General Linear Model for Analyzing fMRI Data

Date: December 20, 2023 10:05 AM

From this course: General Linear Model for Analyzing fMRI Data by Idan Blank

Summary: Theoretical and conceptual basis for General Linear Model fMRI analysis on a single participant, how to execute it in matlab

Example Experiment

Question: which brain regions are engaged in the decoding of semantics, syntax and meaning from sentences?

Test: Reading sentences

Control: Reading nonwords with the same number of words as the sentence

Basic T-test:

T = experiment signal, the brain signal during test condition

C = control signal, brain during control condition

t = mean(T) - mean(C)

       noise

noise = standard deviation ish, based on SSE

want to get a T value that is very big

Predicting signal:

  • time series during task vs nontask, convolved to replicate the BOLD signal

Comparing signals:

called “predictors”:

  • function of baseline (straight line)
    • beta 1
  • function of what you expect a voxel’s BOLD signal to look like if it’s activated by the system you’re looking for
    • beta 2
  • function of what you expect a voxel’s BOLD signal to look like if it’s not activated by system you’re looking for
    • beta 3

This is the X matrix

  • add these three functions together at different weights to approximate what you see in that voxel signal
    • say weight = w for each
    • this weighted sum = appx signal of that voxel
      • b1w1 + b2w2 + b3w3 = approximation(v)
    • difference in weights between nonword signal vs word signal, show you how likely its part of a language system or no
      • w2 - w3
      • comparison of betaweights is called a ‘contrast’
        • formally, a vector indicating which beta weights we are interested in
  • difference between approximation of that voxel and real signal of that voxel is error
    • signal(v) - approximation(v) = error(v)
      • positive error = your approximation is below the real signal, neg error = your appx is above the real signal

GLM:

Screen Shot 2024-02-06 at 10.35.01 AM.png

Formula:

b = regress(BOLD_signal, X)

Noise minimization- add more predictors which are approximations of noise functions:

  • adds a matrix of potential head movement
  • adds a matrix of time derivatives
  • etc. other movement/noise functions
  • can add these to approximate the signal better