# Talairach Transformation File

 Module information Modules BESA Research Basic or higher Version 5.2 or higher

### Overview

The tal file contains the transformation parameters from AC-PC coordinate system to the Talairach coordinate system. The following seven points are listed:

1. Item 1 AP: Distance from x-z-plane at y==AC to anterior point (AP) along the y axis
2. Item 2 PC: Distance from x-z-plane at y==AC to posterior commissure (PC) along the y axis
3. Item 3 PP: Distance from x-z-plane at y==AC to posterior point (PP) along the y axis
4. Item 4 SP: Distance from x-y-plane at z==AC to superior point (SP) along the z axis
5. Item 5 IP: Distance from x-y-plane at z==AC to inferior point (IP) along the z axis
6. Item 6 RP: Distance from y-z-plane at x==AC to right point (RP) along the x axis
7. Item 7 LP: Distance from y-z-plane at x==AC to left point (LP) along the x axis

Example file content:

66.885850 26.500000 102.697017 68.035304 40.421205 65.232346 64.500000

Using these points, the transformation is then performed as shown in the figure and example below.

The default values are as such (all distances in mm):

Distance AC to AP		70
Distance AC to PC		23
Distance AC to PP		102
Distance AC to SP		74
Distance AC to IP		42
Distance AC to RP		68
Distance AC to LP		68

Example of how to apply Talairach values. The principle is followed in all three directions (x, y, z). First the compartment is identified (e.g. for z axis, superior to AC, or inferior to AC). Then the coordinate is scaled with the Talairach value divided by the real value.

For the posterior compartments (y-axis), it is slightly more complicated because there are two posterior compartments: Between AC and PC, and between PC and PP. Once it is decided which compartment is the correct one, the scaling is done for this compartment only; e.g. if the compartment is between PC and PP: First subtract the relevant points from the value, i.e. $|y|’ = |y|-PC$. Then, scale $y’$ with $({PP}_{tal}-{PC}_{tal})/(PP-PC)$. Then add ${PC}_{tal}$. Done!

### Examples

#### AC-PC to Talairach

You want to transform the coordinate in AC-PC coordinate system (-38, -15, 12) to the Talairach coordinate system. The *.tal file contains the values from the above example:

66.885850 26.500000 102.697017 68.035304 40.421205 65.232346 64.500000

This means that the distances have the following relationships:

Point Individual value Talairach standard Ratio in compartment
AP 66.9 70 1.046
PC 26.5 23 0.868
PP 102.7 102 1.037(*)
SP 68.0 74 1.088
IP 40.4 42 1.040
RP 65.2 68 1.043
LP 64.5 68 1.054

(*): For the posterior compartment, the distance between PC and PP is used here.

X value: The coordinate lies in the left compartment. So:

$X_{tal} = x \times \frac{{LP}_{tal}}{LP} = -38 \times 1.054 = -40$

Y value: The coordinate lies in the compartment between AC and PC. So:

$Y_{tal} = y \times \frac{{PC}_{tal}}{PC} = -15 \times 0.868 = -13$

Z-value: The coordinate lies in the top compartment. So:

$Z_{tal} = z \times \frac{{SP}_{tal}}{SP} = 12 \times 1.088 = 13$

#### Transforming an AC-PC coordinate

You want to transform an AC-PC coordinate of (-10, -78, -10).

X value: The coordinate lies in the left compartment. So:

$X_{tal} = x \times \frac{{LP}_{tal}}{LP} = -10 \times 1.054 = -11$

Y value: The coordinate lies in the compartment between PC and PP (we use the individual values to decide on the compartment if we transform from the individual AC-PC coordinate system). This means that we first need to subtract the length of the compartment between AC and PC in the individual coordinate system, and then stretch the remaining value in the rear Talairach compartment. At the end, we need to add the length of the compartment between ACtal and PCtal (in the Talairach coordinate system) again:

$y’ = y – (-PC) = -51.5$

$Y_{tal} = y’ \times \frac{{PP}_{tal} – {PC}_{tal}}{(PP – PC)} + (-{PC}_{tal}) = -51.5 \times 1.037 + (-23) = -53 – 23 = -76$

Z-value: The coordinate lies in the bottom compartment. So:

$Z_{tal} = z \times \frac{{IP}_{tal}}{IP} = -10 \times 1.040 = -10$

#### Generate Talairach transformation (*.tal) file from BESA MRI coregistration (*.sfh) file

If you want to create a *.tal file from a BESA MRI coregistration *.sfh file to (e.g.) add a custom head-model in BESA Research 6.1, you need the Talairach transformation section in the *.sfh file:

AC: 128 128 128
PC: 167 128 128
AP: 71 124 125
PP: 240 130 143
SP: 150 47 128
IP: 210 182 122
RP: 166 128 59
LP: 170 128 202

The values for the *.tal file can be calculated as follows:

1st value: AC(x) - AP(x) = 128 - 71  = 57
2nd value: PC(x) - AC(x) = 167 - 128 = 39
3rd value: PP(x) - AC(x) = 240 - 128 = 112
4th value: AC(y) - SP(y) = 128 - 47  = 81
5th value: IP(y) - AC(y) = 182 - 128 = 54
6th value: AC(z) - RP(z) = 128 - 59  = 69
7th value: AC(z) - LP(z) = 202 - 128 = 74

The content of the *.tal file is then:

57	39	112	81	54	69	74