Analysis of fMRI data with linear models

1
Analysis of fMRI data with linear models
2
Typical fMRI processing steps

• Image reconstruction
• Slice time correction
• Motion correction
• Temporal filtering
• 1st level (individual subject) linear modeling
• Conversion to signal change
• Image normalisation (Talairach/MNI)
• Spatial blurring
• 2nd level (group) linear modeling
• Extraction of activated clusters

3
Typical fMRI processing steps

• Image reconstruction
• Slice time correction
• Motion correction
• Temporal filtering
• 1st level (individual subject) linear modeling
• Conversion to signal change
• Image normalisation (Talairach/MNI)
• Spatial blurring
• 2nd level (group) linear modeling
• Extraction of activated clusters

4
1st level linear modeling
5
1st level linear modeling
Fitting a general linear model to individual
voxel time series We postulate a number of
predictor variables ideal time series that
represent what we think the response should look
like to each type of experimental stimulus. Then
compute the weighted sum of these predictor
variables that produces the closest match to the
actual data time series. Signal ß1F1 ß 2F2
ß3F3 constant error Where F1, F2 and F3
are the postulated predictor variables or
functions.
6
(No Transcript)
7
1st level linear modeling

• Although only one set of predictor variables is
  posited for every voxel in the analysis, the
  model is individually fit for every voxel. This
  gives a unique set of weights (beta coefficients)
  for each voxel.
• Each beta weight for a voxel represents the BOLD
  signal change due to the corresponding
  experimental condition
• We can also form linear contrasts of beta weights
  at each voxel (e.g. the subtraction of one beta
  from another, representing the difference in
  signal change between two conditions)
• Thus we have one or more statistical brain maps
  of beta weights and/or contrasts
• Associated with each beta and contrast is a
  t-statistic, that tells us to what extent such a
  value could be expected by chance alone these
  are only interesting for single subject analyses.

8
2nd level linear modeling

• The goal of 2nd level analysis is to determine
  the extent to which beta-weights or contrasts are
  consistent across subjects in a group, and to
  what extent they differ across different groups
• The method is simply a matter of running t-tests,
  ANOVA or regression on the beta weights or
  contrasts for each voxel
• The result is one or more group statistical maps

9
2nd level linear modeling t-tests

• Used to test whether the means of two groups are
  equal.
• 3 types of t-test
• Unpaired tests equality of means of two
  independent groups
• Paired tests equality of means of two dependent
  groups (e.g. two time points on same group, two
  groups that are pairwise matched)
• Single group tests if mean of one group is
  equal to zero
• Can be used directionally 1-tailed vs. 2-tailed
  test

10
2nd level linear modeling ANOVA

• Used to test whether the means of two or more
  groups are equal.
• 3 types of ANOVA
• Fixed effects
• Random effects
• Mixed effects (i.e. both random and fixed)
• Most usual for fMRI data is mixed effects
• Experimental conditions are fixed
• Subjects are random
• Does not provide directional test must look at
  mean differences

11
2nd level linear modeling regression

• Used to test association between BOLD signal
  change and some external measure (e.g.
  trait/state measure, behavioral measure,
  physiological measure)
• Provides a directional measure of association
• In simplest form is simple correlation
• Can be used to account for undesirable variance
• Very sensitive to outliers you MUST extract the
  voxel values and examine the scatterplots
• Can be used to create more complicated ANOVA
  models, including ANCOVA