is estimated by applying the general formula for a weighted minimum norm:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T}\left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings.''

In LAURA, V contains both a depth weighting term W and a representation of a local autoregressive function A. V is computed as:

<math>\mathrm{V} = \left( \mathrm{U}^{T} \cdot \mathrm{U} \right)^{-1}</math>


Where

<math>\mathrm{U} = \left( \mathrm{W} \cdot \mathrm{A} \right) \otimes \mathrm{I}_{3}</math>


Here, <math>\otimes</math> denotes the Kronecker product. I3 is the [3×3] identity matrix. W is an [s×s] diagonal matrix (with s the number of source locations on the grid), where each diagonal element is the inverse of the maximum singular value of the corresponding regional source's leadfields. The formula for the diagonal components Aii and the off-diagonal components Aik are as follows:

<math>\mathrm{A}_{ii} = \frac{26}{\mathrm{N}_{i}}\sum_{k \subset V_{i}}^{}\frac{1}{\mathrm{d}_{ik}^{2}}</math>


<math>
\mathrm{A}_{ik} =
\begin{cases}
- 1/\operatorname{dist}\left( i,k \right)^{2}, & \text{if } k \subset V_{i} \\
0, & \text{otherwise}
\end{cases}
</math>


Here, Vi is the vicinity around grid point i that includes the 26 direct neighbors.

The LAURA image in BESA Research displays the norm of the 3 components of S at each location r. Using the menu function ''Image / Export Image As... ''you have the option to save this norm of S or alternatively all components separately to disk.

'''Notes:'''

* '''Grid spacing:''' Due to memory limitations, LAURA images require a grid spacing of 7 mm or more.
* '''Computation time:''' Computation speed during the first LAURA image calculation depends on the grid spacing (computation is faster with larger grid spacing). After the first computation of a LAURA image, a '''*.laura''' file is stored in the data folder, containing intermediate results of the LAURA inverse. This file is used during all subsequent LAURA image computations. Thereby, the time needed to obtain the image is substantially reduced.
* '''MEG:''' In the case of MEG data, an additional constraint is implemented in the LAURA algorithm that prevents solutions from containing radial source currents (compare Pascual-Marqui, ISBET Newsletter 1995, 22-29). In MEG, an additional source space regularization is necessary in the inverse matrix operation required compute V
* '''Starting LAURA:''' LAURA can be started from the''' Image''' menu or from the '''Image Selection''' button.
* '''Regularization:''' Please refer to Chapter'' “Regularization of distributed volume images” ''for important information on regularization of distributed inverses.

== LORETA ==

LORETA ("Low Resolution Electromagnetic Tomography") is a distributed inverse method of the family of ''weighted minimum norm'' methods. LORETA was suggested by R.D. Pascual-Marqui (International Journal of Psychophysiology. 1994, 18:49-65). LORETA is characterized by a smoothness constraint, represented by a discrete 3D Laplacian.

The source activity is estimated by applying the general formula for a weighted minimum norm:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T}\left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings.''

In LORETA, V contains both a depth weighting term and a representation of the 3D Laplacian matrix. V is computed as:

<math>\mathrm{V} = \left( \mathrm{U}^{T} \cdot \mathrm{U} \right)^{- 1}</math>


where

<math>\mathrm{U} = \left( \mathrm{W} \cdot \mathrm{A} \right) \otimes \mathrm{I}_{3}</math>


Here, <math>\otimes</math> denotes the Kronecker product. I3 is the [3x3] identity matrix. W is an [sxs] diagonal matrix (with s the number of source locations on the grid), where each diagonal element is the inverse of the maximum singular value of the corresponding regional source's leadfields. A contains the 3D Laplacian and is computed as

<math>\mathrm{A} = \mathrm{Y} - \mathrm{I}_{s}</math>


with Is the [sxs] identity matrix, where s is the number of sources (= three times the number of grid points) and

<math>\mathrm{Y} = \frac{1}{2}\left\{ \mathrm{I}_{s} + \left\lbrack \operatorname{diag}\left( \mathrm{Z} \cdot \left\lbrack 111 \ldots 1 \right\rbrack^{T} \right) \right\rbrack^{- 1} \right\} \cdot \mathrm{Z}</math>


where

<math>
\mathrm{Z}_{ik} =
\begin{cases}
1/6, & \text{if } \operatorname{dist}\left( i,k \right) = 1 \text{ grid point} \\
0, & \text{otherwise}
\end{cases}
</math>


The LORETA image in BESA Research displays the norm of the 3 components of S at each location r. Using the menu function ''Image / Export Image As... ''you have the option to save this norm of S or alternatively all components separately to disk.

'''Notes:'''
* '''Grid spacing:''' Due to memory limitations, LORETA images require a grid spacing of 5 mm or more.
* '''Computation time:''' Computation speed during the first LORETA image calculation depends on the grid spacing (computation is faster with larger grid spacing). After the first computation of a LORETA image, a '''<nowiki>*.loreta</nowiki>''' file is stored in the data folder, containing intermediate results of the LORETA inverse. This file is used during all subsequent LORETA image computations. Thereby, the time needed to obtain the image is substantially reduced.
* '''MEG''': In the case of MEG data, an additional constraint is implemented in the LORETA algorithm that prevents solutions from containing radial source currents (Pascual-Marqui, ISBET Newsletter 1995, 22-29). In MEG, an additional source space regularization is necessary in the inverse matrix operation required compute V.
* '''Starting LORETA:''' LORETA can be started from the''' Image''' menu or from the '''Image Selection '''button.
* '''Regularization:''' Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed source models.

== sLORETA ==

This distributed inverse method consists of a ''standardized, unweighted minimum norm''. The method was originally suggested by R.D. Pascual-Marqui (Methods & Findings in Experimental & Clinical Pharmacology 2002, 24D:5-12) Starting point is an unweighted minimum norm computation:

<math>\mathrm{S}_{\text{MN}}\left( t \right) = \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings''.

This minimum norm estimate is now standardized to produce the sLORETA activity at a certain brain location r:

<math>\mathrm{S}_{\text{sLORETA}, r} = \mathrm{R}_{rr}^{-1/2} \cdot \mathrm{S}_{\text{MN},r}</math>


SsMN,r is the [3x1] (MEG: [2x1]) minimum norm estimate of the 3 (MEG: 2) dipoles at location r. Rrr is the [3x3] (MEG: [2x2]) diagonal block of the resolution matrix R that corresponds to the source components at the target location r. The resolution matrix is defined as:

<math>\mathrm{R} = \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{L}^{T} + \lambda \cdot \mathrm{I} \right)^{-1} \cdot \mathrm{L}</math>


The sLORETA image in BESA Research displays the norm of SsLORETA, r at each location r. Using the menu function ''Image / Export Image As...'' you have the option to save this norm of SsLORETA, r or alternatively all components separately to disk.

'''Notes:'''

* sLORETA can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== swLORETA ==

This distributed inverse method is a ''standardized, depth-weighted minimum norm'' (E. Palmero-Soler et al 2007 Phys. Med. Biol. 52 1783-1800). It differs from sLORETA only by an additional depth weighting.

Starting point is a depth-weighted minimum norm computation:

<math>\mathrm{S}_{\text{MN}}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings''.

V is the diagonal depth weighting matrix. For s grid locations, V is of dimension [3s x 3s] (MEG: [2s x 2s]). Each diagonal element of V is the inverse of the first singular value of the leadfield of the corresponding regional source. Hence, the first 3 (MEG: 2) diagonal elements equal the inverse of the largest eigenvalue of the leadfield matrix of regional source 1, and so on.

This minimum norm estimate is now standardized to produce the swLORETA activity at a certain brain location r:

<math>\mathrm{S}_{\text{swLORETA},r} = \mathrm{R}_{rr}^{-1/2} \cdot \mathrm{S}_{\text{MN},r}</math>


SsMN,r is the [3x1] (MEG: [2x1]) depth-weighted minimum norm estimate of the regional source at location r. Rrr is the [3x3] (MEG: [2x2]) diagonal block of the resolution matrix R that corresponds to the source components at the target location r. The resolution matrix is defined as:

<math>\mathrm{R} = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} + \lambda \cdot \mathrm{I} \right)^{-1} \cdot \mathrm{L}</math>


The swLORETA image in BESA Research displays the norm of SswLORETA, r at each location r. Using the menu function ''Image / Export Image As...'' you have the option to save this norm of SswLORETA, r or alternatively all components separately to disk.

'''Notes:'''

* sLORETA can be started from the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== sSLOFO ==

SSLOFO (standardized shrinking LORETA-FOCUSS) is an iterative application of weighted distributed source images with a reduced source space in each iteration ([https://dx.doi.org/10.1109/TBME.2005.855720 Liu et al., "Standardized shrinking LORETA-FOCUSS (SSLOFO): a new algorithm for spatio-temporal EEG source reconstruction", IEEE Transactions on Biomedical Engineering 52(10), 1681-1691, 2005]).

In an initialization step, an [[#sLORETA | sLORETA]] image is calculated. Then in each iteration the following steps are performed:

# A weighted minimum norm solution is computed according to the formula <math display="inline">\mathrm{S} = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}</math> . Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D is the data at the time point under consideration. V is a diagonal spatial weighting matrix that is computed in the previous iteration step. In the first iteration, the elements of V contain the magnitudes of the initially computed LORETA image.
# Standardization of this weighted minimum norm image is performed with the resolution matrix as in [[#sLORETA | sLORETA]].
# The obtained standardized weighted minimum norm image is being smoothed to get Ssmooth.
# All voxels with amplitudes below a threshold of 1% of the maximum activity get a weight of zero in the next iteration step, thus being effectively eliminated from the source space in the next iteration step.
# For all other voxels, compute the elements of the spatial weighting matrix V to be used in the next iteration as follows: <math display="inline">\mathrm{V}_{ii,\text{next iteration}} = \frac{1}{\left\| \mathrm{L}_{i} \right\|} \cdot \mathrm{S}_{ii,\text{smooth}} \cdot \mathrm{V}_{ii,\text{current iteration}}</math>



The procedure stops after 3 iterations. Please note that you can change all parameters by creating a [[#User-Defined Volume Image | user-defined volume image]].

'''Notes:'''
* '''Starting sSLOFO''': sSLOFO can be started from the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter ''[[#Regularization of distributed volume images | Regularization of distributed volume images]]'' for important information on regularization of distributed inverses.

== User-Defined Volume Image ==

In addition to the predefined 3D imaging methods in BESA Research, it is possible to create user-defined imaging methods based on the general formula for distributed inverses:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. Custom-defined parameters are:* The spatial weighting matrix V: This may include depth weighting, image weighting, or cross-voxel weighting with a 3D Laplacian (as in LORETA) or an autoregressive function (as in LAURA).

* Regularization: The term in parentheses is generally regularized. Note that regularization has a strong effect on the obtained results. Please refer to chapter “''Regularization of Distributed Volume Images” ''for more information.
* Standardization: Optionally, the result of the distributed inverse can be standardized with the resolution matrix (as in sLORETA).
* Iterations: Inverse computations can be applied iteratively. Each iteration is weighted with the image obtained in the previous iteration.

All parameters for the user-defined volume image are specified in the User-Defined Volume Tab of the Image Settings dialog box. Please refer to chapter “''User-Defined Volume Tab”'' for details.

'''Notes:'''
* Starting the user-defined volume image: the image calculation can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== Regularization of distributed volume images ==

Distributed source images require the inversion of a term of the form L V LT. This term is generally regularized before its inversion. In BESA Research, selection can be made between two different regularization approaches (parameters are defined in the ''Image Settings dialog box''):

* '''Tikhonov regularization''': In Tikhonov regularization, the term L V LT is inverted as (L V LT +λ I)-1. Here, l is the regularization constant, and I is the identity matrix.
* One way of determining the optimum regularization constant is by minimizing the ''generalized cross'' ''validation error'' (CVE).
* Alternatively, the regularization constant can be specified manually as a percentage of the trace of the matrix L V LT.
* '''TSVD''': In the truncated singular value decomposition (TSVD) approach, an SVD decomposition of L V LT is computed as  L V LT = U S UT, where the diagonal matrix S contains the singular values. All singular values smaller than the specified percentage of the maximum singular values are set to zero. The inverse is computed as U S-1 UT, where the diagonal elements of S-1 are the inverse of the corresponding non-zero diagonal elements of S.

Regularization has a critical effect on the obtained distributed source images. The results may differ completely with different choices of the regularization parameter (see examples below). Therefore, it is important to evaluate the generated image critically with respect to the regularization constant, and to keep in mind the uncertainties resulting from this fact when interpreting the results. The default setting in BESA Research is a TSVD regularization with a 0.03% threshold. However, this value might need to be adjusted to the specific data set at hand.

The following example illustrates the influence of the regularization parameter on the obtained images. The data used here is condition '''St-Cor of dataset Examples \ TFC-Error-Related-Negativity \ Correct+Error.fsg''' at 176 ms following the visual stimulus. Discrete dipole analysis reveals the main activity in the left and right lateral visual cortex at this latency.

[[Image:SA 3Dimaging (42).gif]]

''Discrete source model at 176 ms: Main activity in the left and right lateral visual cortex, no visual midline activity.''

LORETA images computed at this latency depend critically on the choice of the regularization constant. The following 3D images are created with TSVD regularization with SVD cutoffs of 0.1%, 0.005%, and 0.0001%, respectively. The volume grid size was 9 mm. The example demonstrates the dramatic effect of regularization and demonstrates the typical tradeoff between too strong regularization (leading to too smeared 3D images that tend to show blurred maxima) and too small regularization (resulting in too superficial 3D images with multiple maxima).

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (43).gif|thumb|350px|'''SVD cutoff 0.1%''': Regularization too strong. No separation between sources, mislocalization towards the middle of the brain.]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (44).gif|thumb|350px|'''SVD cutoff 0.005%''': Appropriate regularization. Separation of the bilateral activities. Location in agreement with the discrete multiple source model.]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (45).gif|thumb|350px|'''SVD cutoff 0.0001%''': Too small regularization. Mislocalization, too superficial 3D image. ]] </li>
</ul></div>

The automatic determination of the regularization constant using the CVE approach does not necessarily result in the optimum regularization parameter either. In this example, the unscaled CVE approach rather resembles the TSVD image with a cutoff of 0.0001%, i.e. regularization is too small. Therefore, it is advisable to compare different settings of the regularization parameter and make the final choice based on the above-mentioned considerations.

== Cortical LORETA ==

Cortical LORETA is principally the same technique as LORETA, however, Cortical LORETA is not computed in a 3D volume, but on the cortical surface.

The cortical reconstruction in BESA Research fed from BESA MRI is a closed 2D surface with no boundaries and a very close approximation of the actual cortical form. It consists of an irregular triangulated grid.

The Laplace operator that is used for identifying a smooth solution in a three-dimensional space is exchanged with a Laplace operator that runs on the two-dimensional cortical surface.

There is a wide variety of 2D Laplace operators with different characteristics. The general form of the discrete Laplace operator is

<math>\Delta f\left( p_{i} \right) = \frac{1}{d_{i}}\sum_{j \in N(i)}^{}{w_{ij}\left\lbrack f\left( p_{i} \right) - f\left( p_{j} \right) \right\rbrack},</math>


where '''pi''' is the '''i-th''' node of the triangular mesh, '''f(pi) '''is the value of a function f defined on the cortical mesh at the node '''pi''', '''wij''' is the weight for the connection between the nodes '''pi''' and '''pj''' and '''di''' is a normalization factor for the '''i-th''' row of the operator. Furthermore, '''N(i)''' is the set of indices corresponding to the direct (also called "1-ring") neighbors of '''pi'''.

BESA offers the choice of three Laplace operators with slightly different characteristics.

* '''Unweighted Graph Laplacian''': This is the simplest operator. It takes into account only the adjacency of the nodes and not the geometry of the mesh:

<math>
w_{ij} =
\begin{cases}
1, & \text{if } p_{i} \text{ and } p_{j} \text{ are connected by an edge} \\
0, & \text{otherwise}
\end{cases}
</math>

<math>d_{i} = 1</math>


[[Image:SA 3Dimaging (4).jpg |450px]]

* '''Weighted Graph Laplacian:''' This operator is similar to the unweighted graph Laplacian but with different weights for the different connections. The connections between nearby nodes get larger weights than the connections between farther nodes:

<math>w_{ij} = \frac{1}{\operatorname{dist}\left( p_{i},p_{j} \right)}</math>

<math>d_{i} = \sum_{j \in N(i)}^{} {\operatorname{dist}\left(p_{i}, p_{j} \right)}</math>


where '''dist''' ('''pi''' , '''pj''') is the distance between the nodes '''pi '''and '''pj'''.

[[Image:SA 3Dimaging (6).jpg|450px]]

* '''Geometric Laplacian with mixed area weights''': This operator takes into account the angles in the corresponding triangles into account as well as the area around the nodes in order to determine the connection weights:

<math>w_{ij} = \frac{\cot\left( \alpha_{ij} \right) + \cot\left( \beta_{ij} \right)}{2}</math>

<math>d_{i} = A_{\text{mixed}}</math>


where '''αij''' and '''βij''' denote the two angles opposite to the edge ('''i , j''') and '''Amixed '''is either the Voronoi area, or 1/2 of the triangle area or 1/4 of the triangle area depending on the type of the triangle.

[[Image:SA 3Dimaging (8).jpg|450px]]

'''Regularization and other parameters:'''

[[Image:SA 3Dimaging (46).gif ‎]]

* '''SVD cutoff''': The regularization for the inverse operator as a percent of the largest singular value.
* '''Depth weighting''': Turn depth weighting on or off.
* '''Laplacian type''': Selection of Laplacian operators (see above).

'''Notes:'''
* '''Starting Cortical LORETA''': Cortical LORETA can be started from the sub-menu '''Surface Image''' of the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]''” for important information on regularization of distributed inverses.

== Cortical CLARA ==

Cortical CLARA is principally the same technique as CLARA, but Cortical CLARA is not computed in a 3D volume, but on the cortical surface. Instead of using a LORETA image as the basis for the iterative application, cortical CLARA uses cortical LORETA.

'''Regularization and other parameters:'''

[[Image:SA 3Dimaging (47).gif]]

* '''SVD cutoff''': The regularization for the inverse operator as a percent of the largest singular value.
* '''Depth weighting''': Turn depth weighting on or off.
* '''Laplacian type''': Selection of Laplacian operators (see Cortical LORETA).
* '''No of iterations''': Number of iterations for CLARA. The more iterations are used, the sparser becomes the solution.
* '''Automatic''': The algorithm tries to determine the number of iterations automatically. The goodness of fit (GOF) is calculated after every iteration and if there is a big jump in the GOF then the algorithm will stop. If no jumps appear during the calculations then CLARA iterates until the specified number of iterations is reached.
* '''Regularize iterations''': If one wants to use different regularization for the CLARA iterations than the value specified as "SVD cutoff", this option should be selected.
* '''Amount to clip from img (%)''': Cortical CLARA uses the solution from the previous iteration as an additional weighting matrix for the current iteration. That weighting matrix is constructed by cutting the "low" activity from the solution. This number specifies how much of the activity should be cut from the previous solution in order to construct the weighting matrix. This value is given as a percentage of the maximal activity. Default value is 10%.

'''Notes:'''

* '''Starting Cortical CLARA:''' Cortical CLARA can be started from the sub-menu '''Surface Image''' of the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]''” for important information on regularization of distributed inverses.

== Cortex Inflation ==

The inflated cortex is a smoothened version of the individual cortical surface with minimal metric distortions (Fischl, B. et al. (1999). Cortical Surface-Based Analysis: II: Inflation, Flattening, and a Surface-Based Coordinate System. ''NeuroImage'', 9(2), 195–207). Gyri and sulci are smoothened out. The original distances between each point on the cortex and its neighbors are, however, mostly preserved.

[[Image:SA 3Dimaging (48).gif]]

''Cortical LORETA map overlaid on top of the inflated cortical surface.''

A lighter gray color overlaid on top of the surface image indicates the location of a gyrus of the individual cortex surface, while a darker gray color indicates the location of a sulcus. The inflated cortical surface can be computed in '''BESA MRI 2.0'''. For more details please refer to the BESA MRI 2.0 help.

== Surface Minimum Norm Image ==

'''Introduction'''

The minimum norm approach is a common method to estimate a distributed electrical current image in the brain at each time sample (Hämäläinen & Ilmoniemi 1984). The source activities of a large number of regional sources are computed. The sources are evenly distributed using 1500 standard locations 10% and 30% below the smoothed standard brain surface (when using the standard MRI) or using between 3000-4000 locations on the individual brain surface defined by the gray-white-matter boundary.

Since the number of sources is much larger than the number of sensors in a minimum norm solution, the inverse problem is highly underdetermined and must be stabilized by a mathematical constraint, the minimum norm. Out of the many current distributions that can account for the recorded sensor data, the solution with the minimum L2 norm, i.e. the minimum total power of the current distribution is displayed in BESA Research.

First, the forward solution (leadfield matrix L) of all sources is calculated in the current head model. Then, the source activities S(t) of all source components are computed from the data matrix D(t) using an inverse regularized by the estimated noise covariance matrix:

<math>\mathrm{S}\left( t \right) = \mathrm{R} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{R} \cdot \mathrm{L}^{T} + \mathrm{C}_N \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed regional source model, CN denotes the noise correlation matrix in sensor space, and R is a weighting matrix in source space. R and CN can be designed in different ways in order to optimize the minimum norm result. The total activity of each regional source is computed as the root mean square of the source activities S(t) of its 3 (MEG:2) components. This total source activity is transformed to a color-coded image of the brain surface. (When the standard brain is used, two sources are assigned to each surface location, located 10% and 30% below the surface, respectively. The color that is displayed on the standard brain surface is the larger of the two corresponding source activities.)

'''Weighting options'''

The minimum norm current imaging techniques of BESA Research provide different weighting strategies. Two weighting approaches are available: Depth weighting and spatio-temporal approaches.
* '''Depth weighting:''' Without depth weighting, deep sources appear very smeared in a minimum-norm reconstruction. With depth weighting, both deep and superficial sources produce a similar, more focal result. If this weighting method is selected, the leadfield of each regional source is scaled with the largest singular value of the SVD (singular value decomposition) of the source's leadfield.
* '''Spatio-temporal weighting''': Spatio-temporal weighting tries to assign large weight to sources that are assumed to be more likely to contribute to the recorded data.
** '''Subspace correlation after single source scan''': This method divides the signal into a signal and a noise subspace. The correlation of the leadfield of a regional source i with the signal subspace (pi) is computed to find out if the source location contributes to the measured data. The weighting matrix R becomes a diagonal matrix. Each of the three (MEG: 2) components of a regional source get the same weighting value pi2. This approach is based on the signal subspace correlation measure introduced by J.C. Mosher, R. M. Leahy (Recursive MUSIC: A Framework for EEG and MEG Source Localization, IEEE Trans. On Biomed. Eng. Vol. 45, No. 11, November 1998)
** '''Dale & Sereno 1993:''' In the approach of Dale and Sereno (J Cogn Neurosci, 1993, 5: 162-176) a signal subspace needs not be defined. The correlation pi of the leadfield of regional source i with the inverse of the data covariance matrix is computed along with the largest singular value λmax of the data covariance matrix. The weighting matrix R is a diagonal matrix with weights: [[Image:SA 3Dimaging (50).gif]]. Each of the three (MEG: 2) components of a regional source receives the same weighting value.

'''Noise regularization'''

Two methods to estimate the channel noise correlation matrix CN are provided by the program:
* '''Use baseline:''' Select this option to estimate the noise from the user-definable baseline. The signal is computed from the data at non-baseline latencies.
* '''Use 15% lowest values:''' The baseline activity is computed from the data at those 15% of all displayed latencies that have the lowest global field power. The signal is computed from all displayed latencies.

In each case, the activity (noise or signal, respectively) is defined as root-mean-square across all respective latencies for each channel.

The noise covariance matrix CN is constructed as a diagonal matrix. The entries in the main diagonal are proportional to the noise activity of the individual channels (if selected) or are all equally proportional to the average noise activity over all channels. The noise covariance matrix CN is then scaled such that the ratio of the Frobenius norms of the weighted leadfield projector matrix (LRLT) and the noise covariance matrix CN equals the Signal-to-Noise ratio. This scaling can be multiplied by an additional factor (default=1) to sharpen (<1) or smoothen (>1) the minimum norm image.

'''Applying the Minimum Norm Image'''

The minimum-norm algorithm is started via the ''Surface minimum norm image dialog box'', which is opened from the''' Image''' menu, or by typing the shortcut '''Ctrl-M''': Please refer to Chapter ''“Surface'' ''Minimum Norm Tab”'' for more details.

As opposed to the other 3D images available from the '''Image '''menu, the surface minimum norm image is not computed on a volumetric grid, but rather for locations on the brain surface. Accordingly, the results of the minimum norm image are displayed superimposed to the brain surface mesh rather than to the volumetric MR image.

The figure below shows a minimum norm image computed from the file '''Examples\Epilepsy\Spikes\Spikes-Child4_EEG+MEG_averaged.fsg'''. The EEG spike peak was imaged using the individual brain surface of the subject. A baseline from -300 to -70 ms was used. Minimum norm was computed with depth weighting, Spatio-temporal weighting according to Dale & Sereno 1993 and individual noise weighting with a noise scale factor of 0.01. The minimum norm image reveals the location of the spike generator in the close vicinity of the frontal left-hemispheric lesion in this subject.

[[Image:SA 3Dimaging (51).gif]]

== Multiple Source Probe Scan (MSPS) ==

 
'''Introduction'''

The MSPS function provides a tool for the validation of a given solution. It is based on the following theoretical consideration: If the recorded EEG/MEG data has been modeled adequately, i.e. all active brain regions are represented by a source in the current solution, then any additional probe source added to the solution will not show any activity apart from noise. The only exception occurs if this probe source is placed in close vicinity to one of the sources in the current solution. In that case, the solution's source and the probe source will share the activity of the corresponding brain area. The MSPS applies these considerations by scanning the brain on a pre-defined grid with a regional probe added to the current solution. Grid extent and density can be specified in the Image settings. The power P of the probe source at location r in the signal interval is compared with the power of the probe source in a reference interval, defining a value q:

<math>\mathrm{q}\left( r \right) = \sqrt{\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}} - 1</math>


MSPS can be computed on time domain or time-frequency domain data:
* In the time domain, q(r) is computed from the source waveform of the probe source. Here, P(r) is the mean power of the probe source at location r in the marked latency range, and Pref(r) is the mean probe source power in the user-definable baseline interval.
* In the time-frequency domain, an MSPS image can be computed from the complex cross spectral density matrices. By applying the inverse operator for a source configuration consisting of the current solution and the probe source, the power of the probe source can be computed for the target interval [P(r)] and the reference time-frequency interval [Pref(r)]. In the resulting MSPS image, q-values are shown in %, where q[%] = q*100.

The inverse operator used to determine the probe source power uses different regularization constants for the probe source and the sources in the current solution. The regularization constant of the sources in the current solution can be specified in the Image settings (default 4%). The regularization constant of the probe source is internally set to 0%.

Alternatively to the definition above, q can also be displayed in units of dB:

<math>\mathrm{q}\left\lbrack \text{dB} \right\rbrack = 10 \cdot \log_{10}\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}</math>


Values of q smaller than zero are not shown in the MSPS image.

According to the considerations above, an MSPS of a correct source model should optimally yield image maxima around the sources in the current solution only. If the MSPS image is blurred or shows maxima at locations different from the modeled sources, this indicates a non-sufficient or incorrect solution.

'''Applying the MSPS'''

This chapter illustrates the application of the Multiple Source Probe Scan. The figures are generated with data from file '''Examples/Epilepsy/Spikes/Rolandic-Spike-Child.fsg''' (-300 : +200 ms, filtered from 3 Hz [forward] to 40 Hz [zero-phase]).

'''Time domain versus time-frequency domain MSPS'''

The multiple source probe scan can be computed in the time domain or the time-frequency domain. The latter is possible only when time-frequency domain data is available for the current condition, i.e. if the condition has been created by starting a multiple source beamformer (MSBF) computation from the source coherence window. In this case, evoking the MSPS calculation from the '''Imaging '''button or from the '''Image''' menu will bring up the following dialog window that allows to choose between time- or time-frequency MSPS. If only time domain data is available, this dialog window will not appear and MSPS will be computed in the time domain.

[[Image:SA 3Dimaging (53).gif]]

For a time-frequency domain MSPS, the target and the reference time-frequency interval have been specified already in the Time-Frequency window (see Chapter "''How To Create Beamformer Images''"). For a time-domain MSPS, the target and the reference epoch have to be specified in the Source Analysis window as described below.

'''Time domain MSPS'''

The time-domain MSPS image displays the ratio of the power of a regional probe source in the signal and the baseline interval. The currently set baseline is indicated by a horizontal line in the upper left corner of the channel box.

[[Image:SA 3Dimaging (54).gif|thumb|c|none|330px|The black horizontal bar in the upper part of the channel box (here circled in red) indicates the baseline interval.]]

By default, BESA Research defines the pre-stimulus interval of the current data segment as baseline. The baseline should represent a latency range in which no event-related activity is present in the data. There are several possibilities to modify the baseline interval: by clicking on the horizontal line with the left mouse button or by using the corresponding entry in the '''Condition '''menu or '''Fit Interval''' popup menu.

Mark an interval to define the target epoch, i.e. the time-interval for which the current solution is to be tested. Start the MSPS by selecting it from the '''Image selection '''button or from the '''Image''' menu to start the probe source scan. The''' Image '''menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window. The 3D window opens and displays the scan result.

<div><ul>
<li style="display: inline-block;"> [[Image:SA 3Dimaging (55).gif|thumb|c|none|650px|This figure shows the MSPS image applied on the three left-hemispheric sources in the solution ''''Rolandic-Spike-Child-RS2.bsa''''. The baseline is set from -300ms to -50 ms. The right-hemispheric sources have been switched off. The fit interval is set to the latency range of large overall activity in the data (-43 ms : 117 ms). A realistic FEM model appropriate for the subject's age (12 years, conductivity ratios (cr) 50) is applied. The MSPS image does not show maxima at the modeled source locations and rather shows a spread q-value distribution.]] </li>

<li style="display: inline-block;"> [[Image:SA 3Dimaging (56).gif|thumb|c|none|650px|The MSPS image for the same latency range when the right-hemispheric sources have been included. The MSPS image appears more focal and shows maxima around the modeled brain regions. This indicates the substantial improvement of the solution by adding the right-hemispheric sources that model the propagation of the epileptic spike from the left to the right hemisphere (note the radiological side convention in the 3D window).]] </li>
</ul></div>

'''Time-Resolved MSPS'''

If the MSPS has been computed on time domain data, the image can be shown separately for each latency in the selected interval. After the MSPS has been computed for the marked epoch, double-click anywhere within this epoch to display the ratio of the probe source magnitude at the selected latency and the mean probe source magnitude in the baseline. Scanning the latency range by moving the cursor (e.g. with the left and right arrow cursor keys) provides a time-resolved MSPS image.

Time-resolved MSPS images are not available if the MSPS has been computed on data in the time-frequency domain.

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (57).gif|thumb|450px|MSPS image of the spike peak activity at 0ms. The activity mainly occurs in the left hemisphere. This fact is illustrated by the source waveforms and confirmed in the MSPS image, which shows a focal maximum around the location of the red sources.]] </li>

<li style="display: inline-block;"> [[File:SA 3Dimaging (58).gif|thumb|450px|Around +27 ms, the spike has propagated to the right hemisphere. This becomes evident from the waveforms of the blue sources, which show a significant latency lag with respect to the first three sources, and from the MSPS image, which shows the maximum around blue sources at this latency.]] </li>
</ul></div>



'''Notes:'''

* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image''' menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the''' Image''' menu.
* For scaling options, please refer to the '''scaling buttons''' popup menu .
* Parameters used for the MSPS calculations can be set in the ''General Settings tab'' of the ''Image Settings dialog box.''

== Source Sensitivity ==

'''Introduction'''

The 'Source sensitivity' function displays the sensitivity of the selected source in the current source model to activity in other brain regions. Sensitivity is defined as the fraction of power at the scanned brain location that is mapped onto the selected source.

To compute the source sensitivity, unit brain activity is modeled at different locations (probe source) throughout the brain. To this data, the current source model is applied to compute the source waveforms SCM of all modeled sources:

<math>\mathrm{S}_{\text{CM}} = \mathrm{L}_{\text{CM}}^{-1} \cdot \mathrm{L}_{\text{PS}}</math>


Here LCM-1 is the regularized inverse operator for the current model, and LPS is the leadfield of the regional probe source (dimension [Nx3] for EEG and [Nx2] for MEG, respectively, where N is the number of sensors). The source amplitude SSS of the selected source in the model is a 3x3 (MEG: 2x2) sub-matrix of SCM (if the selected source is a regional source) or a 1x3-matrix (MEG: 1x2) (if the selected source is a dipole). The root mean square of the singular values of SCM is defined as the source sensitivity.

The 3D source sensitivity image displays this value for all locations on a grid specified under '''Image/Settings'''. Grid density can be specified in the Image Settings.

'''Applying the Source Sensitivity Image'''

The Source Sensitivity image is evoked from the '''Image''' menu or by pressing the corresponding hot key (default: '''V''').

This function is enabled only when a solution with an active selected source is present in the Source Analysis window. The source sensitivity image then displays the sensitivity of the selected source to activity in other brain regions.

[[Image:SA 3Dimaging (59).gif]]

''Source Sensitivity image for the selected frontal source (green) in model ''''''High_Intensity_3RS.bsa'''''' in folder 'Examples/ERP_Auditory_Intensity'. The data displayed is the '100dB' condition in file ''''''All_Subjects_cc.fsg''''''. The selected source is sensitive to activity in the frontal brain region (yellow/white), while it is not influenced by activity in the vicinity of the left and right auditory cortex areas, which are modeled by the red and blue source in the model (transparent/gray).''

'''Notes:'''

* The sensitivity image is independent of the recorded sensor signals. It only depends on the current source model, the sensor configuration, the head model, and the regularization constant.
* If the regularization constant is set to zero, each source has a sensitivity of 100% to activity around its own location. With increasing regularization, the spatial filter becomes less focused, and the sensitivity of a source to activity at its location decreases.
* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image''' menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the '''Image''' menu.

{{BESAManualNav}}

Source Analysis 3D Imaging

2019-03-27T12:40:34Z

Jamie: /* sLORETA */

{{BESAInfobox
|title = Module information
|module = BESA Research Standard or higher
|version = 6.1 or higher
}}


== Overview ==

BESA Research features a set of new functions that provide 3D images that are displayed superimposed to the individual subject's anatomy. This chapter introduces these different images and describe their properties and applications.

The 3D images can be divided into three categories:

'''Volume images:'''

* '''The Multiple Source Beamformer (MSBF)''' is a tool for imaging brain activity. It is applied in the time-domain or time-frequency domain. The beamformer technique in time-frequency domain can image not only evoked, but also induced activity, which is not visible in time-domain averages of the data.
* '''Dynamic Imaging of Coherent Sources (DICS)''' can find coherence between any two pairs of voxels in the brain or between an external source and brain voxels. DICS requires time-frequency-transformed data and can find coherence for evoked and induced activity.

The following imaging methods provide an image of brain activity based on a distributed multiple source model:
* '''CLARA''' is an iterative application of LORETA images, focusing the obtained 3D image in each iteration step.
* '''LAURA '''uses a spatial weighting function that has the form of a local autoregressive function.
* '''LORETA''' has the 3D Laplacian operator implemented as spatial weighting prior.
* '''sLORETA''' is an unweighted minimum norm that is standardized by the resolution matrix.
* '''swLORETA '''is equivalent to sLORETA, except for an additional depth weighting.
* '''SSLOFO '''is an iterative application of standardized minimum norm images with consecutive shrinkage of the source space.
* A '''User-defined volume image''' allows to experiment with the different imaging techniques. It is possible to specify user-defined parameters for the family of distributed source images to create a new imaging technique.
* Bayesian source imaging: '''SESAME''' uses a semi-automated Bayesian approach to estimate the number of dipoles along with their parameters.

'''Surface image:'''

* The '''Surface Minimum Norm Image'''. If no individual MRI is available, the minimum norm image is displayed on a standard brain surface and computed for standard source locations. If available, an individual brain surface is used to construct the distributed source model and to image the brain activity.
* '''Cortical LORETA'''. Unlike classical LORETA, cortical LORETA is not computed in a 3D volume, but on the cortical surface.
* '''Cortical CLARA'''. Unlike classical CLARA, cortical CLARA is not computed in a 3D volume, but on the cortical surface.

'''Discrete model probing:'''

These images do not visualize source activity. Rather, they visualize properties of the currently applied discrete source model:
* The '''Multiple Source Probe Scan (MSPS)''' is a tool for the validation of a discrete multiple source model.
* The '''Source Sensitivity image''' displays the sensitivity of a selected source in the current discrete source model and is therefore data independent.

== Multiple Source Beamformer (MSBF) in the Time-frequency Domain ==

 
'''Short mathematical introduction'''

The BESA beamformer is a modified version of the linearly constrained minimum variance vector beamformer in the time-frequency domain as described in [https://dx.doi.org/10.1073/pnas.98.2.694 Gross et al., "Dynamic imaging of coherent sources: Studying neural interactions in the human brain", PNAS 98, 694-699, 2001]. It allows to image evoked and induced oscillatory activity in a user-defined time-frequency range, where time is taken relative to a triggered event.

The computation is based on a transformation of each channel's single trial data from the time domain into the time-frequency domain. This transformation is performed by the BESA Research Source Coherence module and leads to the complex spectral density Si (f,t), where i is the channel index and f and t denote frequency and time, respectively. Complex cross spectral density matrices C are computed for each trial:

<math>\mathrm{C}_{ij}\left( f,t \right) = \mathrm{S}_{i}\left( f,t \right) \cdot \mathrm{S}_{j}^{*}\left( f,t \right)</math>


The output power P of the beamformer for a specific brain region at location r is then computed by the following equation:

<math>\mathrm{P}\left( r \right) = \operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{-1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{-1}</math>


Here, Cr-1 is the inverse of the SVD-regularized average of Cij(f,t) over trials and the time-frequency range of interest; L is the leadfield matrix of the model containing a regional source at target location r and, optionally, additional sources whose interference with the target source is to be minimized; tr'[] is the trace of the [3×3] (MEG:[2×2]) submatrix of the bracketed expression that corresponds to the source at target location r.

In BESA Research, the output power P(r) is normalized with the output power in a reference time-frequency interval Pref(r). A value q ist defined as follows:

<math> \mathrm{q}\left( r \right) =
\begin{cases}
\sqrt{\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}(r)}} - 1 = \sqrt{\frac{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{\text{ref},r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}} - 1, & \text{for }\mathrm{P}(r) \geq \mathrm{P}_{\text{ref}}(r) \\

1 - \sqrt{\frac{\mathrm{P}_{\text{ref}}\left( r \right)}{\mathrm{P}\left( r \right)}} = 1 - \sqrt{\frac{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{\text{ref},r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}}, & \text{for }\mathrm{P}(r) < \mathrm{P}_{\text{ref}}(r)
\end{cases} </math>


Pref can be computed either from the corresponding frequency range in the baseline of the same condition (i.e. the beamformer images event-related power increase or decrease) or from the corresponding time-frequency range in a control condition (i.e. the beamformer images differences between two conditions). The beamformer image is constructed from values q(r) computed for all locations on a grid specified in the '''General Settings tab'''. For MEG data, the innermost grid points within a sphere of approx. 12% of the head diameter are assigned interpolated rather than calculated values).
q-values are shown in %, where where q[%] = q*100. Alternatively to the definition above, q can also be displayed in units of dB:

<math>\mathrm{q}\left\lbrack \text{dB} \right\rbrack = 10 \cdot \log_{10}\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}</math>


A beamformer operator is designed to pass signals from the brain region of interest r without attenuation, while minimizing interference from activity in all other brain regions. Traditional single-source beamformers are known to mislocalize sources if several brain regions have highly correlated activity. Therefore, the BESA beamformer extends the traditional single-source beamformer in order to implicitly suppress activity from possibly correlated brain regions. This is achieved by using a multiple source beamformer calculation that contains not only the leadfields of the source at the location of interest r, but also those of possibly interfering sources. As a default, BESA Research uses a bilateral beamformer, where specifically contributions from the homologue source in the opposite hemisphere are taken into account (the matrix L thus being of dimension N×6 for EEG and N×4 for MEG, respectively, where N is the number of sensors). This allows for imaging of highly correlated bilateral activity in the two hemispheres that commonly occurs during processing of external stimuli.

In addition, the beamformer computation can take into account possibly correlated sources at arbitrary locations that are specified in the current solution. This is achieved by adding their leadfield vectors to the matrix L in the equation above.

'''Applying the Beamformer'''

This chapter illustrates the usage of the BESA beamformer. The displayed figures are generated using the file ''''Examples/Learn-by-Simulations/AC-Coherence/AC-Osc20.foc'''' (see BESA Tutorial 6: "''Time-frequency analysis and Source coherence''").

'''Starting the beamformer from the time-frequency window'''

The BESA beamformer is applied in the time-frequency domain and therefore requires the Source Coherence module to be enabled. The time-frequency beamformer is especially useful to image in- or decrease of induced oscillatory activity. Induced activity cannot be observed in the averaged data, but shows up as enhanced averaged power in the TSE (Temporal-Spectral Evolution) plot. For instructions on how to initiate a beamformer computation in the time-frequency window, please refer to Chapter '''[[Source_Coherence_How_to...#How_to_Start_the_Beamformer_from_the_Time-Frequency_Window|How to Create Beamformer Images]]'''.

After the beamformer computation has been initiated in the time-frequency window, the source analysis window opens with an enlarged 3D image of the q-value computed with a '''bilateral beamformer'''. The result is superimposed onto the MR image assigned to the data set (individual or standard).

[[Image:SA 3Dimaging (5).gif]]

''Beamformer image after starting the computation in the Time-Frequency window. A bilateral pair of sources in the auditory cortex accounts for the highly correlated oscillatory induced activity. Only the bilateral beamformer manages to separate these activities; a traditional single-source beamformer would merge the two sources into one image maximum in the head center instead.''

'''Multiple source beamformer in the Source Analysis window'''

The 3D imaging display is part of the source analysis window. If you press the '''Restore''' button at the right end of the title bar of the 3D window, the window appears at the bottom right of the source analysis window. In the channel box, the averaged (evoked) data of the selected condition is shown. When a control condition was selected, its average is appended to the average of the target condition.

[[Image:SA 3Dimaging (6).gif]]

''Source Analysis window with beamformer image. The two sources have been added using the '''''Switch to''''' '''''Maximum''''' and '''''Add Source '''''toolbar buttons (see below). Source waveforms are computed from the displayed averaged data. Therefore, they do not represent the activity displayed in the beamformer image, which in this simulation example is induced (i.e. not phase-locked to the trigger)!''

When starting the beamformer from the time-frequency window, a bilateral beamformer scan is performed. In the source analysis window, the beamformer computation can be repeated taking into account possibly correlated sources that are specified in the current solution. Interfering activities generated by all sources in the current solution that are in the 'On' state are specifically suppressed ('''they enter the matrix L in the beamformer calculation''', see Chapter ''Short mathematical description'' above). The computation can be started from the '''Image''' menu or from the '''Image selector button''' dropdown menu. The '''Image''' menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window.

[[Image:SA 3Dimaging (7).gif]]

''Multiple source beamformer image calculated in the presence of a source in the left hemisphere. A '''single''' source scan has been performed. The source set in the current solution accounts for the left-hemispheric q-maximum in the data. Accordingly, the beamformer scan reveals only the as yet unmodeled additional activity in the right hemisphere (note the radiological convention in the 3D image display).''

The beamformer scan can be performed with a '''single''' or a '''bilateral''' source scan. The default scan type depends on the current solution:
* When the beamformer is started from the Time-Frequency window, the Source Analysis window opens with a new solution and a '''bilateral''' beamformer scan is performed.
* When the beamformer is started within the Source Analysis window, the default is
** a scan with a '''single''' source in addition to the sources in the current solution, if at least one source is active.
** a '''bilateral''' scan if no source in the current solution is active.

The default scan type is the multiple source beamformer. The non-default scan type can be enforced using the corresponding ''Volume Image / Beamformer'' entry in the '''Image''' menu.

'''Inserting Sources out of the Beamformer Image'''

The beamformer image can be used to add sources to the current solution. A simple double-click anywhere in the 2D- or 3D-view will generate a non-oriented regional source at the corresponding location. However, a better and easier way to create sources at image maxima and minima is to use the toolbar buttons '''Switch to Maximum''' [[Image:SA 3Dimaging (8).gif]] and '''Add Source''' [[Image:SA 3Dimaging (9).gif]].

Use the '''Switch to Maximum''' button to place the red crosshair of the 3D window onto a local image maximum or minimum. Hitting the '''Add Source''' button creates a regional source at the location of the crosshair and therefore ensures the exact placement of the source at the image extremum. Moreover, the '''Add Source''' button generates an oriented regional source. BESA Research automatically estimates the source orientation that contributes most to the power in the target time-frequency interval (or the reference time-frequency interval, if its power is larger than that in the target interval). The accuracy of this orientation estimate depends largely on the noise content of the data. The smaller the signal-to-noise ratio of the data, the lower is the accuracy of the orientation estimate. '''This feature allows to use the beamformer as a tool to create a source montage for source coherence analysis, where it is of advantage to work with oriented sources'''.

'''Notes:'''

* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image '''menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the''' Image''' menu.
* For scaling options, use the [[Image:SA 3Dimaging (10).gif]] and [[Image:SA 3Dimaging (11).gif]] '''Image Scale toolbar''' buttons.
* Parameters used for the beamformer calculations can be set in the '''Standard Volumes''' of the ''Image Settings dialog box.''

== Dynamic Imaging of Coherent Sources (DICS) ==

 
'''Short mathematical introduction'''

Dynamic Imaging of Coherent Sources (DICS) is a sophisticated method for imaging cortico-cortical coherence in the brain, or coherence between an external reference (e.g. EMG channel) and cortical structures. DICS can be applied to localize evoked as well as induced coherent cortical activity in a user-defined time-frequency range.

DICS was implemented in BESA closely following [https://dx.doi.org/10.1073/pnas.98.2.694 Gross et al., "Dynamic imaging of coherent sources: Studying neural interactions in the human brain", PNAS 98, 694-699, 2001].

The computation is based on a transformation of each channel's single trial data from the time domain into the frequency domain. This transformation is performed by the BESA Research Coherence module and results in the complex spectral density matrix that is used for constructing the spatial filter similar to beamforming.

DICS computation yields a 3-D image, each voxel being assigned a coherence value. Coherence values can be described as a neural activity index and do not have a unit. The neural activity index contrasts coherence in a target time-frequency bin with coherence of the same time-frequency bin in a baseline.

'''DICS for cortico-cortical coherence is computed as follows:'''

Let L(r) be the leadfield in voxel r in the brain and C the complex cross-spectral density matrix. The spatial filter W(r) for the voxel r in the head is defined as follows:

<math>W\left( r \right) = \left\lbrack L^{T}\left( r \right) \cdot C^{- 1} \cdot L\left( r \right) \right\rbrack^{- 1} \cdot L^{T}(r) \cdot C^{- 1}</math>


The cross-spectrum between two locations (voxels) r1 and r2 in the head are calculated with the following equation:

<math>C_{s}\left( r_{1},r_{2} \right) = W\left( r_{1} \right) \cdot C \cdot W^{*T}\left( r_{2} \right),</math>


where <nowiki>*T</nowiki> means the transposed complex conjugate of a matrix. The cross-spectral density can then be calculated from the cross spectrum as follows:

<math>c_{s}\left( r_{1},r_{2} \right) = \lambda_{1}\left\{ C_{s}\left( r_{1},r_{2} \right) \right\},</math>


where λ1{} indicates the largest singular value of the cross spectrum. Once the cross spectral density is estimated, the connectivity¹(CON) between the two brain regions r1 and r2 are calculated as follows:

<math>\text{CON}\left( r_{1},r_{2} \right) = \frac{c_{s}^{\text{sig}}\left( r_{1},r_{2} \right) - c_{s}^{\text{bl}}(r_{1},r_{2})}{c_{s}^{\text{sig}}\left( r_{1},r_{2} \right) + c_{s}^{\text{bl}}(r_{1},r_{2})},</math>


where cssig is the cross-spectral density for the signal of interest between the two brain regions r1 and r2, and csbl is the corresponding cross spectral density for the baseline or the control condition, respectively. In the case DICS is computed with a cortical reference, r1 is the reference region (voxel) and remains constant while r2 scans all the grid points within the brain sequentially. In that way, the connectivity between the reference brain region and all other brain regions is estimated. The value of CON(r1, r2) falls in the interval [-1 1]. If the cross-spectral density for the baseline is 0 the connectivity value will be 1. If the cross-spectral density for the signal is 0 the connectivity value will be -1.

¹ Here, the term connectivity is used rather than coherence, as strictly speaking the coherence equation is defined slightly differently. For simplicity reasons the rest of the tutorial uses the term coherence.

'''DICS for cortico-muscular coherence is computed as follows:'''

When using an external reference, the equation for coherence calculation is slightly different compared to the equation for cortico-cortical coherence. First of all, the cross-spectral density matrix is not only computed for the MEG/EEG channels, but the external reference channel is added. This resulting matrix is Call. In this case, the cross-spectral density between the reference signal and all other MEG/EEG

channels is called cref. It is only one column of Call. Hence, the cross-spectrum in voxel r is calculated with the following equation:

<math>C_{s}\left( r \right) = W\left( r \right) \cdot c_{\text{ref}}</math>


and the corresponding cross-spectral density is calculated as the sum of squares of Cs:

<math>c_{s}\left( r \right) = \sum_{i = 1}^{n}{C_{s}\left( r \right)_{i}^{2}},</math>


where n is 2 for MEG and 3 for EEG. This equation can also be described as the squared Euclidean norm of the cross-spectrum:

<math>c_{s}\left( r \right) = \left\| C_{s} \right\|^{2},</math>


The power in voxel r is calculated as in the cortico-cortical case:

<math>p\left( r \right) = \lambda_{1}\left\{ C_{s}(r,r) \right\}.</math>


At last, coherence between the external reference and cortical activity is calculated with the equation:

<math>\text{CON}\left( r \right) = \frac{c_{s}(r)}{p\left( r \right) \cdot C_{\text{all}}(k,k)},</math>


where Call(k, k) is the (k,k)-th diagonal element of the matrix Call.

DICS is particularly useful, if coherence is to be calculated without an a-priory source model (in contrast to source coherence based on pre-defined source montages). However, the recommended analysis strategy for DICS is to use a brain source as a starting point for coherence calculation that is known to contribute to the EEG/MEG signal of interest. For example, one might first run a beamformer on the time-frequency range of interest and use the voxel with the strongest oscillatory activity as a starting point for DICS. The resulting coherence image will again lead to several maxima (ordered by magnitude), which in turn can serve as starting points for DICS calculation. This way, it is possible to detect even weak sources that show coherent activity in the given time-frequency range.

The other significant application for DICS is estimating coherence between an external source and voxels in the brain. For example, an external source can be muscle activity recoded by an electrode placed over the according peripheral region. This way, the direct relationship between muscle activity and brain activation can be measured.

'''Starting DICS computation from the Time-Frequency Window'''

DICS is particularly useful, if coherence in a user-defined time-frequency bin (evoked or induced) is to be calculated between any two brain regions or between an external reference and the brain. DICS runs only on time-frequency decomposed data, so time-frequency analysis needs to be run before starting DICS computation.

To start the DICS computation, left-drag a window over a selected time-frequency bin in the Time-Frequency Window. Right-click and select “Image”. A dialogue will open (see fig. 1) prompting you to specify time and frequency settings as well as the baseline period. It is recommended to use a baseline period of equal length as the data period of interest. Make sure to select “DICS” in the top row and press “'''Go'''”.

[[Image:SA 3Dimaging (21).gif|450px|thumb|c|none|Fig. 1: Time and frequency settings for DICS and MSBF]]

Next, a window will appear allowing you to specify the reference source for coherence calculation (see fig. 2). It is possible to select a channel (e.g. EMG) or a brain source. If a brain source is chosen and no source analysis was computed beforehand, the option “Use current cross-hair position” must be chosen. In case discrete source analysis was computed previously, the selected source can be chosen as the reference for DICS. Please note that DICS can be re-computed with any cross-hair or source position at a later stage.

[[Image:SA 3Dimaging (1).jpg|400px|thumb|c|none|Fig. 2: Possible options for choosing the reference]]

Confirming with “'''OK'''” will start computation of coherence between the selected channel/voxel and all other brain voxels. In case DICS is computed for a reference source in the brain, it can be advantageous to run a beamforming analysis in the selected time-frequency window first and use one of the beamforming maxima as reference for DICS. Fig. 3 shows an example for DICS calculation.

[[Image:SA 3Dimaging (22).gif|500px|thumb|c|none|Fig. 3: Coherence between left-hemispheric auditory areas and the selected voxel in the right auditory cortex.]]

Coherence values range between -1 and 1. If coherence in the signal is much larger than coherence in the baseline (control condition) then the DICS value is going to approach 1. Contrary, if coherence in the baseline is much larger than coherence in the signal, then the DICS value is going to approach -1. At last, if coherence in the signal is equal to coherence in the baseline, then the DICS value is 0.

In case DICS is to be re-computed with a different reference, simply mark the desired reference position by placing the cross-hair in the anatomical view and select “DICS” in the middle panel of the source analysis window (see Fig. 4). In case an external reference is to be selected, click on “DICS” in the middle panel to bring up the DICS dialogue (see. Fig. 2) and select the desired channel. Please note that DICS computation will only be available after running time-frequency analysis.

[[Image:SA 3Dimaging (23).gif|700px|thumb|c|none|Fig. 4: Integration of DICS in the Source Analysis window]]

== Multiple Source Beamformer (MSBF) in the Time Domain ==
''(requires Besa Research 7.0 or higher)''

===Short mathematical introduction===

Beamforming approach can be also applied in the time domain data. This approach was introduced as linearly constrained minimum variance (LCMV) beamformer (Van Veen et al., 1997). It allows to image evoked activity in a user-defined time range, where time is taken relative to a triggered event, and to estimate source waveforms using the calculated spatial weight at locations of interest. For an implementation of the beamformer in the time domain, data covariance matrices are required, while complex cross spectral density matrices are used for the beamformer approaches in the time-frequency domain as described in the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section.

The bilateral beamformer introduced in the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section is also implemented for the time-domain beamformer to take into account contributions from the homologue source in the opposite. This allows for imaging of highly correlated bilateral activity in the two hemispheres that commonly occurs during processing of external stimuli. In addition, the beamformer computation can take into account possibly correlated sources at arbitrary locations.
The beamformer spatial weight W(r) for the voxel r in the brain is defined as follows (Van Veen et al., 1997):

[[File:MSBF1.png]]

where '''C-1''' is the inversed regularized average of covariance matrix over trials, '''L''' is the leadfield matrix of the model containing a regional source at target location r and optionally
additional sources whose interference with the target source is to be minimized. The beamformer spatial weight '''W'''(r) can be applied to the measured data to estimate source
waveform at a location r (beamformer virtual sensor):

[[File:MSBF2.png]]

where '''S'''(r,t) represents the estimated source waveform and '''M'''(t) represents measured EEG or MEG signals.
The output power P of the beamformer for a specific brain region at location r is computed by the following equation:

[[File:MSBF3.png]]

where tr’[ ] is the trace of the [3×3] (MEG: [2×2]) submatrix of the bracketed expression that corresponds to the source at target location r.
Beamformer can suppress noise sources that are correlated across sensors. However, uncorrelated noise will be amplified in a spatially non-uniform manner, with increasing
distortion with increasing distance from the sensors (Van Veen et al., 1997; Sekihara et al., 2001). For this reason, estimated source power should be normalized by a noise power.
In BESA Research, the output power P(r) is normalized with the output power in a baseline interval or with the output power of a uncorrelated noise: P(r) / Pref (r).
The time-domain beamformer image is constructed from values q(r) computed for all locations on a grid specified in the '''General Settings''' tab. A value q(r) is defined as described in
the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section with data covariance matrices instead of cross-spectral density matrices.

===Applying the Beamformer===

This chapter illustrates the usage of the BESA beamformer in the time domain. The displayed figures are generated using the file ‘Examples/ERP-Auditory-Intensity/S1.cnt’.

'''Starting the time-domain beamformer from the Average tab of the Paradigm dialog box'''

The time-domain beamformer is needed data covariance matrices and therefore requires the ERP module to be enabled. After the beamformer computation has been initiated in the
'''Average tab of the Paradigm dialog box''', the source analysis window opens with an enlarged 3D image of the q-value computed with a bilateral beamformer. The result is
superimposed onto the MR image assigned to the data set (individual or standard).

[[File:MSBF44.png]]

''Beamformer image for auditory evoked data after starting the computation in the '''Average tab of the Paradigm dialog box'''. The bilateral beamformer manages to separate the
activities in auditory areas, while a traditional single-source beamformer would merge the two sources into one image maximum in the head center instead.''

'''Multiple-source beamformer in the Source Analysis window'''

The 3D imaging display is part of the source analysis window. In the Channel box, the averaged (evoked) data of the selected condition is shown. Selected covariance intervals in
the ERP module can be checked in the Channel box. The red, gray, and blue rectangles indicate signal, baseline, and common interval, respectively.

[[File:MSBF55.png]]

''Source Analysis window with beamformer image. The two beamformer virtual sensors have been added using the Switch to Maximum and Add Source toolbar buttons (see below).
Source waveforms are computed using the beamformer spatial weights and the displayed averaged data (the noise normalized weights (5% noise) option was used to compute the
beamformer image).''

When starting the beamformer from the '''Average tab of the Paradigm dialog box''', the bilateral beamformer scan is performed. In the source analysis window, the beamformer computation can be repeated taking into account possibly correlated sources that are specified in the current solution. Interfering activities generated by all sources in the current solution that are in the 'On' state are specifically suppressed (they enter the leadfield matrix L in the beamformer calculation). The computation can be started from the '''Image''' menu or from the Image selector button [[File:MSBF_Button.png|22px|Image: 22 pixels]] dropdown menu. The Image menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window.

[[File:MSBF66.png]]

''Multiple-source beamformer image calculated in the presence of a source in the left hemisphere. A single-source scan has been performed instead of a bilateral beamforemr. The
source set in the current solution accounts for the left-hemispheric q-maximum in the data. Accordingly, the beamformer scan reveals only the as yet unmodeled additional activity in
the right hemisphere (note the radiological convention in the 3D image display). The source waveform of the beamformer virtual sensor in the left hemisphere is not shown since the
location (blue square in the figure) is not considered for the multiple-source beamformer.''

The beamformer scan can be performed with a single or a bilateral source scan. The default scan type depends on the current solution:
When the beamformer is started from the '''Average tab of the Paradigm dialog box''' the Source Analysis window opens with a new solution and a bilateral beamformer scan is
performed.
When the beamformer is started within the Source Analysis window, the default is:

* a scan with a single source in addition to the sources in the current solution, if at least one source is active.
* a bilateral scan if no source in the current solution is active.
* a scan with a single source when scalar-type beamformer is selected in the '''beamformer option dialog box'''.

The default scan type is the multiple source beamformer. The non-default scan type can be enforced using the corresponding Volume Image / Beamformer entry in the Image main
menu or in the beamformer option dialog box (only for the time-domain beamformer).

===Inserting Sources as Beamformer Virtual Sensor out of the Beamformer Image===

This is similar to the inserting sources out of the beamformer image in Multiple Source Beamformer (MSBF) in the Time-frequency Domain section.
The beamformer image can be used to add beamformer virtual sensors to the current solution. A simple double-click anywhere in the 3D view (not in the 2D view) will generate a
source at the corresponding location. A better and easier way to create sources at image maxima and minima is to use the toolbar buttons '''Switch to Maximum''' and '''Add Source'''

This feature allows to use the beamformer as a tool to create a source montage for '''source coherence''' analysis. A source montage file (*.mtg) for beamformer virtual sensors can
be saved using File \ Save Source Montage As… entry.

The time-domain beamformer image can be also used to add regional or dipole sources to the current solution. Press '''N''' key when there is no source in the current source array or
there is more than one beamformer virtual sensor. To create a new source array for beamformer virtual sensor, press '''N''' key when there is more than one regional or dipole source in
the current source array.

===Notes===

* You can hide or re-display the last computed image by selecting ''Hide Image'' entry in the '''Image''' menu.
* The current image can be exported to ASCII, ANALYZE, or BrainVoyager (vmp) format from the '''Image''' menu.
* For scaling options, use the and Image Scale toolbar buttons.
* Parameters used for the beamformer calculations can be set in the '''Standard Volume tab of the Image Settings dialog box'''.
* Note that Model, Residual, Order, and Residual variance are not shown for the beamformer virtual sensor type sources.

===References===

* Sekihara, K., Nagarajan, S. S., Poeppel, D., Marantz, A., & Miyashita, Y. (2001). Reconstructing spatio-temporal activities of neural sources using an MEG vector beamformer technique. IEEE Transactions on Biomedical Engineering, 48(7), 760–771.

* Van Veen, B. D., Van Drongelen, W., Yuchtman, M., & Suzuki, A. (1997). Localization of brain electrical activity via linearly constrained minimum variance spatial filtering. IEEE Transactions on Biomedical Engineering, 44(9), 867–880

== CLARA ==

CLARA ('Classical LORETA Analysis Recursively Applied') is an iterative application of weighted LORETA images with a reduced source space in each iteration.

In an initialization step, a LORETA image is calculated. Then in each iteration the following steps are performed:

# The obtained image is spatially smoothed (this step is left out in the first iteration).
# All grid points with amplitudes below a threshold of 1% of the maximum activity are set to zero, thus being effectively eliminated from the source space in the following step.
# The resulting image defines a spatial weighting term (for each voxel the corresponding image amplitude).
# A LORETA image is computed with an additional spatial weighting term for each voxel as computed in step 3. By the default settings in BESA Research, the regularization values used in the iteration steps are slightly higher than that of the initialization LORETA image.

The procedure stops after 2 iterations, and the image computed in the last iteration is displayed. Please note that you can change all parameters by creating a user-defined volume image.

The advantage of CLARA over non-focusing distributed imaging methods is visualized by the figure below. Both images are computed from the N100 response in an auditory oddball experiment (file '''Oddball.fsg''' in subfolder ''fMRI+EEG-RT-Experiment'' of the ''Examples'' folder). The CLARA image is much more focal than the sLORETA image, making it easier to determine the location of the image maxima.

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (24).gif|thumb|350px|sLORETA image]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (25).gif|thumb|350px|CLARA image]] </li>
</ul></div>

'''Notes:'''

* Starting CLARA: CLARA can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter ''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]'' for important information on regularization of distributed inverses.

== LAURA ==

LAURA (Local Auto Regressive Average) belongs to the distributed inverse method of the family of weighted minimum norm methods ([https://doi.org/10.1023/A:1012944913650 Grave de Peralta Menendeza et al., "Noninvasive Localization of Electromagnetic Epileptic Activity. I. Method Descriptions and Simulations", BrainTopography 14(2), 131-137, 2001]). LAURA uses a spatial weighting function that includes depth weighting and that term has the form of a local autoregressive function.

The source activity is estimated by applying the general formula for a weighted minimum norm:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T}\left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings.''

In LAURA, V contains both a depth weighting term W and a representation of a local autoregressive function A. V is computed as:

<math>\mathrm{V} = \left( \mathrm{U}^{T} \cdot \mathrm{U} \right)^{-1}</math>


Where

<math>\mathrm{U} = \left( \mathrm{W} \cdot \mathrm{A} \right) \otimes \mathrm{I}_{3}</math>


Here, <math>\otimes</math> denotes the Kronecker product. I3 is the [3×3] identity matrix. W is an [s×s] diagonal matrix (with s the number of source locations on the grid), where each diagonal element is the inverse of the maximum singular value of the corresponding regional source's leadfields. The formula for the diagonal components Aii and the off-diagonal components Aik are as follows:

<math>\mathrm{A}_{ii} = \frac{26}{\mathrm{N}_{i}}\sum_{k \subset V_{i}}^{}\frac{1}{\mathrm{d}_{ik}^{2}}</math>


<math>
\mathrm{A}_{ik} =
\begin{cases}
- 1/\operatorname{dist}\left( i,k \right)^{2}, & \text{if } k \subset V_{i} \\
0, & \text{otherwise}
\end{cases}
</math>


Here, Vi is the vicinity around grid point i that includes the 26 direct neighbors.

The LAURA image in BESA Research displays the norm of the 3 components of S at each location r. Using the menu function ''Image / Export Image As... ''you have the option to save this norm of S or alternatively all components separately to disk.

'''Notes:'''

* '''Grid spacing:''' Due to memory limitations, LAURA images require a grid spacing of 7 mm or more.
* '''Computation time:''' Computation speed during the first LAURA image calculation depends on the grid spacing (computation is faster with larger grid spacing). After the first computation of a LAURA image, a '''*.laura''' file is stored in the data folder, containing intermediate results of the LAURA inverse. This file is used during all subsequent LAURA image computations. Thereby, the time needed to obtain the image is substantially reduced.
* '''MEG:''' In the case of MEG data, an additional constraint is implemented in the LAURA algorithm that prevents solutions from containing radial source currents (compare Pascual-Marqui, ISBET Newsletter 1995, 22-29). In MEG, an additional source space regularization is necessary in the inverse matrix operation required compute V
* '''Starting LAURA:''' LAURA can be started from the''' Image''' menu or from the '''Image Selection''' button.
* '''Regularization:''' Please refer to Chapter'' “Regularization of distributed volume images” ''for important information on regularization of distributed inverses.

== LORETA ==

LORETA ("Low Resolution Electromagnetic Tomography") is a distributed inverse method of the family of ''weighted minimum norm'' methods. LORETA was suggested by R.D. Pascual-Marqui (International Journal of Psychophysiology. 1994, 18:49-65). LORETA is characterized by a smoothness constraint, represented by a discrete 3D Laplacian.

The source activity is estimated by applying the general formula for a weighted minimum norm:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T}\left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings.''

In LORETA, V contains both a depth weighting term and a representation of the 3D Laplacian matrix. V is computed as:

<math>\mathrm{V} = \left( \mathrm{U}^{T} \cdot \mathrm{U} \right)^{- 1}</math>


where

<math>\mathrm{U} = \left( \mathrm{W} \cdot \mathrm{A} \right) \otimes \mathrm{I}_{3}</math>


Here, <math>\otimes</math> denotes the Kronecker product. I3 is the [3x3] identity matrix. W is an [sxs] diagonal matrix (with s the number of source locations on the grid), where each diagonal element is the inverse of the maximum singular value of the corresponding regional source's leadfields. A contains the 3D Laplacian and is computed as

<math>\mathrm{A} = \mathrm{Y} - \mathrm{I}_{s}</math>


with Is the [sxs] identity matrix, where s is the number of sources (= three times the number of grid points) and

<math>\mathrm{Y} = \frac{1}{2}\left\{ \mathrm{I}_{s} + \left\lbrack \operatorname{diag}\left( \mathrm{Z} \cdot \left\lbrack 111 \ldots 1 \right\rbrack^{T} \right) \right\rbrack^{- 1} \right\} \cdot \mathrm{Z}</math>


where

<math>
\mathrm{Z}_{ik} =
\begin{cases}
1/6, & \text{if } \operatorname{dist}\left( i,k \right) = 1 \text{ grid point} \\
0, & \text{otherwise}
\end{cases}
</math>


The LORETA image in BESA Research displays the norm of the 3 components of S at each location r. Using the menu function ''Image / Export Image As... ''you have the option to save this norm of S or alternatively all components separately to disk.

'''Notes:'''
* '''Grid spacing:''' Due to memory limitations, LORETA images require a grid spacing of 5 mm or more.
* '''Computation time:''' Computation speed during the first LORETA image calculation depends on the grid spacing (computation is faster with larger grid spacing). After the first computation of a LORETA image, a '''<nowiki>*.loreta</nowiki>''' file is stored in the data folder, containing intermediate results of the LORETA inverse. This file is used during all subsequent LORETA image computations. Thereby, the time needed to obtain the image is substantially reduced.
* '''MEG''': In the case of MEG data, an additional constraint is implemented in the LORETA algorithm that prevents solutions from containing radial source currents (Pascual-Marqui, ISBET Newsletter 1995, 22-29). In MEG, an additional source space regularization is necessary in the inverse matrix operation required compute V.
* '''Starting LORETA:''' LORETA can be started from the''' Image''' menu or from the '''Image Selection '''button.
* '''Regularization:''' Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed source models.

== sLORETA ==

This distributed inverse method consists of a ''standardized, unweighted minimum norm''. The method was originally suggested by R.D. Pascual-Marqui (Methods & Findings in Experimental & Clinical Pharmacology 2002, 24D:5-12) Starting point is an unweighted minimum norm computation:

<math>\mathrm{S}_{\text{MN}}\left( t \right) = \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings''.

This minimum norm estimate is now standardized to produce the sLORETA activity at a certain brain location r:

<math>\mathrm{S}_{\text{sLORETA}, r} = \mathrm{R}_{rr}^{-1/2} \cdot \mathrm{S}_{\text{MN},r}</math>


SsMN,r is the [3x1] (MEG: [2x1]) minimum norm estimate of the 3 (MEG: 2) dipoles at location r. Rrr is the [3x3] (MEG: [2x2]) diagonal block of the resolution matrix R that corresponds to the source components at the target location r. The resolution matrix is defined as:

<math>\mathrm{R} = \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{L}^{T} + \lambda \cdot \mathrm{I} \right)^{-1} \cdot \mathrm{L}</math>


The sLORETA image in BESA Research displays the norm of SsLORETA, r at each location r. Using the menu function ''Image / Export Image As...'' you have the option to save this norm of SsLORETA, r or alternatively all components separately to disk.

'''Notes:'''

* sLORETA can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== swLORETA ==

This distributed inverse method is a ''standardized, depth-weighted minimum norm'' (E. Palmero-Soler et al 2007 Phys. Med. Biol. 52 1783-1800). It differs from sLORETA only by an additional depth weighting.

Starting point is a depth-weighted minimum norm computation:

<math>\mathrm{S}_{\text{MN}}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings''.

V is the diagonal depth weighting matrix. For s grid locations, V is of dimension [3s x 3s] (MEG: [2s x 2s]). Each diagonal element of V is the inverse of the first singular value of the leadfield of the corresponding regional source. Hence, the first 3 (MEG: 2) diagonal elements equal the inverse of the largest eigenvalue of the leadfield matrix of regional source 1, and so on.

This minimum norm estimate is now standardized to produce the swLORETA activity at a certain brain location r:

<math>\mathrm{S}_{\text{swLORETA},r} = \mathrm{R}_{rr}^{-1/2} \cdot \mathrm{S}_{\text{MN},r}</math>


SsMN,r is the [3x1] (MEG: [2x1]) depth-weighted minimum norm estimate of the regional source at location r. Rrr is the [3x3] (MEG: [2x2]) diagonal block of the resolution matrix R that corresponds to the source components at the target location r. The resolution matrix is defined as:

<math>\mathrm{R} = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} + \lambda \cdot \mathrm{I} \right)^{-1} \cdot \mathrm{L}</math>


The swLORETA image in BESA Research displays the norm of SswLORETA, r at each location r. Using the menu function ''Image / Export Image As...'' you have the option to save this norm of SswLORETA, r or alternatively all components separately to disk.

'''Notes:'''

* sLORETA can be started from the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== sSLOFO ==

SSLOFO (standardized shrinking LORETA-FOCUSS) is an iterative application of weighted distributed source images with a reduced source space in each iteration ([https://dx.doi.org/10.1109/TBME.2005.855720 Liu et al., "Standardized shrinking LORETA-FOCUSS (SSLOFO): a new algorithm for spatio-temporal EEG source reconstruction", IEEE Transactions on Biomedical Engineering 52(10), 1681-1691, 2005]).

In an initialization step, an [[#sLORETA | sLORETA]] image is calculated. Then in each iteration the following steps are performed:

# A weighted minimum norm solution is computed according to the formula <math display="inline">\mathrm{S} = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}</math> . Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D is the data at the time point under consideration. V is a diagonal spatial weighting matrix that is computed in the previous iteration step. In the first iteration, the elements of V contain the magnitudes of the initially computed LORETA image.
# Standardization of this weighted minimum norm image is performed with the resolution matrix as in [[#sLORETA | sLORETA]].
# The obtained standardized weighted minimum norm image is being smoothed to get Ssmooth.
# All voxels with amplitudes below a threshold of 1% of the maximum activity get a weight of zero in the next iteration step, thus being effectively eliminated from the source space in the next iteration step.
# For all other voxels, compute the elements of the spatial weighting matrix V to be used in the next iteration as follows: <math display="inline">\mathrm{V}_{ii,\text{next iteration}} = \frac{1}{\left\| \mathrm{L}_{i} \right\|} \cdot \mathrm{S}_{ii,\text{smooth}} \cdot \mathrm{V}_{ii,\text{current iteration}}</math>



The procedure stops after 3 iterations. Please note that you can change all parameters by creating a [[#User-Defined Volume Image | user-defined volume image]].

'''Notes:'''
* '''Starting sSLOFO''': sSLOFO can be started from the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter ''[[#Regularization of distributed volume images | Regularization of distributed volume images]]'' for important information on regularization of distributed inverses.

== User-Defined Volume Image ==

In addition to the predefined 3D imaging methods in BESA Research, it is possible to create user-defined imaging methods based on the general formula for distributed inverses:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. Custom-defined parameters are:* The spatial weighting matrix V: This may include depth weighting, image weighting, or cross-voxel weighting with a 3D Laplacian (as in LORETA) or an autoregressive function (as in LAURA).

* Regularization: The term in parentheses is generally regularized. Note that regularization has a strong effect on the obtained results. Please refer to chapter “''Regularization of Distributed Volume Images” ''for more information.
* Standardization: Optionally, the result of the distributed inverse can be standardized with the resolution matrix (as in sLORETA).
* Iterations: Inverse computations can be applied iteratively. Each iteration is weighted with the image obtained in the previous iteration.

All parameters for the user-defined volume image are specified in the User-Defined Volume Tab of the Image Settings dialog box. Please refer to chapter “''User-Defined Volume Tab”'' for details.

'''Notes:'''
* Starting the user-defined volume image: the image calculation can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== Regularization of distributed volume images ==

Distributed source images require the inversion of a term of the form L V LT. This term is generally regularized before its inversion. In BESA Research, selection can be made between two different regularization approaches (parameters are defined in the ''Image Settings dialog box''):

* '''Tikhonov regularization''': In Tikhonov regularization, the term L V LT is inverted as (L V LT +λ I)-1. Here, l is the regularization constant, and I is the identity matrix.
* One way of determining the optimum regularization constant is by minimizing the ''generalized cross'' ''validation error'' (CVE).
* Alternatively, the regularization constant can be specified manually as a percentage of the trace of the matrix L V LT.
* '''TSVD''': In the truncated singular value decomposition (TSVD) approach, an SVD decomposition of L V LT is computed as  L V LT = U S UT, where the diagonal matrix S contains the singular values. All singular values smaller than the specified percentage of the maximum singular values are set to zero. The inverse is computed as U S-1 UT, where the diagonal elements of S-1 are the inverse of the corresponding non-zero diagonal elements of S.

Regularization has a critical effect on the obtained distributed source images. The results may differ completely with different choices of the regularization parameter (see examples below). Therefore, it is important to evaluate the generated image critically with respect to the regularization constant, and to keep in mind the uncertainties resulting from this fact when interpreting the results. The default setting in BESA Research is a TSVD regularization with a 0.03% threshold. However, this value might need to be adjusted to the specific data set at hand.

The following example illustrates the influence of the regularization parameter on the obtained images. The data used here is condition '''St-Cor of dataset Examples \ TFC-Error-Related-Negativity \ Correct+Error.fsg''' at 176 ms following the visual stimulus. Discrete dipole analysis reveals the main activity in the left and right lateral visual cortex at this latency.

[[Image:SA 3Dimaging (42).gif]]

''Discrete source model at 176 ms: Main activity in the left and right lateral visual cortex, no visual midline activity.''

LORETA images computed at this latency depend critically on the choice of the regularization constant. The following 3D images are created with TSVD regularization with SVD cutoffs of 0.1%, 0.005%, and 0.0001%, respectively. The volume grid size was 9 mm. The example demonstrates the dramatic effect of regularization and demonstrates the typical tradeoff between too strong regularization (leading to too smeared 3D images that tend to show blurred maxima) and too small regularization (resulting in too superficial 3D images with multiple maxima).

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (43).gif|thumb|350px|'''SVD cutoff 0.1%''': Regularization too strong. No separation between sources, mislocalization towards the middle of the brain.]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (44).gif|thumb|350px|'''SVD cutoff 0.005%''': Appropriate regularization. Separation of the bilateral activities. Location in agreement with the discrete multiple source model.]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (45).gif|thumb|350px|'''SVD cutoff 0.0001%''': Too small regularization. Mislocalization, too superficial 3D image. ]] </li>
</ul></div>

The automatic determination of the regularization constant using the CVE approach does not necessarily result in the optimum regularization parameter either. In this example, the unscaled CVE approach rather resembles the TSVD image with a cutoff of 0.0001%, i.e. regularization is too small. Therefore, it is advisable to compare different settings of the regularization parameter and make the final choice based on the above-mentioned considerations.

== Cortical LORETA ==

Cortical LORETA is principally the same technique as LORETA, however, Cortical LORETA is not computed in a 3D volume, but on the cortical surface.

The cortical reconstruction in BESA Research fed from BESA MRI is a closed 2D surface with no boundaries and a very close approximation of the actual cortical form. It consists of an irregular triangulated grid.

The Laplace operator that is used for identifying a smooth solution in a three-dimensional space is exchanged with a Laplace operator that runs on the two-dimensional cortical surface.

There is a wide variety of 2D Laplace operators with different characteristics. The general form of the discrete Laplace operator is

<math>\Delta f\left( p_{i} \right) = \frac{1}{d_{i}}\sum_{j \in N(i)}^{}{w_{ij}\left\lbrack f\left( p_{i} \right) - f\left( p_{j} \right) \right\rbrack},</math>


where '''pi''' is the '''i-th''' node of the triangular mesh, '''f(pi) '''is the value of a function f defined on the cortical mesh at the node '''pi''', '''wij''' is the weight for the connection between the nodes '''pi''' and '''pj''' and '''di''' is a normalization factor for the '''i-th''' row of the operator. Furthermore, '''N(i)''' is the set of indices corresponding to the direct (also called "1-ring") neighbors of '''pi'''.

BESA offers the choice of three Laplace operators with slightly different characteristics.

* '''Unweighted Graph Laplacian''': This is the simplest operator. It takes into account only the adjacency of the nodes and not the geometry of the mesh:

<math>
w_{ij} =
\begin{cases}
1, & \text{if } p_{i} \text{ and } p_{j} \text{ are connected by an edge} \\
0, & \text{otherwise}
\end{cases}
</math>

<math>d_{i} = 1</math>


[[Image:SA 3Dimaging (4).jpg |450px]]

* '''Weighted Graph Laplacian:''' This operator is similar to the unweighted graph Laplacian but with different weights for the different connections. The connections between nearby nodes get larger weights than the connections between farther nodes:

<math>w_{ij} = \frac{1}{\operatorname{dist}\left( p_{i},p_{j} \right)}</math>

<math>d_{i} = \sum_{j \in N(i)}^{} {\operatorname{dist}\left(p_{i}, p_{j} \right)}</math>


where '''dist''' ('''pi''' , '''pj''') is the distance between the nodes '''pi '''and '''pj'''.

[[Image:SA 3Dimaging (6).jpg|450px]]

* '''Geometric Laplacian with mixed area weights''': This operator takes into account the angles in the corresponding triangles into account as well as the area around the nodes in order to determine the connection weights:

<math>w_{ij} = \frac{\cot\left( \alpha_{ij} \right) + \cot\left( \beta_{ij} \right)}{2}</math>

<math>d_{i} = A_{\text{mixed}}</math>


where '''αij''' and '''βij''' denote the two angles opposite to the edge ('''i , j''') and '''Amixed '''is either the Voronoi area, or 1/2 of the triangle area or 1/4 of the triangle area depending on the type of the triangle.

[[Image:SA 3Dimaging (8).jpg|450px]]

'''Regularization and other parameters:'''

[[Image:SA 3Dimaging (46).gif ‎]]

* '''SVD cutoff''': The regularization for the inverse operator as a percent of the largest singular value.
* '''Depth weighting''': Turn depth weighting on or off.
* '''Laplacian type''': Selection of Laplacian operators (see above).

'''Notes:'''
* '''Starting Cortical LORETA''': Cortical LORETA can be started from the sub-menu '''Surface Image''' of the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]''” for important information on regularization of distributed inverses.

== Cortical CLARA ==

Cortical CLARA is principally the same technique as CLARA, but Cortical CLARA is not computed in a 3D volume, but on the cortical surface. Instead of using a LORETA image as the basis for the iterative application, cortical CLARA uses cortical LORETA.

'''Regularization and other parameters:'''

[[Image:SA 3Dimaging (47).gif]]

* '''SVD cutoff''': The regularization for the inverse operator as a percent of the largest singular value.
* '''Depth weighting''': Turn depth weighting on or off.
* '''Laplacian type''': Selection of Laplacian operators (see Cortical LORETA).
* '''No of iterations''': Number of iterations for CLARA. The more iterations are used, the sparser becomes the solution.
* '''Automatic''': The algorithm tries to determine the number of iterations automatically. The goodness of fit (GOF) is calculated after every iteration and if there is a big jump in the GOF then the algorithm will stop. If no jumps appear during the calculations then CLARA iterates until the specified number of iterations is reached.
* '''Regularize iterations''': If one wants to use different regularization for the CLARA iterations than the value specified as "SVD cutoff", this option should be selected.
* '''Amount to clip from img (%)''': Cortical CLARA uses the solution from the previous iteration as an additional weighting matrix for the current iteration. That weighting matrix is constructed by cutting the "low" activity from the solution. This number specifies how much of the activity should be cut from the previous solution in order to construct the weighting matrix. This value is given as a percentage of the maximal activity. Default value is 10%.

'''Notes:'''

* '''Starting Cortical CLARA:''' Cortical CLARA can be started from the sub-menu '''Surface Image''' of the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]''” for important information on regularization of distributed inverses.

== Cortex Inflation ==

The inflated cortex is a smoothened version of the individual cortical surface with minimal metric distortions (Fischl, B. et al. (1999). Cortical Surface-Based Analysis: II: Inflation, Flattening, and a Surface-Based Coordinate System. ''NeuroImage'', 9(2), 195–207). Gyri and sulci are smoothened out. The original distances between each point on the cortex and its neighbors are, however, mostly preserved.

[[Image:SA 3Dimaging (48).gif]]

''Cortical LORETA map overlaid on top of the inflated cortical surface.''

A lighter gray color overlaid on top of the surface image indicates the location of a gyrus of the individual cortex surface, while a darker gray color indicates the location of a sulcus. The inflated cortical surface can be computed in '''BESA MRI 2.0'''. For more details please refer to the BESA MRI 2.0 help.

== Surface Minimum Norm Image ==

'''Introduction'''

The minimum norm approach is a common method to estimate a distributed electrical current image in the brain at each time sample (Hämäläinen & Ilmoniemi 1984). The source activities of a large number of regional sources are computed. The sources are evenly distributed using 1500 standard locations 10% and 30% below the smoothed standard brain surface (when using the standard MRI) or using between 3000-4000 locations on the individual brain surface defined by the gray-white-matter boundary.

Since the number of sources is much larger than the number of sensors in a minimum norm solution, the inverse problem is highly underdetermined and must be stabilized by a mathematical constraint, the minimum norm. Out of the many current distributions that can account for the recorded sensor data, the solution with the minimum L2 norm, i.e. the minimum total power of the current distribution is displayed in BESA Research.

First, the forward solution (leadfield matrix L) of all sources is calculated in the current head model. Then, the source activities S(t) of all source components are computed from the data matrix D(t) using an inverse regularized by the estimated noise covariance matrix:

<math>\mathrm{S}\left( t \right) = \mathrm{R} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{R} \cdot \mathrm{L}^{T} + \mathrm{C}_N \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed regional source model, CN denotes the noise correlation matrix in sensor space, and R is a weighting matrix in source space. R and CN can be designed in different ways in order to optimize the minimum norm result. The total activity of each regional source is computed as the root mean square of the source activities S(t) of its 3 (MEG:2) components. This total source activity is transformed to a color-coded image of the brain surface. (When the standard brain is used, two sources are assigned to each surface location, located 10% and 30% below the surface, respectively. The color that is displayed on the standard brain surface is the larger of the two corresponding source activities.)

'''Weighting options'''

The minimum norm current imaging techniques of BESA Research provide different weighting strategies. Two weighting approaches are available: Depth weighting and spatio-temporal approaches.
* '''Depth weighting:''' Without depth weighting, deep sources appear very smeared in a minimum-norm reconstruction. With depth weighting, both deep and superficial sources produce a similar, more focal result. If this weighting method is selected, the leadfield of each regional source is scaled with the largest singular value of the SVD (singular value decomposition) of the source's leadfield.
* '''Spatio-temporal weighting''': Spatio-temporal weighting tries to assign large weight to sources that are assumed to be more likely to contribute to the recorded data.
** '''Subspace correlation after single source scan''': This method divides the signal into a signal and a noise subspace. The correlation of the leadfield of a regional source i with the signal subspace (pi) is computed to find out if the source location contributes to the measured data. The weighting matrix R becomes a diagonal matrix. Each of the three (MEG: 2) components of a regional source get the same weighting value pi2. This approach is based on the signal subspace correlation measure introduced by J.C. Mosher, R. M. Leahy (Recursive MUSIC: A Framework for EEG and MEG Source Localization, IEEE Trans. On Biomed. Eng. Vol. 45, No. 11, November 1998)
** '''Dale & Sereno 1993:''' In the approach of Dale and Sereno (J Cogn Neurosci, 1993, 5: 162-176) a signal subspace needs not be defined. The correlation pi of the leadfield of regional source i with the inverse of the data covariance matrix is computed along with the largest singular value λmax of the data covariance matrix. The weighting matrix R is a diagonal matrix with weights: [[Image:SA 3Dimaging (50).gif]]. Each of the three (MEG: 2) components of a regional source receives the same weighting value.

'''Noise regularization'''

Two methods to estimate the channel noise correlation matrix CN are provided by the program:
* '''Use baseline:''' Select this option to estimate the noise from the user-definable baseline. The signal is computed from the data at non-baseline latencies.
* '''Use 15% lowest values:''' The baseline activity is computed from the data at those 15% of all displayed latencies that have the lowest global field power. The signal is computed from all displayed latencies.

In each case, the activity (noise or signal, respectively) is defined as root-mean-square across all respective latencies for each channel.

The noise covariance matrix CN is constructed as a diagonal matrix. The entries in the main diagonal are proportional to the noise activity of the individual channels (if selected) or are all equally proportional to the average noise activity over all channels. The noise covariance matrix CN is then scaled such that the ratio of the Frobenius norms of the weighted leadfield projector matrix (LRLT) and the noise covariance matrix CN equals the Signal-to-Noise ratio. This scaling can be multiplied by an additional factor (default=1) to sharpen (<1) or smoothen (>1) the minimum norm image.

'''Applying the Minimum Norm Image'''

The minimum-norm algorithm is started via the ''Surface minimum norm image dialog box'', which is opened from the''' Image''' menu, or by typing the shortcut '''Ctrl-M''': Please refer to Chapter ''“Surface'' ''Minimum Norm Tab”'' for more details.

As opposed to the other 3D images available from the '''Image '''menu, the surface minimum norm image is not computed on a volumetric grid, but rather for locations on the brain surface. Accordingly, the results of the minimum norm image are displayed superimposed to the brain surface mesh rather than to the volumetric MR image.

The figure below shows a minimum norm image computed from the file '''Examples\Epilepsy\Spikes\Spikes-Child4_EEG+MEG_averaged.fsg'''. The EEG spike peak was imaged using the individual brain surface of the subject. A baseline from -300 to -70 ms was used. Minimum norm was computed with depth weighting, Spatio-temporal weighting according to Dale & Sereno 1993 and individual noise weighting with a noise scale factor of 0.01. The minimum norm image reveals the location of the spike generator in the close vicinity of the frontal left-hemispheric lesion in this subject.

[[Image:SA 3Dimaging (51).gif]]

== Multiple Source Probe Scan (MSPS) ==

 
'''Introduction'''

The MSPS function provides a tool for the validation of a given solution. It is based on the following theoretical consideration: If the recorded EEG/MEG data has been modeled adequately, i.e. all active brain regions are represented by a source in the current solution, then any additional probe source added to the solution will not show any activity apart from noise. The only exception occurs if this probe source is placed in close vicinity to one of the sources in the current solution. In that case, the solution's source and the probe source will share the activity of the corresponding brain area. The MSPS applies these considerations by scanning the brain on a pre-defined grid with a regional probe added to the current solution. Grid extent and density can be specified in the Image settings. The power P of the probe source at location r in the signal interval is compared with the power of the probe source in a reference interval, defining a value q:

<math>\mathrm{q}\left( r \right) = \sqrt{\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}} - 1</math>


MSPS can be computed on time domain or time-frequency domain data:
* In the time domain, q(r) is computed from the source waveform of the probe source. Here, P(r) is the mean power of the probe source at location r in the marked latency range, and Pref(r) is the mean probe source power in the user-definable baseline interval.
* In the time-frequency domain, an MSPS image can be computed from the complex cross spectral density matrices. By applying the inverse operator for a source configuration consisting of the current solution and the probe source, the power of the probe source can be computed for the target interval [P(r)] and the reference time-frequency interval [Pref(r)]. In the resulting MSPS image, q-values are shown in %, where q[%] = q*100.

The inverse operator used to determine the probe source power uses different regularization constants for the probe source and the sources in the current solution. The regularization constant of the sources in the current solution can be specified in the Image settings (default 4%). The regularization constant of the probe source is internally set to 0%.

Alternatively to the definition above, q can also be displayed in units of dB:

<math>\mathrm{q}\left\lbrack \text{dB} \right\rbrack = 10 \cdot \log_{10}\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}</math>


Values of q smaller than zero are not shown in the MSPS image.

According to the considerations above, an MSPS of a correct source model should optimally yield image maxima around the sources in the current solution only. If the MSPS image is blurred or shows maxima at locations different from the modeled sources, this indicates a non-sufficient or incorrect solution.

'''Applying the MSPS'''

This chapter illustrates the application of the Multiple Source Probe Scan. The figures are generated with data from file '''Examples/Epilepsy/Spikes/Rolandic-Spike-Child.fsg''' (-300 : +200 ms, filtered from 3 Hz [forward] to 40 Hz [zero-phase]).

'''Time domain versus time-frequency domain MSPS'''

The multiple source probe scan can be computed in the time domain or the time-frequency domain. The latter is possible only when time-frequency domain data is available for the current condition, i.e. if the condition has been created by starting a multiple source beamformer (MSBF) computation from the source coherence window. In this case, evoking the MSPS calculation from the '''Imaging '''button or from the '''Image''' menu will bring up the following dialog window that allows to choose between time- or time-frequency MSPS. If only time domain data is available, this dialog window will not appear and MSPS will be computed in the time domain.

[[Image:SA 3Dimaging (53).gif]]

For a time-frequency domain MSPS, the target and the reference time-frequency interval have been specified already in the Time-Frequency window (see Chapter "''How To Create Beamformer Images''"). For a time-domain MSPS, the target and the reference epoch have to be specified in the Source Analysis window as described below.

'''Time domain MSPS'''

The time-domain MSPS image displays the ratio of the power of a regional probe source in the signal and the baseline interval. The currently set baseline is indicated by a horizontal line in the upper left corner of the channel box.

[[Image:SA 3Dimaging (54).gif|thumb|c|none|330px|The black horizontal bar in the upper part of the channel box (here circled in red) indicates the baseline interval.]]

By default, BESA Research defines the pre-stimulus interval of the current data segment as baseline. The baseline should represent a latency range in which no event-related activity is present in the data. There are several possibilities to modify the baseline interval: by clicking on the horizontal line with the left mouse button or by using the corresponding entry in the '''Condition '''menu or '''Fit Interval''' popup menu.

Mark an interval to define the target epoch, i.e. the time-interval for which the current solution is to be tested. Start the MSPS by selecting it from the '''Image selection '''button or from the '''Image''' menu to start the probe source scan. The''' Image '''menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window. The 3D window opens and displays the scan result.

<div><ul>
<li style="display: inline-block;"> [[Image:SA 3Dimaging (55).gif|thumb|c|none|650px|This figure shows the MSPS image applied on the three left-hemispheric sources in the solution ''''Rolandic-Spike-Child-RS2.bsa''''. The baseline is set from -300ms to -50 ms. The right-hemispheric sources have been switched off. The fit interval is set to the latency range of large overall activity in the data (-43 ms : 117 ms). A realistic FEM model appropriate for the subject's age (12 years, conductivity ratios (cr) 50) is applied. The MSPS image does not show maxima at the modeled source locations and rather shows a spread q-value distribution.]] </li>

<li style="display: inline-block;"> [[Image:SA 3Dimaging (56).gif|thumb|c|none|650px|The MSPS image for the same latency range when the right-hemispheric sources have been included. The MSPS image appears more focal and shows maxima around the modeled brain regions. This indicates the substantial improvement of the solution by adding the right-hemispheric sources that model the propagation of the epileptic spike from the left to the right hemisphere (note the radiological side convention in the 3D window).]] </li>
</ul></div>

'''Time-Resolved MSPS'''

If the MSPS has been computed on time domain data, the image can be shown separately for each latency in the selected interval. After the MSPS has been computed for the marked epoch, double-click anywhere within this epoch to display the ratio of the probe source magnitude at the selected latency and the mean probe source magnitude in the baseline. Scanning the latency range by moving the cursor (e.g. with the left and right arrow cursor keys) provides a time-resolved MSPS image.

Time-resolved MSPS images are not available if the MSPS has been computed on data in the time-frequency domain.

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (57).gif|thumb|450px|MSPS image of the spike peak activity at 0ms. The activity mainly occurs in the left hemisphere. This fact is illustrated by the source waveforms and confirmed in the MSPS image, which shows a focal maximum around the location of the red sources.]] </li>

<li style="display: inline-block;"> [[File:SA 3Dimaging (58).gif|thumb|450px|Around +27 ms, the spike has propagated to the right hemisphere. This becomes evident from the waveforms of the blue sources, which show a significant latency lag with respect to the first three sources, and from the MSPS image, which shows the maximum around blue sources at this latency.]] </li>
</ul></div>



'''Notes:'''

* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image''' menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the''' Image''' menu.
* For scaling options, please refer to the '''scaling buttons''' popup menu .
* Parameters used for the MSPS calculations can be set in the ''General Settings tab'' of the ''Image Settings dialog box.''

== Source Sensitivity ==

'''Introduction'''

The 'Source sensitivity' function displays the sensitivity of the selected source in the current source model to activity in other brain regions. Sensitivity is defined as the fraction of power at the scanned brain location that is mapped onto the selected source.

To compute the source sensitivity, unit brain activity is modeled at different locations (probe source) throughout the brain. To this data, the current source model is applied to compute the source waveforms SCM of all modeled sources:

<math>\mathrm{S}_{\text{CM}} = \mathrm{L}_{\text{CM}}^{-1} \cdot \mathrm{L}_{\text{PS}}</math>


Here LCM-1 is the regularized inverse operator for the current model, and LPS is the leadfield of the regional probe source (dimension [Nx3] for EEG and [Nx2] for MEG, respectively, where N is the number of sensors). The source amplitude SSS of the selected source in the model is a 3x3 (MEG: 2x2) sub-matrix of SCM (if the selected source is a regional source) or a 1x3-matrix (MEG: 1x2) (if the selected source is a dipole). The root mean square of the singular values of SCM is defined as the source sensitivity.

The 3D source sensitivity image displays this value for all locations on a grid specified under '''Image/Settings'''. Grid density can be specified in the Image Settings.

'''Applying the Source Sensitivity Image'''

The Source Sensitivity image is evoked from the '''Image''' menu or by pressing the corresponding hot key (default: '''V''').

This function is enabled only when a solution with an active selected source is present in the Source Analysis window. The source sensitivity image then displays the sensitivity of the selected source to activity in other brain regions.

[[Image:SA 3Dimaging (59).gif]]

''Source Sensitivity image for the selected frontal source (green) in model ''''''High_Intensity_3RS.bsa'''''' in folder 'Examples/ERP_Auditory_Intensity'. The data displayed is the '100dB' condition in file ''''''All_Subjects_cc.fsg''''''. The selected source is sensitive to activity in the frontal brain region (yellow/white), while it is not influenced by activity in the vicinity of the left and right auditory cortex areas, which are modeled by the red and blue source in the model (transparent/gray).''

'''Notes:'''

* The sensitivity image is independent of the recorded sensor signals. It only depends on the current source model, the sensor configuration, the head model, and the regularization constant.
* If the regularization constant is set to zero, each source has a sensitivity of 100% to activity around its own location. With increasing regularization, the spatial filter becomes less focused, and the sensitivity of a source to activity at its location decreases.
* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image''' menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the '''Image''' menu.

{{BESAManualNav}}

Source Analysis 3D Imaging

2019-03-27T11:54:34Z

Jamie: /* Notes */

{{BESAInfobox
|title = Module information
|module = BESA Research Standard or higher
|version = 6.1 or higher
}}


== Overview ==

BESA Research features a set of new functions that provide 3D images that are displayed superimposed to the individual subject's anatomy. This chapter introduces these different images and describe their properties and applications.

The 3D images can be divided into three categories:

'''Volume images:'''

* '''The Multiple Source Beamformer (MSBF)''' is a tool for imaging brain activity. It is applied in the time-domain or time-frequency domain. The beamformer technique in time-frequency domain can image not only evoked, but also induced activity, which is not visible in time-domain averages of the data.
* '''Dynamic Imaging of Coherent Sources (DICS)''' can find coherence between any two pairs of voxels in the brain or between an external source and brain voxels. DICS requires time-frequency-transformed data and can find coherence for evoked and induced activity.

The following imaging methods provide an image of brain activity based on a distributed multiple source model:
* '''CLARA''' is an iterative application of LORETA images, focusing the obtained 3D image in each iteration step.
* '''LAURA '''uses a spatial weighting function that has the form of a local autoregressive function.
* '''LORETA''' has the 3D Laplacian operator implemented as spatial weighting prior.
* '''sLORETA''' is an unweighted minimum norm that is standardized by the resolution matrix.
* '''swLORETA '''is equivalent to sLORETA, except for an additional depth weighting.
* '''SSLOFO '''is an iterative application of standardized minimum norm images with consecutive shrinkage of the source space.
* A '''User-defined volume image''' allows to experiment with the different imaging techniques. It is possible to specify user-defined parameters for the family of distributed source images to create a new imaging technique.
* Bayesian source imaging: '''SESAME''' uses a semi-automated Bayesian approach to estimate the number of dipoles along with their parameters.

'''Surface image:'''

* The '''Surface Minimum Norm Image'''. If no individual MRI is available, the minimum norm image is displayed on a standard brain surface and computed for standard source locations. If available, an individual brain surface is used to construct the distributed source model and to image the brain activity.
* '''Cortical LORETA'''. Unlike classical LORETA, cortical LORETA is not computed in a 3D volume, but on the cortical surface.
* '''Cortical CLARA'''. Unlike classical CLARA, cortical CLARA is not computed in a 3D volume, but on the cortical surface.

'''Discrete model probing:'''

These images do not visualize source activity. Rather, they visualize properties of the currently applied discrete source model:
* The '''Multiple Source Probe Scan (MSPS)''' is a tool for the validation of a discrete multiple source model.
* The '''Source Sensitivity image''' displays the sensitivity of a selected source in the current discrete source model and is therefore data independent.

== Multiple Source Beamformer (MSBF) in the Time-frequency Domain ==

 
'''Short mathematical introduction'''

The BESA beamformer is a modified version of the linearly constrained minimum variance vector beamformer in the time-frequency domain as described in [https://dx.doi.org/10.1073/pnas.98.2.694 Gross et al., "Dynamic imaging of coherent sources: Studying neural interactions in the human brain", PNAS 98, 694-699, 2001]. It allows to image evoked and induced oscillatory activity in a user-defined time-frequency range, where time is taken relative to a triggered event.

The computation is based on a transformation of each channel's single trial data from the time domain into the time-frequency domain. This transformation is performed by the BESA Research Source Coherence module and leads to the complex spectral density Si (f,t), where i is the channel index and f and t denote frequency and time, respectively. Complex cross spectral density matrices C are computed for each trial:

<math>\mathrm{C}_{ij}\left( f,t \right) = \mathrm{S}_{i}\left( f,t \right) \cdot \mathrm{S}_{j}^{*}\left( f,t \right)</math>


The output power P of the beamformer for a specific brain region at location r is then computed by the following equation:

<math>\mathrm{P}\left( r \right) = \operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{-1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{-1}</math>


Here, Cr-1 is the inverse of the SVD-regularized average of Cij(f,t) over trials and the time-frequency range of interest; L is the leadfield matrix of the model containing a regional source at target location r and, optionally, additional sources whose interference with the target source is to be minimized; tr'[] is the trace of the [3×3] (MEG:[2×2]) submatrix of the bracketed expression that corresponds to the source at target location r.

In BESA Research, the output power P(r) is normalized with the output power in a reference time-frequency interval Pref(r). A value q ist defined as follows:

<math> \mathrm{q}\left( r \right) =
\begin{cases}
\sqrt{\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}(r)}} - 1 = \sqrt{\frac{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{\text{ref},r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}} - 1, & \text{for }\mathrm{P}(r) \geq \mathrm{P}_{\text{ref}}(r) \\

1 - \sqrt{\frac{\mathrm{P}_{\text{ref}}\left( r \right)}{\mathrm{P}\left( r \right)}} = 1 - \sqrt{\frac{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{\text{ref},r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}}, & \text{for }\mathrm{P}(r) < \mathrm{P}_{\text{ref}}(r)
\end{cases} </math>


Pref can be computed either from the corresponding frequency range in the baseline of the same condition (i.e. the beamformer images event-related power increase or decrease) or from the corresponding time-frequency range in a control condition (i.e. the beamformer images differences between two conditions). The beamformer image is constructed from values q(r) computed for all locations on a grid specified in the '''General Settings tab'''. For MEG data, the innermost grid points within a sphere of approx. 12% of the head diameter are assigned interpolated rather than calculated values).
q-values are shown in %, where where q[%] = q*100. Alternatively to the definition above, q can also be displayed in units of dB:

<math>\mathrm{q}\left\lbrack \text{dB} \right\rbrack = 10 \cdot \log_{10}\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}</math>


A beamformer operator is designed to pass signals from the brain region of interest r without attenuation, while minimizing interference from activity in all other brain regions. Traditional single-source beamformers are known to mislocalize sources if several brain regions have highly correlated activity. Therefore, the BESA beamformer extends the traditional single-source beamformer in order to implicitly suppress activity from possibly correlated brain regions. This is achieved by using a multiple source beamformer calculation that contains not only the leadfields of the source at the location of interest r, but also those of possibly interfering sources. As a default, BESA Research uses a bilateral beamformer, where specifically contributions from the homologue source in the opposite hemisphere are taken into account (the matrix L thus being of dimension N×6 for EEG and N×4 for MEG, respectively, where N is the number of sensors). This allows for imaging of highly correlated bilateral activity in the two hemispheres that commonly occurs during processing of external stimuli.

In addition, the beamformer computation can take into account possibly correlated sources at arbitrary locations that are specified in the current solution. This is achieved by adding their leadfield vectors to the matrix L in the equation above.

'''Applying the Beamformer'''

This chapter illustrates the usage of the BESA beamformer. The displayed figures are generated using the file ''''Examples/Learn-by-Simulations/AC-Coherence/AC-Osc20.foc'''' (see BESA Tutorial 6: "''Time-frequency analysis and Source coherence''").

'''Starting the beamformer from the time-frequency window'''

The BESA beamformer is applied in the time-frequency domain and therefore requires the Source Coherence module to be enabled. The time-frequency beamformer is especially useful to image in- or decrease of induced oscillatory activity. Induced activity cannot be observed in the averaged data, but shows up as enhanced averaged power in the TSE (Temporal-Spectral Evolution) plot. For instructions on how to initiate a beamformer computation in the time-frequency window, please refer to Chapter '''[[Source_Coherence_How_to...#How_to_Start_the_Beamformer_from_the_Time-Frequency_Window|How to Create Beamformer Images]]'''.

After the beamformer computation has been initiated in the time-frequency window, the source analysis window opens with an enlarged 3D image of the q-value computed with a '''bilateral beamformer'''. The result is superimposed onto the MR image assigned to the data set (individual or standard).

[[Image:SA 3Dimaging (5).gif]]

''Beamformer image after starting the computation in the Time-Frequency window. A bilateral pair of sources in the auditory cortex accounts for the highly correlated oscillatory induced activity. Only the bilateral beamformer manages to separate these activities; a traditional single-source beamformer would merge the two sources into one image maximum in the head center instead.''

'''Multiple source beamformer in the Source Analysis window'''

The 3D imaging display is part of the source analysis window. If you press the '''Restore''' button at the right end of the title bar of the 3D window, the window appears at the bottom right of the source analysis window. In the channel box, the averaged (evoked) data of the selected condition is shown. When a control condition was selected, its average is appended to the average of the target condition.

[[Image:SA 3Dimaging (6).gif]]

''Source Analysis window with beamformer image. The two sources have been added using the '''''Switch to''''' '''''Maximum''''' and '''''Add Source '''''toolbar buttons (see below). Source waveforms are computed from the displayed averaged data. Therefore, they do not represent the activity displayed in the beamformer image, which in this simulation example is induced (i.e. not phase-locked to the trigger)!''

When starting the beamformer from the time-frequency window, a bilateral beamformer scan is performed. In the source analysis window, the beamformer computation can be repeated taking into account possibly correlated sources that are specified in the current solution. Interfering activities generated by all sources in the current solution that are in the 'On' state are specifically suppressed ('''they enter the matrix L in the beamformer calculation''', see Chapter ''Short mathematical description'' above). The computation can be started from the '''Image''' menu or from the '''Image selector button''' dropdown menu. The '''Image''' menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window.

[[Image:SA 3Dimaging (7).gif]]

''Multiple source beamformer image calculated in the presence of a source in the left hemisphere. A '''single''' source scan has been performed. The source set in the current solution accounts for the left-hemispheric q-maximum in the data. Accordingly, the beamformer scan reveals only the as yet unmodeled additional activity in the right hemisphere (note the radiological convention in the 3D image display).''

The beamformer scan can be performed with a '''single''' or a '''bilateral''' source scan. The default scan type depends on the current solution:
* When the beamformer is started from the Time-Frequency window, the Source Analysis window opens with a new solution and a '''bilateral''' beamformer scan is performed.
* When the beamformer is started within the Source Analysis window, the default is
** a scan with a '''single''' source in addition to the sources in the current solution, if at least one source is active.
** a '''bilateral''' scan if no source in the current solution is active.

The default scan type is the multiple source beamformer. The non-default scan type can be enforced using the corresponding ''Volume Image / Beamformer'' entry in the '''Image''' menu.

'''Inserting Sources out of the Beamformer Image'''

The beamformer image can be used to add sources to the current solution. A simple double-click anywhere in the 2D- or 3D-view will generate a non-oriented regional source at the corresponding location. However, a better and easier way to create sources at image maxima and minima is to use the toolbar buttons '''Switch to Maximum''' [[Image:SA 3Dimaging (8).gif]] and '''Add Source''' [[Image:SA 3Dimaging (9).gif]].

Use the '''Switch to Maximum''' button to place the red crosshair of the 3D window onto a local image maximum or minimum. Hitting the '''Add Source''' button creates a regional source at the location of the crosshair and therefore ensures the exact placement of the source at the image extremum. Moreover, the '''Add Source''' button generates an oriented regional source. BESA Research automatically estimates the source orientation that contributes most to the power in the target time-frequency interval (or the reference time-frequency interval, if its power is larger than that in the target interval). The accuracy of this orientation estimate depends largely on the noise content of the data. The smaller the signal-to-noise ratio of the data, the lower is the accuracy of the orientation estimate. '''This feature allows to use the beamformer as a tool to create a source montage for source coherence analysis, where it is of advantage to work with oriented sources'''.

'''Notes:'''

* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image '''menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the''' Image''' menu.
* For scaling options, use the [[Image:SA 3Dimaging (10).gif]] and [[Image:SA 3Dimaging (11).gif]] '''Image Scale toolbar''' buttons.
* Parameters used for the beamformer calculations can be set in the '''Standard Volumes''' of the ''Image Settings dialog box.''

== Dynamic Imaging of Coherent Sources (DICS) ==

 
'''Short mathematical introduction'''

Dynamic Imaging of Coherent Sources (DICS) is a sophisticated method for imaging cortico-cortical coherence in the brain, or coherence between an external reference (e.g. EMG channel) and cortical structures. DICS can be applied to localize evoked as well as induced coherent cortical activity in a user-defined time-frequency range.

DICS was implemented in BESA closely following [https://dx.doi.org/10.1073/pnas.98.2.694 Gross et al., "Dynamic imaging of coherent sources: Studying neural interactions in the human brain", PNAS 98, 694-699, 2001].

The computation is based on a transformation of each channel's single trial data from the time domain into the frequency domain. This transformation is performed by the BESA Research Coherence module and results in the complex spectral density matrix that is used for constructing the spatial filter similar to beamforming.

DICS computation yields a 3-D image, each voxel being assigned a coherence value. Coherence values can be described as a neural activity index and do not have a unit. The neural activity index contrasts coherence in a target time-frequency bin with coherence of the same time-frequency bin in a baseline.

'''DICS for cortico-cortical coherence is computed as follows:'''

Let L(r) be the leadfield in voxel r in the brain and C the complex cross-spectral density matrix. The spatial filter W(r) for the voxel r in the head is defined as follows:

<math>W\left( r \right) = \left\lbrack L^{T}\left( r \right) \cdot C^{- 1} \cdot L\left( r \right) \right\rbrack^{- 1} \cdot L^{T}(r) \cdot C^{- 1}</math>


The cross-spectrum between two locations (voxels) r1 and r2 in the head are calculated with the following equation:

<math>C_{s}\left( r_{1},r_{2} \right) = W\left( r_{1} \right) \cdot C \cdot W^{*T}\left( r_{2} \right),</math>


where <nowiki>*T</nowiki> means the transposed complex conjugate of a matrix. The cross-spectral density can then be calculated from the cross spectrum as follows:

<math>c_{s}\left( r_{1},r_{2} \right) = \lambda_{1}\left\{ C_{s}\left( r_{1},r_{2} \right) \right\},</math>


where λ1{} indicates the largest singular value of the cross spectrum. Once the cross spectral density is estimated, the connectivity¹(CON) between the two brain regions r1 and r2 are calculated as follows:

<math>\text{CON}\left( r_{1},r_{2} \right) = \frac{c_{s}^{\text{sig}}\left( r_{1},r_{2} \right) - c_{s}^{\text{bl}}(r_{1},r_{2})}{c_{s}^{\text{sig}}\left( r_{1},r_{2} \right) + c_{s}^{\text{bl}}(r_{1},r_{2})},</math>


where cssig is the cross-spectral density for the signal of interest between the two brain regions r1 and r2, and csbl is the corresponding cross spectral density for the baseline or the control condition, respectively. In the case DICS is computed with a cortical reference, r1 is the reference region (voxel) and remains constant while r2 scans all the grid points within the brain sequentially. In that way, the connectivity between the reference brain region and all other brain regions is estimated. The value of CON(r1, r2) falls in the interval [-1 1]. If the cross-spectral density for the baseline is 0 the connectivity value will be 1. If the cross-spectral density for the signal is 0 the connectivity value will be -1.

¹ Here, the term connectivity is used rather than coherence, as strictly speaking the coherence equation is defined slightly differently. For simplicity reasons the rest of the tutorial uses the term coherence.

'''DICS for cortico-muscular coherence is computed as follows:'''

When using an external reference, the equation for coherence calculation is slightly different compared to the equation for cortico-cortical coherence. First of all, the cross-spectral density matrix is not only computed for the MEG/EEG channels, but the external reference channel is added. This resulting matrix is Call. In this case, the cross-spectral density between the reference signal and all other MEG/EEG

channels is called cref. It is only one column of Call. Hence, the cross-spectrum in voxel r is calculated with the following equation:

<math>C_{s}\left( r \right) = W\left( r \right) \cdot c_{\text{ref}}</math>


and the corresponding cross-spectral density is calculated as the sum of squares of Cs:

<math>c_{s}\left( r \right) = \sum_{i = 1}^{n}{C_{s}\left( r \right)_{i}^{2}},</math>


where n is 2 for MEG and 3 for EEG. This equation can also be described as the squared Euclidean norm of the cross-spectrum:

<math>c_{s}\left( r \right) = \left\| C_{s} \right\|^{2},</math>


The power in voxel r is calculated as in the cortico-cortical case:

<math>p\left( r \right) = \lambda_{1}\left\{ C_{s}(r,r) \right\}.</math>


At last, coherence between the external reference and cortical activity is calculated with the equation:

<math>\text{CON}\left( r \right) = \frac{c_{s}(r)}{p\left( r \right) \cdot C_{\text{all}}(k,k)},</math>


where Call(k, k) is the (k,k)-th diagonal element of the matrix Call.

DICS is particularly useful, if coherence is to be calculated without an a-priory source model (in contrast to source coherence based on pre-defined source montages). However, the recommended analysis strategy for DICS is to use a brain source as a starting point for coherence calculation that is known to contribute to the EEG/MEG signal of interest. For example, one might first run a beamformer on the time-frequency range of interest and use the voxel with the strongest oscillatory activity as a starting point for DICS. The resulting coherence image will again lead to several maxima (ordered by magnitude), which in turn can serve as starting points for DICS calculation. This way, it is possible to detect even weak sources that show coherent activity in the given time-frequency range.

The other significant application for DICS is estimating coherence between an external source and voxels in the brain. For example, an external source can be muscle activity recoded by an electrode placed over the according peripheral region. This way, the direct relationship between muscle activity and brain activation can be measured.

'''Starting DICS computation from the Time-Frequency Window'''

DICS is particularly useful, if coherence in a user-defined time-frequency bin (evoked or induced) is to be calculated between any two brain regions or between an external reference and the brain. DICS runs only on time-frequency decomposed data, so time-frequency analysis needs to be run before starting DICS computation.

To start the DICS computation, left-drag a window over a selected time-frequency bin in the Time-Frequency Window. Right-click and select “Image”. A dialogue will open (see fig. 1) prompting you to specify time and frequency settings as well as the baseline period. It is recommended to use a baseline period of equal length as the data period of interest. Make sure to select “DICS” in the top row and press “'''Go'''”.

[[Image:SA 3Dimaging (21).gif|450px|thumb|c|none|Fig. 1: Time and frequency settings for DICS and MSBF]]

Next, a window will appear allowing you to specify the reference source for coherence calculation (see fig. 2). It is possible to select a channel (e.g. EMG) or a brain source. If a brain source is chosen and no source analysis was computed beforehand, the option “Use current cross-hair position” must be chosen. In case discrete source analysis was computed previously, the selected source can be chosen as the reference for DICS. Please note that DICS can be re-computed with any cross-hair or source position at a later stage.

[[Image:SA 3Dimaging (1).jpg|400px|thumb|c|none|Fig. 2: Possible options for choosing the reference]]

Confirming with “'''OK'''” will start computation of coherence between the selected channel/voxel and all other brain voxels. In case DICS is computed for a reference source in the brain, it can be advantageous to run a beamforming analysis in the selected time-frequency window first and use one of the beamforming maxima as reference for DICS. Fig. 3 shows an example for DICS calculation.

[[Image:SA 3Dimaging (22).gif|500px|thumb|c|none|Fig. 3: Coherence between left-hemispheric auditory areas and the selected voxel in the right auditory cortex.]]

Coherence values range between -1 and 1. If coherence in the signal is much larger than coherence in the baseline (control condition) then the DICS value is going to approach 1. Contrary, if coherence in the baseline is much larger than coherence in the signal, then the DICS value is going to approach -1. At last, if coherence in the signal is equal to coherence in the baseline, then the DICS value is 0.

In case DICS is to be re-computed with a different reference, simply mark the desired reference position by placing the cross-hair in the anatomical view and select “DICS” in the middle panel of the source analysis window (see Fig. 4). In case an external reference is to be selected, click on “DICS” in the middle panel to bring up the DICS dialogue (see. Fig. 2) and select the desired channel. Please note that DICS computation will only be available after running time-frequency analysis.

[[Image:SA 3Dimaging (23).gif|700px|thumb|c|none|Fig. 4: Integration of DICS in the Source Analysis window]]

== Multiple Source Beamformer (MSBF) in the Time Domain ==
''(requires Besa Research 7.0 or higher)''

===Short mathematical introduction===

Beamforming approach can be also applied in the time domain data. This approach was introduced as linearly constrained minimum variance (LCMV) beamformer (Van Veen et al., 1997). It allows to image evoked activity in a user-defined time range, where time is taken relative to a triggered event, and to estimate source waveforms using the calculated spatial weight at locations of interest. For an implementation of the beamformer in the time domain, data covariance matrices are required, while complex cross spectral density matrices are used for the beamformer approaches in the time-frequency domain as described in the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section.

The bilateral beamformer introduced in the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section is also implemented for the time-domain beamformer to take into account contributions from the homologue source in the opposite. This allows for imaging of highly correlated bilateral activity in the two hemispheres that commonly occurs during processing of external stimuli. In addition, the beamformer computation can take into account possibly correlated sources at arbitrary locations.
The beamformer spatial weight W(r) for the voxel r in the brain is defined as follows (Van Veen et al., 1997):

[[File:MSBF1.png]]

where '''C-1''' is the inversed regularized average of covariance matrix over trials, '''L''' is the leadfield matrix of the model containing a regional source at target location r and optionally
additional sources whose interference with the target source is to be minimized. The beamformer spatial weight '''W'''(r) can be applied to the measured data to estimate source
waveform at a location r (beamformer virtual sensor):

[[File:MSBF2.png]]

where '''S'''(r,t) represents the estimated source waveform and '''M'''(t) represents measured EEG or MEG signals.
The output power P of the beamformer for a specific brain region at location r is computed by the following equation:

[[File:MSBF3.png]]

where tr’[ ] is the trace of the [3×3] (MEG: [2×2]) submatrix of the bracketed expression that corresponds to the source at target location r.
Beamformer can suppress noise sources that are correlated across sensors. However, uncorrelated noise will be amplified in a spatially non-uniform manner, with increasing
distortion with increasing distance from the sensors (Van Veen et al., 1997; Sekihara et al., 2001). For this reason, estimated source power should be normalized by a noise power.
In BESA Research, the output power P(r) is normalized with the output power in a baseline interval or with the output power of a uncorrelated noise: P(r) / Pref (r).
The time-domain beamformer image is constructed from values q(r) computed for all locations on a grid specified in the '''General Settings''' tab. A value q(r) is defined as described in
the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section with data covariance matrices instead of cross-spectral density matrices.

===Applying the Beamformer===

This chapter illustrates the usage of the BESA beamformer in the time domain. The displayed figures are generated using the file ‘Examples/ERP-Auditory-Intensity/S1.cnt’.

'''Starting the time-domain beamformer from the Average tab of the Paradigm dialog box'''

The time-domain beamformer is needed data covariance matrices and therefore requires the ERP module to be enabled. After the beamformer computation has been initiated in the
'''Average tab of the Paradigm dialog box''', the source analysis window opens with an enlarged 3D image of the q-value computed with a bilateral beamformer. The result is
superimposed onto the MR image assigned to the data set (individual or standard).

[[File:MSBF44.png]]

''Beamformer image for auditory evoked data after starting the computation in the '''Average tab of the Paradigm dialog box'''. The bilateral beamformer manages to separate the
activities in auditory areas, while a traditional single-source beamformer would merge the two sources into one image maximum in the head center instead.''

'''Multiple-source beamformer in the Source Analysis window'''

The 3D imaging display is part of the source analysis window. In the Channel box, the averaged (evoked) data of the selected condition is shown. Selected covariance intervals in
the ERP module can be checked in the Channel box. The red, gray, and blue rectangles indicate signal, baseline, and common interval, respectively.

[[File:MSBF55.png]]

''Source Analysis window with beamformer image. The two beamformer virtual sensors have been added using the Switch to Maximum and Add Source toolbar buttons (see below).
Source waveforms are computed using the beamformer spatial weights and the displayed averaged data (the noise normalized weights (5% noise) option was used to compute the
beamformer image).''

When starting the beamformer from the '''Average tab of the Paradigm dialog box''', the bilateral beamformer scan is performed. In the source analysis window, the beamformer computation can be repeated taking into account possibly correlated sources that are specified in the current solution. Interfering activities generated by all sources in the current solution that are in the 'On' state are specifically suppressed (they enter the leadfield matrix L in the beamformer calculation). The computation can be started from the '''Image''' menu or from the Image selector button [[File:MSBF_Button.png|22px|Image: 22 pixels]] dropdown menu. The Image menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window.

[[File:MSBF66.png]]

''Multiple-source beamformer image calculated in the presence of a source in the left hemisphere. A single-source scan has been performed instead of a bilateral beamforemr. The
source set in the current solution accounts for the left-hemispheric q-maximum in the data. Accordingly, the beamformer scan reveals only the as yet unmodeled additional activity in
the right hemisphere (note the radiological convention in the 3D image display). The source waveform of the beamformer virtual sensor in the left hemisphere is not shown since the
location (blue square in the figure) is not considered for the multiple-source beamformer.''

The beamformer scan can be performed with a single or a bilateral source scan. The default scan type depends on the current solution:
When the beamformer is started from the '''Average tab of the Paradigm dialog box''' the Source Analysis window opens with a new solution and a bilateral beamformer scan is
performed.
When the beamformer is started within the Source Analysis window, the default is:

* a scan with a single source in addition to the sources in the current solution, if at least one source is active.
* a bilateral scan if no source in the current solution is active.
* a scan with a single source when scalar-type beamformer is selected in the '''beamformer option dialog box'''.

The default scan type is the multiple source beamformer. The non-default scan type can be enforced using the corresponding Volume Image / Beamformer entry in the Image main
menu or in the beamformer option dialog box (only for the time-domain beamformer).

===Inserting Sources as Beamformer Virtual Sensor out of the Beamformer Image===

This is similar to the inserting sources out of the beamformer image in Multiple Source Beamformer (MSBF) in the Time-frequency Domain section.
The beamformer image can be used to add beamformer virtual sensors to the current solution. A simple double-click anywhere in the 3D view (not in the 2D view) will generate a
source at the corresponding location. A better and easier way to create sources at image maxima and minima is to use the toolbar buttons '''Switch to Maximum''' and '''Add Source'''

This feature allows to use the beamformer as a tool to create a source montage for '''source coherence''' analysis. A source montage file (*.mtg) for beamformer virtual sensors can
be saved using File \ Save Source Montage As… entry.

The time-domain beamformer image can be also used to add regional or dipole sources to the current solution. Press '''N''' key when there is no source in the current source array or
there is more than one beamformer virtual sensor. To create a new source array for beamformer virtual sensor, press '''N''' key when there is more than one regional or dipole source in
the current source array.

===Notes===

* You can hide or re-display the last computed image by selecting ''Hide Image'' entry in the '''Image''' menu.
* The current image can be exported to ASCII, ANALYZE, or BrainVoyager (vmp) format from the '''Image''' menu.
* For scaling options, use the and Image Scale toolbar buttons.
* Parameters used for the beamformer calculations can be set in the '''Standard Volume tab of the Image Settings dialog box'''.
* Note that Model, Residual, Order, and Residual variance are not shown for the beamformer virtual sensor type sources.

===References===

* Sekihara, K., Nagarajan, S. S., Poeppel, D., Marantz, A., & Miyashita, Y. (2001). Reconstructing spatio-temporal activities of neural sources using an MEG vector beamformer technique. IEEE Transactions on Biomedical Engineering, 48(7), 760–771.

* Van Veen, B. D., Van Drongelen, W., Yuchtman, M., & Suzuki, A. (1997). Localization of brain electrical activity via linearly constrained minimum variance spatial filtering. IEEE Transactions on Biomedical Engineering, 44(9), 867–880

== CLARA ==

CLARA ('Classical LORETA Analysis Recursively Applied') is an iterative application of weighted LORETA images with a reduced source space in each iteration.

In an initialization step, a LORETA image is calculated. Then in each iteration the following steps are performed:

# The obtained image is spatially smoothed (this step is left out in the first iteration).
# All grid points with amplitudes below a threshold of 1% of the maximum activity are set to zero, thus being effectively eliminated from the source space in the following step.
# The resulting image defines a spatial weighting term (for each voxel the corresponding image amplitude).
# A LORETA image is computed with an additional spatial weighting term for each voxel as computed in step 3. By the default settings in BESA Research, the regularization values used in the iteration steps are slightly higher than that of the initialization LORETA image.

The procedure stops after 2 iterations, and the image computed in the last iteration is displayed. Please note that you can change all parameters by creating a user-defined volume image.

The advantage of CLARA over non-focusing distributed imaging methods is visualized by the figure below. Both images are computed from the N100 response in an auditory oddball experiment (file '''Oddball.fsg''' in subfolder ''fMRI+EEG-RT-Experiment'' of the ''Examples'' folder). The CLARA image is much more focal than the sLORETA image, making it easier to determine the location of the image maxima.

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (24).gif|thumb|350px|sLORETA image]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (25).gif|thumb|350px|CLARA image]] </li>
</ul></div>

'''Notes:'''

* Starting CLARA: CLARA can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter ''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]'' for important information on regularization of distributed inverses.

== LAURA ==

LAURA (Local Auto Regressive Average) belongs to the distributed inverse method of the family of weighted minimum norm methods ([https://doi.org/10.1023/A:1012944913650 Grave de Peralta Menendeza et al., "Noninvasive Localization of Electromagnetic Epileptic Activity. I. Method Descriptions and Simulations", BrainTopography 14(2), 131-137, 2001]). LAURA uses a spatial weighting function that includes depth weighting and that term has the form of a local autoregressive function.

The source activity is estimated by applying the general formula for a weighted minimum norm:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T}\left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings.''

In LAURA, V contains both a depth weighting term W and a representation of a local autoregressive function A. V is computed as:

<math>\mathrm{V} = \left( \mathrm{U}^{T} \cdot \mathrm{U} \right)^{-1}</math>


Where

<math>\mathrm{U} = \left( \mathrm{W} \cdot \mathrm{A} \right) \otimes \mathrm{I}_{3}</math>


Here, <math>\otimes</math> denotes the Kronecker product. I3 is the [3×3] identity matrix. W is an [s×s] diagonal matrix (with s the number of source locations on the grid), where each diagonal element is the inverse of the maximum singular value of the corresponding regional source's leadfields. The formula for the diagonal components Aii and the off-diagonal components Aik are as follows:

<math>\mathrm{A}_{ii} = \frac{26}{\mathrm{N}_{i}}\sum_{k \subset V_{i}}^{}\frac{1}{\mathrm{d}_{ik}^{2}}</math>


<math>
\mathrm{A}_{ik} =
\begin{cases}
- 1/\operatorname{dist}\left( i,k \right)^{2}, & \text{if } k \subset V_{i} \\
0, & \text{otherwise}
\end{cases}
</math>


Here, Vi is the vicinity around grid point i that includes the 26 direct neighbors.

The LAURA image in BESA Research displays the norm of the 3 components of S at each location r. Using the menu function ''Image / Export Image As... ''you have the option to save this norm of S or alternatively all components separately to disk.

'''Notes:'''

* '''Grid spacing:''' Due to memory limitations, LAURA images require a grid spacing of 7 mm or more.
* '''Computation time:''' Computation speed during the first LAURA image calculation depends on the grid spacing (computation is faster with larger grid spacing). After the first computation of a LAURA image, a '''*.laura''' file is stored in the data folder, containing intermediate results of the LAURA inverse. This file is used during all subsequent LAURA image computations. Thereby, the time needed to obtain the image is substantially reduced.
* '''MEG:''' In the case of MEG data, an additional constraint is implemented in the LAURA algorithm that prevents solutions from containing radial source currents (compare Pascual-Marqui, ISBET Newsletter 1995, 22-29). In MEG, an additional source space regularization is necessary in the inverse matrix operation required compute V
* '''Starting LAURA:''' LAURA can be started from the''' Image''' menu or from the '''Image Selection''' button.
* '''Regularization:''' Please refer to Chapter'' “Regularization of distributed volume images” ''for important information on regularization of distributed inverses.

== LORETA ==

LORETA ("Low Resolution Electromagnetic Tomography") is a distributed inverse method of the family of ''weighted minimum norm'' methods. LORETA was suggested by R.D. Pascual-Marqui (International Journal of Psychophysiology. 1994, 18:49-65). LORETA is characterized by a smoothness constraint, represented by a discrete 3D Laplacian.

The source activity is estimated by applying the general formula for a weighted minimum norm:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T}\left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings.''

In LORETA, V contains both a depth weighting term and a representation of the 3D Laplacian matrix. V is computed as:

<math>\mathrm{V} = \left( \mathrm{U}^{T} \cdot \mathrm{U} \right)^{- 1}</math>


where

<math>\mathrm{U} = \left( \mathrm{W} \cdot \mathrm{A} \right) \otimes \mathrm{I}_{3}</math>


Here, <math>\otimes</math> denotes the Kronecker product. I3 is the [3x3] identity matrix. W is an [sxs] diagonal matrix (with s the number of source locations on the grid), where each diagonal element is the inverse of the maximum singular value of the corresponding regional source's leadfields. A contains the 3D Laplacian and is computed as

<math>\mathrm{A} = \mathrm{Y} - \mathrm{I}_{s}</math>


with Is the [sxs] identity matrix, where s is the number of sources (= three times the number of grid points) and

<math>\mathrm{Y} = \frac{1}{2}\left\{ \mathrm{I}_{s} + \left\lbrack \operatorname{diag}\left( \mathrm{Z} \cdot \left\lbrack 111 \ldots 1 \right\rbrack^{T} \right) \right\rbrack^{- 1} \right\} \cdot \mathrm{Z}</math>


where

<math>
\mathrm{Z}_{ik} =
\begin{cases}
1/6, & \text{if } \operatorname{dist}\left( i,k \right) = 1 \text{ grid point} \\
0, & \text{otherwise}
\end{cases}
</math>


The LORETA image in BESA Research displays the norm of the 3 components of S at each location r. Using the menu function ''Image / Export Image As... ''you have the option to save this norm of S or alternatively all components separately to disk.

'''Notes:'''
* '''Grid spacing:''' Due to memory limitations, LORETA images require a grid spacing of 5 mm or more.
* '''Computation time:''' Computation speed during the first LORETA image calculation depends on the grid spacing (computation is faster with larger grid spacing). After the first computation of a LORETA image, a '''<nowiki>*.loreta</nowiki>''' file is stored in the data folder, containing intermediate results of the LORETA inverse. This file is used during all subsequent LORETA image computations. Thereby, the time needed to obtain the image is substantially reduced.
* '''MEG''': In the case of MEG data, an additional constraint is implemented in the LORETA algorithm that prevents solutions from containing radial source currents (Pascual-Marqui, ISBET Newsletter 1995, 22-29). In MEG, an additional source space regularization is necessary in the inverse matrix operation required compute V.
* '''Starting LORETA:''' LORETA can be started from the''' Image''' menu or from the '''Image Selection '''button.
* '''Regularization:''' Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed source models.

== sLORETA ==

This distributed inverse method consists of a ''standardized, unweighted minimum norm''. The method was originally suggested by R.D. Pascual-Marqui (Methods & Findings in Experimental & Clinical Pharmacology 2002, 24D:5-12) Starting point is an unweighted minimum norm computation:

<math>\mathrm{S}_{\text{MN}}\left( t \right) = \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings''.

This minimum norm estimate is now standardized to produce the sLORETA activity at a certain brain location r:

<math>\mathrm{S}_{\text{sLORETA}, r} = \mathrm{R}_{rr}^{-1/2} \cdot \mathrm{S}_{\text{MN},r}</math>


SsMN,r is the [3x1] (MEG: [2x1]) minimum norm estimate of the 3 (MEG: 2) dipoles at location r. Rrr is the [3x3] (MEG: [2x2]) diagonal block of the resolution matrix R that corresponds to the source components at the target location r. The resolution matrix is defined as:

<math>\mathrm{R} = \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{L}^{T} + \lambda \cdot \mathrm{I} \right)^{-1} \cdot \mathrm{L}</math>


The sLORETA image in BESA Research displays the norm of SsLORETA, r at each location r. Using the menu function ''Image / Export Image As...'' you have the option to save this norm of SsLORETA, r or alternatively all components separately to disk.

'''Notes:'''

* sLORETA can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== swLORETA ==

This distributed inverse method is a ''standardized, depth-weighted minimum norm'' (E. Palmero-Soler et al 2007 Phys. Med. Biol. 52 1783-1800). It differs from sLORETA only by an additional depth weighting.

Starting point is a depth-weighted minimum norm computation:

<math>\mathrm{S}_{\text{MN}}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings''.

V is the diagonal depth weighting matrix. For s grid locations, V is of dimension [3s x 3s] (MEG: [2s x 2s]). Each diagonal element of V is the inverse of the first singular value of the leadfield of the corresponding regional source. Hence, the first 3 (MEG: 2) diagonal elements equal the inverse of the largest eigenvalue of the leadfield matrix of regional source 1, and so on.

This minimum norm estimate is now standardized to produce the swLORETA activity at a certain brain location r:

<math>\mathrm{S}_{\text{swLORETA},r} = \mathrm{R}_{rr}^{-1/2} \cdot \mathrm{S}_{\text{MN},r}</math>


SsMN,r is the [3x1] (MEG: [2x1]) depth-weighted minimum norm estimate of the regional source at location r. Rrr is the [3x3] (MEG: [2x2]) diagonal block of the resolution matrix R that corresponds to the source components at the target location r. The resolution matrix is defined as:

<math>\mathrm{R} = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} + \lambda \cdot \mathrm{I} \right)^{-1} \cdot \mathrm{L}</math>


The swLORETA image in BESA Research displays the norm of SswLORETA, r at each location r. Using the menu function ''Image / Export Image As...'' you have the option to save this norm of SswLORETA, r or alternatively all components separately to disk.

'''Notes:'''

* sLORETA can be started from the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== sSLOFO ==

SSLOFO (standardized shrinking LORETA-FOCUSS) is an iterative application of weighted distributed source images with a reduced source space in each iteration ([https://dx.doi.org/10.1109/TBME.2005.855720 Liu et al., "Standardized shrinking LORETA-FOCUSS (SSLOFO): a new algorithm for spatio-temporal EEG source reconstruction", IEEE Transactions on Biomedical Engineering 52(10), 1681-1691, 2005]).

In an initialization step, an [[#sLORETA | sLORETA]] image is calculated. Then in each iteration the following steps are performed:

# A weighted minimum norm solution is computed according to the formula <math display="inline">\mathrm{S} = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}</math> . Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D is the data at the time point under consideration. V is a diagonal spatial weighting matrix that is computed in the previous iteration step. In the first iteration, the elements of V contain the magnitudes of the initially computed LORETA image.
# Standardization of this weighted minimum norm image is performed with the resolution matrix as in [[#sLORETA | sLORETA]].
# The obtained standardized weighted minimum norm image is being smoothed to get Ssmooth.
# All voxels with amplitudes below a threshold of 1% of the maximum activity get a weight of zero in the next iteration step, thus being effectively eliminated from the source space in the next iteration step.
# For all other voxels, compute the elements of the spatial weighting matrix V to be used in the next iteration as follows: <math display="inline">\mathrm{V}_{ii,\text{next iteration}} = \frac{1}{\left\| \mathrm{L}_{i} \right\|} \cdot \mathrm{S}_{ii,\text{smooth}} \cdot \mathrm{V}_{ii,\text{current iteration}}</math>



The procedure stops after 3 iterations. Please note that you can change all parameters by creating a [[#User-Defined Volume Image | user-defined volume image]].

'''Notes:'''
* '''Starting sSLOFO''': sSLOFO can be started from the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter ''[[#Regularization of distributed volume images | Regularization of distributed volume images]]'' for important information on regularization of distributed inverses.

== User-Defined Volume Image ==

In addition to the predefined 3D imaging methods in BESA Research, it is possible to create user-defined imaging methods based on the general formula for distributed inverses:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. Custom-defined parameters are:* The spatial weighting matrix V: This may include depth weighting, image weighting, or cross-voxel weighting with a 3D Laplacian (as in LORETA) or an autoregressive function (as in LAURA).

* Regularization: The term in parentheses is generally regularized. Note that regularization has a strong effect on the obtained results. Please refer to chapter “''Regularization of Distributed Volume Images” ''for more information.
* Standardization: Optionally, the result of the distributed inverse can be standardized with the resolution matrix (as in sLORETA).
* Iterations: Inverse computations can be applied iteratively. Each iteration is weighted with the image obtained in the previous iteration.

All parameters for the user-defined volume image are specified in the User-Defined Volume Tab of the Image Settings dialog box. Please refer to chapter “''User-Defined Volume Tab”'' for details.

'''Notes:'''
* Starting the user-defined volume image: the image calculation can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== Regularization of distributed volume images ==

Distributed source images require the inversion of a term of the form L V LT. This term is generally regularized before its inversion. In BESA Research, selection can be made between two different regularization approaches (parameters are defined in the ''Image Settings dialog box''):

* '''Tikhonov regularization''': In Tikhonov regularization, the term L V LT is inverted as (L V LT +λ I)-1. Here, l is the regularization constant, and I is the identity matrix.
* One way of determining the optimum regularization constant is by minimizing the ''generalized cross'' ''validation error'' (CVE).
* Alternatively, the regularization constant can be specified manually as a percentage of the trace of the matrix L V LT.
* '''TSVD''': In the truncated singular value decomposition (TSVD) approach, an SVD decomposition of L V LT is computed as  L V LT = U S UT, where the diagonal matrix S contains the singular values. All singular values smaller than the specified percentage of the maximum singular values are set to zero. The inverse is computed as U S-1 UT, where the diagonal elements of S-1 are the inverse of the corresponding non-zero diagonal elements of S.

Regularization has a critical effect on the obtained distributed source images. The results may differ completely with different choices of the regularization parameter (see examples below). Therefore, it is important to evaluate the generated image critically with respect to the regularization constant, and to keep in mind the uncertainties resulting from this fact when interpreting the results. The default setting in BESA Research is a TSVD regularization with a 0.03% threshold. However, this value might need to be adjusted to the specific data set at hand.

The following example illustrates the influence of the regularization parameter on the obtained images. The data used here is condition '''St-Cor of dataset Examples \ TFC-Error-Related-Negativity \ Correct+Error.fsg''' at 176 ms following the visual stimulus. Discrete dipole analysis reveals the main activity in the left and right lateral visual cortex at this latency.

[[Image:SA 3Dimaging (42).gif]]

''Discrete source model at 176 ms: Main activity in the left and right lateral visual cortex, no visual midline activity.''

LORETA images computed at this latency depend critically on the choice of the regularization constant. The following 3D images are created with TSVD regularization with SVD cutoffs of 0.1%, 0.005%, and 0.0001%, respectively. The volume grid size was 9 mm. The example demonstrates the dramatic effect of regularization and demonstrates the typical tradeoff between too strong regularization (leading to too smeared 3D images that tend to show blurred maxima) and too small regularization (resulting in too superficial 3D images with multiple maxima).

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (43).gif|thumb|350px|'''SVD cutoff 0.1%''': Regularization too strong. No separation between sources, mislocalization towards the middle of the brain.]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (44).gif|thumb|350px|'''SVD cutoff 0.005%''': Appropriate regularization. Separation of the bilateral activities. Location in agreement with the discrete multiple source model.]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (45).gif|thumb|350px|'''SVD cutoff 0.0001%''': Too small regularization. Mislocalization, too superficial 3D image. ]] </li>
</ul></div>

The automatic determination of the regularization constant using the CVE approach does not necessarily result in the optimum regularization parameter either. In this example, the unscaled CVE approach rather resembles the TSVD image with a cutoff of 0.0001%, i.e. regularization is too small. Therefore, it is advisable to compare different settings of the regularization parameter and make the final choice based on the above-mentioned considerations.

== Cortical LORETA ==

Cortical LORETA is principally the same technique as LORETA, however, Cortical LORETA is not computed in a 3D volume, but on the cortical surface.

The cortical reconstruction in BESA Research fed from BESA MRI is a closed 2D surface with no boundaries and a very close approximation of the actual cortical form. It consists of an irregular triangulated grid.

The Laplace operator that is used for identifying a smooth solution in a three-dimensional space is exchanged with a Laplace operator that runs on the two-dimensional cortical surface.

There is a wide variety of 2D Laplace operators with different characteristics. The general form of the discrete Laplace operator is

<math>\Delta f\left( p_{i} \right) = \frac{1}{d_{i}}\sum_{j \in N(i)}^{}{w_{ij}\left\lbrack f\left( p_{i} \right) - f\left( p_{j} \right) \right\rbrack},</math>


where '''pi''' is the '''i-th''' node of the triangular mesh, '''f(pi) '''is the value of a function f defined on the cortical mesh at the node '''pi''', '''wij''' is the weight for the connection between the nodes '''pi''' and '''pj''' and '''di''' is a normalization factor for the '''i-th''' row of the operator. Furthermore, '''N(i)''' is the set of indices corresponding to the direct (also called "1-ring") neighbors of '''pi'''.

BESA offers the choice of three Laplace operators with slightly different characteristics.

* '''Unweighted Graph Laplacian''': This is the simplest operator. It takes into account only the adjacency of the nodes and not the geometry of the mesh:

<math>
w_{ij} =
\begin{cases}
1, & \text{if } p_{i} \text{ and } p_{j} \text{ are connected by an edge} \\
0, & \text{otherwise}
\end{cases}
</math>

<math>d_{i} = 1</math>


[[Image:SA 3Dimaging (4).jpg |450px]]

* '''Weighted Graph Laplacian:''' This operator is similar to the unweighted graph Laplacian but with different weights for the different connections. The connections between nearby nodes get larger weights than the connections between farther nodes:

<math>w_{ij} = \frac{1}{\operatorname{dist}\left( p_{i},p_{j} \right)}</math>

<math>d_{i} = \sum_{j \in N(i)}^{} {\operatorname{dist}\left(p_{i}, p_{j} \right)}</math>


where '''dist''' ('''pi''' , '''pj''') is the distance between the nodes '''pi '''and '''pj'''.

[[Image:SA 3Dimaging (6).jpg|450px]]

* '''Geometric Laplacian with mixed area weights''': This operator takes into account the angles in the corresponding triangles into account as well as the area around the nodes in order to determine the connection weights:

<math>w_{ij} = \frac{\cot\left( \alpha_{ij} \right) + \cot\left( \beta_{ij} \right)}{2}</math>

<math>d_{i} = A_{\text{mixed}}</math>


where '''αij''' and '''βij''' denote the two angles opposite to the edge ('''i , j''') and '''Amixed '''is either the Voronoi area, or 1/2 of the triangle area or 1/4 of the triangle area depending on the type of the triangle.

[[Image:SA 3Dimaging (8).jpg|450px]]

'''Regularization and other parameters:'''

[[Image:SA 3Dimaging (46).gif ‎]]

* '''SVD cutoff''': The regularization for the inverse operator as a percent of the largest singular value.
* '''Depth weighting''': Turn depth weighting on or off.
* '''Laplacian type''': Selection of Laplacian operators (see above).

'''Notes:'''
* '''Starting Cortical LORETA''': Cortical LORETA can be started from the sub-menu '''Surface Image''' of the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]''” for important information on regularization of distributed inverses.

== Cortical CLARA ==

Cortical CLARA is principally the same technique as CLARA, but Cortical CLARA is not computed in a 3D volume, but on the cortical surface. Instead of using a LORETA image as the basis for the iterative application, cortical CLARA uses cortical LORETA.

'''Regularization and other parameters:'''

[[Image:SA 3Dimaging (47).gif]]

* '''SVD cutoff''': The regularization for the inverse operator as a percent of the largest singular value.
* '''Depth weighting''': Turn depth weighting on or off.
* '''Laplacian type''': Selection of Laplacian operators (see Cortical LORETA).
* '''No of iterations''': Number of iterations for CLARA. The more iterations are used, the sparser becomes the solution.
* '''Automatic''': The algorithm tries to determine the number of iterations automatically. The goodness of fit (GOF) is calculated after every iteration and if there is a big jump in the GOF then the algorithm will stop. If no jumps appear during the calculations then CLARA iterates until the specified number of iterations is reached.
* '''Regularize iterations''': If one wants to use different regularization for the CLARA iterations than the value specified as "SVD cutoff", this option should be selected.
* '''Amount to clip from img (%)''': Cortical CLARA uses the solution from the previous iteration as an additional weighting matrix for the current iteration. That weighting matrix is constructed by cutting the "low" activity from the solution. This number specifies how much of the activity should be cut from the previous solution in order to construct the weighting matrix. This value is given as a percentage of the maximal activity. Default value is 10%.

'''Notes:'''

* '''Starting Cortical CLARA:''' Cortical CLARA can be started from the sub-menu '''Surface Image''' of the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]''” for important information on regularization of distributed inverses.

== Cortex Inflation ==

The inflated cortex is a smoothened version of the individual cortical surface with minimal metric distortions (Fischl, B. et al. (1999). Cortical Surface-Based Analysis: II: Inflation, Flattening, and a Surface-Based Coordinate System. ''NeuroImage'', 9(2), 195–207). Gyri and sulci are smoothened out. The original distances between each point on the cortex and its neighbors are, however, mostly preserved.

[[Image:SA 3Dimaging (48).gif]]

''Cortical LORETA map overlaid on top of the inflated cortical surface.''

A lighter gray color overlaid on top of the surface image indicates the location of a gyrus of the individual cortex surface, while a darker gray color indicates the location of a sulcus. The inflated cortical surface can be computed in '''BESA MRI 2.0'''. For more details please refer to the BESA MRI 2.0 help.

== Surface Minimum Norm Image ==

'''Introduction'''

The minimum norm approach is a common method to estimate a distributed electrical current image in the brain at each time sample (Hämäläinen & Ilmoniemi 1984). The source activities of a large number of regional sources are computed. The sources are evenly distributed using 1500 standard locations 10% and 30% below the smoothed standard brain surface (when using the standard MRI) or using between 3000-4000 locations on the individual brain surface defined by the gray-white-matter boundary.

Since the number of sources is much larger than the number of sensors in a minimum norm solution, the inverse problem is highly underdetermined and must be stabilized by a mathematical constraint, the minimum norm. Out of the many current distributions that can account for the recorded sensor data, the solution with the minimum L2 norm, i.e. the minimum total power of the current distribution is displayed in BESA Research.

First, the forward solution (leadfield matrix L) of all sources is calculated in the current head model. Then, the source activities S(t) of all source components are computed from the data matrix D(t) using an inverse regularized by the estimated noise covariance matrix:

<math>\mathrm{S}\left( t \right) = \mathrm{R} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{R} \cdot \mathrm{L}^{T} + \mathrm{C}_N \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed regional source model, CN denotes the noise correlation matrix in sensor space, and R is a weighting matrix in source space. R and CN can be designed in different ways in order to optimize the minimum norm result. The total activity of each regional source is computed as the root mean square of the source activities S(t) of its 3 (MEG:2) components. This total source activity is transformed to a color-coded image of the brain surface. (When the standard brain is used, two sources are assigned to each surface location, located 10% and 30% below the surface, respectively. The color that is displayed on the standard brain surface is the larger of the two corresponding source activities.)

'''Weighting options'''

The minimum norm current imaging techniques of BESA Research provide different weighting strategies. Two weighting approaches are available: Depth weighting and spatio-temporal approaches.
* '''Depth weighting:''' Without depth weighting, deep sources appear very smeared in a minimum-norm reconstruction. With depth weighting, both deep and superficial sources produce a similar, more focal result. If this weighting method is selected, the leadfield of each regional source is scaled with the largest singular value of the SVD (singular value decomposition) of the source's leadfield.
* '''Spatio-temporal weighting''': Spatio-temporal weighting tries to assign large weight to sources that are assumed to be more likely to contribute to the recorded data.
** '''Subspace correlation after single source scan''': This method divides the signal into a signal and a noise subspace. The correlation of the leadfield of a regional source i with the signal subspace (pi) is computed to find out if the source location contributes to the measured data. The weighting matrix R becomes a diagonal matrix. Each of the three (MEG: 2) components of a regional source get the same weighting value pi2. This approach is based on the signal subspace correlation measure introduced by J.C. Mosher, R. M. Leahy (Recursive MUSIC: A Framework for EEG and MEG Source Localization, IEEE Trans. On Biomed. Eng. Vol. 45, No. 11, November 1998)
** '''Dale & Sereno 1993:''' In the approach of Dale and Sereno (J Cogn Neurosci, 1993, 5: 162-176) a signal subspace needs not be defined. The correlation pi of the leadfield of regional source i with the inverse of the data covariance matrix is computed along with the largest singular value λmax of the data covariance matrix. The weighting matrix R is a diagonal matrix with weights: [[Image:SA 3Dimaging (50).gif]]. Each of the three (MEG: 2) components of a regional source receives the same weighting value.

'''Noise regularization'''

Two methods to estimate the channel noise correlation matrix CN are provided by the program:
* '''Use baseline:''' Select this option to estimate the noise from the user-definable baseline. The signal is computed from the data at non-baseline latencies.
* '''Use 15% lowest values:''' The baseline activity is computed from the data at those 15% of all displayed latencies that have the lowest global field power. The signal is computed from all displayed latencies.

In each case, the activity (noise or signal, respectively) is defined as root-mean-square across all respective latencies for each channel.

The noise covariance matrix CN is constructed as a diagonal matrix. The entries in the main diagonal are proportional to the noise activity of the individual channels (if selected) or are all equally proportional to the average noise activity over all channels. The noise covariance matrix CN is then scaled such that the ratio of the Frobenius norms of the weighted leadfield projector matrix (LRLT) and the noise covariance matrix CN equals the Signal-to-Noise ratio. This scaling can be multiplied by an additional factor (default=1) to sharpen (<1) or smoothen (>1) the minimum norm image.

'''Applying the Minimum Norm Image'''

The minimum-norm algorithm is started via the ''Surface minimum norm image dialog box'', which is opened from the''' Image''' menu, or by typing the shortcut '''Ctrl-M''': Please refer to Chapter ''“Surface'' ''Minimum Norm Tab”'' for more details.

As opposed to the other 3D images available from the '''Image '''menu, the surface minimum norm image is not computed on a volumetric grid, but rather for locations on the brain surface. Accordingly, the results of the minimum norm image are displayed superimposed to the brain surface mesh rather than to the volumetric MR image.

The figure below shows a minimum norm image computed from the file '''Examples\Epilepsy\Spikes\Spikes-Child4_EEG+MEG_averaged.fsg'''. The EEG spike peak was imaged using the individual brain surface of the subject. A baseline from -300 to -70 ms was used. Minimum norm was computed with depth weighting, Spatio-temporal weighting according to Dale & Sereno 1993 and individual noise weighting with a noise scale factor of 0.01. The minimum norm image reveals the location of the spike generator in the close vicinity of the frontal left-hemispheric lesion in this subject.

[[Image:SA 3Dimaging (51).gif]]

== Multiple Source Probe Scan (MSPS) ==

 
'''Introduction'''

The MSPS function provides a tool for the validation of a given solution. It is based on the following theoretical consideration: If the recorded EEG/MEG data has been modeled adequately, i.e. all active brain regions are represented by a source in the current solution, then any additional probe source added to the solution will not show any activity apart from noise. The only exception occurs if this probe source is placed in close vicinity to one of the sources in the current solution. In that case, the solution's source and the probe source will share the activity of the corresponding brain area. The MSPS applies these considerations by scanning the brain on a pre-defined grid with a regional probe added to the current solution. Grid extent and density can be specified in the Image settings. The power P of the probe source at location r in the signal interval is compared with the power of the probe source in a reference interval, defining a value q:

<math>\mathrm{q}\left( r \right) = \sqrt{\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}} - 1</math>


MSPS can be computed on time domain or time-frequency domain data:
* In the time domain, q(r) is computed from the source waveform of the probe source. Here, P(r) is the mean power of the probe source at location r in the marked latency range, and Pref(r) is the mean probe source power in the user-definable baseline interval.
* In the time-frequency domain, an MSPS image can be computed from the complex cross spectral density matrices. By applying the inverse operator for a source configuration consisting of the current solution and the probe source, the power of the probe source can be computed for the target interval [P(r)] and the reference time-frequency interval [Pref(r)]. In the resulting MSPS image, q-values are shown in %, where q[%] = q*100.

The inverse operator used to determine the probe source power uses different regularization constants for the probe source and the sources in the current solution. The regularization constant of the sources in the current solution can be specified in the Image settings (default 4%). The regularization constant of the probe source is internally set to 0%.

Alternatively to the definition above, q can also be displayed in units of dB:

<math>\mathrm{q}\left\lbrack \text{dB} \right\rbrack = 10 \cdot \log_{10}\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}</math>


Values of q smaller than zero are not shown in the MSPS image.

According to the considerations above, an MSPS of a correct source model should optimally yield image maxima around the sources in the current solution only. If the MSPS image is blurred or shows maxima at locations different from the modeled sources, this indicates a non-sufficient or incorrect solution.

'''Applying the MSPS'''

This chapter illustrates the application of the Multiple Source Probe Scan. The figures are generated with data from file '''Examples/Epilepsy/Spikes/Rolandic-Spike-Child.fsg''' (-300 : +200 ms, filtered from 3 Hz [forward] to 40 Hz [zero-phase]).

'''Time domain versus time-frequency domain MSPS'''

The multiple source probe scan can be computed in the time domain or the time-frequency domain. The latter is possible only when time-frequency domain data is available for the current condition, i.e. if the condition has been created by starting a multiple source beamformer (MSBF) computation from the source coherence window. In this case, evoking the MSPS calculation from the '''Imaging '''button or from the '''Image''' menu will bring up the following dialog window that allows to choose between time- or time-frequency MSPS. If only time domain data is available, this dialog window will not appear and MSPS will be computed in the time domain.

[[Image:SA 3Dimaging (53).gif]]

For a time-frequency domain MSPS, the target and the reference time-frequency interval have been specified already in the Time-Frequency window (see Chapter "''How To Create Beamformer Images''"). For a time-domain MSPS, the target and the reference epoch have to be specified in the Source Analysis window as described below.

'''Time domain MSPS'''

The time-domain MSPS image displays the ratio of the power of a regional probe source in the signal and the baseline interval. The currently set baseline is indicated by a horizontal line in the upper left corner of the channel box.

[[Image:SA 3Dimaging (54).gif|thumb|c|none|330px|The black horizontal bar in the upper part of the channel box (here circled in red) indicates the baseline interval.]]

By default, BESA Research defines the pre-stimulus interval of the current data segment as baseline. The baseline should represent a latency range in which no event-related activity is present in the data. There are several possibilities to modify the baseline interval: by clicking on the horizontal line with the left mouse button or by using the corresponding entry in the '''Condition '''menu or '''Fit Interval''' popup menu.

Mark an interval to define the target epoch, i.e. the time-interval for which the current solution is to be tested. Start the MSPS by selecting it from the '''Image selection '''button or from the '''Image''' menu to start the probe source scan. The''' Image '''menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window. The 3D window opens and displays the scan result.

<div><ul>
<li style="display: inline-block;"> [[Image:SA 3Dimaging (55).gif|thumb|c|none|650px|This figure shows the MSPS image applied on the three left-hemispheric sources in the solution ''''Rolandic-Spike-Child-RS2.bsa''''. The baseline is set from -300ms to -50 ms. The right-hemispheric sources have been switched off. The fit interval is set to the latency range of large overall activity in the data (-43 ms : 117 ms). A realistic FEM model appropriate for the subject's age (12 years, conductivity ratios (cr) 50) is applied. The MSPS image does not show maxima at the modeled source locations and rather shows a spread q-value distribution.]] </li>

<li style="display: inline-block;"> [[Image:SA 3Dimaging (56).gif|thumb|c|none|650px|The MSPS image for the same latency range when the right-hemispheric sources have been included. The MSPS image appears more focal and shows maxima around the modeled brain regions. This indicates the substantial improvement of the solution by adding the right-hemispheric sources that model the propagation of the epileptic spike from the left to the right hemisphere (note the radiological side convention in the 3D window).]] </li>
</ul></div>

'''Time-Resolved MSPS'''

If the MSPS has been computed on time domain data, the image can be shown separately for each latency in the selected interval. After the MSPS has been computed for the marked epoch, double-click anywhere within this epoch to display the ratio of the probe source magnitude at the selected latency and the mean probe source magnitude in the baseline. Scanning the latency range by moving the cursor (e.g. with the left and right arrow cursor keys) provides a time-resolved MSPS image.

Time-resolved MSPS images are not available if the MSPS has been computed on data in the time-frequency domain.

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (57).gif|thumb|450px|MSPS image of the spike peak activity at 0ms. The activity mainly occurs in the left hemisphere. This fact is illustrated by the source waveforms and confirmed in the MSPS image, which shows a focal maximum around the location of the red sources.]] </li>

<li style="display: inline-block;"> [[File:SA 3Dimaging (58).gif|thumb|450px|Around +27 ms, the spike has propagated to the right hemisphere. This becomes evident from the waveforms of the blue sources, which show a significant latency lag with respect to the first three sources, and from the MSPS image, which shows the maximum around blue sources at this latency.]] </li>
</ul></div>



'''Notes:'''

* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image''' menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the''' Image''' menu.
* For scaling options, please refer to the '''scaling buttons''' popup menu .
* Parameters used for the MSPS calculations can be set in the ''General Settings tab'' of the ''Image Settings dialog box.''

== Source Sensitivity ==

'''Introduction'''

The 'Source sensitivity' function displays the sensitivity of the selected source in the current source model to activity in other brain regions. Sensitivity is defined as the fraction of power at the scanned brain location that is mapped onto the selected source.

To compute the source sensitivity, unit brain activity is modeled at different locations (probe source) throughout the brain. To this data, the current source model is applied to compute the source waveforms SCM of all modeled sources:

<math>\mathrm{S}_{\text{CM}} = \mathrm{L}_{\text{CM}}^{-1} \cdot \mathrm{L}_{\text{PS}}</math>


Here LCM-1 is the regularized inverse operator for the current model, and LPS is the leadfield of the regional probe source (dimension [Nx3] for EEG and [Nx2] for MEG, respectively, where N is the number of sensors). The source amplitude SSS of the selected source in the model is a 3x3 (MEG: 2x2) sub-matrix of SCM (if the selected source is a regional source) or a 1x3-matrix (MEG: 1x2) (if the selected source is a dipole). The root mean square of the singular values of SCM is defined as the source sensitivity.

The 3D source sensitivity image displays this value for all locations on a grid specified under '''Image/Settings'''. Grid density can be specified in the Image Settings.

'''Applying the Source Sensitivity Image'''

The Source Sensitivity image is evoked from the '''Image''' menu or by pressing the corresponding hot key (default: '''V''').

This function is enabled only when a solution with an active selected source is present in the Source Analysis window. The source sensitivity image then displays the sensitivity of the selected source to activity in other brain regions.

[[Image:SA 3Dimaging (59).gif]]

''Source Sensitivity image for the selected frontal source (green) in model ''''''High_Intensity_3RS.bsa'''''' in folder 'Examples/ERP_Auditory_Intensity'. The data displayed is the '100dB' condition in file ''''''All_Subjects_cc.fsg''''''. The selected source is sensitive to activity in the frontal brain region (yellow/white), while it is not influenced by activity in the vicinity of the left and right auditory cortex areas, which are modeled by the red and blue source in the model (transparent/gray).''

'''Notes:'''

* The sensitivity image is independent of the recorded sensor signals. It only depends on the current source model, the sensor configuration, the head model, and the regularization constant.
* If the regularization constant is set to zero, each source has a sensitivity of 100% to activity around its own location. With increasing regularization, the spatial filter becomes less focused, and the sensitivity of a source to activity at its location decreases.
* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image''' menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the '''Image''' menu.

{{BESAManualNav}}

Source Analysis 3D Imaging

2019-03-27T11:51:40Z

Jamie: /* Inserting Sources as Beamformer Virtual Sensor out of the Beamformer Image */

{{BESAInfobox
|title = Module information
|module = BESA Research Standard or higher
|version = 6.1 or higher
}}


== Overview ==

BESA Research features a set of new functions that provide 3D images that are displayed superimposed to the individual subject's anatomy. This chapter introduces these different images and describe their properties and applications.

The 3D images can be divided into three categories:

'''Volume images:'''

* '''The Multiple Source Beamformer (MSBF)''' is a tool for imaging brain activity. It is applied in the time-domain or time-frequency domain. The beamformer technique in time-frequency domain can image not only evoked, but also induced activity, which is not visible in time-domain averages of the data.
* '''Dynamic Imaging of Coherent Sources (DICS)''' can find coherence between any two pairs of voxels in the brain or between an external source and brain voxels. DICS requires time-frequency-transformed data and can find coherence for evoked and induced activity.

The following imaging methods provide an image of brain activity based on a distributed multiple source model:
* '''CLARA''' is an iterative application of LORETA images, focusing the obtained 3D image in each iteration step.
* '''LAURA '''uses a spatial weighting function that has the form of a local autoregressive function.
* '''LORETA''' has the 3D Laplacian operator implemented as spatial weighting prior.
* '''sLORETA''' is an unweighted minimum norm that is standardized by the resolution matrix.
* '''swLORETA '''is equivalent to sLORETA, except for an additional depth weighting.
* '''SSLOFO '''is an iterative application of standardized minimum norm images with consecutive shrinkage of the source space.
* A '''User-defined volume image''' allows to experiment with the different imaging techniques. It is possible to specify user-defined parameters for the family of distributed source images to create a new imaging technique.
* Bayesian source imaging: '''SESAME''' uses a semi-automated Bayesian approach to estimate the number of dipoles along with their parameters.

'''Surface image:'''

* The '''Surface Minimum Norm Image'''. If no individual MRI is available, the minimum norm image is displayed on a standard brain surface and computed for standard source locations. If available, an individual brain surface is used to construct the distributed source model and to image the brain activity.
* '''Cortical LORETA'''. Unlike classical LORETA, cortical LORETA is not computed in a 3D volume, but on the cortical surface.
* '''Cortical CLARA'''. Unlike classical CLARA, cortical CLARA is not computed in a 3D volume, but on the cortical surface.

'''Discrete model probing:'''

These images do not visualize source activity. Rather, they visualize properties of the currently applied discrete source model:
* The '''Multiple Source Probe Scan (MSPS)''' is a tool for the validation of a discrete multiple source model.
* The '''Source Sensitivity image''' displays the sensitivity of a selected source in the current discrete source model and is therefore data independent.

== Multiple Source Beamformer (MSBF) in the Time-frequency Domain ==

 
'''Short mathematical introduction'''

The BESA beamformer is a modified version of the linearly constrained minimum variance vector beamformer in the time-frequency domain as described in [https://dx.doi.org/10.1073/pnas.98.2.694 Gross et al., "Dynamic imaging of coherent sources: Studying neural interactions in the human brain", PNAS 98, 694-699, 2001]. It allows to image evoked and induced oscillatory activity in a user-defined time-frequency range, where time is taken relative to a triggered event.

The computation is based on a transformation of each channel's single trial data from the time domain into the time-frequency domain. This transformation is performed by the BESA Research Source Coherence module and leads to the complex spectral density Si (f,t), where i is the channel index and f and t denote frequency and time, respectively. Complex cross spectral density matrices C are computed for each trial:

<math>\mathrm{C}_{ij}\left( f,t \right) = \mathrm{S}_{i}\left( f,t \right) \cdot \mathrm{S}_{j}^{*}\left( f,t \right)</math>


The output power P of the beamformer for a specific brain region at location r is then computed by the following equation:

<math>\mathrm{P}\left( r \right) = \operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{-1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{-1}</math>


Here, Cr-1 is the inverse of the SVD-regularized average of Cij(f,t) over trials and the time-frequency range of interest; L is the leadfield matrix of the model containing a regional source at target location r and, optionally, additional sources whose interference with the target source is to be minimized; tr'[] is the trace of the [3×3] (MEG:[2×2]) submatrix of the bracketed expression that corresponds to the source at target location r.

In BESA Research, the output power P(r) is normalized with the output power in a reference time-frequency interval Pref(r). A value q ist defined as follows:

<math> \mathrm{q}\left( r \right) =
\begin{cases}
\sqrt{\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}(r)}} - 1 = \sqrt{\frac{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{\text{ref},r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}} - 1, & \text{for }\mathrm{P}(r) \geq \mathrm{P}_{\text{ref}}(r) \\

1 - \sqrt{\frac{\mathrm{P}_{\text{ref}}\left( r \right)}{\mathrm{P}\left( r \right)}} = 1 - \sqrt{\frac{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{\text{ref},r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}}, & \text{for }\mathrm{P}(r) < \mathrm{P}_{\text{ref}}(r)
\end{cases} </math>


Pref can be computed either from the corresponding frequency range in the baseline of the same condition (i.e. the beamformer images event-related power increase or decrease) or from the corresponding time-frequency range in a control condition (i.e. the beamformer images differences between two conditions). The beamformer image is constructed from values q(r) computed for all locations on a grid specified in the '''General Settings tab'''. For MEG data, the innermost grid points within a sphere of approx. 12% of the head diameter are assigned interpolated rather than calculated values).
q-values are shown in %, where where q[%] = q*100. Alternatively to the definition above, q can also be displayed in units of dB:

<math>\mathrm{q}\left\lbrack \text{dB} \right\rbrack = 10 \cdot \log_{10}\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}</math>


A beamformer operator is designed to pass signals from the brain region of interest r without attenuation, while minimizing interference from activity in all other brain regions. Traditional single-source beamformers are known to mislocalize sources if several brain regions have highly correlated activity. Therefore, the BESA beamformer extends the traditional single-source beamformer in order to implicitly suppress activity from possibly correlated brain regions. This is achieved by using a multiple source beamformer calculation that contains not only the leadfields of the source at the location of interest r, but also those of possibly interfering sources. As a default, BESA Research uses a bilateral beamformer, where specifically contributions from the homologue source in the opposite hemisphere are taken into account (the matrix L thus being of dimension N×6 for EEG and N×4 for MEG, respectively, where N is the number of sensors). This allows for imaging of highly correlated bilateral activity in the two hemispheres that commonly occurs during processing of external stimuli.

In addition, the beamformer computation can take into account possibly correlated sources at arbitrary locations that are specified in the current solution. This is achieved by adding their leadfield vectors to the matrix L in the equation above.

'''Applying the Beamformer'''

This chapter illustrates the usage of the BESA beamformer. The displayed figures are generated using the file ''''Examples/Learn-by-Simulations/AC-Coherence/AC-Osc20.foc'''' (see BESA Tutorial 6: "''Time-frequency analysis and Source coherence''").

'''Starting the beamformer from the time-frequency window'''

The BESA beamformer is applied in the time-frequency domain and therefore requires the Source Coherence module to be enabled. The time-frequency beamformer is especially useful to image in- or decrease of induced oscillatory activity. Induced activity cannot be observed in the averaged data, but shows up as enhanced averaged power in the TSE (Temporal-Spectral Evolution) plot. For instructions on how to initiate a beamformer computation in the time-frequency window, please refer to Chapter '''[[Source_Coherence_How_to...#How_to_Start_the_Beamformer_from_the_Time-Frequency_Window|How to Create Beamformer Images]]'''.

After the beamformer computation has been initiated in the time-frequency window, the source analysis window opens with an enlarged 3D image of the q-value computed with a '''bilateral beamformer'''. The result is superimposed onto the MR image assigned to the data set (individual or standard).

[[Image:SA 3Dimaging (5).gif]]

''Beamformer image after starting the computation in the Time-Frequency window. A bilateral pair of sources in the auditory cortex accounts for the highly correlated oscillatory induced activity. Only the bilateral beamformer manages to separate these activities; a traditional single-source beamformer would merge the two sources into one image maximum in the head center instead.''

'''Multiple source beamformer in the Source Analysis window'''

The 3D imaging display is part of the source analysis window. If you press the '''Restore''' button at the right end of the title bar of the 3D window, the window appears at the bottom right of the source analysis window. In the channel box, the averaged (evoked) data of the selected condition is shown. When a control condition was selected, its average is appended to the average of the target condition.

[[Image:SA 3Dimaging (6).gif]]

''Source Analysis window with beamformer image. The two sources have been added using the '''''Switch to''''' '''''Maximum''''' and '''''Add Source '''''toolbar buttons (see below). Source waveforms are computed from the displayed averaged data. Therefore, they do not represent the activity displayed in the beamformer image, which in this simulation example is induced (i.e. not phase-locked to the trigger)!''

When starting the beamformer from the time-frequency window, a bilateral beamformer scan is performed. In the source analysis window, the beamformer computation can be repeated taking into account possibly correlated sources that are specified in the current solution. Interfering activities generated by all sources in the current solution that are in the 'On' state are specifically suppressed ('''they enter the matrix L in the beamformer calculation''', see Chapter ''Short mathematical description'' above). The computation can be started from the '''Image''' menu or from the '''Image selector button''' dropdown menu. The '''Image''' menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window.

[[Image:SA 3Dimaging (7).gif]]

''Multiple source beamformer image calculated in the presence of a source in the left hemisphere. A '''single''' source scan has been performed. The source set in the current solution accounts for the left-hemispheric q-maximum in the data. Accordingly, the beamformer scan reveals only the as yet unmodeled additional activity in the right hemisphere (note the radiological convention in the 3D image display).''

The beamformer scan can be performed with a '''single''' or a '''bilateral''' source scan. The default scan type depends on the current solution:
* When the beamformer is started from the Time-Frequency window, the Source Analysis window opens with a new solution and a '''bilateral''' beamformer scan is performed.
* When the beamformer is started within the Source Analysis window, the default is
** a scan with a '''single''' source in addition to the sources in the current solution, if at least one source is active.
** a '''bilateral''' scan if no source in the current solution is active.

The default scan type is the multiple source beamformer. The non-default scan type can be enforced using the corresponding ''Volume Image / Beamformer'' entry in the '''Image''' menu.

'''Inserting Sources out of the Beamformer Image'''

The beamformer image can be used to add sources to the current solution. A simple double-click anywhere in the 2D- or 3D-view will generate a non-oriented regional source at the corresponding location. However, a better and easier way to create sources at image maxima and minima is to use the toolbar buttons '''Switch to Maximum''' [[Image:SA 3Dimaging (8).gif]] and '''Add Source''' [[Image:SA 3Dimaging (9).gif]].

Use the '''Switch to Maximum''' button to place the red crosshair of the 3D window onto a local image maximum or minimum. Hitting the '''Add Source''' button creates a regional source at the location of the crosshair and therefore ensures the exact placement of the source at the image extremum. Moreover, the '''Add Source''' button generates an oriented regional source. BESA Research automatically estimates the source orientation that contributes most to the power in the target time-frequency interval (or the reference time-frequency interval, if its power is larger than that in the target interval). The accuracy of this orientation estimate depends largely on the noise content of the data. The smaller the signal-to-noise ratio of the data, the lower is the accuracy of the orientation estimate. '''This feature allows to use the beamformer as a tool to create a source montage for source coherence analysis, where it is of advantage to work with oriented sources'''.

'''Notes:'''

* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image '''menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the''' Image''' menu.
* For scaling options, use the [[Image:SA 3Dimaging (10).gif]] and [[Image:SA 3Dimaging (11).gif]] '''Image Scale toolbar''' buttons.
* Parameters used for the beamformer calculations can be set in the '''Standard Volumes''' of the ''Image Settings dialog box.''

== Dynamic Imaging of Coherent Sources (DICS) ==

 
'''Short mathematical introduction'''

Dynamic Imaging of Coherent Sources (DICS) is a sophisticated method for imaging cortico-cortical coherence in the brain, or coherence between an external reference (e.g. EMG channel) and cortical structures. DICS can be applied to localize evoked as well as induced coherent cortical activity in a user-defined time-frequency range.

DICS was implemented in BESA closely following [https://dx.doi.org/10.1073/pnas.98.2.694 Gross et al., "Dynamic imaging of coherent sources: Studying neural interactions in the human brain", PNAS 98, 694-699, 2001].

The computation is based on a transformation of each channel's single trial data from the time domain into the frequency domain. This transformation is performed by the BESA Research Coherence module and results in the complex spectral density matrix that is used for constructing the spatial filter similar to beamforming.

DICS computation yields a 3-D image, each voxel being assigned a coherence value. Coherence values can be described as a neural activity index and do not have a unit. The neural activity index contrasts coherence in a target time-frequency bin with coherence of the same time-frequency bin in a baseline.

'''DICS for cortico-cortical coherence is computed as follows:'''

Let L(r) be the leadfield in voxel r in the brain and C the complex cross-spectral density matrix. The spatial filter W(r) for the voxel r in the head is defined as follows:

<math>W\left( r \right) = \left\lbrack L^{T}\left( r \right) \cdot C^{- 1} \cdot L\left( r \right) \right\rbrack^{- 1} \cdot L^{T}(r) \cdot C^{- 1}</math>


The cross-spectrum between two locations (voxels) r1 and r2 in the head are calculated with the following equation:

<math>C_{s}\left( r_{1},r_{2} \right) = W\left( r_{1} \right) \cdot C \cdot W^{*T}\left( r_{2} \right),</math>


where <nowiki>*T</nowiki> means the transposed complex conjugate of a matrix. The cross-spectral density can then be calculated from the cross spectrum as follows:

<math>c_{s}\left( r_{1},r_{2} \right) = \lambda_{1}\left\{ C_{s}\left( r_{1},r_{2} \right) \right\},</math>


where λ1{} indicates the largest singular value of the cross spectrum. Once the cross spectral density is estimated, the connectivity¹(CON) between the two brain regions r1 and r2 are calculated as follows:

<math>\text{CON}\left( r_{1},r_{2} \right) = \frac{c_{s}^{\text{sig}}\left( r_{1},r_{2} \right) - c_{s}^{\text{bl}}(r_{1},r_{2})}{c_{s}^{\text{sig}}\left( r_{1},r_{2} \right) + c_{s}^{\text{bl}}(r_{1},r_{2})},</math>


where cssig is the cross-spectral density for the signal of interest between the two brain regions r1 and r2, and csbl is the corresponding cross spectral density for the baseline or the control condition, respectively. In the case DICS is computed with a cortical reference, r1 is the reference region (voxel) and remains constant while r2 scans all the grid points within the brain sequentially. In that way, the connectivity between the reference brain region and all other brain regions is estimated. The value of CON(r1, r2) falls in the interval [-1 1]. If the cross-spectral density for the baseline is 0 the connectivity value will be 1. If the cross-spectral density for the signal is 0 the connectivity value will be -1.

¹ Here, the term connectivity is used rather than coherence, as strictly speaking the coherence equation is defined slightly differently. For simplicity reasons the rest of the tutorial uses the term coherence.

'''DICS for cortico-muscular coherence is computed as follows:'''

When using an external reference, the equation for coherence calculation is slightly different compared to the equation for cortico-cortical coherence. First of all, the cross-spectral density matrix is not only computed for the MEG/EEG channels, but the external reference channel is added. This resulting matrix is Call. In this case, the cross-spectral density between the reference signal and all other MEG/EEG

channels is called cref. It is only one column of Call. Hence, the cross-spectrum in voxel r is calculated with the following equation:

<math>C_{s}\left( r \right) = W\left( r \right) \cdot c_{\text{ref}}</math>


and the corresponding cross-spectral density is calculated as the sum of squares of Cs:

<math>c_{s}\left( r \right) = \sum_{i = 1}^{n}{C_{s}\left( r \right)_{i}^{2}},</math>


where n is 2 for MEG and 3 for EEG. This equation can also be described as the squared Euclidean norm of the cross-spectrum:

<math>c_{s}\left( r \right) = \left\| C_{s} \right\|^{2},</math>


The power in voxel r is calculated as in the cortico-cortical case:

<math>p\left( r \right) = \lambda_{1}\left\{ C_{s}(r,r) \right\}.</math>


At last, coherence between the external reference and cortical activity is calculated with the equation:

<math>\text{CON}\left( r \right) = \frac{c_{s}(r)}{p\left( r \right) \cdot C_{\text{all}}(k,k)},</math>


where Call(k, k) is the (k,k)-th diagonal element of the matrix Call.

DICS is particularly useful, if coherence is to be calculated without an a-priory source model (in contrast to source coherence based on pre-defined source montages). However, the recommended analysis strategy for DICS is to use a brain source as a starting point for coherence calculation that is known to contribute to the EEG/MEG signal of interest. For example, one might first run a beamformer on the time-frequency range of interest and use the voxel with the strongest oscillatory activity as a starting point for DICS. The resulting coherence image will again lead to several maxima (ordered by magnitude), which in turn can serve as starting points for DICS calculation. This way, it is possible to detect even weak sources that show coherent activity in the given time-frequency range.

The other significant application for DICS is estimating coherence between an external source and voxels in the brain. For example, an external source can be muscle activity recoded by an electrode placed over the according peripheral region. This way, the direct relationship between muscle activity and brain activation can be measured.

'''Starting DICS computation from the Time-Frequency Window'''

DICS is particularly useful, if coherence in a user-defined time-frequency bin (evoked or induced) is to be calculated between any two brain regions or between an external reference and the brain. DICS runs only on time-frequency decomposed data, so time-frequency analysis needs to be run before starting DICS computation.

To start the DICS computation, left-drag a window over a selected time-frequency bin in the Time-Frequency Window. Right-click and select “Image”. A dialogue will open (see fig. 1) prompting you to specify time and frequency settings as well as the baseline period. It is recommended to use a baseline period of equal length as the data period of interest. Make sure to select “DICS” in the top row and press “'''Go'''”.

[[Image:SA 3Dimaging (21).gif|450px|thumb|c|none|Fig. 1: Time and frequency settings for DICS and MSBF]]

Next, a window will appear allowing you to specify the reference source for coherence calculation (see fig. 2). It is possible to select a channel (e.g. EMG) or a brain source. If a brain source is chosen and no source analysis was computed beforehand, the option “Use current cross-hair position” must be chosen. In case discrete source analysis was computed previously, the selected source can be chosen as the reference for DICS. Please note that DICS can be re-computed with any cross-hair or source position at a later stage.

[[Image:SA 3Dimaging (1).jpg|400px|thumb|c|none|Fig. 2: Possible options for choosing the reference]]

Confirming with “'''OK'''” will start computation of coherence between the selected channel/voxel and all other brain voxels. In case DICS is computed for a reference source in the brain, it can be advantageous to run a beamforming analysis in the selected time-frequency window first and use one of the beamforming maxima as reference for DICS. Fig. 3 shows an example for DICS calculation.

[[Image:SA 3Dimaging (22).gif|500px|thumb|c|none|Fig. 3: Coherence between left-hemispheric auditory areas and the selected voxel in the right auditory cortex.]]

Coherence values range between -1 and 1. If coherence in the signal is much larger than coherence in the baseline (control condition) then the DICS value is going to approach 1. Contrary, if coherence in the baseline is much larger than coherence in the signal, then the DICS value is going to approach -1. At last, if coherence in the signal is equal to coherence in the baseline, then the DICS value is 0.

In case DICS is to be re-computed with a different reference, simply mark the desired reference position by placing the cross-hair in the anatomical view and select “DICS” in the middle panel of the source analysis window (see Fig. 4). In case an external reference is to be selected, click on “DICS” in the middle panel to bring up the DICS dialogue (see. Fig. 2) and select the desired channel. Please note that DICS computation will only be available after running time-frequency analysis.

[[Image:SA 3Dimaging (23).gif|700px|thumb|c|none|Fig. 4: Integration of DICS in the Source Analysis window]]

== Multiple Source Beamformer (MSBF) in the Time Domain ==
''(requires Besa Research 7.0 or higher)''

===Short mathematical introduction===

Beamforming approach can be also applied in the time domain data. This approach was introduced as linearly constrained minimum variance (LCMV) beamformer (Van Veen et al., 1997). It allows to image evoked activity in a user-defined time range, where time is taken relative to a triggered event, and to estimate source waveforms using the calculated spatial weight at locations of interest. For an implementation of the beamformer in the time domain, data covariance matrices are required, while complex cross spectral density matrices are used for the beamformer approaches in the time-frequency domain as described in the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section.

The bilateral beamformer introduced in the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section is also implemented for the time-domain beamformer to take into account contributions from the homologue source in the opposite. This allows for imaging of highly correlated bilateral activity in the two hemispheres that commonly occurs during processing of external stimuli. In addition, the beamformer computation can take into account possibly correlated sources at arbitrary locations.
The beamformer spatial weight W(r) for the voxel r in the brain is defined as follows (Van Veen et al., 1997):

[[File:MSBF1.png]]

where '''C-1''' is the inversed regularized average of covariance matrix over trials, '''L''' is the leadfield matrix of the model containing a regional source at target location r and optionally
additional sources whose interference with the target source is to be minimized. The beamformer spatial weight '''W'''(r) can be applied to the measured data to estimate source
waveform at a location r (beamformer virtual sensor):

[[File:MSBF2.png]]

where '''S'''(r,t) represents the estimated source waveform and '''M'''(t) represents measured EEG or MEG signals.
The output power P of the beamformer for a specific brain region at location r is computed by the following equation:

[[File:MSBF3.png]]

where tr’[ ] is the trace of the [3×3] (MEG: [2×2]) submatrix of the bracketed expression that corresponds to the source at target location r.
Beamformer can suppress noise sources that are correlated across sensors. However, uncorrelated noise will be amplified in a spatially non-uniform manner, with increasing
distortion with increasing distance from the sensors (Van Veen et al., 1997; Sekihara et al., 2001). For this reason, estimated source power should be normalized by a noise power.
In BESA Research, the output power P(r) is normalized with the output power in a baseline interval or with the output power of a uncorrelated noise: P(r) / Pref (r).
The time-domain beamformer image is constructed from values q(r) computed for all locations on a grid specified in the '''General Settings''' tab. A value q(r) is defined as described in
the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section with data covariance matrices instead of cross-spectral density matrices.

===Applying the Beamformer===

This chapter illustrates the usage of the BESA beamformer in the time domain. The displayed figures are generated using the file ‘Examples/ERP-Auditory-Intensity/S1.cnt’.

'''Starting the time-domain beamformer from the Average tab of the Paradigm dialog box'''

The time-domain beamformer is needed data covariance matrices and therefore requires the ERP module to be enabled. After the beamformer computation has been initiated in the
'''Average tab of the Paradigm dialog box''', the source analysis window opens with an enlarged 3D image of the q-value computed with a bilateral beamformer. The result is
superimposed onto the MR image assigned to the data set (individual or standard).

[[File:MSBF44.png]]

''Beamformer image for auditory evoked data after starting the computation in the '''Average tab of the Paradigm dialog box'''. The bilateral beamformer manages to separate the
activities in auditory areas, while a traditional single-source beamformer would merge the two sources into one image maximum in the head center instead.''

'''Multiple-source beamformer in the Source Analysis window'''

The 3D imaging display is part of the source analysis window. In the Channel box, the averaged (evoked) data of the selected condition is shown. Selected covariance intervals in
the ERP module can be checked in the Channel box. The red, gray, and blue rectangles indicate signal, baseline, and common interval, respectively.

[[File:MSBF55.png]]

''Source Analysis window with beamformer image. The two beamformer virtual sensors have been added using the Switch to Maximum and Add Source toolbar buttons (see below).
Source waveforms are computed using the beamformer spatial weights and the displayed averaged data (the noise normalized weights (5% noise) option was used to compute the
beamformer image).''

When starting the beamformer from the '''Average tab of the Paradigm dialog box''', the bilateral beamformer scan is performed. In the source analysis window, the beamformer computation can be repeated taking into account possibly correlated sources that are specified in the current solution. Interfering activities generated by all sources in the current solution that are in the 'On' state are specifically suppressed (they enter the leadfield matrix L in the beamformer calculation). The computation can be started from the '''Image''' menu or from the Image selector button [[File:MSBF_Button.png|22px|Image: 22 pixels]] dropdown menu. The Image menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window.

[[File:MSBF66.png]]

''Multiple-source beamformer image calculated in the presence of a source in the left hemisphere. A single-source scan has been performed instead of a bilateral beamforemr. The
source set in the current solution accounts for the left-hemispheric q-maximum in the data. Accordingly, the beamformer scan reveals only the as yet unmodeled additional activity in
the right hemisphere (note the radiological convention in the 3D image display). The source waveform of the beamformer virtual sensor in the left hemisphere is not shown since the
location (blue square in the figure) is not considered for the multiple-source beamformer.''

The beamformer scan can be performed with a single or a bilateral source scan. The default scan type depends on the current solution:
When the beamformer is started from the '''Average tab of the Paradigm dialog box''' the Source Analysis window opens with a new solution and a bilateral beamformer scan is
performed.
When the beamformer is started within the Source Analysis window, the default is:

* a scan with a single source in addition to the sources in the current solution, if at least one source is active.
* a bilateral scan if no source in the current solution is active.
* a scan with a single source when scalar-type beamformer is selected in the '''beamformer option dialog box'''.

The default scan type is the multiple source beamformer. The non-default scan type can be enforced using the corresponding Volume Image / Beamformer entry in the Image main
menu or in the beamformer option dialog box (only for the time-domain beamformer).

===Inserting Sources as Beamformer Virtual Sensor out of the Beamformer Image===

This is similar to the inserting sources out of the beamformer image in Multiple Source Beamformer (MSBF) in the Time-frequency Domain section.
The beamformer image can be used to add beamformer virtual sensors to the current solution. A simple double-click anywhere in the 3D view (not in the 2D view) will generate a
source at the corresponding location. A better and easier way to create sources at image maxima and minima is to use the toolbar buttons '''Switch to Maximum''' and '''Add Source'''

This feature allows to use the beamformer as a tool to create a source montage for '''source coherence''' analysis. A source montage file (*.mtg) for beamformer virtual sensors can
be saved using File \ Save Source Montage As… entry.

The time-domain beamformer image can be also used to add regional or dipole sources to the current solution. Press '''N''' key when there is no source in the current source array or
there is more than one beamformer virtual sensor. To create a new source array for beamformer virtual sensor, press '''N''' key when there is more than one regional or dipole source in
the current source array.

===Notes===

* You can hide or re-display the last computed image by selecting Hide Image entry in the Image menu.
* The current image can be exported to ASCII, ANALYZE, or BrainVoyager (vmp) format from the Image menu.
* For scaling options, use the and Image Scale toolbar buttons.
* Parameters used for the beamformer calculations can be set in the Standard Volume tab of the Image Settings dialog box.
* Note that Model, Residual, Order, and Residual variance are not shown for the beamformer virtual sensor type sources.

===References===

* Sekihara, K., Nagarajan, S. S., Poeppel, D., Marantz, A., & Miyashita, Y. (2001). Reconstructing spatio-temporal activities of neural sources using an MEG vector beamformer technique. IEEE Transactions on Biomedical Engineering, 48(7), 760–771.

* Van Veen, B. D., Van Drongelen, W., Yuchtman, M., & Suzuki, A. (1997). Localization of brain electrical activity via linearly constrained minimum variance spatial filtering. IEEE Transactions on Biomedical Engineering, 44(9), 867–880

== CLARA ==

CLARA ('Classical LORETA Analysis Recursively Applied') is an iterative application of weighted LORETA images with a reduced source space in each iteration.

In an initialization step, a LORETA image is calculated. Then in each iteration the following steps are performed:

# The obtained image is spatially smoothed (this step is left out in the first iteration).
# All grid points with amplitudes below a threshold of 1% of the maximum activity are set to zero, thus being effectively eliminated from the source space in the following step.
# The resulting image defines a spatial weighting term (for each voxel the corresponding image amplitude).
# A LORETA image is computed with an additional spatial weighting term for each voxel as computed in step 3. By the default settings in BESA Research, the regularization values used in the iteration steps are slightly higher than that of the initialization LORETA image.

The procedure stops after 2 iterations, and the image computed in the last iteration is displayed. Please note that you can change all parameters by creating a user-defined volume image.

The advantage of CLARA over non-focusing distributed imaging methods is visualized by the figure below. Both images are computed from the N100 response in an auditory oddball experiment (file '''Oddball.fsg''' in subfolder ''fMRI+EEG-RT-Experiment'' of the ''Examples'' folder). The CLARA image is much more focal than the sLORETA image, making it easier to determine the location of the image maxima.

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (24).gif|thumb|350px|sLORETA image]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (25).gif|thumb|350px|CLARA image]] </li>
</ul></div>

'''Notes:'''

* Starting CLARA: CLARA can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter ''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]'' for important information on regularization of distributed inverses.

== LAURA ==

LAURA (Local Auto Regressive Average) belongs to the distributed inverse method of the family of weighted minimum norm methods ([https://doi.org/10.1023/A:1012944913650 Grave de Peralta Menendeza et al., "Noninvasive Localization of Electromagnetic Epileptic Activity. I. Method Descriptions and Simulations", BrainTopography 14(2), 131-137, 2001]). LAURA uses a spatial weighting function that includes depth weighting and that term has the form of a local autoregressive function.

The source activity is estimated by applying the general formula for a weighted minimum norm:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T}\left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings.''

In LAURA, V contains both a depth weighting term W and a representation of a local autoregressive function A. V is computed as:

<math>\mathrm{V} = \left( \mathrm{U}^{T} \cdot \mathrm{U} \right)^{-1}</math>


Where

<math>\mathrm{U} = \left( \mathrm{W} \cdot \mathrm{A} \right) \otimes \mathrm{I}_{3}</math>


Here, <math>\otimes</math> denotes the Kronecker product. I3 is the [3×3] identity matrix. W is an [s×s] diagonal matrix (with s the number of source locations on the grid), where each diagonal element is the inverse of the maximum singular value of the corresponding regional source's leadfields. The formula for the diagonal components Aii and the off-diagonal components Aik are as follows:

<math>\mathrm{A}_{ii} = \frac{26}{\mathrm{N}_{i}}\sum_{k \subset V_{i}}^{}\frac{1}{\mathrm{d}_{ik}^{2}}</math>


<math>
\mathrm{A}_{ik} =
\begin{cases}
- 1/\operatorname{dist}\left( i,k \right)^{2}, & \text{if } k \subset V_{i} \\
0, & \text{otherwise}
\end{cases}
</math>


Here, Vi is the vicinity around grid point i that includes the 26 direct neighbors.

The LAURA image in BESA Research displays the norm of the 3 components of S at each location r. Using the menu function ''Image / Export Image As... ''you have the option to save this norm of S or alternatively all components separately to disk.

'''Notes:'''

* '''Grid spacing:''' Due to memory limitations, LAURA images require a grid spacing of 7 mm or more.
* '''Computation time:''' Computation speed during the first LAURA image calculation depends on the grid spacing (computation is faster with larger grid spacing). After the first computation of a LAURA image, a '''*.laura''' file is stored in the data folder, containing intermediate results of the LAURA inverse. This file is used during all subsequent LAURA image computations. Thereby, the time needed to obtain the image is substantially reduced.
* '''MEG:''' In the case of MEG data, an additional constraint is implemented in the LAURA algorithm that prevents solutions from containing radial source currents (compare Pascual-Marqui, ISBET Newsletter 1995, 22-29). In MEG, an additional source space regularization is necessary in the inverse matrix operation required compute V
* '''Starting LAURA:''' LAURA can be started from the''' Image''' menu or from the '''Image Selection''' button.
* '''Regularization:''' Please refer to Chapter'' “Regularization of distributed volume images” ''for important information on regularization of distributed inverses.

== LORETA ==

LORETA ("Low Resolution Electromagnetic Tomography") is a distributed inverse method of the family of ''weighted minimum norm'' methods. LORETA was suggested by R.D. Pascual-Marqui (International Journal of Psychophysiology. 1994, 18:49-65). LORETA is characterized by a smoothness constraint, represented by a discrete 3D Laplacian.

The source activity is estimated by applying the general formula for a weighted minimum norm:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T}\left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings.''

In LORETA, V contains both a depth weighting term and a representation of the 3D Laplacian matrix. V is computed as:

<math>\mathrm{V} = \left( \mathrm{U}^{T} \cdot \mathrm{U} \right)^{- 1}</math>


where

<math>\mathrm{U} = \left( \mathrm{W} \cdot \mathrm{A} \right) \otimes \mathrm{I}_{3}</math>


Here, <math>\otimes</math> denotes the Kronecker product. I3 is the [3x3] identity matrix. W is an [sxs] diagonal matrix (with s the number of source locations on the grid), where each diagonal element is the inverse of the maximum singular value of the corresponding regional source's leadfields. A contains the 3D Laplacian and is computed as

<math>\mathrm{A} = \mathrm{Y} - \mathrm{I}_{s}</math>


with Is the [sxs] identity matrix, where s is the number of sources (= three times the number of grid points) and

<math>\mathrm{Y} = \frac{1}{2}\left\{ \mathrm{I}_{s} + \left\lbrack \operatorname{diag}\left( \mathrm{Z} \cdot \left\lbrack 111 \ldots 1 \right\rbrack^{T} \right) \right\rbrack^{- 1} \right\} \cdot \mathrm{Z}</math>


where

<math>
\mathrm{Z}_{ik} =
\begin{cases}
1/6, & \text{if } \operatorname{dist}\left( i,k \right) = 1 \text{ grid point} \\
0, & \text{otherwise}
\end{cases}
</math>


The LORETA image in BESA Research displays the norm of the 3 components of S at each location r. Using the menu function ''Image / Export Image As... ''you have the option to save this norm of S or alternatively all components separately to disk.

'''Notes:'''
* '''Grid spacing:''' Due to memory limitations, LORETA images require a grid spacing of 5 mm or more.
* '''Computation time:''' Computation speed during the first LORETA image calculation depends on the grid spacing (computation is faster with larger grid spacing). After the first computation of a LORETA image, a '''<nowiki>*.loreta</nowiki>''' file is stored in the data folder, containing intermediate results of the LORETA inverse. This file is used during all subsequent LORETA image computations. Thereby, the time needed to obtain the image is substantially reduced.
* '''MEG''': In the case of MEG data, an additional constraint is implemented in the LORETA algorithm that prevents solutions from containing radial source currents (Pascual-Marqui, ISBET Newsletter 1995, 22-29). In MEG, an additional source space regularization is necessary in the inverse matrix operation required compute V.
* '''Starting LORETA:''' LORETA can be started from the''' Image''' menu or from the '''Image Selection '''button.
* '''Regularization:''' Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed source models.

== sLORETA ==

This distributed inverse method consists of a ''standardized, unweighted minimum norm''. The method was originally suggested by R.D. Pascual-Marqui (Methods & Findings in Experimental & Clinical Pharmacology 2002, 24D:5-12) Starting point is an unweighted minimum norm computation:

<math>\mathrm{S}_{\text{MN}}\left( t \right) = \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings''.

This minimum norm estimate is now standardized to produce the sLORETA activity at a certain brain location r:

<math>\mathrm{S}_{\text{sLORETA}, r} = \mathrm{R}_{rr}^{-1/2} \cdot \mathrm{S}_{\text{MN},r}</math>


SsMN,r is the [3x1] (MEG: [2x1]) minimum norm estimate of the 3 (MEG: 2) dipoles at location r. Rrr is the [3x3] (MEG: [2x2]) diagonal block of the resolution matrix R that corresponds to the source components at the target location r. The resolution matrix is defined as:

<math>\mathrm{R} = \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{L}^{T} + \lambda \cdot \mathrm{I} \right)^{-1} \cdot \mathrm{L}</math>


The sLORETA image in BESA Research displays the norm of SsLORETA, r at each location r. Using the menu function ''Image / Export Image As...'' you have the option to save this norm of SsLORETA, r or alternatively all components separately to disk.

'''Notes:'''

* sLORETA can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== swLORETA ==

This distributed inverse method is a ''standardized, depth-weighted minimum norm'' (E. Palmero-Soler et al 2007 Phys. Med. Biol. 52 1783-1800). It differs from sLORETA only by an additional depth weighting.

Starting point is a depth-weighted minimum norm computation:

<math>\mathrm{S}_{\text{MN}}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings''.

V is the diagonal depth weighting matrix. For s grid locations, V is of dimension [3s x 3s] (MEG: [2s x 2s]). Each diagonal element of V is the inverse of the first singular value of the leadfield of the corresponding regional source. Hence, the first 3 (MEG: 2) diagonal elements equal the inverse of the largest eigenvalue of the leadfield matrix of regional source 1, and so on.

This minimum norm estimate is now standardized to produce the swLORETA activity at a certain brain location r:

<math>\mathrm{S}_{\text{swLORETA},r} = \mathrm{R}_{rr}^{-1/2} \cdot \mathrm{S}_{\text{MN},r}</math>


SsMN,r is the [3x1] (MEG: [2x1]) depth-weighted minimum norm estimate of the regional source at location r. Rrr is the [3x3] (MEG: [2x2]) diagonal block of the resolution matrix R that corresponds to the source components at the target location r. The resolution matrix is defined as:

<math>\mathrm{R} = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} + \lambda \cdot \mathrm{I} \right)^{-1} \cdot \mathrm{L}</math>


The swLORETA image in BESA Research displays the norm of SswLORETA, r at each location r. Using the menu function ''Image / Export Image As...'' you have the option to save this norm of SswLORETA, r or alternatively all components separately to disk.

'''Notes:'''

* sLORETA can be started from the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== sSLOFO ==

SSLOFO (standardized shrinking LORETA-FOCUSS) is an iterative application of weighted distributed source images with a reduced source space in each iteration ([https://dx.doi.org/10.1109/TBME.2005.855720 Liu et al., "Standardized shrinking LORETA-FOCUSS (SSLOFO): a new algorithm for spatio-temporal EEG source reconstruction", IEEE Transactions on Biomedical Engineering 52(10), 1681-1691, 2005]).

In an initialization step, an [[#sLORETA | sLORETA]] image is calculated. Then in each iteration the following steps are performed:

# A weighted minimum norm solution is computed according to the formula <math display="inline">\mathrm{S} = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}</math> . Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D is the data at the time point under consideration. V is a diagonal spatial weighting matrix that is computed in the previous iteration step. In the first iteration, the elements of V contain the magnitudes of the initially computed LORETA image.
# Standardization of this weighted minimum norm image is performed with the resolution matrix as in [[#sLORETA | sLORETA]].
# The obtained standardized weighted minimum norm image is being smoothed to get Ssmooth.
# All voxels with amplitudes below a threshold of 1% of the maximum activity get a weight of zero in the next iteration step, thus being effectively eliminated from the source space in the next iteration step.
# For all other voxels, compute the elements of the spatial weighting matrix V to be used in the next iteration as follows: <math display="inline">\mathrm{V}_{ii,\text{next iteration}} = \frac{1}{\left\| \mathrm{L}_{i} \right\|} \cdot \mathrm{S}_{ii,\text{smooth}} \cdot \mathrm{V}_{ii,\text{current iteration}}</math>



The procedure stops after 3 iterations. Please note that you can change all parameters by creating a [[#User-Defined Volume Image | user-defined volume image]].

'''Notes:'''
* '''Starting sSLOFO''': sSLOFO can be started from the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter ''[[#Regularization of distributed volume images | Regularization of distributed volume images]]'' for important information on regularization of distributed inverses.

== User-Defined Volume Image ==

In addition to the predefined 3D imaging methods in BESA Research, it is possible to create user-defined imaging methods based on the general formula for distributed inverses:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. Custom-defined parameters are:* The spatial weighting matrix V: This may include depth weighting, image weighting, or cross-voxel weighting with a 3D Laplacian (as in LORETA) or an autoregressive function (as in LAURA).

* Regularization: The term in parentheses is generally regularized. Note that regularization has a strong effect on the obtained results. Please refer to chapter “''Regularization of Distributed Volume Images” ''for more information.
* Standardization: Optionally, the result of the distributed inverse can be standardized with the resolution matrix (as in sLORETA).
* Iterations: Inverse computations can be applied iteratively. Each iteration is weighted with the image obtained in the previous iteration.

All parameters for the user-defined volume image are specified in the User-Defined Volume Tab of the Image Settings dialog box. Please refer to chapter “''User-Defined Volume Tab”'' for details.

'''Notes:'''
* Starting the user-defined volume image: the image calculation can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== Regularization of distributed volume images ==

Distributed source images require the inversion of a term of the form L V LT. This term is generally regularized before its inversion. In BESA Research, selection can be made between two different regularization approaches (parameters are defined in the ''Image Settings dialog box''):

* '''Tikhonov regularization''': In Tikhonov regularization, the term L V LT is inverted as (L V LT +λ I)-1. Here, l is the regularization constant, and I is the identity matrix.
* One way of determining the optimum regularization constant is by minimizing the ''generalized cross'' ''validation error'' (CVE).
* Alternatively, the regularization constant can be specified manually as a percentage of the trace of the matrix L V LT.
* '''TSVD''': In the truncated singular value decomposition (TSVD) approach, an SVD decomposition of L V LT is computed as  L V LT = U S UT, where the diagonal matrix S contains the singular values. All singular values smaller than the specified percentage of the maximum singular values are set to zero. The inverse is computed as U S-1 UT, where the diagonal elements of S-1 are the inverse of the corresponding non-zero diagonal elements of S.

Regularization has a critical effect on the obtained distributed source images. The results may differ completely with different choices of the regularization parameter (see examples below). Therefore, it is important to evaluate the generated image critically with respect to the regularization constant, and to keep in mind the uncertainties resulting from this fact when interpreting the results. The default setting in BESA Research is a TSVD regularization with a 0.03% threshold. However, this value might need to be adjusted to the specific data set at hand.

The following example illustrates the influence of the regularization parameter on the obtained images. The data used here is condition '''St-Cor of dataset Examples \ TFC-Error-Related-Negativity \ Correct+Error.fsg''' at 176 ms following the visual stimulus. Discrete dipole analysis reveals the main activity in the left and right lateral visual cortex at this latency.

[[Image:SA 3Dimaging (42).gif]]

''Discrete source model at 176 ms: Main activity in the left and right lateral visual cortex, no visual midline activity.''

LORETA images computed at this latency depend critically on the choice of the regularization constant. The following 3D images are created with TSVD regularization with SVD cutoffs of 0.1%, 0.005%, and 0.0001%, respectively. The volume grid size was 9 mm. The example demonstrates the dramatic effect of regularization and demonstrates the typical tradeoff between too strong regularization (leading to too smeared 3D images that tend to show blurred maxima) and too small regularization (resulting in too superficial 3D images with multiple maxima).

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (43).gif|thumb|350px|'''SVD cutoff 0.1%''': Regularization too strong. No separation between sources, mislocalization towards the middle of the brain.]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (44).gif|thumb|350px|'''SVD cutoff 0.005%''': Appropriate regularization. Separation of the bilateral activities. Location in agreement with the discrete multiple source model.]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (45).gif|thumb|350px|'''SVD cutoff 0.0001%''': Too small regularization. Mislocalization, too superficial 3D image. ]] </li>
</ul></div>

The automatic determination of the regularization constant using the CVE approach does not necessarily result in the optimum regularization parameter either. In this example, the unscaled CVE approach rather resembles the TSVD image with a cutoff of 0.0001%, i.e. regularization is too small. Therefore, it is advisable to compare different settings of the regularization parameter and make the final choice based on the above-mentioned considerations.

== Cortical LORETA ==

Cortical LORETA is principally the same technique as LORETA, however, Cortical LORETA is not computed in a 3D volume, but on the cortical surface.

The cortical reconstruction in BESA Research fed from BESA MRI is a closed 2D surface with no boundaries and a very close approximation of the actual cortical form. It consists of an irregular triangulated grid.

The Laplace operator that is used for identifying a smooth solution in a three-dimensional space is exchanged with a Laplace operator that runs on the two-dimensional cortical surface.

There is a wide variety of 2D Laplace operators with different characteristics. The general form of the discrete Laplace operator is

<math>\Delta f\left( p_{i} \right) = \frac{1}{d_{i}}\sum_{j \in N(i)}^{}{w_{ij}\left\lbrack f\left( p_{i} \right) - f\left( p_{j} \right) \right\rbrack},</math>


where '''pi''' is the '''i-th''' node of the triangular mesh, '''f(pi) '''is the value of a function f defined on the cortical mesh at the node '''pi''', '''wij''' is the weight for the connection between the nodes '''pi''' and '''pj''' and '''di''' is a normalization factor for the '''i-th''' row of the operator. Furthermore, '''N(i)''' is the set of indices corresponding to the direct (also called "1-ring") neighbors of '''pi'''.

BESA offers the choice of three Laplace operators with slightly different characteristics.

* '''Unweighted Graph Laplacian''': This is the simplest operator. It takes into account only the adjacency of the nodes and not the geometry of the mesh:

<math>
w_{ij} =
\begin{cases}
1, & \text{if } p_{i} \text{ and } p_{j} \text{ are connected by an edge} \\
0, & \text{otherwise}
\end{cases}
</math>

<math>d_{i} = 1</math>


[[Image:SA 3Dimaging (4).jpg |450px]]

* '''Weighted Graph Laplacian:''' This operator is similar to the unweighted graph Laplacian but with different weights for the different connections. The connections between nearby nodes get larger weights than the connections between farther nodes:

<math>w_{ij} = \frac{1}{\operatorname{dist}\left( p_{i},p_{j} \right)}</math>

<math>d_{i} = \sum_{j \in N(i)}^{} {\operatorname{dist}\left(p_{i}, p_{j} \right)}</math>


where '''dist''' ('''pi''' , '''pj''') is the distance between the nodes '''pi '''and '''pj'''.

[[Image:SA 3Dimaging (6).jpg|450px]]

* '''Geometric Laplacian with mixed area weights''': This operator takes into account the angles in the corresponding triangles into account as well as the area around the nodes in order to determine the connection weights:

<math>w_{ij} = \frac{\cot\left( \alpha_{ij} \right) + \cot\left( \beta_{ij} \right)}{2}</math>

<math>d_{i} = A_{\text{mixed}}</math>


where '''αij''' and '''βij''' denote the two angles opposite to the edge ('''i , j''') and '''Amixed '''is either the Voronoi area, or 1/2 of the triangle area or 1/4 of the triangle area depending on the type of the triangle.

[[Image:SA 3Dimaging (8).jpg|450px]]

'''Regularization and other parameters:'''

[[Image:SA 3Dimaging (46).gif ‎]]

* '''SVD cutoff''': The regularization for the inverse operator as a percent of the largest singular value.
* '''Depth weighting''': Turn depth weighting on or off.
* '''Laplacian type''': Selection of Laplacian operators (see above).

'''Notes:'''
* '''Starting Cortical LORETA''': Cortical LORETA can be started from the sub-menu '''Surface Image''' of the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]''” for important information on regularization of distributed inverses.

== Cortical CLARA ==

Cortical CLARA is principally the same technique as CLARA, but Cortical CLARA is not computed in a 3D volume, but on the cortical surface. Instead of using a LORETA image as the basis for the iterative application, cortical CLARA uses cortical LORETA.

'''Regularization and other parameters:'''

[[Image:SA 3Dimaging (47).gif]]

* '''SVD cutoff''': The regularization for the inverse operator as a percent of the largest singular value.
* '''Depth weighting''': Turn depth weighting on or off.
* '''Laplacian type''': Selection of Laplacian operators (see Cortical LORETA).
* '''No of iterations''': Number of iterations for CLARA. The more iterations are used, the sparser becomes the solution.
* '''Automatic''': The algorithm tries to determine the number of iterations automatically. The goodness of fit (GOF) is calculated after every iteration and if there is a big jump in the GOF then the algorithm will stop. If no jumps appear during the calculations then CLARA iterates until the specified number of iterations is reached.
* '''Regularize iterations''': If one wants to use different regularization for the CLARA iterations than the value specified as "SVD cutoff", this option should be selected.
* '''Amount to clip from img (%)''': Cortical CLARA uses the solution from the previous iteration as an additional weighting matrix for the current iteration. That weighting matrix is constructed by cutting the "low" activity from the solution. This number specifies how much of the activity should be cut from the previous solution in order to construct the weighting matrix. This value is given as a percentage of the maximal activity. Default value is 10%.

'''Notes:'''

* '''Starting Cortical CLARA:''' Cortical CLARA can be started from the sub-menu '''Surface Image''' of the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]''” for important information on regularization of distributed inverses.

== Cortex Inflation ==

The inflated cortex is a smoothened version of the individual cortical surface with minimal metric distortions (Fischl, B. et al. (1999). Cortical Surface-Based Analysis: II: Inflation, Flattening, and a Surface-Based Coordinate System. ''NeuroImage'', 9(2), 195–207). Gyri and sulci are smoothened out. The original distances between each point on the cortex and its neighbors are, however, mostly preserved.

[[Image:SA 3Dimaging (48).gif]]

''Cortical LORETA map overlaid on top of the inflated cortical surface.''

A lighter gray color overlaid on top of the surface image indicates the location of a gyrus of the individual cortex surface, while a darker gray color indicates the location of a sulcus. The inflated cortical surface can be computed in '''BESA MRI 2.0'''. For more details please refer to the BESA MRI 2.0 help.

== Surface Minimum Norm Image ==

'''Introduction'''

The minimum norm approach is a common method to estimate a distributed electrical current image in the brain at each time sample (Hämäläinen & Ilmoniemi 1984). The source activities of a large number of regional sources are computed. The sources are evenly distributed using 1500 standard locations 10% and 30% below the smoothed standard brain surface (when using the standard MRI) or using between 3000-4000 locations on the individual brain surface defined by the gray-white-matter boundary.

Since the number of sources is much larger than the number of sensors in a minimum norm solution, the inverse problem is highly underdetermined and must be stabilized by a mathematical constraint, the minimum norm. Out of the many current distributions that can account for the recorded sensor data, the solution with the minimum L2 norm, i.e. the minimum total power of the current distribution is displayed in BESA Research.

First, the forward solution (leadfield matrix L) of all sources is calculated in the current head model. Then, the source activities S(t) of all source components are computed from the data matrix D(t) using an inverse regularized by the estimated noise covariance matrix:

<math>\mathrm{S}\left( t \right) = \mathrm{R} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{R} \cdot \mathrm{L}^{T} + \mathrm{C}_N \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed regional source model, CN denotes the noise correlation matrix in sensor space, and R is a weighting matrix in source space. R and CN can be designed in different ways in order to optimize the minimum norm result. The total activity of each regional source is computed as the root mean square of the source activities S(t) of its 3 (MEG:2) components. This total source activity is transformed to a color-coded image of the brain surface. (When the standard brain is used, two sources are assigned to each surface location, located 10% and 30% below the surface, respectively. The color that is displayed on the standard brain surface is the larger of the two corresponding source activities.)

'''Weighting options'''

The minimum norm current imaging techniques of BESA Research provide different weighting strategies. Two weighting approaches are available: Depth weighting and spatio-temporal approaches.
* '''Depth weighting:''' Without depth weighting, deep sources appear very smeared in a minimum-norm reconstruction. With depth weighting, both deep and superficial sources produce a similar, more focal result. If this weighting method is selected, the leadfield of each regional source is scaled with the largest singular value of the SVD (singular value decomposition) of the source's leadfield.
* '''Spatio-temporal weighting''': Spatio-temporal weighting tries to assign large weight to sources that are assumed to be more likely to contribute to the recorded data.
** '''Subspace correlation after single source scan''': This method divides the signal into a signal and a noise subspace. The correlation of the leadfield of a regional source i with the signal subspace (pi) is computed to find out if the source location contributes to the measured data. The weighting matrix R becomes a diagonal matrix. Each of the three (MEG: 2) components of a regional source get the same weighting value pi2. This approach is based on the signal subspace correlation measure introduced by J.C. Mosher, R. M. Leahy (Recursive MUSIC: A Framework for EEG and MEG Source Localization, IEEE Trans. On Biomed. Eng. Vol. 45, No. 11, November 1998)
** '''Dale & Sereno 1993:''' In the approach of Dale and Sereno (J Cogn Neurosci, 1993, 5: 162-176) a signal subspace needs not be defined. The correlation pi of the leadfield of regional source i with the inverse of the data covariance matrix is computed along with the largest singular value λmax of the data covariance matrix. The weighting matrix R is a diagonal matrix with weights: [[Image:SA 3Dimaging (50).gif]]. Each of the three (MEG: 2) components of a regional source receives the same weighting value.

'''Noise regularization'''

Two methods to estimate the channel noise correlation matrix CN are provided by the program:
* '''Use baseline:''' Select this option to estimate the noise from the user-definable baseline. The signal is computed from the data at non-baseline latencies.
* '''Use 15% lowest values:''' The baseline activity is computed from the data at those 15% of all displayed latencies that have the lowest global field power. The signal is computed from all displayed latencies.

In each case, the activity (noise or signal, respectively) is defined as root-mean-square across all respective latencies for each channel.

The noise covariance matrix CN is constructed as a diagonal matrix. The entries in the main diagonal are proportional to the noise activity of the individual channels (if selected) or are all equally proportional to the average noise activity over all channels. The noise covariance matrix CN is then scaled such that the ratio of the Frobenius norms of the weighted leadfield projector matrix (LRLT) and the noise covariance matrix CN equals the Signal-to-Noise ratio. This scaling can be multiplied by an additional factor (default=1) to sharpen (<1) or smoothen (>1) the minimum norm image.

'''Applying the Minimum Norm Image'''

The minimum-norm algorithm is started via the ''Surface minimum norm image dialog box'', which is opened from the''' Image''' menu, or by typing the shortcut '''Ctrl-M''': Please refer to Chapter ''“Surface'' ''Minimum Norm Tab”'' for more details.

As opposed to the other 3D images available from the '''Image '''menu, the surface minimum norm image is not computed on a volumetric grid, but rather for locations on the brain surface. Accordingly, the results of the minimum norm image are displayed superimposed to the brain surface mesh rather than to the volumetric MR image.

The figure below shows a minimum norm image computed from the file '''Examples\Epilepsy\Spikes\Spikes-Child4_EEG+MEG_averaged.fsg'''. The EEG spike peak was imaged using the individual brain surface of the subject. A baseline from -300 to -70 ms was used. Minimum norm was computed with depth weighting, Spatio-temporal weighting according to Dale & Sereno 1993 and individual noise weighting with a noise scale factor of 0.01. The minimum norm image reveals the location of the spike generator in the close vicinity of the frontal left-hemispheric lesion in this subject.

[[Image:SA 3Dimaging (51).gif]]

== Multiple Source Probe Scan (MSPS) ==

 
'''Introduction'''

The MSPS function provides a tool for the validation of a given solution. It is based on the following theoretical consideration: If the recorded EEG/MEG data has been modeled adequately, i.e. all active brain regions are represented by a source in the current solution, then any additional probe source added to the solution will not show any activity apart from noise. The only exception occurs if this probe source is placed in close vicinity to one of the sources in the current solution. In that case, the solution's source and the probe source will share the activity of the corresponding brain area. The MSPS applies these considerations by scanning the brain on a pre-defined grid with a regional probe added to the current solution. Grid extent and density can be specified in the Image settings. The power P of the probe source at location r in the signal interval is compared with the power of the probe source in a reference interval, defining a value q:

<math>\mathrm{q}\left( r \right) = \sqrt{\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}} - 1</math>


MSPS can be computed on time domain or time-frequency domain data:
* In the time domain, q(r) is computed from the source waveform of the probe source. Here, P(r) is the mean power of the probe source at location r in the marked latency range, and Pref(r) is the mean probe source power in the user-definable baseline interval.
* In the time-frequency domain, an MSPS image can be computed from the complex cross spectral density matrices. By applying the inverse operator for a source configuration consisting of the current solution and the probe source, the power of the probe source can be computed for the target interval [P(r)] and the reference time-frequency interval [Pref(r)]. In the resulting MSPS image, q-values are shown in %, where q[%] = q*100.

The inverse operator used to determine the probe source power uses different regularization constants for the probe source and the sources in the current solution. The regularization constant of the sources in the current solution can be specified in the Image settings (default 4%). The regularization constant of the probe source is internally set to 0%.

Alternatively to the definition above, q can also be displayed in units of dB:

<math>\mathrm{q}\left\lbrack \text{dB} \right\rbrack = 10 \cdot \log_{10}\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}</math>


Values of q smaller than zero are not shown in the MSPS image.

According to the considerations above, an MSPS of a correct source model should optimally yield image maxima around the sources in the current solution only. If the MSPS image is blurred or shows maxima at locations different from the modeled sources, this indicates a non-sufficient or incorrect solution.

'''Applying the MSPS'''

This chapter illustrates the application of the Multiple Source Probe Scan. The figures are generated with data from file '''Examples/Epilepsy/Spikes/Rolandic-Spike-Child.fsg''' (-300 : +200 ms, filtered from 3 Hz [forward] to 40 Hz [zero-phase]).

'''Time domain versus time-frequency domain MSPS'''

The multiple source probe scan can be computed in the time domain or the time-frequency domain. The latter is possible only when time-frequency domain data is available for the current condition, i.e. if the condition has been created by starting a multiple source beamformer (MSBF) computation from the source coherence window. In this case, evoking the MSPS calculation from the '''Imaging '''button or from the '''Image''' menu will bring up the following dialog window that allows to choose between time- or time-frequency MSPS. If only time domain data is available, this dialog window will not appear and MSPS will be computed in the time domain.

[[Image:SA 3Dimaging (53).gif]]

For a time-frequency domain MSPS, the target and the reference time-frequency interval have been specified already in the Time-Frequency window (see Chapter "''How To Create Beamformer Images''"). For a time-domain MSPS, the target and the reference epoch have to be specified in the Source Analysis window as described below.

'''Time domain MSPS'''

The time-domain MSPS image displays the ratio of the power of a regional probe source in the signal and the baseline interval. The currently set baseline is indicated by a horizontal line in the upper left corner of the channel box.

[[Image:SA 3Dimaging (54).gif|thumb|c|none|330px|The black horizontal bar in the upper part of the channel box (here circled in red) indicates the baseline interval.]]

By default, BESA Research defines the pre-stimulus interval of the current data segment as baseline. The baseline should represent a latency range in which no event-related activity is present in the data. There are several possibilities to modify the baseline interval: by clicking on the horizontal line with the left mouse button or by using the corresponding entry in the '''Condition '''menu or '''Fit Interval''' popup menu.

Mark an interval to define the target epoch, i.e. the time-interval for which the current solution is to be tested. Start the MSPS by selecting it from the '''Image selection '''button or from the '''Image''' menu to start the probe source scan. The''' Image '''menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window. The 3D window opens and displays the scan result.

<div><ul>
<li style="display: inline-block;"> [[Image:SA 3Dimaging (55).gif|thumb|c|none|650px|This figure shows the MSPS image applied on the three left-hemispheric sources in the solution ''''Rolandic-Spike-Child-RS2.bsa''''. The baseline is set from -300ms to -50 ms. The right-hemispheric sources have been switched off. The fit interval is set to the latency range of large overall activity in the data (-43 ms : 117 ms). A realistic FEM model appropriate for the subject's age (12 years, conductivity ratios (cr) 50) is applied. The MSPS image does not show maxima at the modeled source locations and rather shows a spread q-value distribution.]] </li>

<li style="display: inline-block;"> [[Image:SA 3Dimaging (56).gif|thumb|c|none|650px|The MSPS image for the same latency range when the right-hemispheric sources have been included. The MSPS image appears more focal and shows maxima around the modeled brain regions. This indicates the substantial improvement of the solution by adding the right-hemispheric sources that model the propagation of the epileptic spike from the left to the right hemisphere (note the radiological side convention in the 3D window).]] </li>
</ul></div>

'''Time-Resolved MSPS'''

If the MSPS has been computed on time domain data, the image can be shown separately for each latency in the selected interval. After the MSPS has been computed for the marked epoch, double-click anywhere within this epoch to display the ratio of the probe source magnitude at the selected latency and the mean probe source magnitude in the baseline. Scanning the latency range by moving the cursor (e.g. with the left and right arrow cursor keys) provides a time-resolved MSPS image.

Time-resolved MSPS images are not available if the MSPS has been computed on data in the time-frequency domain.

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (57).gif|thumb|450px|MSPS image of the spike peak activity at 0ms. The activity mainly occurs in the left hemisphere. This fact is illustrated by the source waveforms and confirmed in the MSPS image, which shows a focal maximum around the location of the red sources.]] </li>

<li style="display: inline-block;"> [[File:SA 3Dimaging (58).gif|thumb|450px|Around +27 ms, the spike has propagated to the right hemisphere. This becomes evident from the waveforms of the blue sources, which show a significant latency lag with respect to the first three sources, and from the MSPS image, which shows the maximum around blue sources at this latency.]] </li>
</ul></div>



'''Notes:'''

* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image''' menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the''' Image''' menu.
* For scaling options, please refer to the '''scaling buttons''' popup menu .
* Parameters used for the MSPS calculations can be set in the ''General Settings tab'' of the ''Image Settings dialog box.''

== Source Sensitivity ==

'''Introduction'''

The 'Source sensitivity' function displays the sensitivity of the selected source in the current source model to activity in other brain regions. Sensitivity is defined as the fraction of power at the scanned brain location that is mapped onto the selected source.

To compute the source sensitivity, unit brain activity is modeled at different locations (probe source) throughout the brain. To this data, the current source model is applied to compute the source waveforms SCM of all modeled sources:

<math>\mathrm{S}_{\text{CM}} = \mathrm{L}_{\text{CM}}^{-1} \cdot \mathrm{L}_{\text{PS}}</math>


Here LCM-1 is the regularized inverse operator for the current model, and LPS is the leadfield of the regional probe source (dimension [Nx3] for EEG and [Nx2] for MEG, respectively, where N is the number of sensors). The source amplitude SSS of the selected source in the model is a 3x3 (MEG: 2x2) sub-matrix of SCM (if the selected source is a regional source) or a 1x3-matrix (MEG: 1x2) (if the selected source is a dipole). The root mean square of the singular values of SCM is defined as the source sensitivity.

The 3D source sensitivity image displays this value for all locations on a grid specified under '''Image/Settings'''. Grid density can be specified in the Image Settings.

'''Applying the Source Sensitivity Image'''

The Source Sensitivity image is evoked from the '''Image''' menu or by pressing the corresponding hot key (default: '''V''').

This function is enabled only when a solution with an active selected source is present in the Source Analysis window. The source sensitivity image then displays the sensitivity of the selected source to activity in other brain regions.

[[Image:SA 3Dimaging (59).gif]]

''Source Sensitivity image for the selected frontal source (green) in model ''''''High_Intensity_3RS.bsa'''''' in folder 'Examples/ERP_Auditory_Intensity'. The data displayed is the '100dB' condition in file ''''''All_Subjects_cc.fsg''''''. The selected source is sensitive to activity in the frontal brain region (yellow/white), while it is not influenced by activity in the vicinity of the left and right auditory cortex areas, which are modeled by the red and blue source in the model (transparent/gray).''

'''Notes:'''

* The sensitivity image is independent of the recorded sensor signals. It only depends on the current source model, the sensor configuration, the head model, and the regularization constant.
* If the regularization constant is set to zero, each source has a sensitivity of 100% to activity around its own location. With increasing regularization, the spatial filter becomes less focused, and the sensitivity of a source to activity at its location decreases.
* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image''' menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the '''Image''' menu.

{{BESAManualNav}}

Source Analysis 3D Imaging

2019-03-27T11:42:36Z

Jamie: /* Applying the Beamformer */

{{BESAInfobox
|title = Module information
|module = BESA Research Standard or higher
|version = 6.1 or higher
}}


== Overview ==

BESA Research features a set of new functions that provide 3D images that are displayed superimposed to the individual subject's anatomy. This chapter introduces these different images and describe their properties and applications.

The 3D images can be divided into three categories:

'''Volume images:'''

* '''The Multiple Source Beamformer (MSBF)''' is a tool for imaging brain activity. It is applied in the time-domain or time-frequency domain. The beamformer technique in time-frequency domain can image not only evoked, but also induced activity, which is not visible in time-domain averages of the data.
* '''Dynamic Imaging of Coherent Sources (DICS)''' can find coherence between any two pairs of voxels in the brain or between an external source and brain voxels. DICS requires time-frequency-transformed data and can find coherence for evoked and induced activity.

The following imaging methods provide an image of brain activity based on a distributed multiple source model:
* '''CLARA''' is an iterative application of LORETA images, focusing the obtained 3D image in each iteration step.
* '''LAURA '''uses a spatial weighting function that has the form of a local autoregressive function.
* '''LORETA''' has the 3D Laplacian operator implemented as spatial weighting prior.
* '''sLORETA''' is an unweighted minimum norm that is standardized by the resolution matrix.
* '''swLORETA '''is equivalent to sLORETA, except for an additional depth weighting.
* '''SSLOFO '''is an iterative application of standardized minimum norm images with consecutive shrinkage of the source space.
* A '''User-defined volume image''' allows to experiment with the different imaging techniques. It is possible to specify user-defined parameters for the family of distributed source images to create a new imaging technique.
* Bayesian source imaging: '''SESAME''' uses a semi-automated Bayesian approach to estimate the number of dipoles along with their parameters.

'''Surface image:'''

* The '''Surface Minimum Norm Image'''. If no individual MRI is available, the minimum norm image is displayed on a standard brain surface and computed for standard source locations. If available, an individual brain surface is used to construct the distributed source model and to image the brain activity.
* '''Cortical LORETA'''. Unlike classical LORETA, cortical LORETA is not computed in a 3D volume, but on the cortical surface.
* '''Cortical CLARA'''. Unlike classical CLARA, cortical CLARA is not computed in a 3D volume, but on the cortical surface.

'''Discrete model probing:'''

These images do not visualize source activity. Rather, they visualize properties of the currently applied discrete source model:
* The '''Multiple Source Probe Scan (MSPS)''' is a tool for the validation of a discrete multiple source model.
* The '''Source Sensitivity image''' displays the sensitivity of a selected source in the current discrete source model and is therefore data independent.

== Multiple Source Beamformer (MSBF) in the Time-frequency Domain ==

 
'''Short mathematical introduction'''

The BESA beamformer is a modified version of the linearly constrained minimum variance vector beamformer in the time-frequency domain as described in [https://dx.doi.org/10.1073/pnas.98.2.694 Gross et al., "Dynamic imaging of coherent sources: Studying neural interactions in the human brain", PNAS 98, 694-699, 2001]. It allows to image evoked and induced oscillatory activity in a user-defined time-frequency range, where time is taken relative to a triggered event.

The computation is based on a transformation of each channel's single trial data from the time domain into the time-frequency domain. This transformation is performed by the BESA Research Source Coherence module and leads to the complex spectral density Si (f,t), where i is the channel index and f and t denote frequency and time, respectively. Complex cross spectral density matrices C are computed for each trial:

<math>\mathrm{C}_{ij}\left( f,t \right) = \mathrm{S}_{i}\left( f,t \right) \cdot \mathrm{S}_{j}^{*}\left( f,t \right)</math>


The output power P of the beamformer for a specific brain region at location r is then computed by the following equation:

<math>\mathrm{P}\left( r \right) = \operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{-1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{-1}</math>


Here, Cr-1 is the inverse of the SVD-regularized average of Cij(f,t) over trials and the time-frequency range of interest; L is the leadfield matrix of the model containing a regional source at target location r and, optionally, additional sources whose interference with the target source is to be minimized; tr'[] is the trace of the [3×3] (MEG:[2×2]) submatrix of the bracketed expression that corresponds to the source at target location r.

In BESA Research, the output power P(r) is normalized with the output power in a reference time-frequency interval Pref(r). A value q ist defined as follows:

<math> \mathrm{q}\left( r \right) =
\begin{cases}
\sqrt{\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}(r)}} - 1 = \sqrt{\frac{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{\text{ref},r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}} - 1, & \text{for }\mathrm{P}(r) \geq \mathrm{P}_{\text{ref}}(r) \\

1 - \sqrt{\frac{\mathrm{P}_{\text{ref}}\left( r \right)}{\mathrm{P}\left( r \right)}} = 1 - \sqrt{\frac{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{\text{ref},r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}}, & \text{for }\mathrm{P}(r) < \mathrm{P}_{\text{ref}}(r)
\end{cases} </math>


Pref can be computed either from the corresponding frequency range in the baseline of the same condition (i.e. the beamformer images event-related power increase or decrease) or from the corresponding time-frequency range in a control condition (i.e. the beamformer images differences between two conditions). The beamformer image is constructed from values q(r) computed for all locations on a grid specified in the '''General Settings tab'''. For MEG data, the innermost grid points within a sphere of approx. 12% of the head diameter are assigned interpolated rather than calculated values).
q-values are shown in %, where where q[%] = q*100. Alternatively to the definition above, q can also be displayed in units of dB:

<math>\mathrm{q}\left\lbrack \text{dB} \right\rbrack = 10 \cdot \log_{10}\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}</math>


A beamformer operator is designed to pass signals from the brain region of interest r without attenuation, while minimizing interference from activity in all other brain regions. Traditional single-source beamformers are known to mislocalize sources if several brain regions have highly correlated activity. Therefore, the BESA beamformer extends the traditional single-source beamformer in order to implicitly suppress activity from possibly correlated brain regions. This is achieved by using a multiple source beamformer calculation that contains not only the leadfields of the source at the location of interest r, but also those of possibly interfering sources. As a default, BESA Research uses a bilateral beamformer, where specifically contributions from the homologue source in the opposite hemisphere are taken into account (the matrix L thus being of dimension N×6 for EEG and N×4 for MEG, respectively, where N is the number of sensors). This allows for imaging of highly correlated bilateral activity in the two hemispheres that commonly occurs during processing of external stimuli.

In addition, the beamformer computation can take into account possibly correlated sources at arbitrary locations that are specified in the current solution. This is achieved by adding their leadfield vectors to the matrix L in the equation above.

'''Applying the Beamformer'''

This chapter illustrates the usage of the BESA beamformer. The displayed figures are generated using the file ''''Examples/Learn-by-Simulations/AC-Coherence/AC-Osc20.foc'''' (see BESA Tutorial 6: "''Time-frequency analysis and Source coherence''").

'''Starting the beamformer from the time-frequency window'''

The BESA beamformer is applied in the time-frequency domain and therefore requires the Source Coherence module to be enabled. The time-frequency beamformer is especially useful to image in- or decrease of induced oscillatory activity. Induced activity cannot be observed in the averaged data, but shows up as enhanced averaged power in the TSE (Temporal-Spectral Evolution) plot. For instructions on how to initiate a beamformer computation in the time-frequency window, please refer to Chapter '''[[Source_Coherence_How_to...#How_to_Start_the_Beamformer_from_the_Time-Frequency_Window|How to Create Beamformer Images]]'''.

After the beamformer computation has been initiated in the time-frequency window, the source analysis window opens with an enlarged 3D image of the q-value computed with a '''bilateral beamformer'''. The result is superimposed onto the MR image assigned to the data set (individual or standard).

[[Image:SA 3Dimaging (5).gif]]

''Beamformer image after starting the computation in the Time-Frequency window. A bilateral pair of sources in the auditory cortex accounts for the highly correlated oscillatory induced activity. Only the bilateral beamformer manages to separate these activities; a traditional single-source beamformer would merge the two sources into one image maximum in the head center instead.''

'''Multiple source beamformer in the Source Analysis window'''

The 3D imaging display is part of the source analysis window. If you press the '''Restore''' button at the right end of the title bar of the 3D window, the window appears at the bottom right of the source analysis window. In the channel box, the averaged (evoked) data of the selected condition is shown. When a control condition was selected, its average is appended to the average of the target condition.

[[Image:SA 3Dimaging (6).gif]]

''Source Analysis window with beamformer image. The two sources have been added using the '''''Switch to''''' '''''Maximum''''' and '''''Add Source '''''toolbar buttons (see below). Source waveforms are computed from the displayed averaged data. Therefore, they do not represent the activity displayed in the beamformer image, which in this simulation example is induced (i.e. not phase-locked to the trigger)!''

When starting the beamformer from the time-frequency window, a bilateral beamformer scan is performed. In the source analysis window, the beamformer computation can be repeated taking into account possibly correlated sources that are specified in the current solution. Interfering activities generated by all sources in the current solution that are in the 'On' state are specifically suppressed ('''they enter the matrix L in the beamformer calculation''', see Chapter ''Short mathematical description'' above). The computation can be started from the '''Image''' menu or from the '''Image selector button''' dropdown menu. The '''Image''' menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window.

[[Image:SA 3Dimaging (7).gif]]

''Multiple source beamformer image calculated in the presence of a source in the left hemisphere. A '''single''' source scan has been performed. The source set in the current solution accounts for the left-hemispheric q-maximum in the data. Accordingly, the beamformer scan reveals only the as yet unmodeled additional activity in the right hemisphere (note the radiological convention in the 3D image display).''

The beamformer scan can be performed with a '''single''' or a '''bilateral''' source scan. The default scan type depends on the current solution:
* When the beamformer is started from the Time-Frequency window, the Source Analysis window opens with a new solution and a '''bilateral''' beamformer scan is performed.
* When the beamformer is started within the Source Analysis window, the default is
** a scan with a '''single''' source in addition to the sources in the current solution, if at least one source is active.
** a '''bilateral''' scan if no source in the current solution is active.

The default scan type is the multiple source beamformer. The non-default scan type can be enforced using the corresponding ''Volume Image / Beamformer'' entry in the '''Image''' menu.

'''Inserting Sources out of the Beamformer Image'''

The beamformer image can be used to add sources to the current solution. A simple double-click anywhere in the 2D- or 3D-view will generate a non-oriented regional source at the corresponding location. However, a better and easier way to create sources at image maxima and minima is to use the toolbar buttons '''Switch to Maximum''' [[Image:SA 3Dimaging (8).gif]] and '''Add Source''' [[Image:SA 3Dimaging (9).gif]].

Use the '''Switch to Maximum''' button to place the red crosshair of the 3D window onto a local image maximum or minimum. Hitting the '''Add Source''' button creates a regional source at the location of the crosshair and therefore ensures the exact placement of the source at the image extremum. Moreover, the '''Add Source''' button generates an oriented regional source. BESA Research automatically estimates the source orientation that contributes most to the power in the target time-frequency interval (or the reference time-frequency interval, if its power is larger than that in the target interval). The accuracy of this orientation estimate depends largely on the noise content of the data. The smaller the signal-to-noise ratio of the data, the lower is the accuracy of the orientation estimate. '''This feature allows to use the beamformer as a tool to create a source montage for source coherence analysis, where it is of advantage to work with oriented sources'''.

'''Notes:'''

* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image '''menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the''' Image''' menu.
* For scaling options, use the [[Image:SA 3Dimaging (10).gif]] and [[Image:SA 3Dimaging (11).gif]] '''Image Scale toolbar''' buttons.
* Parameters used for the beamformer calculations can be set in the '''Standard Volumes''' of the ''Image Settings dialog box.''

== Dynamic Imaging of Coherent Sources (DICS) ==

 
'''Short mathematical introduction'''

Dynamic Imaging of Coherent Sources (DICS) is a sophisticated method for imaging cortico-cortical coherence in the brain, or coherence between an external reference (e.g. EMG channel) and cortical structures. DICS can be applied to localize evoked as well as induced coherent cortical activity in a user-defined time-frequency range.

DICS was implemented in BESA closely following [https://dx.doi.org/10.1073/pnas.98.2.694 Gross et al., "Dynamic imaging of coherent sources: Studying neural interactions in the human brain", PNAS 98, 694-699, 2001].

The computation is based on a transformation of each channel's single trial data from the time domain into the frequency domain. This transformation is performed by the BESA Research Coherence module and results in the complex spectral density matrix that is used for constructing the spatial filter similar to beamforming.

DICS computation yields a 3-D image, each voxel being assigned a coherence value. Coherence values can be described as a neural activity index and do not have a unit. The neural activity index contrasts coherence in a target time-frequency bin with coherence of the same time-frequency bin in a baseline.

'''DICS for cortico-cortical coherence is computed as follows:'''

Let L(r) be the leadfield in voxel r in the brain and C the complex cross-spectral density matrix. The spatial filter W(r) for the voxel r in the head is defined as follows:

<math>W\left( r \right) = \left\lbrack L^{T}\left( r \right) \cdot C^{- 1} \cdot L\left( r \right) \right\rbrack^{- 1} \cdot L^{T}(r) \cdot C^{- 1}</math>


The cross-spectrum between two locations (voxels) r1 and r2 in the head are calculated with the following equation:

<math>C_{s}\left( r_{1},r_{2} \right) = W\left( r_{1} \right) \cdot C \cdot W^{*T}\left( r_{2} \right),</math>


where <nowiki>*T</nowiki> means the transposed complex conjugate of a matrix. The cross-spectral density can then be calculated from the cross spectrum as follows:

<math>c_{s}\left( r_{1},r_{2} \right) = \lambda_{1}\left\{ C_{s}\left( r_{1},r_{2} \right) \right\},</math>


where λ1{} indicates the largest singular value of the cross spectrum. Once the cross spectral density is estimated, the connectivity¹(CON) between the two brain regions r1 and r2 are calculated as follows:

<math>\text{CON}\left( r_{1},r_{2} \right) = \frac{c_{s}^{\text{sig}}\left( r_{1},r_{2} \right) - c_{s}^{\text{bl}}(r_{1},r_{2})}{c_{s}^{\text{sig}}\left( r_{1},r_{2} \right) + c_{s}^{\text{bl}}(r_{1},r_{2})},</math>


where cssig is the cross-spectral density for the signal of interest between the two brain regions r1 and r2, and csbl is the corresponding cross spectral density for the baseline or the control condition, respectively. In the case DICS is computed with a cortical reference, r1 is the reference region (voxel) and remains constant while r2 scans all the grid points within the brain sequentially. In that way, the connectivity between the reference brain region and all other brain regions is estimated. The value of CON(r1, r2) falls in the interval [-1 1]. If the cross-spectral density for the baseline is 0 the connectivity value will be 1. If the cross-spectral density for the signal is 0 the connectivity value will be -1.

¹ Here, the term connectivity is used rather than coherence, as strictly speaking the coherence equation is defined slightly differently. For simplicity reasons the rest of the tutorial uses the term coherence.

'''DICS for cortico-muscular coherence is computed as follows:'''

When using an external reference, the equation for coherence calculation is slightly different compared to the equation for cortico-cortical coherence. First of all, the cross-spectral density matrix is not only computed for the MEG/EEG channels, but the external reference channel is added. This resulting matrix is Call. In this case, the cross-spectral density between the reference signal and all other MEG/EEG

channels is called cref. It is only one column of Call. Hence, the cross-spectrum in voxel r is calculated with the following equation:

<math>C_{s}\left( r \right) = W\left( r \right) \cdot c_{\text{ref}}</math>


and the corresponding cross-spectral density is calculated as the sum of squares of Cs:

<math>c_{s}\left( r \right) = \sum_{i = 1}^{n}{C_{s}\left( r \right)_{i}^{2}},</math>


where n is 2 for MEG and 3 for EEG. This equation can also be described as the squared Euclidean norm of the cross-spectrum:

<math>c_{s}\left( r \right) = \left\| C_{s} \right\|^{2},</math>


The power in voxel r is calculated as in the cortico-cortical case:

<math>p\left( r \right) = \lambda_{1}\left\{ C_{s}(r,r) \right\}.</math>


At last, coherence between the external reference and cortical activity is calculated with the equation:

<math>\text{CON}\left( r \right) = \frac{c_{s}(r)}{p\left( r \right) \cdot C_{\text{all}}(k,k)},</math>


where Call(k, k) is the (k,k)-th diagonal element of the matrix Call.

DICS is particularly useful, if coherence is to be calculated without an a-priory source model (in contrast to source coherence based on pre-defined source montages). However, the recommended analysis strategy for DICS is to use a brain source as a starting point for coherence calculation that is known to contribute to the EEG/MEG signal of interest. For example, one might first run a beamformer on the time-frequency range of interest and use the voxel with the strongest oscillatory activity as a starting point for DICS. The resulting coherence image will again lead to several maxima (ordered by magnitude), which in turn can serve as starting points for DICS calculation. This way, it is possible to detect even weak sources that show coherent activity in the given time-frequency range.

The other significant application for DICS is estimating coherence between an external source and voxels in the brain. For example, an external source can be muscle activity recoded by an electrode placed over the according peripheral region. This way, the direct relationship between muscle activity and brain activation can be measured.

'''Starting DICS computation from the Time-Frequency Window'''

DICS is particularly useful, if coherence in a user-defined time-frequency bin (evoked or induced) is to be calculated between any two brain regions or between an external reference and the brain. DICS runs only on time-frequency decomposed data, so time-frequency analysis needs to be run before starting DICS computation.

To start the DICS computation, left-drag a window over a selected time-frequency bin in the Time-Frequency Window. Right-click and select “Image”. A dialogue will open (see fig. 1) prompting you to specify time and frequency settings as well as the baseline period. It is recommended to use a baseline period of equal length as the data period of interest. Make sure to select “DICS” in the top row and press “'''Go'''”.

[[Image:SA 3Dimaging (21).gif|450px|thumb|c|none|Fig. 1: Time and frequency settings for DICS and MSBF]]

Next, a window will appear allowing you to specify the reference source for coherence calculation (see fig. 2). It is possible to select a channel (e.g. EMG) or a brain source. If a brain source is chosen and no source analysis was computed beforehand, the option “Use current cross-hair position” must be chosen. In case discrete source analysis was computed previously, the selected source can be chosen as the reference for DICS. Please note that DICS can be re-computed with any cross-hair or source position at a later stage.

[[Image:SA 3Dimaging (1).jpg|400px|thumb|c|none|Fig. 2: Possible options for choosing the reference]]

Confirming with “'''OK'''” will start computation of coherence between the selected channel/voxel and all other brain voxels. In case DICS is computed for a reference source in the brain, it can be advantageous to run a beamforming analysis in the selected time-frequency window first and use one of the beamforming maxima as reference for DICS. Fig. 3 shows an example for DICS calculation.

[[Image:SA 3Dimaging (22).gif|500px|thumb|c|none|Fig. 3: Coherence between left-hemispheric auditory areas and the selected voxel in the right auditory cortex.]]

Coherence values range between -1 and 1. If coherence in the signal is much larger than coherence in the baseline (control condition) then the DICS value is going to approach 1. Contrary, if coherence in the baseline is much larger than coherence in the signal, then the DICS value is going to approach -1. At last, if coherence in the signal is equal to coherence in the baseline, then the DICS value is 0.

In case DICS is to be re-computed with a different reference, simply mark the desired reference position by placing the cross-hair in the anatomical view and select “DICS” in the middle panel of the source analysis window (see Fig. 4). In case an external reference is to be selected, click on “DICS” in the middle panel to bring up the DICS dialogue (see. Fig. 2) and select the desired channel. Please note that DICS computation will only be available after running time-frequency analysis.

[[Image:SA 3Dimaging (23).gif|700px|thumb|c|none|Fig. 4: Integration of DICS in the Source Analysis window]]

== Multiple Source Beamformer (MSBF) in the Time Domain ==
''(requires Besa Research 7.0 or higher)''

===Short mathematical introduction===

Beamforming approach can be also applied in the time domain data. This approach was introduced as linearly constrained minimum variance (LCMV) beamformer (Van Veen et al., 1997). It allows to image evoked activity in a user-defined time range, where time is taken relative to a triggered event, and to estimate source waveforms using the calculated spatial weight at locations of interest. For an implementation of the beamformer in the time domain, data covariance matrices are required, while complex cross spectral density matrices are used for the beamformer approaches in the time-frequency domain as described in the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section.

The bilateral beamformer introduced in the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section is also implemented for the time-domain beamformer to take into account contributions from the homologue source in the opposite. This allows for imaging of highly correlated bilateral activity in the two hemispheres that commonly occurs during processing of external stimuli. In addition, the beamformer computation can take into account possibly correlated sources at arbitrary locations.
The beamformer spatial weight W(r) for the voxel r in the brain is defined as follows (Van Veen et al., 1997):

[[File:MSBF1.png]]

where '''C-1''' is the inversed regularized average of covariance matrix over trials, '''L''' is the leadfield matrix of the model containing a regional source at target location r and optionally
additional sources whose interference with the target source is to be minimized. The beamformer spatial weight '''W'''(r) can be applied to the measured data to estimate source
waveform at a location r (beamformer virtual sensor):

[[File:MSBF2.png]]

where '''S'''(r,t) represents the estimated source waveform and '''M'''(t) represents measured EEG or MEG signals.
The output power P of the beamformer for a specific brain region at location r is computed by the following equation:

[[File:MSBF3.png]]

where tr’[ ] is the trace of the [3×3] (MEG: [2×2]) submatrix of the bracketed expression that corresponds to the source at target location r.
Beamformer can suppress noise sources that are correlated across sensors. However, uncorrelated noise will be amplified in a spatially non-uniform manner, with increasing
distortion with increasing distance from the sensors (Van Veen et al., 1997; Sekihara et al., 2001). For this reason, estimated source power should be normalized by a noise power.
In BESA Research, the output power P(r) is normalized with the output power in a baseline interval or with the output power of a uncorrelated noise: P(r) / Pref (r).
The time-domain beamformer image is constructed from values q(r) computed for all locations on a grid specified in the '''General Settings''' tab. A value q(r) is defined as described in
the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section with data covariance matrices instead of cross-spectral density matrices.

===Applying the Beamformer===

This chapter illustrates the usage of the BESA beamformer in the time domain. The displayed figures are generated using the file ‘Examples/ERP-Auditory-Intensity/S1.cnt’.

'''Starting the time-domain beamformer from the Average tab of the Paradigm dialog box'''

The time-domain beamformer is needed data covariance matrices and therefore requires the ERP module to be enabled. After the beamformer computation has been initiated in the
'''Average tab of the Paradigm dialog box''', the source analysis window opens with an enlarged 3D image of the q-value computed with a bilateral beamformer. The result is
superimposed onto the MR image assigned to the data set (individual or standard).

[[File:MSBF44.png]]

''Beamformer image for auditory evoked data after starting the computation in the '''Average tab of the Paradigm dialog box'''. The bilateral beamformer manages to separate the
activities in auditory areas, while a traditional single-source beamformer would merge the two sources into one image maximum in the head center instead.''

'''Multiple-source beamformer in the Source Analysis window'''

The 3D imaging display is part of the source analysis window. In the Channel box, the averaged (evoked) data of the selected condition is shown. Selected covariance intervals in
the ERP module can be checked in the Channel box. The red, gray, and blue rectangles indicate signal, baseline, and common interval, respectively.

[[File:MSBF55.png]]

''Source Analysis window with beamformer image. The two beamformer virtual sensors have been added using the Switch to Maximum and Add Source toolbar buttons (see below).
Source waveforms are computed using the beamformer spatial weights and the displayed averaged data (the noise normalized weights (5% noise) option was used to compute the
beamformer image).''

When starting the beamformer from the '''Average tab of the Paradigm dialog box''', the bilateral beamformer scan is performed. In the source analysis window, the beamformer computation can be repeated taking into account possibly correlated sources that are specified in the current solution. Interfering activities generated by all sources in the current solution that are in the 'On' state are specifically suppressed (they enter the leadfield matrix L in the beamformer calculation). The computation can be started from the '''Image''' menu or from the Image selector button [[File:MSBF_Button.png|22px|Image: 22 pixels]] dropdown menu. The Image menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window.

[[File:MSBF66.png]]

''Multiple-source beamformer image calculated in the presence of a source in the left hemisphere. A single-source scan has been performed instead of a bilateral beamforemr. The
source set in the current solution accounts for the left-hemispheric q-maximum in the data. Accordingly, the beamformer scan reveals only the as yet unmodeled additional activity in
the right hemisphere (note the radiological convention in the 3D image display). The source waveform of the beamformer virtual sensor in the left hemisphere is not shown since the
location (blue square in the figure) is not considered for the multiple-source beamformer.''

The beamformer scan can be performed with a single or a bilateral source scan. The default scan type depends on the current solution:
When the beamformer is started from the '''Average tab of the Paradigm dialog box''' the Source Analysis window opens with a new solution and a bilateral beamformer scan is
performed.
When the beamformer is started within the Source Analysis window, the default is:

* a scan with a single source in addition to the sources in the current solution, if at least one source is active.
* a bilateral scan if no source in the current solution is active.
* a scan with a single source when scalar-type beamformer is selected in the '''beamformer option dialog box'''.

The default scan type is the multiple source beamformer. The non-default scan type can be enforced using the corresponding Volume Image / Beamformer entry in the Image main
menu or in the beamformer option dialog box (only for the time-domain beamformer).

===Inserting Sources as Beamformer Virtual Sensor out of the Beamformer Image===

This is similar to the inserting sources out of the beamformer image in Multiple Source Beamformer (MSBF) in the Time-frequency Domain section.
The beamformer image can be used to add beamformer virtual sensors to the current solution. A simple double-click anywhere in the 3D view (not in the 2D view) will generate a
source at the corresponding location. A better and easier way to create sources at image maxima and minima is to use the toolbar buttons Switch to Maximum and Add Source

This feature allows to use the beamformer as a tool to create a source montage for source coherence analysis. A source montage file (*.mtg) for beamformer virtual sensors can
be saved using File \ Save Source Montage As… entry.

The time-domain beamformer image can be also used to add regional or dipole sources to the current solution. Press N key when there is no source in the current source array or
there is more than one beamformer virtual sensor. To create a new source array for beamformer virtual sensor, press N key when there is more than one regional or dipole source in
the current source array.

===Notes===

* You can hide or re-display the last computed image by selecting Hide Image entry in the Image menu.
* The current image can be exported to ASCII, ANALYZE, or BrainVoyager (vmp) format from the Image menu.
* For scaling options, use the and Image Scale toolbar buttons.
* Parameters used for the beamformer calculations can be set in the Standard Volume tab of the Image Settings dialog box.
* Note that Model, Residual, Order, and Residual variance are not shown for the beamformer virtual sensor type sources.

===References===

* Sekihara, K., Nagarajan, S. S., Poeppel, D., Marantz, A., & Miyashita, Y. (2001). Reconstructing spatio-temporal activities of neural sources using an MEG vector beamformer technique. IEEE Transactions on Biomedical Engineering, 48(7), 760–771.

* Van Veen, B. D., Van Drongelen, W., Yuchtman, M., & Suzuki, A. (1997). Localization of brain electrical activity via linearly constrained minimum variance spatial filtering. IEEE Transactions on Biomedical Engineering, 44(9), 867–880

== CLARA ==

CLARA ('Classical LORETA Analysis Recursively Applied') is an iterative application of weighted LORETA images with a reduced source space in each iteration.

In an initialization step, a LORETA image is calculated. Then in each iteration the following steps are performed:

# The obtained image is spatially smoothed (this step is left out in the first iteration).
# All grid points with amplitudes below a threshold of 1% of the maximum activity are set to zero, thus being effectively eliminated from the source space in the following step.
# The resulting image defines a spatial weighting term (for each voxel the corresponding image amplitude).
# A LORETA image is computed with an additional spatial weighting term for each voxel as computed in step 3. By the default settings in BESA Research, the regularization values used in the iteration steps are slightly higher than that of the initialization LORETA image.

The procedure stops after 2 iterations, and the image computed in the last iteration is displayed. Please note that you can change all parameters by creating a user-defined volume image.

The advantage of CLARA over non-focusing distributed imaging methods is visualized by the figure below. Both images are computed from the N100 response in an auditory oddball experiment (file '''Oddball.fsg''' in subfolder ''fMRI+EEG-RT-Experiment'' of the ''Examples'' folder). The CLARA image is much more focal than the sLORETA image, making it easier to determine the location of the image maxima.

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (24).gif|thumb|350px|sLORETA image]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (25).gif|thumb|350px|CLARA image]] </li>
</ul></div>

'''Notes:'''

* Starting CLARA: CLARA can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter ''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]'' for important information on regularization of distributed inverses.

== LAURA ==

LAURA (Local Auto Regressive Average) belongs to the distributed inverse method of the family of weighted minimum norm methods ([https://doi.org/10.1023/A:1012944913650 Grave de Peralta Menendeza et al., "Noninvasive Localization of Electromagnetic Epileptic Activity. I. Method Descriptions and Simulations", BrainTopography 14(2), 131-137, 2001]). LAURA uses a spatial weighting function that includes depth weighting and that term has the form of a local autoregressive function.

The source activity is estimated by applying the general formula for a weighted minimum norm:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T}\left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings.''

In LAURA, V contains both a depth weighting term W and a representation of a local autoregressive function A. V is computed as:

<math>\mathrm{V} = \left( \mathrm{U}^{T} \cdot \mathrm{U} \right)^{-1}</math>


Where

<math>\mathrm{U} = \left( \mathrm{W} \cdot \mathrm{A} \right) \otimes \mathrm{I}_{3}</math>


Here, <math>\otimes</math> denotes the Kronecker product. I3 is the [3×3] identity matrix. W is an [s×s] diagonal matrix (with s the number of source locations on the grid), where each diagonal element is the inverse of the maximum singular value of the corresponding regional source's leadfields. The formula for the diagonal components Aii and the off-diagonal components Aik are as follows:

<math>\mathrm{A}_{ii} = \frac{26}{\mathrm{N}_{i}}\sum_{k \subset V_{i}}^{}\frac{1}{\mathrm{d}_{ik}^{2}}</math>


<math>
\mathrm{A}_{ik} =
\begin{cases}
- 1/\operatorname{dist}\left( i,k \right)^{2}, & \text{if } k \subset V_{i} \\
0, & \text{otherwise}
\end{cases}
</math>


Here, Vi is the vicinity around grid point i that includes the 26 direct neighbors.

The LAURA image in BESA Research displays the norm of the 3 components of S at each location r. Using the menu function ''Image / Export Image As... ''you have the option to save this norm of S or alternatively all components separately to disk.

'''Notes:'''

* '''Grid spacing:''' Due to memory limitations, LAURA images require a grid spacing of 7 mm or more.
* '''Computation time:''' Computation speed during the first LAURA image calculation depends on the grid spacing (computation is faster with larger grid spacing). After the first computation of a LAURA image, a '''*.laura''' file is stored in the data folder, containing intermediate results of the LAURA inverse. This file is used during all subsequent LAURA image computations. Thereby, the time needed to obtain the image is substantially reduced.
* '''MEG:''' In the case of MEG data, an additional constraint is implemented in the LAURA algorithm that prevents solutions from containing radial source currents (compare Pascual-Marqui, ISBET Newsletter 1995, 22-29). In MEG, an additional source space regularization is necessary in the inverse matrix operation required compute V
* '''Starting LAURA:''' LAURA can be started from the''' Image''' menu or from the '''Image Selection''' button.
* '''Regularization:''' Please refer to Chapter'' “Regularization of distributed volume images” ''for important information on regularization of distributed inverses.

== LORETA ==

LORETA ("Low Resolution Electromagnetic Tomography") is a distributed inverse method of the family of ''weighted minimum norm'' methods. LORETA was suggested by R.D. Pascual-Marqui (International Journal of Psychophysiology. 1994, 18:49-65). LORETA is characterized by a smoothness constraint, represented by a discrete 3D Laplacian.

The source activity is estimated by applying the general formula for a weighted minimum norm:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T}\left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings.''

In LORETA, V contains both a depth weighting term and a representation of the 3D Laplacian matrix. V is computed as:

<math>\mathrm{V} = \left( \mathrm{U}^{T} \cdot \mathrm{U} \right)^{- 1}</math>


where

<math>\mathrm{U} = \left( \mathrm{W} \cdot \mathrm{A} \right) \otimes \mathrm{I}_{3}</math>


Here, <math>\otimes</math> denotes the Kronecker product. I3 is the [3x3] identity matrix. W is an [sxs] diagonal matrix (with s the number of source locations on the grid), where each diagonal element is the inverse of the maximum singular value of the corresponding regional source's leadfields. A contains the 3D Laplacian and is computed as

<math>\mathrm{A} = \mathrm{Y} - \mathrm{I}_{s}</math>


with Is the [sxs] identity matrix, where s is the number of sources (= three times the number of grid points) and

<math>\mathrm{Y} = \frac{1}{2}\left\{ \mathrm{I}_{s} + \left\lbrack \operatorname{diag}\left( \mathrm{Z} \cdot \left\lbrack 111 \ldots 1 \right\rbrack^{T} \right) \right\rbrack^{- 1} \right\} \cdot \mathrm{Z}</math>


where

<math>
\mathrm{Z}_{ik} =
\begin{cases}
1/6, & \text{if } \operatorname{dist}\left( i,k \right) = 1 \text{ grid point} \\
0, & \text{otherwise}
\end{cases}
</math>


The LORETA image in BESA Research displays the norm of the 3 components of S at each location r. Using the menu function ''Image / Export Image As... ''you have the option to save this norm of S or alternatively all components separately to disk.

'''Notes:'''
* '''Grid spacing:''' Due to memory limitations, LORETA images require a grid spacing of 5 mm or more.
* '''Computation time:''' Computation speed during the first LORETA image calculation depends on the grid spacing (computation is faster with larger grid spacing). After the first computation of a LORETA image, a '''<nowiki>*.loreta</nowiki>''' file is stored in the data folder, containing intermediate results of the LORETA inverse. This file is used during all subsequent LORETA image computations. Thereby, the time needed to obtain the image is substantially reduced.
* '''MEG''': In the case of MEG data, an additional constraint is implemented in the LORETA algorithm that prevents solutions from containing radial source currents (Pascual-Marqui, ISBET Newsletter 1995, 22-29). In MEG, an additional source space regularization is necessary in the inverse matrix operation required compute V.
* '''Starting LORETA:''' LORETA can be started from the''' Image''' menu or from the '''Image Selection '''button.
* '''Regularization:''' Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed source models.

== sLORETA ==

This distributed inverse method consists of a ''standardized, unweighted minimum norm''. The method was originally suggested by R.D. Pascual-Marqui (Methods & Findings in Experimental & Clinical Pharmacology 2002, 24D:5-12) Starting point is an unweighted minimum norm computation:

<math>\mathrm{S}_{\text{MN}}\left( t \right) = \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings''.

This minimum norm estimate is now standardized to produce the sLORETA activity at a certain brain location r:

<math>\mathrm{S}_{\text{sLORETA}, r} = \mathrm{R}_{rr}^{-1/2} \cdot \mathrm{S}_{\text{MN},r}</math>


SsMN,r is the [3x1] (MEG: [2x1]) minimum norm estimate of the 3 (MEG: 2) dipoles at location r. Rrr is the [3x3] (MEG: [2x2]) diagonal block of the resolution matrix R that corresponds to the source components at the target location r. The resolution matrix is defined as:

<math>\mathrm{R} = \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{L}^{T} + \lambda \cdot \mathrm{I} \right)^{-1} \cdot \mathrm{L}</math>


The sLORETA image in BESA Research displays the norm of SsLORETA, r at each location r. Using the menu function ''Image / Export Image As...'' you have the option to save this norm of SsLORETA, r or alternatively all components separately to disk.

'''Notes:'''

* sLORETA can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== swLORETA ==

This distributed inverse method is a ''standardized, depth-weighted minimum norm'' (E. Palmero-Soler et al 2007 Phys. Med. Biol. 52 1783-1800). It differs from sLORETA only by an additional depth weighting.

Starting point is a depth-weighted minimum norm computation:

<math>\mathrm{S}_{\text{MN}}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings''.

V is the diagonal depth weighting matrix. For s grid locations, V is of dimension [3s x 3s] (MEG: [2s x 2s]). Each diagonal element of V is the inverse of the first singular value of the leadfield of the corresponding regional source. Hence, the first 3 (MEG: 2) diagonal elements equal the inverse of the largest eigenvalue of the leadfield matrix of regional source 1, and so on.

This minimum norm estimate is now standardized to produce the swLORETA activity at a certain brain location r:

<math>\mathrm{S}_{\text{swLORETA},r} = \mathrm{R}_{rr}^{-1/2} \cdot \mathrm{S}_{\text{MN},r}</math>


SsMN,r is the [3x1] (MEG: [2x1]) depth-weighted minimum norm estimate of the regional source at location r. Rrr is the [3x3] (MEG: [2x2]) diagonal block of the resolution matrix R that corresponds to the source components at the target location r. The resolution matrix is defined as:

<math>\mathrm{R} = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} + \lambda \cdot \mathrm{I} \right)^{-1} \cdot \mathrm{L}</math>


The swLORETA image in BESA Research displays the norm of SswLORETA, r at each location r. Using the menu function ''Image / Export Image As...'' you have the option to save this norm of SswLORETA, r or alternatively all components separately to disk.

'''Notes:'''

* sLORETA can be started from the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== sSLOFO ==

SSLOFO (standardized shrinking LORETA-FOCUSS) is an iterative application of weighted distributed source images with a reduced source space in each iteration ([https://dx.doi.org/10.1109/TBME.2005.855720 Liu et al., "Standardized shrinking LORETA-FOCUSS (SSLOFO): a new algorithm for spatio-temporal EEG source reconstruction", IEEE Transactions on Biomedical Engineering 52(10), 1681-1691, 2005]).

In an initialization step, an [[#sLORETA | sLORETA]] image is calculated. Then in each iteration the following steps are performed:

# A weighted minimum norm solution is computed according to the formula <math display="inline">\mathrm{S} = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}</math> . Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D is the data at the time point under consideration. V is a diagonal spatial weighting matrix that is computed in the previous iteration step. In the first iteration, the elements of V contain the magnitudes of the initially computed LORETA image.
# Standardization of this weighted minimum norm image is performed with the resolution matrix as in [[#sLORETA | sLORETA]].
# The obtained standardized weighted minimum norm image is being smoothed to get Ssmooth.
# All voxels with amplitudes below a threshold of 1% of the maximum activity get a weight of zero in the next iteration step, thus being effectively eliminated from the source space in the next iteration step.
# For all other voxels, compute the elements of the spatial weighting matrix V to be used in the next iteration as follows: <math display="inline">\mathrm{V}_{ii,\text{next iteration}} = \frac{1}{\left\| \mathrm{L}_{i} \right\|} \cdot \mathrm{S}_{ii,\text{smooth}} \cdot \mathrm{V}_{ii,\text{current iteration}}</math>



The procedure stops after 3 iterations. Please note that you can change all parameters by creating a [[#User-Defined Volume Image | user-defined volume image]].

'''Notes:'''
* '''Starting sSLOFO''': sSLOFO can be started from the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter ''[[#Regularization of distributed volume images | Regularization of distributed volume images]]'' for important information on regularization of distributed inverses.

== User-Defined Volume Image ==

In addition to the predefined 3D imaging methods in BESA Research, it is possible to create user-defined imaging methods based on the general formula for distributed inverses:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. Custom-defined parameters are:* The spatial weighting matrix V: This may include depth weighting, image weighting, or cross-voxel weighting with a 3D Laplacian (as in LORETA) or an autoregressive function (as in LAURA).

* Regularization: The term in parentheses is generally regularized. Note that regularization has a strong effect on the obtained results. Please refer to chapter “''Regularization of Distributed Volume Images” ''for more information.
* Standardization: Optionally, the result of the distributed inverse can be standardized with the resolution matrix (as in sLORETA).
* Iterations: Inverse computations can be applied iteratively. Each iteration is weighted with the image obtained in the previous iteration.

All parameters for the user-defined volume image are specified in the User-Defined Volume Tab of the Image Settings dialog box. Please refer to chapter “''User-Defined Volume Tab”'' for details.

'''Notes:'''
* Starting the user-defined volume image: the image calculation can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== Regularization of distributed volume images ==

Distributed source images require the inversion of a term of the form L V LT. This term is generally regularized before its inversion. In BESA Research, selection can be made between two different regularization approaches (parameters are defined in the ''Image Settings dialog box''):

* '''Tikhonov regularization''': In Tikhonov regularization, the term L V LT is inverted as (L V LT +λ I)-1. Here, l is the regularization constant, and I is the identity matrix.
* One way of determining the optimum regularization constant is by minimizing the ''generalized cross'' ''validation error'' (CVE).
* Alternatively, the regularization constant can be specified manually as a percentage of the trace of the matrix L V LT.
* '''TSVD''': In the truncated singular value decomposition (TSVD) approach, an SVD decomposition of L V LT is computed as  L V LT = U S UT, where the diagonal matrix S contains the singular values. All singular values smaller than the specified percentage of the maximum singular values are set to zero. The inverse is computed as U S-1 UT, where the diagonal elements of S-1 are the inverse of the corresponding non-zero diagonal elements of S.

Regularization has a critical effect on the obtained distributed source images. The results may differ completely with different choices of the regularization parameter (see examples below). Therefore, it is important to evaluate the generated image critically with respect to the regularization constant, and to keep in mind the uncertainties resulting from this fact when interpreting the results. The default setting in BESA Research is a TSVD regularization with a 0.03% threshold. However, this value might need to be adjusted to the specific data set at hand.

The following example illustrates the influence of the regularization parameter on the obtained images. The data used here is condition '''St-Cor of dataset Examples \ TFC-Error-Related-Negativity \ Correct+Error.fsg''' at 176 ms following the visual stimulus. Discrete dipole analysis reveals the main activity in the left and right lateral visual cortex at this latency.

[[Image:SA 3Dimaging (42).gif]]

''Discrete source model at 176 ms: Main activity in the left and right lateral visual cortex, no visual midline activity.''

LORETA images computed at this latency depend critically on the choice of the regularization constant. The following 3D images are created with TSVD regularization with SVD cutoffs of 0.1%, 0.005%, and 0.0001%, respectively. The volume grid size was 9 mm. The example demonstrates the dramatic effect of regularization and demonstrates the typical tradeoff between too strong regularization (leading to too smeared 3D images that tend to show blurred maxima) and too small regularization (resulting in too superficial 3D images with multiple maxima).

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (43).gif|thumb|350px|'''SVD cutoff 0.1%''': Regularization too strong. No separation between sources, mislocalization towards the middle of the brain.]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (44).gif|thumb|350px|'''SVD cutoff 0.005%''': Appropriate regularization. Separation of the bilateral activities. Location in agreement with the discrete multiple source model.]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (45).gif|thumb|350px|'''SVD cutoff 0.0001%''': Too small regularization. Mislocalization, too superficial 3D image. ]] </li>
</ul></div>

The automatic determination of the regularization constant using the CVE approach does not necessarily result in the optimum regularization parameter either. In this example, the unscaled CVE approach rather resembles the TSVD image with a cutoff of 0.0001%, i.e. regularization is too small. Therefore, it is advisable to compare different settings of the regularization parameter and make the final choice based on the above-mentioned considerations.

== Cortical LORETA ==

Cortical LORETA is principally the same technique as LORETA, however, Cortical LORETA is not computed in a 3D volume, but on the cortical surface.

The cortical reconstruction in BESA Research fed from BESA MRI is a closed 2D surface with no boundaries and a very close approximation of the actual cortical form. It consists of an irregular triangulated grid.

The Laplace operator that is used for identifying a smooth solution in a three-dimensional space is exchanged with a Laplace operator that runs on the two-dimensional cortical surface.

There is a wide variety of 2D Laplace operators with different characteristics. The general form of the discrete Laplace operator is

<math>\Delta f\left( p_{i} \right) = \frac{1}{d_{i}}\sum_{j \in N(i)}^{}{w_{ij}\left\lbrack f\left( p_{i} \right) - f\left( p_{j} \right) \right\rbrack},</math>


where '''pi''' is the '''i-th''' node of the triangular mesh, '''f(pi) '''is the value of a function f defined on the cortical mesh at the node '''pi''', '''wij''' is the weight for the connection between the nodes '''pi''' and '''pj''' and '''di''' is a normalization factor for the '''i-th''' row of the operator. Furthermore, '''N(i)''' is the set of indices corresponding to the direct (also called "1-ring") neighbors of '''pi'''.

BESA offers the choice of three Laplace operators with slightly different characteristics.

* '''Unweighted Graph Laplacian''': This is the simplest operator. It takes into account only the adjacency of the nodes and not the geometry of the mesh:

<math>
w_{ij} =
\begin{cases}
1, & \text{if } p_{i} \text{ and } p_{j} \text{ are connected by an edge} \\
0, & \text{otherwise}
\end{cases}
</math>

<math>d_{i} = 1</math>


[[Image:SA 3Dimaging (4).jpg |450px]]

* '''Weighted Graph Laplacian:''' This operator is similar to the unweighted graph Laplacian but with different weights for the different connections. The connections between nearby nodes get larger weights than the connections between farther nodes:

<math>w_{ij} = \frac{1}{\operatorname{dist}\left( p_{i},p_{j} \right)}</math>

<math>d_{i} = \sum_{j \in N(i)}^{} {\operatorname{dist}\left(p_{i}, p_{j} \right)}</math>


where '''dist''' ('''pi''' , '''pj''') is the distance between the nodes '''pi '''and '''pj'''.

[[Image:SA 3Dimaging (6).jpg|450px]]

* '''Geometric Laplacian with mixed area weights''': This operator takes into account the angles in the corresponding triangles into account as well as the area around the nodes in order to determine the connection weights:

<math>w_{ij} = \frac{\cot\left( \alpha_{ij} \right) + \cot\left( \beta_{ij} \right)}{2}</math>

<math>d_{i} = A_{\text{mixed}}</math>


where '''αij''' and '''βij''' denote the two angles opposite to the edge ('''i , j''') and '''Amixed '''is either the Voronoi area, or 1/2 of the triangle area or 1/4 of the triangle area depending on the type of the triangle.

[[Image:SA 3Dimaging (8).jpg|450px]]

'''Regularization and other parameters:'''

[[Image:SA 3Dimaging (46).gif ‎]]

* '''SVD cutoff''': The regularization for the inverse operator as a percent of the largest singular value.
* '''Depth weighting''': Turn depth weighting on or off.
* '''Laplacian type''': Selection of Laplacian operators (see above).

'''Notes:'''
* '''Starting Cortical LORETA''': Cortical LORETA can be started from the sub-menu '''Surface Image''' of the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]''” for important information on regularization of distributed inverses.

== Cortical CLARA ==

Cortical CLARA is principally the same technique as CLARA, but Cortical CLARA is not computed in a 3D volume, but on the cortical surface. Instead of using a LORETA image as the basis for the iterative application, cortical CLARA uses cortical LORETA.

'''Regularization and other parameters:'''

[[Image:SA 3Dimaging (47).gif]]

* '''SVD cutoff''': The regularization for the inverse operator as a percent of the largest singular value.
* '''Depth weighting''': Turn depth weighting on or off.
* '''Laplacian type''': Selection of Laplacian operators (see Cortical LORETA).
* '''No of iterations''': Number of iterations for CLARA. The more iterations are used, the sparser becomes the solution.
* '''Automatic''': The algorithm tries to determine the number of iterations automatically. The goodness of fit (GOF) is calculated after every iteration and if there is a big jump in the GOF then the algorithm will stop. If no jumps appear during the calculations then CLARA iterates until the specified number of iterations is reached.
* '''Regularize iterations''': If one wants to use different regularization for the CLARA iterations than the value specified as "SVD cutoff", this option should be selected.
* '''Amount to clip from img (%)''': Cortical CLARA uses the solution from the previous iteration as an additional weighting matrix for the current iteration. That weighting matrix is constructed by cutting the "low" activity from the solution. This number specifies how much of the activity should be cut from the previous solution in order to construct the weighting matrix. This value is given as a percentage of the maximal activity. Default value is 10%.

'''Notes:'''

* '''Starting Cortical CLARA:''' Cortical CLARA can be started from the sub-menu '''Surface Image''' of the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]''” for important information on regularization of distributed inverses.

== Cortex Inflation ==

The inflated cortex is a smoothened version of the individual cortical surface with minimal metric distortions (Fischl, B. et al. (1999). Cortical Surface-Based Analysis: II: Inflation, Flattening, and a Surface-Based Coordinate System. ''NeuroImage'', 9(2), 195–207). Gyri and sulci are smoothened out. The original distances between each point on the cortex and its neighbors are, however, mostly preserved.

[[Image:SA 3Dimaging (48).gif]]

''Cortical LORETA map overlaid on top of the inflated cortical surface.''

A lighter gray color overlaid on top of the surface image indicates the location of a gyrus of the individual cortex surface, while a darker gray color indicates the location of a sulcus. The inflated cortical surface can be computed in '''BESA MRI 2.0'''. For more details please refer to the BESA MRI 2.0 help.

== Surface Minimum Norm Image ==

'''Introduction'''

The minimum norm approach is a common method to estimate a distributed electrical current image in the brain at each time sample (Hämäläinen & Ilmoniemi 1984). The source activities of a large number of regional sources are computed. The sources are evenly distributed using 1500 standard locations 10% and 30% below the smoothed standard brain surface (when using the standard MRI) or using between 3000-4000 locations on the individual brain surface defined by the gray-white-matter boundary.

Since the number of sources is much larger than the number of sensors in a minimum norm solution, the inverse problem is highly underdetermined and must be stabilized by a mathematical constraint, the minimum norm. Out of the many current distributions that can account for the recorded sensor data, the solution with the minimum L2 norm, i.e. the minimum total power of the current distribution is displayed in BESA Research.

First, the forward solution (leadfield matrix L) of all sources is calculated in the current head model. Then, the source activities S(t) of all source components are computed from the data matrix D(t) using an inverse regularized by the estimated noise covariance matrix:

<math>\mathrm{S}\left( t \right) = \mathrm{R} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{R} \cdot \mathrm{L}^{T} + \mathrm{C}_N \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed regional source model, CN denotes the noise correlation matrix in sensor space, and R is a weighting matrix in source space. R and CN can be designed in different ways in order to optimize the minimum norm result. The total activity of each regional source is computed as the root mean square of the source activities S(t) of its 3 (MEG:2) components. This total source activity is transformed to a color-coded image of the brain surface. (When the standard brain is used, two sources are assigned to each surface location, located 10% and 30% below the surface, respectively. The color that is displayed on the standard brain surface is the larger of the two corresponding source activities.)

'''Weighting options'''

The minimum norm current imaging techniques of BESA Research provide different weighting strategies. Two weighting approaches are available: Depth weighting and spatio-temporal approaches.
* '''Depth weighting:''' Without depth weighting, deep sources appear very smeared in a minimum-norm reconstruction. With depth weighting, both deep and superficial sources produce a similar, more focal result. If this weighting method is selected, the leadfield of each regional source is scaled with the largest singular value of the SVD (singular value decomposition) of the source's leadfield.
* '''Spatio-temporal weighting''': Spatio-temporal weighting tries to assign large weight to sources that are assumed to be more likely to contribute to the recorded data.
** '''Subspace correlation after single source scan''': This method divides the signal into a signal and a noise subspace. The correlation of the leadfield of a regional source i with the signal subspace (pi) is computed to find out if the source location contributes to the measured data. The weighting matrix R becomes a diagonal matrix. Each of the three (MEG: 2) components of a regional source get the same weighting value pi2. This approach is based on the signal subspace correlation measure introduced by J.C. Mosher, R. M. Leahy (Recursive MUSIC: A Framework for EEG and MEG Source Localization, IEEE Trans. On Biomed. Eng. Vol. 45, No. 11, November 1998)
** '''Dale & Sereno 1993:''' In the approach of Dale and Sereno (J Cogn Neurosci, 1993, 5: 162-176) a signal subspace needs not be defined. The correlation pi of the leadfield of regional source i with the inverse of the data covariance matrix is computed along with the largest singular value λmax of the data covariance matrix. The weighting matrix R is a diagonal matrix with weights: [[Image:SA 3Dimaging (50).gif]]. Each of the three (MEG: 2) components of a regional source receives the same weighting value.

'''Noise regularization'''

Two methods to estimate the channel noise correlation matrix CN are provided by the program:
* '''Use baseline:''' Select this option to estimate the noise from the user-definable baseline. The signal is computed from the data at non-baseline latencies.
* '''Use 15% lowest values:''' The baseline activity is computed from the data at those 15% of all displayed latencies that have the lowest global field power. The signal is computed from all displayed latencies.

In each case, the activity (noise or signal, respectively) is defined as root-mean-square across all respective latencies for each channel.

The noise covariance matrix CN is constructed as a diagonal matrix. The entries in the main diagonal are proportional to the noise activity of the individual channels (if selected) or are all equally proportional to the average noise activity over all channels. The noise covariance matrix CN is then scaled such that the ratio of the Frobenius norms of the weighted leadfield projector matrix (LRLT) and the noise covariance matrix CN equals the Signal-to-Noise ratio. This scaling can be multiplied by an additional factor (default=1) to sharpen (<1) or smoothen (>1) the minimum norm image.

'''Applying the Minimum Norm Image'''

The minimum-norm algorithm is started via the ''Surface minimum norm image dialog box'', which is opened from the''' Image''' menu, or by typing the shortcut '''Ctrl-M''': Please refer to Chapter ''“Surface'' ''Minimum Norm Tab”'' for more details.

As opposed to the other 3D images available from the '''Image '''menu, the surface minimum norm image is not computed on a volumetric grid, but rather for locations on the brain surface. Accordingly, the results of the minimum norm image are displayed superimposed to the brain surface mesh rather than to the volumetric MR image.

The figure below shows a minimum norm image computed from the file '''Examples\Epilepsy\Spikes\Spikes-Child4_EEG+MEG_averaged.fsg'''. The EEG spike peak was imaged using the individual brain surface of the subject. A baseline from -300 to -70 ms was used. Minimum norm was computed with depth weighting, Spatio-temporal weighting according to Dale & Sereno 1993 and individual noise weighting with a noise scale factor of 0.01. The minimum norm image reveals the location of the spike generator in the close vicinity of the frontal left-hemispheric lesion in this subject.

[[Image:SA 3Dimaging (51).gif]]

== Multiple Source Probe Scan (MSPS) ==

 
'''Introduction'''

The MSPS function provides a tool for the validation of a given solution. It is based on the following theoretical consideration: If the recorded EEG/MEG data has been modeled adequately, i.e. all active brain regions are represented by a source in the current solution, then any additional probe source added to the solution will not show any activity apart from noise. The only exception occurs if this probe source is placed in close vicinity to one of the sources in the current solution. In that case, the solution's source and the probe source will share the activity of the corresponding brain area. The MSPS applies these considerations by scanning the brain on a pre-defined grid with a regional probe added to the current solution. Grid extent and density can be specified in the Image settings. The power P of the probe source at location r in the signal interval is compared with the power of the probe source in a reference interval, defining a value q:

<math>\mathrm{q}\left( r \right) = \sqrt{\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}} - 1</math>


MSPS can be computed on time domain or time-frequency domain data:
* In the time domain, q(r) is computed from the source waveform of the probe source. Here, P(r) is the mean power of the probe source at location r in the marked latency range, and Pref(r) is the mean probe source power in the user-definable baseline interval.
* In the time-frequency domain, an MSPS image can be computed from the complex cross spectral density matrices. By applying the inverse operator for a source configuration consisting of the current solution and the probe source, the power of the probe source can be computed for the target interval [P(r)] and the reference time-frequency interval [Pref(r)]. In the resulting MSPS image, q-values are shown in %, where q[%] = q*100.

The inverse operator used to determine the probe source power uses different regularization constants for the probe source and the sources in the current solution. The regularization constant of the sources in the current solution can be specified in the Image settings (default 4%). The regularization constant of the probe source is internally set to 0%.

Alternatively to the definition above, q can also be displayed in units of dB:

<math>\mathrm{q}\left\lbrack \text{dB} \right\rbrack = 10 \cdot \log_{10}\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}</math>


Values of q smaller than zero are not shown in the MSPS image.

According to the considerations above, an MSPS of a correct source model should optimally yield image maxima around the sources in the current solution only. If the MSPS image is blurred or shows maxima at locations different from the modeled sources, this indicates a non-sufficient or incorrect solution.

'''Applying the MSPS'''

This chapter illustrates the application of the Multiple Source Probe Scan. The figures are generated with data from file '''Examples/Epilepsy/Spikes/Rolandic-Spike-Child.fsg''' (-300 : +200 ms, filtered from 3 Hz [forward] to 40 Hz [zero-phase]).

'''Time domain versus time-frequency domain MSPS'''

The multiple source probe scan can be computed in the time domain or the time-frequency domain. The latter is possible only when time-frequency domain data is available for the current condition, i.e. if the condition has been created by starting a multiple source beamformer (MSBF) computation from the source coherence window. In this case, evoking the MSPS calculation from the '''Imaging '''button or from the '''Image''' menu will bring up the following dialog window that allows to choose between time- or time-frequency MSPS. If only time domain data is available, this dialog window will not appear and MSPS will be computed in the time domain.

[[Image:SA 3Dimaging (53).gif]]

For a time-frequency domain MSPS, the target and the reference time-frequency interval have been specified already in the Time-Frequency window (see Chapter "''How To Create Beamformer Images''"). For a time-domain MSPS, the target and the reference epoch have to be specified in the Source Analysis window as described below.

'''Time domain MSPS'''

The time-domain MSPS image displays the ratio of the power of a regional probe source in the signal and the baseline interval. The currently set baseline is indicated by a horizontal line in the upper left corner of the channel box.

[[Image:SA 3Dimaging (54).gif|thumb|c|none|330px|The black horizontal bar in the upper part of the channel box (here circled in red) indicates the baseline interval.]]

By default, BESA Research defines the pre-stimulus interval of the current data segment as baseline. The baseline should represent a latency range in which no event-related activity is present in the data. There are several possibilities to modify the baseline interval: by clicking on the horizontal line with the left mouse button or by using the corresponding entry in the '''Condition '''menu or '''Fit Interval''' popup menu.

Mark an interval to define the target epoch, i.e. the time-interval for which the current solution is to be tested. Start the MSPS by selecting it from the '''Image selection '''button or from the '''Image''' menu to start the probe source scan. The''' Image '''menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window. The 3D window opens and displays the scan result.

<div><ul>
<li style="display: inline-block;"> [[Image:SA 3Dimaging (55).gif|thumb|c|none|650px|This figure shows the MSPS image applied on the three left-hemispheric sources in the solution ''''Rolandic-Spike-Child-RS2.bsa''''. The baseline is set from -300ms to -50 ms. The right-hemispheric sources have been switched off. The fit interval is set to the latency range of large overall activity in the data (-43 ms : 117 ms). A realistic FEM model appropriate for the subject's age (12 years, conductivity ratios (cr) 50) is applied. The MSPS image does not show maxima at the modeled source locations and rather shows a spread q-value distribution.]] </li>

<li style="display: inline-block;"> [[Image:SA 3Dimaging (56).gif|thumb|c|none|650px|The MSPS image for the same latency range when the right-hemispheric sources have been included. The MSPS image appears more focal and shows maxima around the modeled brain regions. This indicates the substantial improvement of the solution by adding the right-hemispheric sources that model the propagation of the epileptic spike from the left to the right hemisphere (note the radiological side convention in the 3D window).]] </li>
</ul></div>

'''Time-Resolved MSPS'''

If the MSPS has been computed on time domain data, the image can be shown separately for each latency in the selected interval. After the MSPS has been computed for the marked epoch, double-click anywhere within this epoch to display the ratio of the probe source magnitude at the selected latency and the mean probe source magnitude in the baseline. Scanning the latency range by moving the cursor (e.g. with the left and right arrow cursor keys) provides a time-resolved MSPS image.

Time-resolved MSPS images are not available if the MSPS has been computed on data in the time-frequency domain.

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (57).gif|thumb|450px|MSPS image of the spike peak activity at 0ms. The activity mainly occurs in the left hemisphere. This fact is illustrated by the source waveforms and confirmed in the MSPS image, which shows a focal maximum around the location of the red sources.]] </li>

<li style="display: inline-block;"> [[File:SA 3Dimaging (58).gif|thumb|450px|Around +27 ms, the spike has propagated to the right hemisphere. This becomes evident from the waveforms of the blue sources, which show a significant latency lag with respect to the first three sources, and from the MSPS image, which shows the maximum around blue sources at this latency.]] </li>
</ul></div>



'''Notes:'''

* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image''' menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the''' Image''' menu.
* For scaling options, please refer to the '''scaling buttons''' popup menu .
* Parameters used for the MSPS calculations can be set in the ''General Settings tab'' of the ''Image Settings dialog box.''

== Source Sensitivity ==

'''Introduction'''

The 'Source sensitivity' function displays the sensitivity of the selected source in the current source model to activity in other brain regions. Sensitivity is defined as the fraction of power at the scanned brain location that is mapped onto the selected source.

To compute the source sensitivity, unit brain activity is modeled at different locations (probe source) throughout the brain. To this data, the current source model is applied to compute the source waveforms SCM of all modeled sources:

<math>\mathrm{S}_{\text{CM}} = \mathrm{L}_{\text{CM}}^{-1} \cdot \mathrm{L}_{\text{PS}}</math>


Here LCM-1 is the regularized inverse operator for the current model, and LPS is the leadfield of the regional probe source (dimension [Nx3] for EEG and [Nx2] for MEG, respectively, where N is the number of sensors). The source amplitude SSS of the selected source in the model is a 3x3 (MEG: 2x2) sub-matrix of SCM (if the selected source is a regional source) or a 1x3-matrix (MEG: 1x2) (if the selected source is a dipole). The root mean square of the singular values of SCM is defined as the source sensitivity.

The 3D source sensitivity image displays this value for all locations on a grid specified under '''Image/Settings'''. Grid density can be specified in the Image Settings.

'''Applying the Source Sensitivity Image'''

The Source Sensitivity image is evoked from the '''Image''' menu or by pressing the corresponding hot key (default: '''V''').

This function is enabled only when a solution with an active selected source is present in the Source Analysis window. The source sensitivity image then displays the sensitivity of the selected source to activity in other brain regions.

[[Image:SA 3Dimaging (59).gif]]

''Source Sensitivity image for the selected frontal source (green) in model ''''''High_Intensity_3RS.bsa'''''' in folder 'Examples/ERP_Auditory_Intensity'. The data displayed is the '100dB' condition in file ''''''All_Subjects_cc.fsg''''''. The selected source is sensitive to activity in the frontal brain region (yellow/white), while it is not influenced by activity in the vicinity of the left and right auditory cortex areas, which are modeled by the red and blue source in the model (transparent/gray).''

'''Notes:'''

* The sensitivity image is independent of the recorded sensor signals. It only depends on the current source model, the sensor configuration, the head model, and the regularization constant.
* If the regularization constant is set to zero, each source has a sensitivity of 100% to activity around its own location. With increasing regularization, the spatial filter becomes less focused, and the sensitivity of a source to activity at its location decreases.
* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image''' menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the '''Image''' menu.

{{BESAManualNav}}

Source Analysis 3D Imaging

2019-03-27T11:35:57Z

Jamie: /* Multiple Source Beamformer (MSBF) in the Time Domain */

{{BESAInfobox
|title = Module information
|module = BESA Research Standard or higher
|version = 6.1 or higher
}}


== Overview ==

BESA Research features a set of new functions that provide 3D images that are displayed superimposed to the individual subject's anatomy. This chapter introduces these different images and describe their properties and applications.

The 3D images can be divided into three categories:

'''Volume images:'''

* '''The Multiple Source Beamformer (MSBF)''' is a tool for imaging brain activity. It is applied in the time-domain or time-frequency domain. The beamformer technique in time-frequency domain can image not only evoked, but also induced activity, which is not visible in time-domain averages of the data.
* '''Dynamic Imaging of Coherent Sources (DICS)''' can find coherence between any two pairs of voxels in the brain or between an external source and brain voxels. DICS requires time-frequency-transformed data and can find coherence for evoked and induced activity.

The following imaging methods provide an image of brain activity based on a distributed multiple source model:
* '''CLARA''' is an iterative application of LORETA images, focusing the obtained 3D image in each iteration step.
* '''LAURA '''uses a spatial weighting function that has the form of a local autoregressive function.
* '''LORETA''' has the 3D Laplacian operator implemented as spatial weighting prior.
* '''sLORETA''' is an unweighted minimum norm that is standardized by the resolution matrix.
* '''swLORETA '''is equivalent to sLORETA, except for an additional depth weighting.
* '''SSLOFO '''is an iterative application of standardized minimum norm images with consecutive shrinkage of the source space.
* A '''User-defined volume image''' allows to experiment with the different imaging techniques. It is possible to specify user-defined parameters for the family of distributed source images to create a new imaging technique.
* Bayesian source imaging: '''SESAME''' uses a semi-automated Bayesian approach to estimate the number of dipoles along with their parameters.

'''Surface image:'''

* The '''Surface Minimum Norm Image'''. If no individual MRI is available, the minimum norm image is displayed on a standard brain surface and computed for standard source locations. If available, an individual brain surface is used to construct the distributed source model and to image the brain activity.
* '''Cortical LORETA'''. Unlike classical LORETA, cortical LORETA is not computed in a 3D volume, but on the cortical surface.
* '''Cortical CLARA'''. Unlike classical CLARA, cortical CLARA is not computed in a 3D volume, but on the cortical surface.

'''Discrete model probing:'''

These images do not visualize source activity. Rather, they visualize properties of the currently applied discrete source model:
* The '''Multiple Source Probe Scan (MSPS)''' is a tool for the validation of a discrete multiple source model.
* The '''Source Sensitivity image''' displays the sensitivity of a selected source in the current discrete source model and is therefore data independent.

== Multiple Source Beamformer (MSBF) in the Time-frequency Domain ==

 
'''Short mathematical introduction'''

The BESA beamformer is a modified version of the linearly constrained minimum variance vector beamformer in the time-frequency domain as described in [https://dx.doi.org/10.1073/pnas.98.2.694 Gross et al., "Dynamic imaging of coherent sources: Studying neural interactions in the human brain", PNAS 98, 694-699, 2001]. It allows to image evoked and induced oscillatory activity in a user-defined time-frequency range, where time is taken relative to a triggered event.

The computation is based on a transformation of each channel's single trial data from the time domain into the time-frequency domain. This transformation is performed by the BESA Research Source Coherence module and leads to the complex spectral density Si (f,t), where i is the channel index and f and t denote frequency and time, respectively. Complex cross spectral density matrices C are computed for each trial:

<math>\mathrm{C}_{ij}\left( f,t \right) = \mathrm{S}_{i}\left( f,t \right) \cdot \mathrm{S}_{j}^{*}\left( f,t \right)</math>


The output power P of the beamformer for a specific brain region at location r is then computed by the following equation:

<math>\mathrm{P}\left( r \right) = \operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{-1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{-1}</math>


Here, Cr-1 is the inverse of the SVD-regularized average of Cij(f,t) over trials and the time-frequency range of interest; L is the leadfield matrix of the model containing a regional source at target location r and, optionally, additional sources whose interference with the target source is to be minimized; tr'[] is the trace of the [3×3] (MEG:[2×2]) submatrix of the bracketed expression that corresponds to the source at target location r.

In BESA Research, the output power P(r) is normalized with the output power in a reference time-frequency interval Pref(r). A value q ist defined as follows:

<math> \mathrm{q}\left( r \right) =
\begin{cases}
\sqrt{\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}(r)}} - 1 = \sqrt{\frac{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{\text{ref},r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}} - 1, & \text{for }\mathrm{P}(r) \geq \mathrm{P}_{\text{ref}}(r) \\

1 - \sqrt{\frac{\mathrm{P}_{\text{ref}}\left( r \right)}{\mathrm{P}\left( r \right)}} = 1 - \sqrt{\frac{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{\text{ref},r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}}, & \text{for }\mathrm{P}(r) < \mathrm{P}_{\text{ref}}(r)
\end{cases} </math>


Pref can be computed either from the corresponding frequency range in the baseline of the same condition (i.e. the beamformer images event-related power increase or decrease) or from the corresponding time-frequency range in a control condition (i.e. the beamformer images differences between two conditions). The beamformer image is constructed from values q(r) computed for all locations on a grid specified in the '''General Settings tab'''. For MEG data, the innermost grid points within a sphere of approx. 12% of the head diameter are assigned interpolated rather than calculated values).
q-values are shown in %, where where q[%] = q*100. Alternatively to the definition above, q can also be displayed in units of dB:

<math>\mathrm{q}\left\lbrack \text{dB} \right\rbrack = 10 \cdot \log_{10}\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}</math>


A beamformer operator is designed to pass signals from the brain region of interest r without attenuation, while minimizing interference from activity in all other brain regions. Traditional single-source beamformers are known to mislocalize sources if several brain regions have highly correlated activity. Therefore, the BESA beamformer extends the traditional single-source beamformer in order to implicitly suppress activity from possibly correlated brain regions. This is achieved by using a multiple source beamformer calculation that contains not only the leadfields of the source at the location of interest r, but also those of possibly interfering sources. As a default, BESA Research uses a bilateral beamformer, where specifically contributions from the homologue source in the opposite hemisphere are taken into account (the matrix L thus being of dimension N×6 for EEG and N×4 for MEG, respectively, where N is the number of sensors). This allows for imaging of highly correlated bilateral activity in the two hemispheres that commonly occurs during processing of external stimuli.

In addition, the beamformer computation can take into account possibly correlated sources at arbitrary locations that are specified in the current solution. This is achieved by adding their leadfield vectors to the matrix L in the equation above.

'''Applying the Beamformer'''

This chapter illustrates the usage of the BESA beamformer. The displayed figures are generated using the file ''''Examples/Learn-by-Simulations/AC-Coherence/AC-Osc20.foc'''' (see BESA Tutorial 6: "''Time-frequency analysis and Source coherence''").

'''Starting the beamformer from the time-frequency window'''

The BESA beamformer is applied in the time-frequency domain and therefore requires the Source Coherence module to be enabled. The time-frequency beamformer is especially useful to image in- or decrease of induced oscillatory activity. Induced activity cannot be observed in the averaged data, but shows up as enhanced averaged power in the TSE (Temporal-Spectral Evolution) plot. For instructions on how to initiate a beamformer computation in the time-frequency window, please refer to Chapter '''[[Source_Coherence_How_to...#How_to_Start_the_Beamformer_from_the_Time-Frequency_Window|How to Create Beamformer Images]]'''.

After the beamformer computation has been initiated in the time-frequency window, the source analysis window opens with an enlarged 3D image of the q-value computed with a '''bilateral beamformer'''. The result is superimposed onto the MR image assigned to the data set (individual or standard).

[[Image:SA 3Dimaging (5).gif]]

''Beamformer image after starting the computation in the Time-Frequency window. A bilateral pair of sources in the auditory cortex accounts for the highly correlated oscillatory induced activity. Only the bilateral beamformer manages to separate these activities; a traditional single-source beamformer would merge the two sources into one image maximum in the head center instead.''

'''Multiple source beamformer in the Source Analysis window'''

The 3D imaging display is part of the source analysis window. If you press the '''Restore''' button at the right end of the title bar of the 3D window, the window appears at the bottom right of the source analysis window. In the channel box, the averaged (evoked) data of the selected condition is shown. When a control condition was selected, its average is appended to the average of the target condition.

[[Image:SA 3Dimaging (6).gif]]

''Source Analysis window with beamformer image. The two sources have been added using the '''''Switch to''''' '''''Maximum''''' and '''''Add Source '''''toolbar buttons (see below). Source waveforms are computed from the displayed averaged data. Therefore, they do not represent the activity displayed in the beamformer image, which in this simulation example is induced (i.e. not phase-locked to the trigger)!''

When starting the beamformer from the time-frequency window, a bilateral beamformer scan is performed. In the source analysis window, the beamformer computation can be repeated taking into account possibly correlated sources that are specified in the current solution. Interfering activities generated by all sources in the current solution that are in the 'On' state are specifically suppressed ('''they enter the matrix L in the beamformer calculation''', see Chapter ''Short mathematical description'' above). The computation can be started from the '''Image''' menu or from the '''Image selector button''' dropdown menu. The '''Image''' menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window.

[[Image:SA 3Dimaging (7).gif]]

''Multiple source beamformer image calculated in the presence of a source in the left hemisphere. A '''single''' source scan has been performed. The source set in the current solution accounts for the left-hemispheric q-maximum in the data. Accordingly, the beamformer scan reveals only the as yet unmodeled additional activity in the right hemisphere (note the radiological convention in the 3D image display).''

The beamformer scan can be performed with a '''single''' or a '''bilateral''' source scan. The default scan type depends on the current solution:
* When the beamformer is started from the Time-Frequency window, the Source Analysis window opens with a new solution and a '''bilateral''' beamformer scan is performed.
* When the beamformer is started within the Source Analysis window, the default is
** a scan with a '''single''' source in addition to the sources in the current solution, if at least one source is active.
** a '''bilateral''' scan if no source in the current solution is active.

The default scan type is the multiple source beamformer. The non-default scan type can be enforced using the corresponding ''Volume Image / Beamformer'' entry in the '''Image''' menu.

'''Inserting Sources out of the Beamformer Image'''

The beamformer image can be used to add sources to the current solution. A simple double-click anywhere in the 2D- or 3D-view will generate a non-oriented regional source at the corresponding location. However, a better and easier way to create sources at image maxima and minima is to use the toolbar buttons '''Switch to Maximum''' [[Image:SA 3Dimaging (8).gif]] and '''Add Source''' [[Image:SA 3Dimaging (9).gif]].

Use the '''Switch to Maximum''' button to place the red crosshair of the 3D window onto a local image maximum or minimum. Hitting the '''Add Source''' button creates a regional source at the location of the crosshair and therefore ensures the exact placement of the source at the image extremum. Moreover, the '''Add Source''' button generates an oriented regional source. BESA Research automatically estimates the source orientation that contributes most to the power in the target time-frequency interval (or the reference time-frequency interval, if its power is larger than that in the target interval). The accuracy of this orientation estimate depends largely on the noise content of the data. The smaller the signal-to-noise ratio of the data, the lower is the accuracy of the orientation estimate. '''This feature allows to use the beamformer as a tool to create a source montage for source coherence analysis, where it is of advantage to work with oriented sources'''.

'''Notes:'''

* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image '''menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the''' Image''' menu.
* For scaling options, use the [[Image:SA 3Dimaging (10).gif]] and [[Image:SA 3Dimaging (11).gif]] '''Image Scale toolbar''' buttons.
* Parameters used for the beamformer calculations can be set in the '''Standard Volumes''' of the ''Image Settings dialog box.''

== Dynamic Imaging of Coherent Sources (DICS) ==

 
'''Short mathematical introduction'''

Dynamic Imaging of Coherent Sources (DICS) is a sophisticated method for imaging cortico-cortical coherence in the brain, or coherence between an external reference (e.g. EMG channel) and cortical structures. DICS can be applied to localize evoked as well as induced coherent cortical activity in a user-defined time-frequency range.

DICS was implemented in BESA closely following [https://dx.doi.org/10.1073/pnas.98.2.694 Gross et al., "Dynamic imaging of coherent sources: Studying neural interactions in the human brain", PNAS 98, 694-699, 2001].

The computation is based on a transformation of each channel's single trial data from the time domain into the frequency domain. This transformation is performed by the BESA Research Coherence module and results in the complex spectral density matrix that is used for constructing the spatial filter similar to beamforming.

DICS computation yields a 3-D image, each voxel being assigned a coherence value. Coherence values can be described as a neural activity index and do not have a unit. The neural activity index contrasts coherence in a target time-frequency bin with coherence of the same time-frequency bin in a baseline.

'''DICS for cortico-cortical coherence is computed as follows:'''

Let L(r) be the leadfield in voxel r in the brain and C the complex cross-spectral density matrix. The spatial filter W(r) for the voxel r in the head is defined as follows:

<math>W\left( r \right) = \left\lbrack L^{T}\left( r \right) \cdot C^{- 1} \cdot L\left( r \right) \right\rbrack^{- 1} \cdot L^{T}(r) \cdot C^{- 1}</math>


The cross-spectrum between two locations (voxels) r1 and r2 in the head are calculated with the following equation:

<math>C_{s}\left( r_{1},r_{2} \right) = W\left( r_{1} \right) \cdot C \cdot W^{*T}\left( r_{2} \right),</math>


where <nowiki>*T</nowiki> means the transposed complex conjugate of a matrix. The cross-spectral density can then be calculated from the cross spectrum as follows:

<math>c_{s}\left( r_{1},r_{2} \right) = \lambda_{1}\left\{ C_{s}\left( r_{1},r_{2} \right) \right\},</math>


where λ1{} indicates the largest singular value of the cross spectrum. Once the cross spectral density is estimated, the connectivity¹(CON) between the two brain regions r1 and r2 are calculated as follows:

<math>\text{CON}\left( r_{1},r_{2} \right) = \frac{c_{s}^{\text{sig}}\left( r_{1},r_{2} \right) - c_{s}^{\text{bl}}(r_{1},r_{2})}{c_{s}^{\text{sig}}\left( r_{1},r_{2} \right) + c_{s}^{\text{bl}}(r_{1},r_{2})},</math>


where cssig is the cross-spectral density for the signal of interest between the two brain regions r1 and r2, and csbl is the corresponding cross spectral density for the baseline or the control condition, respectively. In the case DICS is computed with a cortical reference, r1 is the reference region (voxel) and remains constant while r2 scans all the grid points within the brain sequentially. In that way, the connectivity between the reference brain region and all other brain regions is estimated. The value of CON(r1, r2) falls in the interval [-1 1]. If the cross-spectral density for the baseline is 0 the connectivity value will be 1. If the cross-spectral density for the signal is 0 the connectivity value will be -1.

¹ Here, the term connectivity is used rather than coherence, as strictly speaking the coherence equation is defined slightly differently. For simplicity reasons the rest of the tutorial uses the term coherence.

'''DICS for cortico-muscular coherence is computed as follows:'''

When using an external reference, the equation for coherence calculation is slightly different compared to the equation for cortico-cortical coherence. First of all, the cross-spectral density matrix is not only computed for the MEG/EEG channels, but the external reference channel is added. This resulting matrix is Call. In this case, the cross-spectral density between the reference signal and all other MEG/EEG

channels is called cref. It is only one column of Call. Hence, the cross-spectrum in voxel r is calculated with the following equation:

<math>C_{s}\left( r \right) = W\left( r \right) \cdot c_{\text{ref}}</math>


and the corresponding cross-spectral density is calculated as the sum of squares of Cs:

<math>c_{s}\left( r \right) = \sum_{i = 1}^{n}{C_{s}\left( r \right)_{i}^{2}},</math>


where n is 2 for MEG and 3 for EEG. This equation can also be described as the squared Euclidean norm of the cross-spectrum:

<math>c_{s}\left( r \right) = \left\| C_{s} \right\|^{2},</math>


The power in voxel r is calculated as in the cortico-cortical case:

<math>p\left( r \right) = \lambda_{1}\left\{ C_{s}(r,r) \right\}.</math>


At last, coherence between the external reference and cortical activity is calculated with the equation:

<math>\text{CON}\left( r \right) = \frac{c_{s}(r)}{p\left( r \right) \cdot C_{\text{all}}(k,k)},</math>


where Call(k, k) is the (k,k)-th diagonal element of the matrix Call.

DICS is particularly useful, if coherence is to be calculated without an a-priory source model (in contrast to source coherence based on pre-defined source montages). However, the recommended analysis strategy for DICS is to use a brain source as a starting point for coherence calculation that is known to contribute to the EEG/MEG signal of interest. For example, one might first run a beamformer on the time-frequency range of interest and use the voxel with the strongest oscillatory activity as a starting point for DICS. The resulting coherence image will again lead to several maxima (ordered by magnitude), which in turn can serve as starting points for DICS calculation. This way, it is possible to detect even weak sources that show coherent activity in the given time-frequency range.

The other significant application for DICS is estimating coherence between an external source and voxels in the brain. For example, an external source can be muscle activity recoded by an electrode placed over the according peripheral region. This way, the direct relationship between muscle activity and brain activation can be measured.

'''Starting DICS computation from the Time-Frequency Window'''

DICS is particularly useful, if coherence in a user-defined time-frequency bin (evoked or induced) is to be calculated between any two brain regions or between an external reference and the brain. DICS runs only on time-frequency decomposed data, so time-frequency analysis needs to be run before starting DICS computation.

To start the DICS computation, left-drag a window over a selected time-frequency bin in the Time-Frequency Window. Right-click and select “Image”. A dialogue will open (see fig. 1) prompting you to specify time and frequency settings as well as the baseline period. It is recommended to use a baseline period of equal length as the data period of interest. Make sure to select “DICS” in the top row and press “'''Go'''”.

[[Image:SA 3Dimaging (21).gif|450px|thumb|c|none|Fig. 1: Time and frequency settings for DICS and MSBF]]

Next, a window will appear allowing you to specify the reference source for coherence calculation (see fig. 2). It is possible to select a channel (e.g. EMG) or a brain source. If a brain source is chosen and no source analysis was computed beforehand, the option “Use current cross-hair position” must be chosen. In case discrete source analysis was computed previously, the selected source can be chosen as the reference for DICS. Please note that DICS can be re-computed with any cross-hair or source position at a later stage.

[[Image:SA 3Dimaging (1).jpg|400px|thumb|c|none|Fig. 2: Possible options for choosing the reference]]

Confirming with “'''OK'''” will start computation of coherence between the selected channel/voxel and all other brain voxels. In case DICS is computed for a reference source in the brain, it can be advantageous to run a beamforming analysis in the selected time-frequency window first and use one of the beamforming maxima as reference for DICS. Fig. 3 shows an example for DICS calculation.

[[Image:SA 3Dimaging (22).gif|500px|thumb|c|none|Fig. 3: Coherence between left-hemispheric auditory areas and the selected voxel in the right auditory cortex.]]

Coherence values range between -1 and 1. If coherence in the signal is much larger than coherence in the baseline (control condition) then the DICS value is going to approach 1. Contrary, if coherence in the baseline is much larger than coherence in the signal, then the DICS value is going to approach -1. At last, if coherence in the signal is equal to coherence in the baseline, then the DICS value is 0.

In case DICS is to be re-computed with a different reference, simply mark the desired reference position by placing the cross-hair in the anatomical view and select “DICS” in the middle panel of the source analysis window (see Fig. 4). In case an external reference is to be selected, click on “DICS” in the middle panel to bring up the DICS dialogue (see. Fig. 2) and select the desired channel. Please note that DICS computation will only be available after running time-frequency analysis.

[[Image:SA 3Dimaging (23).gif|700px|thumb|c|none|Fig. 4: Integration of DICS in the Source Analysis window]]

== Multiple Source Beamformer (MSBF) in the Time Domain ==
''(requires Besa Research 7.0 or higher)''

===Short mathematical introduction===

Beamforming approach can be also applied in the time domain data. This approach was introduced as linearly constrained minimum variance (LCMV) beamformer (Van Veen et al., 1997). It allows to image evoked activity in a user-defined time range, where time is taken relative to a triggered event, and to estimate source waveforms using the calculated spatial weight at locations of interest. For an implementation of the beamformer in the time domain, data covariance matrices are required, while complex cross spectral density matrices are used for the beamformer approaches in the time-frequency domain as described in the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section.

The bilateral beamformer introduced in the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section is also implemented for the time-domain beamformer to take into account contributions from the homologue source in the opposite. This allows for imaging of highly correlated bilateral activity in the two hemispheres that commonly occurs during processing of external stimuli. In addition, the beamformer computation can take into account possibly correlated sources at arbitrary locations.
The beamformer spatial weight W(r) for the voxel r in the brain is defined as follows (Van Veen et al., 1997):

[[File:MSBF1.png]]

where '''C-1''' is the inversed regularized average of covariance matrix over trials, '''L''' is the leadfield matrix of the model containing a regional source at target location r and optionally
additional sources whose interference with the target source is to be minimized. The beamformer spatial weight '''W'''(r) can be applied to the measured data to estimate source
waveform at a location r (beamformer virtual sensor):

[[File:MSBF2.png]]

where '''S'''(r,t) represents the estimated source waveform and '''M'''(t) represents measured EEG or MEG signals.
The output power P of the beamformer for a specific brain region at location r is computed by the following equation:

[[File:MSBF3.png]]

where tr’[ ] is the trace of the [3×3] (MEG: [2×2]) submatrix of the bracketed expression that corresponds to the source at target location r.
Beamformer can suppress noise sources that are correlated across sensors. However, uncorrelated noise will be amplified in a spatially non-uniform manner, with increasing
distortion with increasing distance from the sensors (Van Veen et al., 1997; Sekihara et al., 2001). For this reason, estimated source power should be normalized by a noise power.
In BESA Research, the output power P(r) is normalized with the output power in a baseline interval or with the output power of a uncorrelated noise: P(r) / Pref (r).
The time-domain beamformer image is constructed from values q(r) computed for all locations on a grid specified in the '''General Settings''' tab. A value q(r) is defined as described in
the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section with data covariance matrices instead of cross-spectral density matrices.

===Applying the Beamformer===

This chapter illustrates the usage of the BESA beamformer in the time domain. The displayed figures are generated using the file ‘Examples/ERP-Auditory-Intensity/S1.cnt’.

'''Starting the time-domain beamformer from the Average tap of the Paradigm dialog box'''

The time-domain beamformer is needed data covariance matrices and therefore requires the ERP module to be enabled. After the beamformer computation has been initiated in the
'''Average tap of the Paradigm dialog box''', the source analysis window opens with an enlarged 3D image of the q-value computed with a bilateral beamformer. The result is
superimposed onto the MR image assigned to the data set (individual or standard).

[[File:MSBF44.png]]

''Beamformer image for auditory evoked data after starting the computation in the '''Average tap of the Paradigm dialog box'''. The bilateral beamformer manages to separate the
activities in auditory areas, while a traditional single-source beamformer would merge the two sources into one image maximum in the head center instead.''

'''Multiple-source beamformer in the Source Analysis window'''

The 3D imaging display is part of the source analysis window. In the Channel box, the averaged (evoked) data of the selected condition is shown. Selected covariance intervals in
the ERP module can be checked in the Channel box. The red, gray, and blue rectangles indicate signal, baseline, and common interval, respectively.

[[File:MSBF55.png]]

''Source Analysis window with beamformer image. The two beamformer virtual sensors have been added using the Switch to Maximum and Add Source toolbar buttons (see below).
Source waveforms are computed using the beamformer spatial weights and the displayed averaged data (the noise normalized weights (5% noise) option was used to compute the
beamformer image).''

When starting the beamformer from the '''Average tap of the Paradigm dialog box''', the bilateral beamformer scan is performed. In the source analysis window, the beamformer computation can be repeated taking into account possibly correlated sources that are specified in the current solution. Interfering activities generated by all sources in the current solution that are in the 'On' state are specifically suppressed (they enter the leadfield matrix L in the beamformer calculation). The computation can be started from the '''Image''' menu or from the Image selector button [[File:MSBF_Button.png|22px|Image: 22 pixels]] dropdown menu. The Image menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window.

[[File:MSBF66.png]]

''Multiple-source beamformer image calculated in the presence of a source in the left hemisphere. A single-source scan has been performed instead of a bilateral beamforemr. The
source set in the current solution accounts for the left-hemispheric q-maximum in the data. Accordingly, the beamformer scan reveals only the as yet unmodeled additional activity in
the right hemisphere (note the radiological convention in the 3D image display). The source waveform of the beamformer virtual sensor in the left hemisphere is not shown since the
location (blue square in the figure) is not considered for the multiple-source beamformer.''

The beamformer scan can be performed with a single or a bilateral source scan. The default scan type depends on the current solution:
When the beamformer is started from the '''Average tap of the Paradigm dialog box''' the Source Analysis window opens with a new solution and a bilateral beamformer scan is
performed.
When the beamformer is started within the Source Analysis window, the default is:

* a scan with a single source in addition to the sources in the current solution, if at least one source is active.
* a bilateral scan if no source in the current solution is active.
* a scan with a single source when scalar-type beamformer is selected in the '''beamformer option dialog box'''.

The default scan type is the multiple source beamformer. The non-default scan type can be enforced using the corresponding Volume Image / Beamformer entry in the Image main
menu or in the beamformer option dialog box (only for the time-domain beamformer).

===Inserting Sources as Beamformer Virtual Sensor out of the Beamformer Image===

This is similar to the inserting sources out of the beamformer image in Multiple Source Beamformer (MSBF) in the Time-frequency Domain section.
The beamformer image can be used to add beamformer virtual sensors to the current solution. A simple double-click anywhere in the 3D view (not in the 2D view) will generate a
source at the corresponding location. A better and easier way to create sources at image maxima and minima is to use the toolbar buttons Switch to Maximum and Add Source

This feature allows to use the beamformer as a tool to create a source montage for source coherence analysis. A source montage file (*.mtg) for beamformer virtual sensors can
be saved using File \ Save Source Montage As… entry.

The time-domain beamformer image can be also used to add regional or dipole sources to the current solution. Press N key when there is no source in the current source array or
there is more than one beamformer virtual sensor. To create a new source array for beamformer virtual sensor, press N key when there is more than one regional or dipole source in
the current source array.

===Notes===

* You can hide or re-display the last computed image by selecting Hide Image entry in the Image menu.
* The current image can be exported to ASCII, ANALYZE, or BrainVoyager (vmp) format from the Image menu.
* For scaling options, use the and Image Scale toolbar buttons.
* Parameters used for the beamformer calculations can be set in the Standard Volume tab of the Image Settings dialog box.
* Note that Model, Residual, Order, and Residual variance are not shown for the beamformer virtual sensor type sources.

===References===

* Sekihara, K., Nagarajan, S. S., Poeppel, D., Marantz, A., & Miyashita, Y. (2001). Reconstructing spatio-temporal activities of neural sources using an MEG vector beamformer technique. IEEE Transactions on Biomedical Engineering, 48(7), 760–771.

* Van Veen, B. D., Van Drongelen, W., Yuchtman, M., & Suzuki, A. (1997). Localization of brain electrical activity via linearly constrained minimum variance spatial filtering. IEEE Transactions on Biomedical Engineering, 44(9), 867–880

== CLARA ==

CLARA ('Classical LORETA Analysis Recursively Applied') is an iterative application of weighted LORETA images with a reduced source space in each iteration.

In an initialization step, a LORETA image is calculated. Then in each iteration the following steps are performed:

# The obtained image is spatially smoothed (this step is left out in the first iteration).
# All grid points with amplitudes below a threshold of 1% of the maximum activity are set to zero, thus being effectively eliminated from the source space in the following step.
# The resulting image defines a spatial weighting term (for each voxel the corresponding image amplitude).
# A LORETA image is computed with an additional spatial weighting term for each voxel as computed in step 3. By the default settings in BESA Research, the regularization values used in the iteration steps are slightly higher than that of the initialization LORETA image.

The procedure stops after 2 iterations, and the image computed in the last iteration is displayed. Please note that you can change all parameters by creating a user-defined volume image.

The advantage of CLARA over non-focusing distributed imaging methods is visualized by the figure below. Both images are computed from the N100 response in an auditory oddball experiment (file '''Oddball.fsg''' in subfolder ''fMRI+EEG-RT-Experiment'' of the ''Examples'' folder). The CLARA image is much more focal than the sLORETA image, making it easier to determine the location of the image maxima.

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (24).gif|thumb|350px|sLORETA image]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (25).gif|thumb|350px|CLARA image]] </li>
</ul></div>

'''Notes:'''

* Starting CLARA: CLARA can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter ''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]'' for important information on regularization of distributed inverses.

== LAURA ==

LAURA (Local Auto Regressive Average) belongs to the distributed inverse method of the family of weighted minimum norm methods ([https://doi.org/10.1023/A:1012944913650 Grave de Peralta Menendeza et al., "Noninvasive Localization of Electromagnetic Epileptic Activity. I. Method Descriptions and Simulations", BrainTopography 14(2), 131-137, 2001]). LAURA uses a spatial weighting function that includes depth weighting and that term has the form of a local autoregressive function.

The source activity is estimated by applying the general formula for a weighted minimum norm:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T}\left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings.''

In LAURA, V contains both a depth weighting term W and a representation of a local autoregressive function A. V is computed as:

<math>\mathrm{V} = \left( \mathrm{U}^{T} \cdot \mathrm{U} \right)^{-1}</math>


Where

<math>\mathrm{U} = \left( \mathrm{W} \cdot \mathrm{A} \right) \otimes \mathrm{I}_{3}</math>


Here, <math>\otimes</math> denotes the Kronecker product. I3 is the [3×3] identity matrix. W is an [s×s] diagonal matrix (with s the number of source locations on the grid), where each diagonal element is the inverse of the maximum singular value of the corresponding regional source's leadfields. The formula for the diagonal components Aii and the off-diagonal components Aik are as follows:

<math>\mathrm{A}_{ii} = \frac{26}{\mathrm{N}_{i}}\sum_{k \subset V_{i}}^{}\frac{1}{\mathrm{d}_{ik}^{2}}</math>


<math>
\mathrm{A}_{ik} =
\begin{cases}
- 1/\operatorname{dist}\left( i,k \right)^{2}, & \text{if } k \subset V_{i} \\
0, & \text{otherwise}
\end{cases}
</math>


Here, Vi is the vicinity around grid point i that includes the 26 direct neighbors.

The LAURA image in BESA Research displays the norm of the 3 components of S at each location r. Using the menu function ''Image / Export Image As... ''you have the option to save this norm of S or alternatively all components separately to disk.

'''Notes:'''

* '''Grid spacing:''' Due to memory limitations, LAURA images require a grid spacing of 7 mm or more.
* '''Computation time:''' Computation speed during the first LAURA image calculation depends on the grid spacing (computation is faster with larger grid spacing). After the first computation of a LAURA image, a '''*.laura''' file is stored in the data folder, containing intermediate results of the LAURA inverse. This file is used during all subsequent LAURA image computations. Thereby, the time needed to obtain the image is substantially reduced.
* '''MEG:''' In the case of MEG data, an additional constraint is implemented in the LAURA algorithm that prevents solutions from containing radial source currents (compare Pascual-Marqui, ISBET Newsletter 1995, 22-29). In MEG, an additional source space regularization is necessary in the inverse matrix operation required compute V
* '''Starting LAURA:''' LAURA can be started from the''' Image''' menu or from the '''Image Selection''' button.
* '''Regularization:''' Please refer to Chapter'' “Regularization of distributed volume images” ''for important information on regularization of distributed inverses.

== LORETA ==

LORETA ("Low Resolution Electromagnetic Tomography") is a distributed inverse method of the family of ''weighted minimum norm'' methods. LORETA was suggested by R.D. Pascual-Marqui (International Journal of Psychophysiology. 1994, 18:49-65). LORETA is characterized by a smoothness constraint, represented by a discrete 3D Laplacian.

The source activity is estimated by applying the general formula for a weighted minimum norm:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T}\left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings.''

In LORETA, V contains both a depth weighting term and a representation of the 3D Laplacian matrix. V is computed as:

<math>\mathrm{V} = \left( \mathrm{U}^{T} \cdot \mathrm{U} \right)^{- 1}</math>


where

<math>\mathrm{U} = \left( \mathrm{W} \cdot \mathrm{A} \right) \otimes \mathrm{I}_{3}</math>


Here, <math>\otimes</math> denotes the Kronecker product. I3 is the [3x3] identity matrix. W is an [sxs] diagonal matrix (with s the number of source locations on the grid), where each diagonal element is the inverse of the maximum singular value of the corresponding regional source's leadfields. A contains the 3D Laplacian and is computed as

<math>\mathrm{A} = \mathrm{Y} - \mathrm{I}_{s}</math>


with Is the [sxs] identity matrix, where s is the number of sources (= three times the number of grid points) and

<math>\mathrm{Y} = \frac{1}{2}\left\{ \mathrm{I}_{s} + \left\lbrack \operatorname{diag}\left( \mathrm{Z} \cdot \left\lbrack 111 \ldots 1 \right\rbrack^{T} \right) \right\rbrack^{- 1} \right\} \cdot \mathrm{Z}</math>


where

<math>
\mathrm{Z}_{ik} =
\begin{cases}
1/6, & \text{if } \operatorname{dist}\left( i,k \right) = 1 \text{ grid point} \\
0, & \text{otherwise}
\end{cases}
</math>


The LORETA image in BESA Research displays the norm of the 3 components of S at each location r. Using the menu function ''Image / Export Image As... ''you have the option to save this norm of S or alternatively all components separately to disk.

'''Notes:'''
* '''Grid spacing:''' Due to memory limitations, LORETA images require a grid spacing of 5 mm or more.
* '''Computation time:''' Computation speed during the first LORETA image calculation depends on the grid spacing (computation is faster with larger grid spacing). After the first computation of a LORETA image, a '''<nowiki>*.loreta</nowiki>''' file is stored in the data folder, containing intermediate results of the LORETA inverse. This file is used during all subsequent LORETA image computations. Thereby, the time needed to obtain the image is substantially reduced.
* '''MEG''': In the case of MEG data, an additional constraint is implemented in the LORETA algorithm that prevents solutions from containing radial source currents (Pascual-Marqui, ISBET Newsletter 1995, 22-29). In MEG, an additional source space regularization is necessary in the inverse matrix operation required compute V.
* '''Starting LORETA:''' LORETA can be started from the''' Image''' menu or from the '''Image Selection '''button.
* '''Regularization:''' Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed source models.

== sLORETA ==

This distributed inverse method consists of a ''standardized, unweighted minimum norm''. The method was originally suggested by R.D. Pascual-Marqui (Methods & Findings in Experimental & Clinical Pharmacology 2002, 24D:5-12) Starting point is an unweighted minimum norm computation:

<math>\mathrm{S}_{\text{MN}}\left( t \right) = \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings''.

This minimum norm estimate is now standardized to produce the sLORETA activity at a certain brain location r:

<math>\mathrm{S}_{\text{sLORETA}, r} = \mathrm{R}_{rr}^{-1/2} \cdot \mathrm{S}_{\text{MN},r}</math>


SsMN,r is the [3x1] (MEG: [2x1]) minimum norm estimate of the 3 (MEG: 2) dipoles at location r. Rrr is the [3x3] (MEG: [2x2]) diagonal block of the resolution matrix R that corresponds to the source components at the target location r. The resolution matrix is defined as:

<math>\mathrm{R} = \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{L}^{T} + \lambda \cdot \mathrm{I} \right)^{-1} \cdot \mathrm{L}</math>


The sLORETA image in BESA Research displays the norm of SsLORETA, r at each location r. Using the menu function ''Image / Export Image As...'' you have the option to save this norm of SsLORETA, r or alternatively all components separately to disk.

'''Notes:'''

* sLORETA can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== swLORETA ==

This distributed inverse method is a ''standardized, depth-weighted minimum norm'' (E. Palmero-Soler et al 2007 Phys. Med. Biol. 52 1783-1800). It differs from sLORETA only by an additional depth weighting.

Starting point is a depth-weighted minimum norm computation:

<math>\mathrm{S}_{\text{MN}}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings''.

V is the diagonal depth weighting matrix. For s grid locations, V is of dimension [3s x 3s] (MEG: [2s x 2s]). Each diagonal element of V is the inverse of the first singular value of the leadfield of the corresponding regional source. Hence, the first 3 (MEG: 2) diagonal elements equal the inverse of the largest eigenvalue of the leadfield matrix of regional source 1, and so on.

This minimum norm estimate is now standardized to produce the swLORETA activity at a certain brain location r:

<math>\mathrm{S}_{\text{swLORETA},r} = \mathrm{R}_{rr}^{-1/2} \cdot \mathrm{S}_{\text{MN},r}</math>


SsMN,r is the [3x1] (MEG: [2x1]) depth-weighted minimum norm estimate of the regional source at location r. Rrr is the [3x3] (MEG: [2x2]) diagonal block of the resolution matrix R that corresponds to the source components at the target location r. The resolution matrix is defined as:

<math>\mathrm{R} = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} + \lambda \cdot \mathrm{I} \right)^{-1} \cdot \mathrm{L}</math>


The swLORETA image in BESA Research displays the norm of SswLORETA, r at each location r. Using the menu function ''Image / Export Image As...'' you have the option to save this norm of SswLORETA, r or alternatively all components separately to disk.

'''Notes:'''

* sLORETA can be started from the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== sSLOFO ==

SSLOFO (standardized shrinking LORETA-FOCUSS) is an iterative application of weighted distributed source images with a reduced source space in each iteration ([https://dx.doi.org/10.1109/TBME.2005.855720 Liu et al., "Standardized shrinking LORETA-FOCUSS (SSLOFO): a new algorithm for spatio-temporal EEG source reconstruction", IEEE Transactions on Biomedical Engineering 52(10), 1681-1691, 2005]).

In an initialization step, an [[#sLORETA | sLORETA]] image is calculated. Then in each iteration the following steps are performed:

# A weighted minimum norm solution is computed according to the formula <math display="inline">\mathrm{S} = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}</math> . Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D is the data at the time point under consideration. V is a diagonal spatial weighting matrix that is computed in the previous iteration step. In the first iteration, the elements of V contain the magnitudes of the initially computed LORETA image.
# Standardization of this weighted minimum norm image is performed with the resolution matrix as in [[#sLORETA | sLORETA]].
# The obtained standardized weighted minimum norm image is being smoothed to get Ssmooth.
# All voxels with amplitudes below a threshold of 1% of the maximum activity get a weight of zero in the next iteration step, thus being effectively eliminated from the source space in the next iteration step.
# For all other voxels, compute the elements of the spatial weighting matrix V to be used in the next iteration as follows: <math display="inline">\mathrm{V}_{ii,\text{next iteration}} = \frac{1}{\left\| \mathrm{L}_{i} \right\|} \cdot \mathrm{S}_{ii,\text{smooth}} \cdot \mathrm{V}_{ii,\text{current iteration}}</math>



The procedure stops after 3 iterations. Please note that you can change all parameters by creating a [[#User-Defined Volume Image | user-defined volume image]].

'''Notes:'''
* '''Starting sSLOFO''': sSLOFO can be started from the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter ''[[#Regularization of distributed volume images | Regularization of distributed volume images]]'' for important information on regularization of distributed inverses.

== User-Defined Volume Image ==

In addition to the predefined 3D imaging methods in BESA Research, it is possible to create user-defined imaging methods based on the general formula for distributed inverses:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. Custom-defined parameters are:* The spatial weighting matrix V: This may include depth weighting, image weighting, or cross-voxel weighting with a 3D Laplacian (as in LORETA) or an autoregressive function (as in LAURA).

* Regularization: The term in parentheses is generally regularized. Note that regularization has a strong effect on the obtained results. Please refer to chapter “''Regularization of Distributed Volume Images” ''for more information.
* Standardization: Optionally, the result of the distributed inverse can be standardized with the resolution matrix (as in sLORETA).
* Iterations: Inverse computations can be applied iteratively. Each iteration is weighted with the image obtained in the previous iteration.

All parameters for the user-defined volume image are specified in the User-Defined Volume Tab of the Image Settings dialog box. Please refer to chapter “''User-Defined Volume Tab”'' for details.

'''Notes:'''
* Starting the user-defined volume image: the image calculation can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== Regularization of distributed volume images ==

Distributed source images require the inversion of a term of the form L V LT. This term is generally regularized before its inversion. In BESA Research, selection can be made between two different regularization approaches (parameters are defined in the ''Image Settings dialog box''):

* '''Tikhonov regularization''': In Tikhonov regularization, the term L V LT is inverted as (L V LT +λ I)-1. Here, l is the regularization constant, and I is the identity matrix.
* One way of determining the optimum regularization constant is by minimizing the ''generalized cross'' ''validation error'' (CVE).
* Alternatively, the regularization constant can be specified manually as a percentage of the trace of the matrix L V LT.
* '''TSVD''': In the truncated singular value decomposition (TSVD) approach, an SVD decomposition of L V LT is computed as  L V LT = U S UT, where the diagonal matrix S contains the singular values. All singular values smaller than the specified percentage of the maximum singular values are set to zero. The inverse is computed as U S-1 UT, where the diagonal elements of S-1 are the inverse of the corresponding non-zero diagonal elements of S.

Regularization has a critical effect on the obtained distributed source images. The results may differ completely with different choices of the regularization parameter (see examples below). Therefore, it is important to evaluate the generated image critically with respect to the regularization constant, and to keep in mind the uncertainties resulting from this fact when interpreting the results. The default setting in BESA Research is a TSVD regularization with a 0.03% threshold. However, this value might need to be adjusted to the specific data set at hand.

The following example illustrates the influence of the regularization parameter on the obtained images. The data used here is condition '''St-Cor of dataset Examples \ TFC-Error-Related-Negativity \ Correct+Error.fsg''' at 176 ms following the visual stimulus. Discrete dipole analysis reveals the main activity in the left and right lateral visual cortex at this latency.

[[Image:SA 3Dimaging (42).gif]]

''Discrete source model at 176 ms: Main activity in the left and right lateral visual cortex, no visual midline activity.''

LORETA images computed at this latency depend critically on the choice of the regularization constant. The following 3D images are created with TSVD regularization with SVD cutoffs of 0.1%, 0.005%, and 0.0001%, respectively. The volume grid size was 9 mm. The example demonstrates the dramatic effect of regularization and demonstrates the typical tradeoff between too strong regularization (leading to too smeared 3D images that tend to show blurred maxima) and too small regularization (resulting in too superficial 3D images with multiple maxima).

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (43).gif|thumb|350px|'''SVD cutoff 0.1%''': Regularization too strong. No separation between sources, mislocalization towards the middle of the brain.]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (44).gif|thumb|350px|'''SVD cutoff 0.005%''': Appropriate regularization. Separation of the bilateral activities. Location in agreement with the discrete multiple source model.]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (45).gif|thumb|350px|'''SVD cutoff 0.0001%''': Too small regularization. Mislocalization, too superficial 3D image. ]] </li>
</ul></div>

The automatic determination of the regularization constant using the CVE approach does not necessarily result in the optimum regularization parameter either. In this example, the unscaled CVE approach rather resembles the TSVD image with a cutoff of 0.0001%, i.e. regularization is too small. Therefore, it is advisable to compare different settings of the regularization parameter and make the final choice based on the above-mentioned considerations.

== Cortical LORETA ==

Cortical LORETA is principally the same technique as LORETA, however, Cortical LORETA is not computed in a 3D volume, but on the cortical surface.

The cortical reconstruction in BESA Research fed from BESA MRI is a closed 2D surface with no boundaries and a very close approximation of the actual cortical form. It consists of an irregular triangulated grid.

The Laplace operator that is used for identifying a smooth solution in a three-dimensional space is exchanged with a Laplace operator that runs on the two-dimensional cortical surface.

There is a wide variety of 2D Laplace operators with different characteristics. The general form of the discrete Laplace operator is

<math>\Delta f\left( p_{i} \right) = \frac{1}{d_{i}}\sum_{j \in N(i)}^{}{w_{ij}\left\lbrack f\left( p_{i} \right) - f\left( p_{j} \right) \right\rbrack},</math>


where '''pi''' is the '''i-th''' node of the triangular mesh, '''f(pi) '''is the value of a function f defined on the cortical mesh at the node '''pi''', '''wij''' is the weight for the connection between the nodes '''pi''' and '''pj''' and '''di''' is a normalization factor for the '''i-th''' row of the operator. Furthermore, '''N(i)''' is the set of indices corresponding to the direct (also called "1-ring") neighbors of '''pi'''.

BESA offers the choice of three Laplace operators with slightly different characteristics.

* '''Unweighted Graph Laplacian''': This is the simplest operator. It takes into account only the adjacency of the nodes and not the geometry of the mesh:

<math>
w_{ij} =
\begin{cases}
1, & \text{if } p_{i} \text{ and } p_{j} \text{ are connected by an edge} \\
0, & \text{otherwise}
\end{cases}
</math>

<math>d_{i} = 1</math>


[[Image:SA 3Dimaging (4).jpg |450px]]

* '''Weighted Graph Laplacian:''' This operator is similar to the unweighted graph Laplacian but with different weights for the different connections. The connections between nearby nodes get larger weights than the connections between farther nodes:

<math>w_{ij} = \frac{1}{\operatorname{dist}\left( p_{i},p_{j} \right)}</math>

<math>d_{i} = \sum_{j \in N(i)}^{} {\operatorname{dist}\left(p_{i}, p_{j} \right)}</math>


where '''dist''' ('''pi''' , '''pj''') is the distance between the nodes '''pi '''and '''pj'''.

[[Image:SA 3Dimaging (6).jpg|450px]]

* '''Geometric Laplacian with mixed area weights''': This operator takes into account the angles in the corresponding triangles into account as well as the area around the nodes in order to determine the connection weights:

<math>w_{ij} = \frac{\cot\left( \alpha_{ij} \right) + \cot\left( \beta_{ij} \right)}{2}</math>

<math>d_{i} = A_{\text{mixed}}</math>


where '''αij''' and '''βij''' denote the two angles opposite to the edge ('''i , j''') and '''Amixed '''is either the Voronoi area, or 1/2 of the triangle area or 1/4 of the triangle area depending on the type of the triangle.

[[Image:SA 3Dimaging (8).jpg|450px]]

'''Regularization and other parameters:'''

[[Image:SA 3Dimaging (46).gif ‎]]

* '''SVD cutoff''': The regularization for the inverse operator as a percent of the largest singular value.
* '''Depth weighting''': Turn depth weighting on or off.
* '''Laplacian type''': Selection of Laplacian operators (see above).

'''Notes:'''
* '''Starting Cortical LORETA''': Cortical LORETA can be started from the sub-menu '''Surface Image''' of the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]''” for important information on regularization of distributed inverses.

== Cortical CLARA ==

Cortical CLARA is principally the same technique as CLARA, but Cortical CLARA is not computed in a 3D volume, but on the cortical surface. Instead of using a LORETA image as the basis for the iterative application, cortical CLARA uses cortical LORETA.

'''Regularization and other parameters:'''

[[Image:SA 3Dimaging (47).gif]]

* '''SVD cutoff''': The regularization for the inverse operator as a percent of the largest singular value.
* '''Depth weighting''': Turn depth weighting on or off.
* '''Laplacian type''': Selection of Laplacian operators (see Cortical LORETA).
* '''No of iterations''': Number of iterations for CLARA. The more iterations are used, the sparser becomes the solution.
* '''Automatic''': The algorithm tries to determine the number of iterations automatically. The goodness of fit (GOF) is calculated after every iteration and if there is a big jump in the GOF then the algorithm will stop. If no jumps appear during the calculations then CLARA iterates until the specified number of iterations is reached.
* '''Regularize iterations''': If one wants to use different regularization for the CLARA iterations than the value specified as "SVD cutoff", this option should be selected.
* '''Amount to clip from img (%)''': Cortical CLARA uses the solution from the previous iteration as an additional weighting matrix for the current iteration. That weighting matrix is constructed by cutting the "low" activity from the solution. This number specifies how much of the activity should be cut from the previous solution in order to construct the weighting matrix. This value is given as a percentage of the maximal activity. Default value is 10%.

'''Notes:'''

* '''Starting Cortical CLARA:''' Cortical CLARA can be started from the sub-menu '''Surface Image''' of the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]''” for important information on regularization of distributed inverses.

== Cortex Inflation ==

The inflated cortex is a smoothened version of the individual cortical surface with minimal metric distortions (Fischl, B. et al. (1999). Cortical Surface-Based Analysis: II: Inflation, Flattening, and a Surface-Based Coordinate System. ''NeuroImage'', 9(2), 195–207). Gyri and sulci are smoothened out. The original distances between each point on the cortex and its neighbors are, however, mostly preserved.

[[Image:SA 3Dimaging (48).gif]]

''Cortical LORETA map overlaid on top of the inflated cortical surface.''

A lighter gray color overlaid on top of the surface image indicates the location of a gyrus of the individual cortex surface, while a darker gray color indicates the location of a sulcus. The inflated cortical surface can be computed in '''BESA MRI 2.0'''. For more details please refer to the BESA MRI 2.0 help.

== Surface Minimum Norm Image ==

'''Introduction'''

The minimum norm approach is a common method to estimate a distributed electrical current image in the brain at each time sample (Hämäläinen & Ilmoniemi 1984). The source activities of a large number of regional sources are computed. The sources are evenly distributed using 1500 standard locations 10% and 30% below the smoothed standard brain surface (when using the standard MRI) or using between 3000-4000 locations on the individual brain surface defined by the gray-white-matter boundary.

Since the number of sources is much larger than the number of sensors in a minimum norm solution, the inverse problem is highly underdetermined and must be stabilized by a mathematical constraint, the minimum norm. Out of the many current distributions that can account for the recorded sensor data, the solution with the minimum L2 norm, i.e. the minimum total power of the current distribution is displayed in BESA Research.

First, the forward solution (leadfield matrix L) of all sources is calculated in the current head model. Then, the source activities S(t) of all source components are computed from the data matrix D(t) using an inverse regularized by the estimated noise covariance matrix:

<math>\mathrm{S}\left( t \right) = \mathrm{R} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{R} \cdot \mathrm{L}^{T} + \mathrm{C}_N \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed regional source model, CN denotes the noise correlation matrix in sensor space, and R is a weighting matrix in source space. R and CN can be designed in different ways in order to optimize the minimum norm result. The total activity of each regional source is computed as the root mean square of the source activities S(t) of its 3 (MEG:2) components. This total source activity is transformed to a color-coded image of the brain surface. (When the standard brain is used, two sources are assigned to each surface location, located 10% and 30% below the surface, respectively. The color that is displayed on the standard brain surface is the larger of the two corresponding source activities.)

'''Weighting options'''

The minimum norm current imaging techniques of BESA Research provide different weighting strategies. Two weighting approaches are available: Depth weighting and spatio-temporal approaches.
* '''Depth weighting:''' Without depth weighting, deep sources appear very smeared in a minimum-norm reconstruction. With depth weighting, both deep and superficial sources produce a similar, more focal result. If this weighting method is selected, the leadfield of each regional source is scaled with the largest singular value of the SVD (singular value decomposition) of the source's leadfield.
* '''Spatio-temporal weighting''': Spatio-temporal weighting tries to assign large weight to sources that are assumed to be more likely to contribute to the recorded data.
** '''Subspace correlation after single source scan''': This method divides the signal into a signal and a noise subspace. The correlation of the leadfield of a regional source i with the signal subspace (pi) is computed to find out if the source location contributes to the measured data. The weighting matrix R becomes a diagonal matrix. Each of the three (MEG: 2) components of a regional source get the same weighting value pi2. This approach is based on the signal subspace correlation measure introduced by J.C. Mosher, R. M. Leahy (Recursive MUSIC: A Framework for EEG and MEG Source Localization, IEEE Trans. On Biomed. Eng. Vol. 45, No. 11, November 1998)
** '''Dale & Sereno 1993:''' In the approach of Dale and Sereno (J Cogn Neurosci, 1993, 5: 162-176) a signal subspace needs not be defined. The correlation pi of the leadfield of regional source i with the inverse of the data covariance matrix is computed along with the largest singular value λmax of the data covariance matrix. The weighting matrix R is a diagonal matrix with weights: [[Image:SA 3Dimaging (50).gif]]. Each of the three (MEG: 2) components of a regional source receives the same weighting value.

'''Noise regularization'''

Two methods to estimate the channel noise correlation matrix CN are provided by the program:
* '''Use baseline:''' Select this option to estimate the noise from the user-definable baseline. The signal is computed from the data at non-baseline latencies.
* '''Use 15% lowest values:''' The baseline activity is computed from the data at those 15% of all displayed latencies that have the lowest global field power. The signal is computed from all displayed latencies.

In each case, the activity (noise or signal, respectively) is defined as root-mean-square across all respective latencies for each channel.

The noise covariance matrix CN is constructed as a diagonal matrix. The entries in the main diagonal are proportional to the noise activity of the individual channels (if selected) or are all equally proportional to the average noise activity over all channels. The noise covariance matrix CN is then scaled such that the ratio of the Frobenius norms of the weighted leadfield projector matrix (LRLT) and the noise covariance matrix CN equals the Signal-to-Noise ratio. This scaling can be multiplied by an additional factor (default=1) to sharpen (<1) or smoothen (>1) the minimum norm image.

'''Applying the Minimum Norm Image'''

The minimum-norm algorithm is started via the ''Surface minimum norm image dialog box'', which is opened from the''' Image''' menu, or by typing the shortcut '''Ctrl-M''': Please refer to Chapter ''“Surface'' ''Minimum Norm Tab”'' for more details.

As opposed to the other 3D images available from the '''Image '''menu, the surface minimum norm image is not computed on a volumetric grid, but rather for locations on the brain surface. Accordingly, the results of the minimum norm image are displayed superimposed to the brain surface mesh rather than to the volumetric MR image.

The figure below shows a minimum norm image computed from the file '''Examples\Epilepsy\Spikes\Spikes-Child4_EEG+MEG_averaged.fsg'''. The EEG spike peak was imaged using the individual brain surface of the subject. A baseline from -300 to -70 ms was used. Minimum norm was computed with depth weighting, Spatio-temporal weighting according to Dale & Sereno 1993 and individual noise weighting with a noise scale factor of 0.01. The minimum norm image reveals the location of the spike generator in the close vicinity of the frontal left-hemispheric lesion in this subject.

[[Image:SA 3Dimaging (51).gif]]

== Multiple Source Probe Scan (MSPS) ==

 
'''Introduction'''

The MSPS function provides a tool for the validation of a given solution. It is based on the following theoretical consideration: If the recorded EEG/MEG data has been modeled adequately, i.e. all active brain regions are represented by a source in the current solution, then any additional probe source added to the solution will not show any activity apart from noise. The only exception occurs if this probe source is placed in close vicinity to one of the sources in the current solution. In that case, the solution's source and the probe source will share the activity of the corresponding brain area. The MSPS applies these considerations by scanning the brain on a pre-defined grid with a regional probe added to the current solution. Grid extent and density can be specified in the Image settings. The power P of the probe source at location r in the signal interval is compared with the power of the probe source in a reference interval, defining a value q:

<math>\mathrm{q}\left( r \right) = \sqrt{\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}} - 1</math>


MSPS can be computed on time domain or time-frequency domain data:
* In the time domain, q(r) is computed from the source waveform of the probe source. Here, P(r) is the mean power of the probe source at location r in the marked latency range, and Pref(r) is the mean probe source power in the user-definable baseline interval.
* In the time-frequency domain, an MSPS image can be computed from the complex cross spectral density matrices. By applying the inverse operator for a source configuration consisting of the current solution and the probe source, the power of the probe source can be computed for the target interval [P(r)] and the reference time-frequency interval [Pref(r)]. In the resulting MSPS image, q-values are shown in %, where q[%] = q*100.

The inverse operator used to determine the probe source power uses different regularization constants for the probe source and the sources in the current solution. The regularization constant of the sources in the current solution can be specified in the Image settings (default 4%). The regularization constant of the probe source is internally set to 0%.

Alternatively to the definition above, q can also be displayed in units of dB:

<math>\mathrm{q}\left\lbrack \text{dB} \right\rbrack = 10 \cdot \log_{10}\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}</math>


Values of q smaller than zero are not shown in the MSPS image.

According to the considerations above, an MSPS of a correct source model should optimally yield image maxima around the sources in the current solution only. If the MSPS image is blurred or shows maxima at locations different from the modeled sources, this indicates a non-sufficient or incorrect solution.

'''Applying the MSPS'''

This chapter illustrates the application of the Multiple Source Probe Scan. The figures are generated with data from file '''Examples/Epilepsy/Spikes/Rolandic-Spike-Child.fsg''' (-300 : +200 ms, filtered from 3 Hz [forward] to 40 Hz [zero-phase]).

'''Time domain versus time-frequency domain MSPS'''

The multiple source probe scan can be computed in the time domain or the time-frequency domain. The latter is possible only when time-frequency domain data is available for the current condition, i.e. if the condition has been created by starting a multiple source beamformer (MSBF) computation from the source coherence window. In this case, evoking the MSPS calculation from the '''Imaging '''button or from the '''Image''' menu will bring up the following dialog window that allows to choose between time- or time-frequency MSPS. If only time domain data is available, this dialog window will not appear and MSPS will be computed in the time domain.

[[Image:SA 3Dimaging (53).gif]]

For a time-frequency domain MSPS, the target and the reference time-frequency interval have been specified already in the Time-Frequency window (see Chapter "''How To Create Beamformer Images''"). For a time-domain MSPS, the target and the reference epoch have to be specified in the Source Analysis window as described below.

'''Time domain MSPS'''

The time-domain MSPS image displays the ratio of the power of a regional probe source in the signal and the baseline interval. The currently set baseline is indicated by a horizontal line in the upper left corner of the channel box.

[[Image:SA 3Dimaging (54).gif|thumb|c|none|330px|The black horizontal bar in the upper part of the channel box (here circled in red) indicates the baseline interval.]]

By default, BESA Research defines the pre-stimulus interval of the current data segment as baseline. The baseline should represent a latency range in which no event-related activity is present in the data. There are several possibilities to modify the baseline interval: by clicking on the horizontal line with the left mouse button or by using the corresponding entry in the '''Condition '''menu or '''Fit Interval''' popup menu.

Mark an interval to define the target epoch, i.e. the time-interval for which the current solution is to be tested. Start the MSPS by selecting it from the '''Image selection '''button or from the '''Image''' menu to start the probe source scan. The''' Image '''menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window. The 3D window opens and displays the scan result.

<div><ul>
<li style="display: inline-block;"> [[Image:SA 3Dimaging (55).gif|thumb|c|none|650px|This figure shows the MSPS image applied on the three left-hemispheric sources in the solution ''''Rolandic-Spike-Child-RS2.bsa''''. The baseline is set from -300ms to -50 ms. The right-hemispheric sources have been switched off. The fit interval is set to the latency range of large overall activity in the data (-43 ms : 117 ms). A realistic FEM model appropriate for the subject's age (12 years, conductivity ratios (cr) 50) is applied. The MSPS image does not show maxima at the modeled source locations and rather shows a spread q-value distribution.]] </li>

<li style="display: inline-block;"> [[Image:SA 3Dimaging (56).gif|thumb|c|none|650px|The MSPS image for the same latency range when the right-hemispheric sources have been included. The MSPS image appears more focal and shows maxima around the modeled brain regions. This indicates the substantial improvement of the solution by adding the right-hemispheric sources that model the propagation of the epileptic spike from the left to the right hemisphere (note the radiological side convention in the 3D window).]] </li>
</ul></div>

'''Time-Resolved MSPS'''

If the MSPS has been computed on time domain data, the image can be shown separately for each latency in the selected interval. After the MSPS has been computed for the marked epoch, double-click anywhere within this epoch to display the ratio of the probe source magnitude at the selected latency and the mean probe source magnitude in the baseline. Scanning the latency range by moving the cursor (e.g. with the left and right arrow cursor keys) provides a time-resolved MSPS image.

Time-resolved MSPS images are not available if the MSPS has been computed on data in the time-frequency domain.

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (57).gif|thumb|450px|MSPS image of the spike peak activity at 0ms. The activity mainly occurs in the left hemisphere. This fact is illustrated by the source waveforms and confirmed in the MSPS image, which shows a focal maximum around the location of the red sources.]] </li>

<li style="display: inline-block;"> [[File:SA 3Dimaging (58).gif|thumb|450px|Around +27 ms, the spike has propagated to the right hemisphere. This becomes evident from the waveforms of the blue sources, which show a significant latency lag with respect to the first three sources, and from the MSPS image, which shows the maximum around blue sources at this latency.]] </li>
</ul></div>



'''Notes:'''

* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image''' menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the''' Image''' menu.
* For scaling options, please refer to the '''scaling buttons''' popup menu .
* Parameters used for the MSPS calculations can be set in the ''General Settings tab'' of the ''Image Settings dialog box.''

== Source Sensitivity ==

'''Introduction'''

The 'Source sensitivity' function displays the sensitivity of the selected source in the current source model to activity in other brain regions. Sensitivity is defined as the fraction of power at the scanned brain location that is mapped onto the selected source.

To compute the source sensitivity, unit brain activity is modeled at different locations (probe source) throughout the brain. To this data, the current source model is applied to compute the source waveforms SCM of all modeled sources:

<math>\mathrm{S}_{\text{CM}} = \mathrm{L}_{\text{CM}}^{-1} \cdot \mathrm{L}_{\text{PS}}</math>


Here LCM-1 is the regularized inverse operator for the current model, and LPS is the leadfield of the regional probe source (dimension [Nx3] for EEG and [Nx2] for MEG, respectively, where N is the number of sensors). The source amplitude SSS of the selected source in the model is a 3x3 (MEG: 2x2) sub-matrix of SCM (if the selected source is a regional source) or a 1x3-matrix (MEG: 1x2) (if the selected source is a dipole). The root mean square of the singular values of SCM is defined as the source sensitivity.

The 3D source sensitivity image displays this value for all locations on a grid specified under '''Image/Settings'''. Grid density can be specified in the Image Settings.

'''Applying the Source Sensitivity Image'''

The Source Sensitivity image is evoked from the '''Image''' menu or by pressing the corresponding hot key (default: '''V''').

This function is enabled only when a solution with an active selected source is present in the Source Analysis window. The source sensitivity image then displays the sensitivity of the selected source to activity in other brain regions.

[[Image:SA 3Dimaging (59).gif]]

''Source Sensitivity image for the selected frontal source (green) in model ''''''High_Intensity_3RS.bsa'''''' in folder 'Examples/ERP_Auditory_Intensity'. The data displayed is the '100dB' condition in file ''''''All_Subjects_cc.fsg''''''. The selected source is sensitive to activity in the frontal brain region (yellow/white), while it is not influenced by activity in the vicinity of the left and right auditory cortex areas, which are modeled by the red and blue source in the model (transparent/gray).''

'''Notes:'''

* The sensitivity image is independent of the recorded sensor signals. It only depends on the current source model, the sensor configuration, the head model, and the regularization constant.
* If the regularization constant is set to zero, each source has a sensitivity of 100% to activity around its own location. With increasing regularization, the spatial filter becomes less focused, and the sensitivity of a source to activity at its location decreases.
* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image''' menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the '''Image''' menu.

{{BESAManualNav}}

Source Analysis 3D Imaging

2019-03-27T11:32:09Z

Jamie: /* Applying the Beamformer */

{{BESAInfobox
|title = Module information
|module = BESA Research Standard or higher
|version = 6.1 or higher
}}


== Overview ==

BESA Research features a set of new functions that provide 3D images that are displayed superimposed to the individual subject's anatomy. This chapter introduces these different images and describe their properties and applications.

The 3D images can be divided into three categories:

'''Volume images:'''

* '''The Multiple Source Beamformer (MSBF)''' is a tool for imaging brain activity. It is applied in the time-domain or time-frequency domain. The beamformer technique in time-frequency domain can image not only evoked, but also induced activity, which is not visible in time-domain averages of the data.
* '''Dynamic Imaging of Coherent Sources (DICS)''' can find coherence between any two pairs of voxels in the brain or between an external source and brain voxels. DICS requires time-frequency-transformed data and can find coherence for evoked and induced activity.

The following imaging methods provide an image of brain activity based on a distributed multiple source model:
* '''CLARA''' is an iterative application of LORETA images, focusing the obtained 3D image in each iteration step.
* '''LAURA '''uses a spatial weighting function that has the form of a local autoregressive function.
* '''LORETA''' has the 3D Laplacian operator implemented as spatial weighting prior.
* '''sLORETA''' is an unweighted minimum norm that is standardized by the resolution matrix.
* '''swLORETA '''is equivalent to sLORETA, except for an additional depth weighting.
* '''SSLOFO '''is an iterative application of standardized minimum norm images with consecutive shrinkage of the source space.
* A '''User-defined volume image''' allows to experiment with the different imaging techniques. It is possible to specify user-defined parameters for the family of distributed source images to create a new imaging technique.
* Bayesian source imaging: '''SESAME''' uses a semi-automated Bayesian approach to estimate the number of dipoles along with their parameters.

'''Surface image:'''

* The '''Surface Minimum Norm Image'''. If no individual MRI is available, the minimum norm image is displayed on a standard brain surface and computed for standard source locations. If available, an individual brain surface is used to construct the distributed source model and to image the brain activity.
* '''Cortical LORETA'''. Unlike classical LORETA, cortical LORETA is not computed in a 3D volume, but on the cortical surface.
* '''Cortical CLARA'''. Unlike classical CLARA, cortical CLARA is not computed in a 3D volume, but on the cortical surface.

'''Discrete model probing:'''

These images do not visualize source activity. Rather, they visualize properties of the currently applied discrete source model:
* The '''Multiple Source Probe Scan (MSPS)''' is a tool for the validation of a discrete multiple source model.
* The '''Source Sensitivity image''' displays the sensitivity of a selected source in the current discrete source model and is therefore data independent.

== Multiple Source Beamformer (MSBF) in the Time-frequency Domain ==

 
'''Short mathematical introduction'''

The BESA beamformer is a modified version of the linearly constrained minimum variance vector beamformer in the time-frequency domain as described in [https://dx.doi.org/10.1073/pnas.98.2.694 Gross et al., "Dynamic imaging of coherent sources: Studying neural interactions in the human brain", PNAS 98, 694-699, 2001]. It allows to image evoked and induced oscillatory activity in a user-defined time-frequency range, where time is taken relative to a triggered event.

The computation is based on a transformation of each channel's single trial data from the time domain into the time-frequency domain. This transformation is performed by the BESA Research Source Coherence module and leads to the complex spectral density Si (f,t), where i is the channel index and f and t denote frequency and time, respectively. Complex cross spectral density matrices C are computed for each trial:

<math>\mathrm{C}_{ij}\left( f,t \right) = \mathrm{S}_{i}\left( f,t \right) \cdot \mathrm{S}_{j}^{*}\left( f,t \right)</math>


The output power P of the beamformer for a specific brain region at location r is then computed by the following equation:

<math>\mathrm{P}\left( r \right) = \operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{-1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{-1}</math>


Here, Cr-1 is the inverse of the SVD-regularized average of Cij(f,t) over trials and the time-frequency range of interest; L is the leadfield matrix of the model containing a regional source at target location r and, optionally, additional sources whose interference with the target source is to be minimized; tr'[] is the trace of the [3×3] (MEG:[2×2]) submatrix of the bracketed expression that corresponds to the source at target location r.

In BESA Research, the output power P(r) is normalized with the output power in a reference time-frequency interval Pref(r). A value q ist defined as follows:

<math> \mathrm{q}\left( r \right) =
\begin{cases}
\sqrt{\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}(r)}} - 1 = \sqrt{\frac{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{\text{ref},r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}} - 1, & \text{for }\mathrm{P}(r) \geq \mathrm{P}_{\text{ref}}(r) \\

1 - \sqrt{\frac{\mathrm{P}_{\text{ref}}\left( r \right)}{\mathrm{P}\left( r \right)}} = 1 - \sqrt{\frac{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{\text{ref},r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}{\operatorname{tr^{'}}\left\lbrack \mathrm{L}^{T}\left( r \right) \cdot \mathrm{C}_{r}^{- 1} \cdot \mathrm{L}\left( r \right) \right\rbrack^{- 1}}}, & \text{for }\mathrm{P}(r) < \mathrm{P}_{\text{ref}}(r)
\end{cases} </math>


Pref can be computed either from the corresponding frequency range in the baseline of the same condition (i.e. the beamformer images event-related power increase or decrease) or from the corresponding time-frequency range in a control condition (i.e. the beamformer images differences between two conditions). The beamformer image is constructed from values q(r) computed for all locations on a grid specified in the '''General Settings tab'''. For MEG data, the innermost grid points within a sphere of approx. 12% of the head diameter are assigned interpolated rather than calculated values).
q-values are shown in %, where where q[%] = q*100. Alternatively to the definition above, q can also be displayed in units of dB:

<math>\mathrm{q}\left\lbrack \text{dB} \right\rbrack = 10 \cdot \log_{10}\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}</math>


A beamformer operator is designed to pass signals from the brain region of interest r without attenuation, while minimizing interference from activity in all other brain regions. Traditional single-source beamformers are known to mislocalize sources if several brain regions have highly correlated activity. Therefore, the BESA beamformer extends the traditional single-source beamformer in order to implicitly suppress activity from possibly correlated brain regions. This is achieved by using a multiple source beamformer calculation that contains not only the leadfields of the source at the location of interest r, but also those of possibly interfering sources. As a default, BESA Research uses a bilateral beamformer, where specifically contributions from the homologue source in the opposite hemisphere are taken into account (the matrix L thus being of dimension N×6 for EEG and N×4 for MEG, respectively, where N is the number of sensors). This allows for imaging of highly correlated bilateral activity in the two hemispheres that commonly occurs during processing of external stimuli.

In addition, the beamformer computation can take into account possibly correlated sources at arbitrary locations that are specified in the current solution. This is achieved by adding their leadfield vectors to the matrix L in the equation above.

'''Applying the Beamformer'''

This chapter illustrates the usage of the BESA beamformer. The displayed figures are generated using the file ''''Examples/Learn-by-Simulations/AC-Coherence/AC-Osc20.foc'''' (see BESA Tutorial 6: "''Time-frequency analysis and Source coherence''").

'''Starting the beamformer from the time-frequency window'''

The BESA beamformer is applied in the time-frequency domain and therefore requires the Source Coherence module to be enabled. The time-frequency beamformer is especially useful to image in- or decrease of induced oscillatory activity. Induced activity cannot be observed in the averaged data, but shows up as enhanced averaged power in the TSE (Temporal-Spectral Evolution) plot. For instructions on how to initiate a beamformer computation in the time-frequency window, please refer to Chapter '''[[Source_Coherence_How_to...#How_to_Start_the_Beamformer_from_the_Time-Frequency_Window|How to Create Beamformer Images]]'''.

After the beamformer computation has been initiated in the time-frequency window, the source analysis window opens with an enlarged 3D image of the q-value computed with a '''bilateral beamformer'''. The result is superimposed onto the MR image assigned to the data set (individual or standard).

[[Image:SA 3Dimaging (5).gif]]

''Beamformer image after starting the computation in the Time-Frequency window. A bilateral pair of sources in the auditory cortex accounts for the highly correlated oscillatory induced activity. Only the bilateral beamformer manages to separate these activities; a traditional single-source beamformer would merge the two sources into one image maximum in the head center instead.''

'''Multiple source beamformer in the Source Analysis window'''

The 3D imaging display is part of the source analysis window. If you press the '''Restore''' button at the right end of the title bar of the 3D window, the window appears at the bottom right of the source analysis window. In the channel box, the averaged (evoked) data of the selected condition is shown. When a control condition was selected, its average is appended to the average of the target condition.

[[Image:SA 3Dimaging (6).gif]]

''Source Analysis window with beamformer image. The two sources have been added using the '''''Switch to''''' '''''Maximum''''' and '''''Add Source '''''toolbar buttons (see below). Source waveforms are computed from the displayed averaged data. Therefore, they do not represent the activity displayed in the beamformer image, which in this simulation example is induced (i.e. not phase-locked to the trigger)!''

When starting the beamformer from the time-frequency window, a bilateral beamformer scan is performed. In the source analysis window, the beamformer computation can be repeated taking into account possibly correlated sources that are specified in the current solution. Interfering activities generated by all sources in the current solution that are in the 'On' state are specifically suppressed ('''they enter the matrix L in the beamformer calculation''', see Chapter ''Short mathematical description'' above). The computation can be started from the '''Image''' menu or from the '''Image selector button''' dropdown menu. The '''Image''' menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window.

[[Image:SA 3Dimaging (7).gif]]

''Multiple source beamformer image calculated in the presence of a source in the left hemisphere. A '''single''' source scan has been performed. The source set in the current solution accounts for the left-hemispheric q-maximum in the data. Accordingly, the beamformer scan reveals only the as yet unmodeled additional activity in the right hemisphere (note the radiological convention in the 3D image display).''

The beamformer scan can be performed with a '''single''' or a '''bilateral''' source scan. The default scan type depends on the current solution:
* When the beamformer is started from the Time-Frequency window, the Source Analysis window opens with a new solution and a '''bilateral''' beamformer scan is performed.
* When the beamformer is started within the Source Analysis window, the default is
** a scan with a '''single''' source in addition to the sources in the current solution, if at least one source is active.
** a '''bilateral''' scan if no source in the current solution is active.

The default scan type is the multiple source beamformer. The non-default scan type can be enforced using the corresponding ''Volume Image / Beamformer'' entry in the '''Image''' menu.

'''Inserting Sources out of the Beamformer Image'''

The beamformer image can be used to add sources to the current solution. A simple double-click anywhere in the 2D- or 3D-view will generate a non-oriented regional source at the corresponding location. However, a better and easier way to create sources at image maxima and minima is to use the toolbar buttons '''Switch to Maximum''' [[Image:SA 3Dimaging (8).gif]] and '''Add Source''' [[Image:SA 3Dimaging (9).gif]].

Use the '''Switch to Maximum''' button to place the red crosshair of the 3D window onto a local image maximum or minimum. Hitting the '''Add Source''' button creates a regional source at the location of the crosshair and therefore ensures the exact placement of the source at the image extremum. Moreover, the '''Add Source''' button generates an oriented regional source. BESA Research automatically estimates the source orientation that contributes most to the power in the target time-frequency interval (or the reference time-frequency interval, if its power is larger than that in the target interval). The accuracy of this orientation estimate depends largely on the noise content of the data. The smaller the signal-to-noise ratio of the data, the lower is the accuracy of the orientation estimate. '''This feature allows to use the beamformer as a tool to create a source montage for source coherence analysis, where it is of advantage to work with oriented sources'''.

'''Notes:'''

* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image '''menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the''' Image''' menu.
* For scaling options, use the [[Image:SA 3Dimaging (10).gif]] and [[Image:SA 3Dimaging (11).gif]] '''Image Scale toolbar''' buttons.
* Parameters used for the beamformer calculations can be set in the '''Standard Volumes''' of the ''Image Settings dialog box.''

== Dynamic Imaging of Coherent Sources (DICS) ==

 
'''Short mathematical introduction'''

Dynamic Imaging of Coherent Sources (DICS) is a sophisticated method for imaging cortico-cortical coherence in the brain, or coherence between an external reference (e.g. EMG channel) and cortical structures. DICS can be applied to localize evoked as well as induced coherent cortical activity in a user-defined time-frequency range.

DICS was implemented in BESA closely following [https://dx.doi.org/10.1073/pnas.98.2.694 Gross et al., "Dynamic imaging of coherent sources: Studying neural interactions in the human brain", PNAS 98, 694-699, 2001].

The computation is based on a transformation of each channel's single trial data from the time domain into the frequency domain. This transformation is performed by the BESA Research Coherence module and results in the complex spectral density matrix that is used for constructing the spatial filter similar to beamforming.

DICS computation yields a 3-D image, each voxel being assigned a coherence value. Coherence values can be described as a neural activity index and do not have a unit. The neural activity index contrasts coherence in a target time-frequency bin with coherence of the same time-frequency bin in a baseline.

'''DICS for cortico-cortical coherence is computed as follows:'''

Let L(r) be the leadfield in voxel r in the brain and C the complex cross-spectral density matrix. The spatial filter W(r) for the voxel r in the head is defined as follows:

<math>W\left( r \right) = \left\lbrack L^{T}\left( r \right) \cdot C^{- 1} \cdot L\left( r \right) \right\rbrack^{- 1} \cdot L^{T}(r) \cdot C^{- 1}</math>


The cross-spectrum between two locations (voxels) r1 and r2 in the head are calculated with the following equation:

<math>C_{s}\left( r_{1},r_{2} \right) = W\left( r_{1} \right) \cdot C \cdot W^{*T}\left( r_{2} \right),</math>


where <nowiki>*T</nowiki> means the transposed complex conjugate of a matrix. The cross-spectral density can then be calculated from the cross spectrum as follows:

<math>c_{s}\left( r_{1},r_{2} \right) = \lambda_{1}\left\{ C_{s}\left( r_{1},r_{2} \right) \right\},</math>


where λ1{} indicates the largest singular value of the cross spectrum. Once the cross spectral density is estimated, the connectivity¹(CON) between the two brain regions r1 and r2 are calculated as follows:

<math>\text{CON}\left( r_{1},r_{2} \right) = \frac{c_{s}^{\text{sig}}\left( r_{1},r_{2} \right) - c_{s}^{\text{bl}}(r_{1},r_{2})}{c_{s}^{\text{sig}}\left( r_{1},r_{2} \right) + c_{s}^{\text{bl}}(r_{1},r_{2})},</math>


where cssig is the cross-spectral density for the signal of interest between the two brain regions r1 and r2, and csbl is the corresponding cross spectral density for the baseline or the control condition, respectively. In the case DICS is computed with a cortical reference, r1 is the reference region (voxel) and remains constant while r2 scans all the grid points within the brain sequentially. In that way, the connectivity between the reference brain region and all other brain regions is estimated. The value of CON(r1, r2) falls in the interval [-1 1]. If the cross-spectral density for the baseline is 0 the connectivity value will be 1. If the cross-spectral density for the signal is 0 the connectivity value will be -1.

¹ Here, the term connectivity is used rather than coherence, as strictly speaking the coherence equation is defined slightly differently. For simplicity reasons the rest of the tutorial uses the term coherence.

'''DICS for cortico-muscular coherence is computed as follows:'''

When using an external reference, the equation for coherence calculation is slightly different compared to the equation for cortico-cortical coherence. First of all, the cross-spectral density matrix is not only computed for the MEG/EEG channels, but the external reference channel is added. This resulting matrix is Call. In this case, the cross-spectral density between the reference signal and all other MEG/EEG

channels is called cref. It is only one column of Call. Hence, the cross-spectrum in voxel r is calculated with the following equation:

<math>C_{s}\left( r \right) = W\left( r \right) \cdot c_{\text{ref}}</math>


and the corresponding cross-spectral density is calculated as the sum of squares of Cs:

<math>c_{s}\left( r \right) = \sum_{i = 1}^{n}{C_{s}\left( r \right)_{i}^{2}},</math>


where n is 2 for MEG and 3 for EEG. This equation can also be described as the squared Euclidean norm of the cross-spectrum:

<math>c_{s}\left( r \right) = \left\| C_{s} \right\|^{2},</math>


The power in voxel r is calculated as in the cortico-cortical case:

<math>p\left( r \right) = \lambda_{1}\left\{ C_{s}(r,r) \right\}.</math>


At last, coherence between the external reference and cortical activity is calculated with the equation:

<math>\text{CON}\left( r \right) = \frac{c_{s}(r)}{p\left( r \right) \cdot C_{\text{all}}(k,k)},</math>


where Call(k, k) is the (k,k)-th diagonal element of the matrix Call.

DICS is particularly useful, if coherence is to be calculated without an a-priory source model (in contrast to source coherence based on pre-defined source montages). However, the recommended analysis strategy for DICS is to use a brain source as a starting point for coherence calculation that is known to contribute to the EEG/MEG signal of interest. For example, one might first run a beamformer on the time-frequency range of interest and use the voxel with the strongest oscillatory activity as a starting point for DICS. The resulting coherence image will again lead to several maxima (ordered by magnitude), which in turn can serve as starting points for DICS calculation. This way, it is possible to detect even weak sources that show coherent activity in the given time-frequency range.

The other significant application for DICS is estimating coherence between an external source and voxels in the brain. For example, an external source can be muscle activity recoded by an electrode placed over the according peripheral region. This way, the direct relationship between muscle activity and brain activation can be measured.

'''Starting DICS computation from the Time-Frequency Window'''

DICS is particularly useful, if coherence in a user-defined time-frequency bin (evoked or induced) is to be calculated between any two brain regions or between an external reference and the brain. DICS runs only on time-frequency decomposed data, so time-frequency analysis needs to be run before starting DICS computation.

To start the DICS computation, left-drag a window over a selected time-frequency bin in the Time-Frequency Window. Right-click and select “Image”. A dialogue will open (see fig. 1) prompting you to specify time and frequency settings as well as the baseline period. It is recommended to use a baseline period of equal length as the data period of interest. Make sure to select “DICS” in the top row and press “'''Go'''”.

[[Image:SA 3Dimaging (21).gif|450px|thumb|c|none|Fig. 1: Time and frequency settings for DICS and MSBF]]

Next, a window will appear allowing you to specify the reference source for coherence calculation (see fig. 2). It is possible to select a channel (e.g. EMG) or a brain source. If a brain source is chosen and no source analysis was computed beforehand, the option “Use current cross-hair position” must be chosen. In case discrete source analysis was computed previously, the selected source can be chosen as the reference for DICS. Please note that DICS can be re-computed with any cross-hair or source position at a later stage.

[[Image:SA 3Dimaging (1).jpg|400px|thumb|c|none|Fig. 2: Possible options for choosing the reference]]

Confirming with “'''OK'''” will start computation of coherence between the selected channel/voxel and all other brain voxels. In case DICS is computed for a reference source in the brain, it can be advantageous to run a beamforming analysis in the selected time-frequency window first and use one of the beamforming maxima as reference for DICS. Fig. 3 shows an example for DICS calculation.

[[Image:SA 3Dimaging (22).gif|500px|thumb|c|none|Fig. 3: Coherence between left-hemispheric auditory areas and the selected voxel in the right auditory cortex.]]

Coherence values range between -1 and 1. If coherence in the signal is much larger than coherence in the baseline (control condition) then the DICS value is going to approach 1. Contrary, if coherence in the baseline is much larger than coherence in the signal, then the DICS value is going to approach -1. At last, if coherence in the signal is equal to coherence in the baseline, then the DICS value is 0.

In case DICS is to be re-computed with a different reference, simply mark the desired reference position by placing the cross-hair in the anatomical view and select “DICS” in the middle panel of the source analysis window (see Fig. 4). In case an external reference is to be selected, click on “DICS” in the middle panel to bring up the DICS dialogue (see. Fig. 2) and select the desired channel. Please note that DICS computation will only be available after running time-frequency analysis.

[[Image:SA 3Dimaging (23).gif|700px|thumb|c|none|Fig. 4: Integration of DICS in the Source Analysis window]]

== Multiple Source Beamformer (MSBF) in the Time Domain ==

===Short mathematical introduction===

Beamforming approach can be also applied in the time domain data. This approach was introduced as linearly constrained minimum variance (LCMV) beamformer (Van Veen et al., 1997). It allows to image evoked activity in a user-defined time range, where time is taken relative to a triggered event, and to estimate source waveforms using the calculated spatial weight at locations of interest. For an implementation of the beamformer in the time domain, data covariance matrices are required, while complex cross spectral density matrices are used for the beamformer approaches in the time-frequency domain as described in the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section.

The bilateral beamformer introduced in the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section is also implemented for the time-domain beamformer to take into account contributions from the homologue source in the opposite. This allows for imaging of highly correlated bilateral activity in the two hemispheres that commonly occurs during processing of external stimuli. In addition, the beamformer computation can take into account possibly correlated sources at arbitrary locations.
The beamformer spatial weight W(r) for the voxel r in the brain is defined as follows (Van Veen et al., 1997):

[[File:MSBF1.png]]

where '''C-1''' is the inversed regularized average of covariance matrix over trials, '''L''' is the leadfield matrix of the model containing a regional source at target location r and optionally
additional sources whose interference with the target source is to be minimized. The beamformer spatial weight '''W'''(r) can be applied to the measured data to estimate source
waveform at a location r (beamformer virtual sensor):

[[File:MSBF2.png]]

where '''S'''(r,t) represents the estimated source waveform and '''M'''(t) represents measured EEG or MEG signals.
The output power P of the beamformer for a specific brain region at location r is computed by the following equation:

[[File:MSBF3.png]]

where tr’[ ] is the trace of the [3×3] (MEG: [2×2]) submatrix of the bracketed expression that corresponds to the source at target location r.
Beamformer can suppress noise sources that are correlated across sensors. However, uncorrelated noise will be amplified in a spatially non-uniform manner, with increasing
distortion with increasing distance from the sensors (Van Veen et al., 1997; Sekihara et al., 2001). For this reason, estimated source power should be normalized by a noise power.
In BESA Research, the output power P(r) is normalized with the output power in a baseline interval or with the output power of a uncorrelated noise: P(r) / Pref (r).
The time-domain beamformer image is constructed from values q(r) computed for all locations on a grid specified in the '''General Settings''' tab. A value q(r) is defined as described in
the ''[[#See also|Multiple Source Beamformer (MSBF) in the Time-frequency Domain]]'' section with data covariance matrices instead of cross-spectral density matrices.

===Applying the Beamformer===

This chapter illustrates the usage of the BESA beamformer in the time domain. The displayed figures are generated using the file ‘Examples/ERP-Auditory-Intensity/S1.cnt’.

'''Starting the time-domain beamformer from the Average tap of the Paradigm dialog box'''

The time-domain beamformer is needed data covariance matrices and therefore requires the ERP module to be enabled. After the beamformer computation has been initiated in the
'''Average tap of the Paradigm dialog box''', the source analysis window opens with an enlarged 3D image of the q-value computed with a bilateral beamformer. The result is
superimposed onto the MR image assigned to the data set (individual or standard).

[[File:MSBF44.png]]

''Beamformer image for auditory evoked data after starting the computation in the '''Average tap of the Paradigm dialog box'''. The bilateral beamformer manages to separate the
activities in auditory areas, while a traditional single-source beamformer would merge the two sources into one image maximum in the head center instead.''

'''Multiple-source beamformer in the Source Analysis window'''

The 3D imaging display is part of the source analysis window. In the Channel box, the averaged (evoked) data of the selected condition is shown. Selected covariance intervals in
the ERP module can be checked in the Channel box. The red, gray, and blue rectangles indicate signal, baseline, and common interval, respectively.

[[File:MSBF55.png]]

''Source Analysis window with beamformer image. The two beamformer virtual sensors have been added using the Switch to Maximum and Add Source toolbar buttons (see below).
Source waveforms are computed using the beamformer spatial weights and the displayed averaged data (the noise normalized weights (5% noise) option was used to compute the
beamformer image).''

When starting the beamformer from the '''Average tap of the Paradigm dialog box''', the bilateral beamformer scan is performed. In the source analysis window, the beamformer computation can be repeated taking into account possibly correlated sources that are specified in the current solution. Interfering activities generated by all sources in the current solution that are in the 'On' state are specifically suppressed (they enter the leadfield matrix L in the beamformer calculation). The computation can be started from the '''Image''' menu or from the Image selector button [[File:MSBF_Button.png|22px|Image: 22 pixels]] dropdown menu. The Image menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window.

[[File:MSBF66.png]]

''Multiple-source beamformer image calculated in the presence of a source in the left hemisphere. A single-source scan has been performed instead of a bilateral beamforemr. The
source set in the current solution accounts for the left-hemispheric q-maximum in the data. Accordingly, the beamformer scan reveals only the as yet unmodeled additional activity in
the right hemisphere (note the radiological convention in the 3D image display). The source waveform of the beamformer virtual sensor in the left hemisphere is not shown since the
location (blue square in the figure) is not considered for the multiple-source beamformer.''

The beamformer scan can be performed with a single or a bilateral source scan. The default scan type depends on the current solution:
When the beamformer is started from the '''Average tap of the Paradigm dialog box''' the Source Analysis window opens with a new solution and a bilateral beamformer scan is
performed.
When the beamformer is started within the Source Analysis window, the default is:

* a scan with a single source in addition to the sources in the current solution, if at least one source is active.
* a bilateral scan if no source in the current solution is active.
* a scan with a single source when scalar-type beamformer is selected in the '''beamformer option dialog box'''.

The default scan type is the multiple source beamformer. The non-default scan type can be enforced using the corresponding Volume Image / Beamformer entry in the Image main
menu or in the beamformer option dialog box (only for the time-domain beamformer).

===Inserting Sources as Beamformer Virtual Sensor out of the Beamformer Image===

This is similar to the inserting sources out of the beamformer image in Multiple Source Beamformer (MSBF) in the Time-frequency Domain section.
The beamformer image can be used to add beamformer virtual sensors to the current solution. A simple double-click anywhere in the 3D view (not in the 2D view) will generate a
source at the corresponding location. A better and easier way to create sources at image maxima and minima is to use the toolbar buttons Switch to Maximum and Add Source

This feature allows to use the beamformer as a tool to create a source montage for source coherence analysis. A source montage file (*.mtg) for beamformer virtual sensors can
be saved using File \ Save Source Montage As… entry.

The time-domain beamformer image can be also used to add regional or dipole sources to the current solution. Press N key when there is no source in the current source array or
there is more than one beamformer virtual sensor. To create a new source array for beamformer virtual sensor, press N key when there is more than one regional or dipole source in
the current source array.

===Notes===

* You can hide or re-display the last computed image by selecting Hide Image entry in the Image menu.
* The current image can be exported to ASCII, ANALYZE, or BrainVoyager (vmp) format from the Image menu.
* For scaling options, use the and Image Scale toolbar buttons.
* Parameters used for the beamformer calculations can be set in the Standard Volume tab of the Image Settings dialog box.
* Note that Model, Residual, Order, and Residual variance are not shown for the beamformer virtual sensor type sources.

===References===

* Sekihara, K., Nagarajan, S. S., Poeppel, D., Marantz, A., & Miyashita, Y. (2001). Reconstructing spatio-temporal activities of neural sources using an MEG vector beamformer technique. IEEE Transactions on Biomedical Engineering, 48(7), 760–771.

* Van Veen, B. D., Van Drongelen, W., Yuchtman, M., & Suzuki, A. (1997). Localization of brain electrical activity via linearly constrained minimum variance spatial filtering. IEEE Transactions on Biomedical Engineering, 44(9), 867–880

== CLARA ==

CLARA ('Classical LORETA Analysis Recursively Applied') is an iterative application of weighted LORETA images with a reduced source space in each iteration.

In an initialization step, a LORETA image is calculated. Then in each iteration the following steps are performed:

# The obtained image is spatially smoothed (this step is left out in the first iteration).
# All grid points with amplitudes below a threshold of 1% of the maximum activity are set to zero, thus being effectively eliminated from the source space in the following step.
# The resulting image defines a spatial weighting term (for each voxel the corresponding image amplitude).
# A LORETA image is computed with an additional spatial weighting term for each voxel as computed in step 3. By the default settings in BESA Research, the regularization values used in the iteration steps are slightly higher than that of the initialization LORETA image.

The procedure stops after 2 iterations, and the image computed in the last iteration is displayed. Please note that you can change all parameters by creating a user-defined volume image.

The advantage of CLARA over non-focusing distributed imaging methods is visualized by the figure below. Both images are computed from the N100 response in an auditory oddball experiment (file '''Oddball.fsg''' in subfolder ''fMRI+EEG-RT-Experiment'' of the ''Examples'' folder). The CLARA image is much more focal than the sLORETA image, making it easier to determine the location of the image maxima.

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (24).gif|thumb|350px|sLORETA image]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (25).gif|thumb|350px|CLARA image]] </li>
</ul></div>

'''Notes:'''

* Starting CLARA: CLARA can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter ''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]'' for important information on regularization of distributed inverses.

== LAURA ==

LAURA (Local Auto Regressive Average) belongs to the distributed inverse method of the family of weighted minimum norm methods ([https://doi.org/10.1023/A:1012944913650 Grave de Peralta Menendeza et al., "Noninvasive Localization of Electromagnetic Epileptic Activity. I. Method Descriptions and Simulations", BrainTopography 14(2), 131-137, 2001]). LAURA uses a spatial weighting function that includes depth weighting and that term has the form of a local autoregressive function.

The source activity is estimated by applying the general formula for a weighted minimum norm:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T}\left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings.''

In LAURA, V contains both a depth weighting term W and a representation of a local autoregressive function A. V is computed as:

<math>\mathrm{V} = \left( \mathrm{U}^{T} \cdot \mathrm{U} \right)^{-1}</math>


Where

<math>\mathrm{U} = \left( \mathrm{W} \cdot \mathrm{A} \right) \otimes \mathrm{I}_{3}</math>


Here, <math>\otimes</math> denotes the Kronecker product. I3 is the [3×3] identity matrix. W is an [s×s] diagonal matrix (with s the number of source locations on the grid), where each diagonal element is the inverse of the maximum singular value of the corresponding regional source's leadfields. The formula for the diagonal components Aii and the off-diagonal components Aik are as follows:

<math>\mathrm{A}_{ii} = \frac{26}{\mathrm{N}_{i}}\sum_{k \subset V_{i}}^{}\frac{1}{\mathrm{d}_{ik}^{2}}</math>


<math>
\mathrm{A}_{ik} =
\begin{cases}
- 1/\operatorname{dist}\left( i,k \right)^{2}, & \text{if } k \subset V_{i} \\
0, & \text{otherwise}
\end{cases}
</math>


Here, Vi is the vicinity around grid point i that includes the 26 direct neighbors.

The LAURA image in BESA Research displays the norm of the 3 components of S at each location r. Using the menu function ''Image / Export Image As... ''you have the option to save this norm of S or alternatively all components separately to disk.

'''Notes:'''

* '''Grid spacing:''' Due to memory limitations, LAURA images require a grid spacing of 7 mm or more.
* '''Computation time:''' Computation speed during the first LAURA image calculation depends on the grid spacing (computation is faster with larger grid spacing). After the first computation of a LAURA image, a '''*.laura''' file is stored in the data folder, containing intermediate results of the LAURA inverse. This file is used during all subsequent LAURA image computations. Thereby, the time needed to obtain the image is substantially reduced.
* '''MEG:''' In the case of MEG data, an additional constraint is implemented in the LAURA algorithm that prevents solutions from containing radial source currents (compare Pascual-Marqui, ISBET Newsletter 1995, 22-29). In MEG, an additional source space regularization is necessary in the inverse matrix operation required compute V
* '''Starting LAURA:''' LAURA can be started from the''' Image''' menu or from the '''Image Selection''' button.
* '''Regularization:''' Please refer to Chapter'' “Regularization of distributed volume images” ''for important information on regularization of distributed inverses.

== LORETA ==

LORETA ("Low Resolution Electromagnetic Tomography") is a distributed inverse method of the family of ''weighted minimum norm'' methods. LORETA was suggested by R.D. Pascual-Marqui (International Journal of Psychophysiology. 1994, 18:49-65). LORETA is characterized by a smoothness constraint, represented by a discrete 3D Laplacian.

The source activity is estimated by applying the general formula for a weighted minimum norm:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T}\left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings.''

In LORETA, V contains both a depth weighting term and a representation of the 3D Laplacian matrix. V is computed as:

<math>\mathrm{V} = \left( \mathrm{U}^{T} \cdot \mathrm{U} \right)^{- 1}</math>


where

<math>\mathrm{U} = \left( \mathrm{W} \cdot \mathrm{A} \right) \otimes \mathrm{I}_{3}</math>


Here, <math>\otimes</math> denotes the Kronecker product. I3 is the [3x3] identity matrix. W is an [sxs] diagonal matrix (with s the number of source locations on the grid), where each diagonal element is the inverse of the maximum singular value of the corresponding regional source's leadfields. A contains the 3D Laplacian and is computed as

<math>\mathrm{A} = \mathrm{Y} - \mathrm{I}_{s}</math>


with Is the [sxs] identity matrix, where s is the number of sources (= three times the number of grid points) and

<math>\mathrm{Y} = \frac{1}{2}\left\{ \mathrm{I}_{s} + \left\lbrack \operatorname{diag}\left( \mathrm{Z} \cdot \left\lbrack 111 \ldots 1 \right\rbrack^{T} \right) \right\rbrack^{- 1} \right\} \cdot \mathrm{Z}</math>


where

<math>
\mathrm{Z}_{ik} =
\begin{cases}
1/6, & \text{if } \operatorname{dist}\left( i,k \right) = 1 \text{ grid point} \\
0, & \text{otherwise}
\end{cases}
</math>


The LORETA image in BESA Research displays the norm of the 3 components of S at each location r. Using the menu function ''Image / Export Image As... ''you have the option to save this norm of S or alternatively all components separately to disk.

'''Notes:'''
* '''Grid spacing:''' Due to memory limitations, LORETA images require a grid spacing of 5 mm or more.
* '''Computation time:''' Computation speed during the first LORETA image calculation depends on the grid spacing (computation is faster with larger grid spacing). After the first computation of a LORETA image, a '''<nowiki>*.loreta</nowiki>''' file is stored in the data folder, containing intermediate results of the LORETA inverse. This file is used during all subsequent LORETA image computations. Thereby, the time needed to obtain the image is substantially reduced.
* '''MEG''': In the case of MEG data, an additional constraint is implemented in the LORETA algorithm that prevents solutions from containing radial source currents (Pascual-Marqui, ISBET Newsletter 1995, 22-29). In MEG, an additional source space regularization is necessary in the inverse matrix operation required compute V.
* '''Starting LORETA:''' LORETA can be started from the''' Image''' menu or from the '''Image Selection '''button.
* '''Regularization:''' Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed source models.

== sLORETA ==

This distributed inverse method consists of a ''standardized, unweighted minimum norm''. The method was originally suggested by R.D. Pascual-Marqui (Methods & Findings in Experimental & Clinical Pharmacology 2002, 24D:5-12) Starting point is an unweighted minimum norm computation:

<math>\mathrm{S}_{\text{MN}}\left( t \right) = \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{L}^{T} \right)^{- 1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings''.

This minimum norm estimate is now standardized to produce the sLORETA activity at a certain brain location r:

<math>\mathrm{S}_{\text{sLORETA}, r} = \mathrm{R}_{rr}^{-1/2} \cdot \mathrm{S}_{\text{MN},r}</math>


SsMN,r is the [3x1] (MEG: [2x1]) minimum norm estimate of the 3 (MEG: 2) dipoles at location r. Rrr is the [3x3] (MEG: [2x2]) diagonal block of the resolution matrix R that corresponds to the source components at the target location r. The resolution matrix is defined as:

<math>\mathrm{R} = \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{L}^{T} + \lambda \cdot \mathrm{I} \right)^{-1} \cdot \mathrm{L}</math>


The sLORETA image in BESA Research displays the norm of SsLORETA, r at each location r. Using the menu function ''Image / Export Image As...'' you have the option to save this norm of SsLORETA, r or alternatively all components separately to disk.

'''Notes:'''

* sLORETA can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== swLORETA ==

This distributed inverse method is a ''standardized, depth-weighted minimum norm'' (E. Palmero-Soler et al 2007 Phys. Med. Biol. 52 1783-1800). It differs from sLORETA only by an additional depth weighting.

Starting point is a depth-weighted minimum norm computation:

<math>\mathrm{S}_{\text{MN}}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. The term in parentheses is generally regularized. Regularization parameters can be specified in the ''Image Settings''.

V is the diagonal depth weighting matrix. For s grid locations, V is of dimension [3s x 3s] (MEG: [2s x 2s]). Each diagonal element of V is the inverse of the first singular value of the leadfield of the corresponding regional source. Hence, the first 3 (MEG: 2) diagonal elements equal the inverse of the largest eigenvalue of the leadfield matrix of regional source 1, and so on.

This minimum norm estimate is now standardized to produce the swLORETA activity at a certain brain location r:

<math>\mathrm{S}_{\text{swLORETA},r} = \mathrm{R}_{rr}^{-1/2} \cdot \mathrm{S}_{\text{MN},r}</math>


SsMN,r is the [3x1] (MEG: [2x1]) depth-weighted minimum norm estimate of the regional source at location r. Rrr is the [3x3] (MEG: [2x2]) diagonal block of the resolution matrix R that corresponds to the source components at the target location r. The resolution matrix is defined as:

<math>\mathrm{R} = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} + \lambda \cdot \mathrm{I} \right)^{-1} \cdot \mathrm{L}</math>


The swLORETA image in BESA Research displays the norm of SswLORETA, r at each location r. Using the menu function ''Image / Export Image As...'' you have the option to save this norm of SswLORETA, r or alternatively all components separately to disk.

'''Notes:'''

* sLORETA can be started from the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== sSLOFO ==

SSLOFO (standardized shrinking LORETA-FOCUSS) is an iterative application of weighted distributed source images with a reduced source space in each iteration ([https://dx.doi.org/10.1109/TBME.2005.855720 Liu et al., "Standardized shrinking LORETA-FOCUSS (SSLOFO): a new algorithm for spatio-temporal EEG source reconstruction", IEEE Transactions on Biomedical Engineering 52(10), 1681-1691, 2005]).

In an initialization step, an [[#sLORETA | sLORETA]] image is calculated. Then in each iteration the following steps are performed:

# A weighted minimum norm solution is computed according to the formula <math display="inline">\mathrm{S} = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}</math> . Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D is the data at the time point under consideration. V is a diagonal spatial weighting matrix that is computed in the previous iteration step. In the first iteration, the elements of V contain the magnitudes of the initially computed LORETA image.
# Standardization of this weighted minimum norm image is performed with the resolution matrix as in [[#sLORETA | sLORETA]].
# The obtained standardized weighted minimum norm image is being smoothed to get Ssmooth.
# All voxels with amplitudes below a threshold of 1% of the maximum activity get a weight of zero in the next iteration step, thus being effectively eliminated from the source space in the next iteration step.
# For all other voxels, compute the elements of the spatial weighting matrix V to be used in the next iteration as follows: <math display="inline">\mathrm{V}_{ii,\text{next iteration}} = \frac{1}{\left\| \mathrm{L}_{i} \right\|} \cdot \mathrm{S}_{ii,\text{smooth}} \cdot \mathrm{V}_{ii,\text{current iteration}}</math>



The procedure stops after 3 iterations. Please note that you can change all parameters by creating a [[#User-Defined Volume Image | user-defined volume image]].

'''Notes:'''
* '''Starting sSLOFO''': sSLOFO can be started from the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter ''[[#Regularization of distributed volume images | Regularization of distributed volume images]]'' for important information on regularization of distributed inverses.

== User-Defined Volume Image ==

In addition to the predefined 3D imaging methods in BESA Research, it is possible to create user-defined imaging methods based on the general formula for distributed inverses:

<math>\mathrm{S}\left( t \right) = \mathrm{V} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{V} \cdot \mathrm{L}^{T} \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed source model with regional sources distributed on a regular cubic grid. D(t) is the data at time point t. Custom-defined parameters are:* The spatial weighting matrix V: This may include depth weighting, image weighting, or cross-voxel weighting with a 3D Laplacian (as in LORETA) or an autoregressive function (as in LAURA).

* Regularization: The term in parentheses is generally regularized. Note that regularization has a strong effect on the obtained results. Please refer to chapter “''Regularization of Distributed Volume Images” ''for more information.
* Standardization: Optionally, the result of the distributed inverse can be standardized with the resolution matrix (as in sLORETA).
* Iterations: Inverse computations can be applied iteratively. Each iteration is weighted with the image obtained in the previous iteration.

All parameters for the user-defined volume image are specified in the User-Defined Volume Tab of the Image Settings dialog box. Please refer to chapter “''User-Defined Volume Tab”'' for details.

'''Notes:'''
* Starting the user-defined volume image: the image calculation can be started from the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''Regularization of distributed volume images”'' for important information on regularization of distributed inverses.

== Regularization of distributed volume images ==

Distributed source images require the inversion of a term of the form L V LT. This term is generally regularized before its inversion. In BESA Research, selection can be made between two different regularization approaches (parameters are defined in the ''Image Settings dialog box''):

* '''Tikhonov regularization''': In Tikhonov regularization, the term L V LT is inverted as (L V LT +λ I)-1. Here, l is the regularization constant, and I is the identity matrix.
* One way of determining the optimum regularization constant is by minimizing the ''generalized cross'' ''validation error'' (CVE).
* Alternatively, the regularization constant can be specified manually as a percentage of the trace of the matrix L V LT.
* '''TSVD''': In the truncated singular value decomposition (TSVD) approach, an SVD decomposition of L V LT is computed as  L V LT = U S UT, where the diagonal matrix S contains the singular values. All singular values smaller than the specified percentage of the maximum singular values are set to zero. The inverse is computed as U S-1 UT, where the diagonal elements of S-1 are the inverse of the corresponding non-zero diagonal elements of S.

Regularization has a critical effect on the obtained distributed source images. The results may differ completely with different choices of the regularization parameter (see examples below). Therefore, it is important to evaluate the generated image critically with respect to the regularization constant, and to keep in mind the uncertainties resulting from this fact when interpreting the results. The default setting in BESA Research is a TSVD regularization with a 0.03% threshold. However, this value might need to be adjusted to the specific data set at hand.

The following example illustrates the influence of the regularization parameter on the obtained images. The data used here is condition '''St-Cor of dataset Examples \ TFC-Error-Related-Negativity \ Correct+Error.fsg''' at 176 ms following the visual stimulus. Discrete dipole analysis reveals the main activity in the left and right lateral visual cortex at this latency.

[[Image:SA 3Dimaging (42).gif]]

''Discrete source model at 176 ms: Main activity in the left and right lateral visual cortex, no visual midline activity.''

LORETA images computed at this latency depend critically on the choice of the regularization constant. The following 3D images are created with TSVD regularization with SVD cutoffs of 0.1%, 0.005%, and 0.0001%, respectively. The volume grid size was 9 mm. The example demonstrates the dramatic effect of regularization and demonstrates the typical tradeoff between too strong regularization (leading to too smeared 3D images that tend to show blurred maxima) and too small regularization (resulting in too superficial 3D images with multiple maxima).

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (43).gif|thumb|350px|'''SVD cutoff 0.1%''': Regularization too strong. No separation between sources, mislocalization towards the middle of the brain.]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (44).gif|thumb|350px|'''SVD cutoff 0.005%''': Appropriate regularization. Separation of the bilateral activities. Location in agreement with the discrete multiple source model.]] </li>
<li style="display: inline-block;"> [[File:SA 3Dimaging (45).gif|thumb|350px|'''SVD cutoff 0.0001%''': Too small regularization. Mislocalization, too superficial 3D image. ]] </li>
</ul></div>

The automatic determination of the regularization constant using the CVE approach does not necessarily result in the optimum regularization parameter either. In this example, the unscaled CVE approach rather resembles the TSVD image with a cutoff of 0.0001%, i.e. regularization is too small. Therefore, it is advisable to compare different settings of the regularization parameter and make the final choice based on the above-mentioned considerations.

== Cortical LORETA ==

Cortical LORETA is principally the same technique as LORETA, however, Cortical LORETA is not computed in a 3D volume, but on the cortical surface.

The cortical reconstruction in BESA Research fed from BESA MRI is a closed 2D surface with no boundaries and a very close approximation of the actual cortical form. It consists of an irregular triangulated grid.

The Laplace operator that is used for identifying a smooth solution in a three-dimensional space is exchanged with a Laplace operator that runs on the two-dimensional cortical surface.

There is a wide variety of 2D Laplace operators with different characteristics. The general form of the discrete Laplace operator is

<math>\Delta f\left( p_{i} \right) = \frac{1}{d_{i}}\sum_{j \in N(i)}^{}{w_{ij}\left\lbrack f\left( p_{i} \right) - f\left( p_{j} \right) \right\rbrack},</math>


where '''pi''' is the '''i-th''' node of the triangular mesh, '''f(pi) '''is the value of a function f defined on the cortical mesh at the node '''pi''', '''wij''' is the weight for the connection between the nodes '''pi''' and '''pj''' and '''di''' is a normalization factor for the '''i-th''' row of the operator. Furthermore, '''N(i)''' is the set of indices corresponding to the direct (also called "1-ring") neighbors of '''pi'''.

BESA offers the choice of three Laplace operators with slightly different characteristics.

* '''Unweighted Graph Laplacian''': This is the simplest operator. It takes into account only the adjacency of the nodes and not the geometry of the mesh:

<math>
w_{ij} =
\begin{cases}
1, & \text{if } p_{i} \text{ and } p_{j} \text{ are connected by an edge} \\
0, & \text{otherwise}
\end{cases}
</math>

<math>d_{i} = 1</math>


[[Image:SA 3Dimaging (4).jpg |450px]]

* '''Weighted Graph Laplacian:''' This operator is similar to the unweighted graph Laplacian but with different weights for the different connections. The connections between nearby nodes get larger weights than the connections between farther nodes:

<math>w_{ij} = \frac{1}{\operatorname{dist}\left( p_{i},p_{j} \right)}</math>

<math>d_{i} = \sum_{j \in N(i)}^{} {\operatorname{dist}\left(p_{i}, p_{j} \right)}</math>


where '''dist''' ('''pi''' , '''pj''') is the distance between the nodes '''pi '''and '''pj'''.

[[Image:SA 3Dimaging (6).jpg|450px]]

* '''Geometric Laplacian with mixed area weights''': This operator takes into account the angles in the corresponding triangles into account as well as the area around the nodes in order to determine the connection weights:

<math>w_{ij} = \frac{\cot\left( \alpha_{ij} \right) + \cot\left( \beta_{ij} \right)}{2}</math>

<math>d_{i} = A_{\text{mixed}}</math>


where '''αij''' and '''βij''' denote the two angles opposite to the edge ('''i , j''') and '''Amixed '''is either the Voronoi area, or 1/2 of the triangle area or 1/4 of the triangle area depending on the type of the triangle.

[[Image:SA 3Dimaging (8).jpg|450px]]

'''Regularization and other parameters:'''

[[Image:SA 3Dimaging (46).gif ‎]]

* '''SVD cutoff''': The regularization for the inverse operator as a percent of the largest singular value.
* '''Depth weighting''': Turn depth weighting on or off.
* '''Laplacian type''': Selection of Laplacian operators (see above).

'''Notes:'''
* '''Starting Cortical LORETA''': Cortical LORETA can be started from the sub-menu '''Surface Image''' of the '''Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]''” for important information on regularization of distributed inverses.

== Cortical CLARA ==

Cortical CLARA is principally the same technique as CLARA, but Cortical CLARA is not computed in a 3D volume, but on the cortical surface. Instead of using a LORETA image as the basis for the iterative application, cortical CLARA uses cortical LORETA.

'''Regularization and other parameters:'''

[[Image:SA 3Dimaging (47).gif]]

* '''SVD cutoff''': The regularization for the inverse operator as a percent of the largest singular value.
* '''Depth weighting''': Turn depth weighting on or off.
* '''Laplacian type''': Selection of Laplacian operators (see Cortical LORETA).
* '''No of iterations''': Number of iterations for CLARA. The more iterations are used, the sparser becomes the solution.
* '''Automatic''': The algorithm tries to determine the number of iterations automatically. The goodness of fit (GOF) is calculated after every iteration and if there is a big jump in the GOF then the algorithm will stop. If no jumps appear during the calculations then CLARA iterates until the specified number of iterations is reached.
* '''Regularize iterations''': If one wants to use different regularization for the CLARA iterations than the value specified as "SVD cutoff", this option should be selected.
* '''Amount to clip from img (%)''': Cortical CLARA uses the solution from the previous iteration as an additional weighting matrix for the current iteration. That weighting matrix is constructed by cutting the "low" activity from the solution. This number specifies how much of the activity should be cut from the previous solution in order to construct the weighting matrix. This value is given as a percentage of the maximal activity. Default value is 10%.

'''Notes:'''

* '''Starting Cortical CLARA:''' Cortical CLARA can be started from the sub-menu '''Surface Image''' of the''' Image''' menu or from the '''Image Selection''' button.
* Please refer to Chapter “''[[Source_Analysis_3D_Imaging#Regularization_of_distributed_volume_images|Regularization of distributed volume images]]''” for important information on regularization of distributed inverses.

== Cortex Inflation ==

The inflated cortex is a smoothened version of the individual cortical surface with minimal metric distortions (Fischl, B. et al. (1999). Cortical Surface-Based Analysis: II: Inflation, Flattening, and a Surface-Based Coordinate System. ''NeuroImage'', 9(2), 195–207). Gyri and sulci are smoothened out. The original distances between each point on the cortex and its neighbors are, however, mostly preserved.

[[Image:SA 3Dimaging (48).gif]]

''Cortical LORETA map overlaid on top of the inflated cortical surface.''

A lighter gray color overlaid on top of the surface image indicates the location of a gyrus of the individual cortex surface, while a darker gray color indicates the location of a sulcus. The inflated cortical surface can be computed in '''BESA MRI 2.0'''. For more details please refer to the BESA MRI 2.0 help.

== Surface Minimum Norm Image ==

'''Introduction'''

The minimum norm approach is a common method to estimate a distributed electrical current image in the brain at each time sample (Hämäläinen & Ilmoniemi 1984). The source activities of a large number of regional sources are computed. The sources are evenly distributed using 1500 standard locations 10% and 30% below the smoothed standard brain surface (when using the standard MRI) or using between 3000-4000 locations on the individual brain surface defined by the gray-white-matter boundary.

Since the number of sources is much larger than the number of sensors in a minimum norm solution, the inverse problem is highly underdetermined and must be stabilized by a mathematical constraint, the minimum norm. Out of the many current distributions that can account for the recorded sensor data, the solution with the minimum L2 norm, i.e. the minimum total power of the current distribution is displayed in BESA Research.

First, the forward solution (leadfield matrix L) of all sources is calculated in the current head model. Then, the source activities S(t) of all source components are computed from the data matrix D(t) using an inverse regularized by the estimated noise covariance matrix:

<math>\mathrm{S}\left( t \right) = \mathrm{R} \cdot \mathrm{L}^{T} \cdot \left( \mathrm{L} \cdot \mathrm{R} \cdot \mathrm{L}^{T} + \mathrm{C}_N \right)^{-1} \cdot \mathrm{D}(t)</math>


Here, L is the leadfield matrix of the distributed regional source model, CN denotes the noise correlation matrix in sensor space, and R is a weighting matrix in source space. R and CN can be designed in different ways in order to optimize the minimum norm result. The total activity of each regional source is computed as the root mean square of the source activities S(t) of its 3 (MEG:2) components. This total source activity is transformed to a color-coded image of the brain surface. (When the standard brain is used, two sources are assigned to each surface location, located 10% and 30% below the surface, respectively. The color that is displayed on the standard brain surface is the larger of the two corresponding source activities.)

'''Weighting options'''

The minimum norm current imaging techniques of BESA Research provide different weighting strategies. Two weighting approaches are available: Depth weighting and spatio-temporal approaches.
* '''Depth weighting:''' Without depth weighting, deep sources appear very smeared in a minimum-norm reconstruction. With depth weighting, both deep and superficial sources produce a similar, more focal result. If this weighting method is selected, the leadfield of each regional source is scaled with the largest singular value of the SVD (singular value decomposition) of the source's leadfield.
* '''Spatio-temporal weighting''': Spatio-temporal weighting tries to assign large weight to sources that are assumed to be more likely to contribute to the recorded data.
** '''Subspace correlation after single source scan''': This method divides the signal into a signal and a noise subspace. The correlation of the leadfield of a regional source i with the signal subspace (pi) is computed to find out if the source location contributes to the measured data. The weighting matrix R becomes a diagonal matrix. Each of the three (MEG: 2) components of a regional source get the same weighting value pi2. This approach is based on the signal subspace correlation measure introduced by J.C. Mosher, R. M. Leahy (Recursive MUSIC: A Framework for EEG and MEG Source Localization, IEEE Trans. On Biomed. Eng. Vol. 45, No. 11, November 1998)
** '''Dale & Sereno 1993:''' In the approach of Dale and Sereno (J Cogn Neurosci, 1993, 5: 162-176) a signal subspace needs not be defined. The correlation pi of the leadfield of regional source i with the inverse of the data covariance matrix is computed along with the largest singular value λmax of the data covariance matrix. The weighting matrix R is a diagonal matrix with weights: [[Image:SA 3Dimaging (50).gif]]. Each of the three (MEG: 2) components of a regional source receives the same weighting value.

'''Noise regularization'''

Two methods to estimate the channel noise correlation matrix CN are provided by the program:
* '''Use baseline:''' Select this option to estimate the noise from the user-definable baseline. The signal is computed from the data at non-baseline latencies.
* '''Use 15% lowest values:''' The baseline activity is computed from the data at those 15% of all displayed latencies that have the lowest global field power. The signal is computed from all displayed latencies.

In each case, the activity (noise or signal, respectively) is defined as root-mean-square across all respective latencies for each channel.

The noise covariance matrix CN is constructed as a diagonal matrix. The entries in the main diagonal are proportional to the noise activity of the individual channels (if selected) or are all equally proportional to the average noise activity over all channels. The noise covariance matrix CN is then scaled such that the ratio of the Frobenius norms of the weighted leadfield projector matrix (LRLT) and the noise covariance matrix CN equals the Signal-to-Noise ratio. This scaling can be multiplied by an additional factor (default=1) to sharpen (<1) or smoothen (>1) the minimum norm image.

'''Applying the Minimum Norm Image'''

The minimum-norm algorithm is started via the ''Surface minimum norm image dialog box'', which is opened from the''' Image''' menu, or by typing the shortcut '''Ctrl-M''': Please refer to Chapter ''“Surface'' ''Minimum Norm Tab”'' for more details.

As opposed to the other 3D images available from the '''Image '''menu, the surface minimum norm image is not computed on a volumetric grid, but rather for locations on the brain surface. Accordingly, the results of the minimum norm image are displayed superimposed to the brain surface mesh rather than to the volumetric MR image.

The figure below shows a minimum norm image computed from the file '''Examples\Epilepsy\Spikes\Spikes-Child4_EEG+MEG_averaged.fsg'''. The EEG spike peak was imaged using the individual brain surface of the subject. A baseline from -300 to -70 ms was used. Minimum norm was computed with depth weighting, Spatio-temporal weighting according to Dale & Sereno 1993 and individual noise weighting with a noise scale factor of 0.01. The minimum norm image reveals the location of the spike generator in the close vicinity of the frontal left-hemispheric lesion in this subject.

[[Image:SA 3Dimaging (51).gif]]

== Multiple Source Probe Scan (MSPS) ==

 
'''Introduction'''

The MSPS function provides a tool for the validation of a given solution. It is based on the following theoretical consideration: If the recorded EEG/MEG data has been modeled adequately, i.e. all active brain regions are represented by a source in the current solution, then any additional probe source added to the solution will not show any activity apart from noise. The only exception occurs if this probe source is placed in close vicinity to one of the sources in the current solution. In that case, the solution's source and the probe source will share the activity of the corresponding brain area. The MSPS applies these considerations by scanning the brain on a pre-defined grid with a regional probe added to the current solution. Grid extent and density can be specified in the Image settings. The power P of the probe source at location r in the signal interval is compared with the power of the probe source in a reference interval, defining a value q:

<math>\mathrm{q}\left( r \right) = \sqrt{\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}} - 1</math>


MSPS can be computed on time domain or time-frequency domain data:
* In the time domain, q(r) is computed from the source waveform of the probe source. Here, P(r) is the mean power of the probe source at location r in the marked latency range, and Pref(r) is the mean probe source power in the user-definable baseline interval.
* In the time-frequency domain, an MSPS image can be computed from the complex cross spectral density matrices. By applying the inverse operator for a source configuration consisting of the current solution and the probe source, the power of the probe source can be computed for the target interval [P(r)] and the reference time-frequency interval [Pref(r)]. In the resulting MSPS image, q-values are shown in %, where q[%] = q*100.

The inverse operator used to determine the probe source power uses different regularization constants for the probe source and the sources in the current solution. The regularization constant of the sources in the current solution can be specified in the Image settings (default 4%). The regularization constant of the probe source is internally set to 0%.

Alternatively to the definition above, q can also be displayed in units of dB:

<math>\mathrm{q}\left\lbrack \text{dB} \right\rbrack = 10 \cdot \log_{10}\frac{\mathrm{P}\left( r \right)}{\mathrm{P}_{\text{ref}}\left( r \right)}</math>


Values of q smaller than zero are not shown in the MSPS image.

According to the considerations above, an MSPS of a correct source model should optimally yield image maxima around the sources in the current solution only. If the MSPS image is blurred or shows maxima at locations different from the modeled sources, this indicates a non-sufficient or incorrect solution.

'''Applying the MSPS'''

This chapter illustrates the application of the Multiple Source Probe Scan. The figures are generated with data from file '''Examples/Epilepsy/Spikes/Rolandic-Spike-Child.fsg''' (-300 : +200 ms, filtered from 3 Hz [forward] to 40 Hz [zero-phase]).

'''Time domain versus time-frequency domain MSPS'''

The multiple source probe scan can be computed in the time domain or the time-frequency domain. The latter is possible only when time-frequency domain data is available for the current condition, i.e. if the condition has been created by starting a multiple source beamformer (MSBF) computation from the source coherence window. In this case, evoking the MSPS calculation from the '''Imaging '''button or from the '''Image''' menu will bring up the following dialog window that allows to choose between time- or time-frequency MSPS. If only time domain data is available, this dialog window will not appear and MSPS will be computed in the time domain.

[[Image:SA 3Dimaging (53).gif]]

For a time-frequency domain MSPS, the target and the reference time-frequency interval have been specified already in the Time-Frequency window (see Chapter "''How To Create Beamformer Images''"). For a time-domain MSPS, the target and the reference epoch have to be specified in the Source Analysis window as described below.

'''Time domain MSPS'''

The time-domain MSPS image displays the ratio of the power of a regional probe source in the signal and the baseline interval. The currently set baseline is indicated by a horizontal line in the upper left corner of the channel box.

[[Image:SA 3Dimaging (54).gif|thumb|c|none|330px|The black horizontal bar in the upper part of the channel box (here circled in red) indicates the baseline interval.]]

By default, BESA Research defines the pre-stimulus interval of the current data segment as baseline. The baseline should represent a latency range in which no event-related activity is present in the data. There are several possibilities to modify the baseline interval: by clicking on the horizontal line with the left mouse button or by using the corresponding entry in the '''Condition '''menu or '''Fit Interval''' popup menu.

Mark an interval to define the target epoch, i.e. the time-interval for which the current solution is to be tested. Start the MSPS by selecting it from the '''Image selection '''button or from the '''Image''' menu to start the probe source scan. The''' Image '''menu can be evoked either from the menu bar or by right-clicking anywhere in the source analysis window. The 3D window opens and displays the scan result.

<div><ul>
<li style="display: inline-block;"> [[Image:SA 3Dimaging (55).gif|thumb|c|none|650px|This figure shows the MSPS image applied on the three left-hemispheric sources in the solution ''''Rolandic-Spike-Child-RS2.bsa''''. The baseline is set from -300ms to -50 ms. The right-hemispheric sources have been switched off. The fit interval is set to the latency range of large overall activity in the data (-43 ms : 117 ms). A realistic FEM model appropriate for the subject's age (12 years, conductivity ratios (cr) 50) is applied. The MSPS image does not show maxima at the modeled source locations and rather shows a spread q-value distribution.]] </li>

<li style="display: inline-block;"> [[Image:SA 3Dimaging (56).gif|thumb|c|none|650px|The MSPS image for the same latency range when the right-hemispheric sources have been included. The MSPS image appears more focal and shows maxima around the modeled brain regions. This indicates the substantial improvement of the solution by adding the right-hemispheric sources that model the propagation of the epileptic spike from the left to the right hemisphere (note the radiological side convention in the 3D window).]] </li>
</ul></div>

'''Time-Resolved MSPS'''

If the MSPS has been computed on time domain data, the image can be shown separately for each latency in the selected interval. After the MSPS has been computed for the marked epoch, double-click anywhere within this epoch to display the ratio of the probe source magnitude at the selected latency and the mean probe source magnitude in the baseline. Scanning the latency range by moving the cursor (e.g. with the left and right arrow cursor keys) provides a time-resolved MSPS image.

Time-resolved MSPS images are not available if the MSPS has been computed on data in the time-frequency domain.

<div><ul>
<li style="display: inline-block;"> [[File:SA 3Dimaging (57).gif|thumb|450px|MSPS image of the spike peak activity at 0ms. The activity mainly occurs in the left hemisphere. This fact is illustrated by the source waveforms and confirmed in the MSPS image, which shows a focal maximum around the location of the red sources.]] </li>

<li style="display: inline-block;"> [[File:SA 3Dimaging (58).gif|thumb|450px|Around +27 ms, the spike has propagated to the right hemisphere. This becomes evident from the waveforms of the blue sources, which show a significant latency lag with respect to the first three sources, and from the MSPS image, which shows the maximum around blue sources at this latency.]] </li>
</ul></div>



'''Notes:'''

* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image''' menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the''' Image''' menu.
* For scaling options, please refer to the '''scaling buttons''' popup menu .
* Parameters used for the MSPS calculations can be set in the ''General Settings tab'' of the ''Image Settings dialog box.''

== Source Sensitivity ==

'''Introduction'''

The 'Source sensitivity' function displays the sensitivity of the selected source in the current source model to activity in other brain regions. Sensitivity is defined as the fraction of power at the scanned brain location that is mapped onto the selected source.

To compute the source sensitivity, unit brain activity is modeled at different locations (probe source) throughout the brain. To this data, the current source model is applied to compute the source waveforms SCM of all modeled sources:

<math>\mathrm{S}_{\text{CM}} = \mathrm{L}_{\text{CM}}^{-1} \cdot \mathrm{L}_{\text{PS}}</math>


Here LCM-1 is the regularized inverse operator for the current model, and LPS is the leadfield of the regional probe source (dimension [Nx3] for EEG and [Nx2] for MEG, respectively, where N is the number of sensors). The source amplitude SSS of the selected source in the model is a 3x3 (MEG: 2x2) sub-matrix of SCM (if the selected source is a regional source) or a 1x3-matrix (MEG: 1x2) (if the selected source is a dipole). The root mean square of the singular values of SCM is defined as the source sensitivity.

The 3D source sensitivity image displays this value for all locations on a grid specified under '''Image/Settings'''. Grid density can be specified in the Image Settings.

'''Applying the Source Sensitivity Image'''

The Source Sensitivity image is evoked from the '''Image''' menu or by pressing the corresponding hot key (default: '''V''').

This function is enabled only when a solution with an active selected source is present in the Source Analysis window. The source sensitivity image then displays the sensitivity of the selected source to activity in other brain regions.

[[Image:SA 3Dimaging (59).gif]]

''Source Sensitivity image for the selected frontal source (green) in model ''''''High_Intensity_3RS.bsa'''''' in folder 'Examples/ERP_Auditory_Intensity'. The data displayed is the '100dB' condition in file ''''''All_Subjects_cc.fsg''''''. The selected source is sensitive to activity in the frontal brain region (yellow/white), while it is not influenced by activity in the vicinity of the left and right auditory cortex areas, which are modeled by the red and blue source in the model (transparent/gray).''

'''Notes:'''

* The sensitivity image is independent of the recorded sensor signals. It only depends on the current source model, the sensor configuration, the head model, and the regularization constant.
* If the regularization constant is set to zero, each source has a sensitivity of 100% to activity around its own location. With increasing regularization, the spatial filter becomes less focused, and the sensitivity of a source to activity at its location decreases.
* You can hide or re-display the last computed image by selecting the corresponding entry in the '''Image''' menu.
* The current image can be exported to ASCII or BrainVoyager vmp-format from the '''Image''' menu.

{{BESAManualNav}}