1. 1st level analysis - Design matrix, contrasts & inference
Nico Bunzeck,
Katya Woollett

2. 1st level data analysis in SPM5
(i) Specification of the GLM design matrix, fMRI data files and filtering
(ii) estimation of GLM parameters using classical or Bayesian approaches
(iii) interrogation of results using contrast vectors to produce Statistical Parametric Maps (SPMs) or Posterior Probability Maps (PPMs)

3. (i) fMRI model specification

4. (i) fMRI model specification
Timing parameters: to construct the design matrix
Units for design: onset of the events or blocks (in sec or scans)
Interscan interval: TR in sec; = time between acquiring a plane for one volume and the same plane in the next volume; constant
Microtime resolution: (t) the number of time-bins per scan used when building the regressors (default = 16)
Microtime onset: (t0) the first time-bin at which the regressors are resampled to coincide with data acquisition (default = 1)
MTR: Do not change this parameter unless you
have a long TR and wish to shift
regressors so that they are aligned to a
particular slice.
acquisition.
If t0 = 1 then the
regressors will be appropriate for the
first slice. If you want to temporally
realign the regressors so that they
match responses in the middle slice then
make t0 = t/2 (assuming there is a
negligible gap between volume
acquisitions).
Do not change the default setting unless
you have a long TR.

5. (i) fMRI model specification
Data & Design matrix: defines the experimental design and the nature of the hypothesis testing
matrix: organized in rows (each scans) and columns (for each effect of explanatory variable = regressor or stimulus function)
can be replicated and/or manipulated for each subject/session
The design matrix has one row for each
scan and one column for each effect or
explanatory variable. (e.g. regressor or
stimulus function).

6. (i) fMRI model specification
Subjects/Session:
Scans: select the images for the model that has to be estimated

7. (i) fMRI model specification
Condition: can be event-related, blocked design or a combination of both – they are modelled in the same way -> they are later convolved with a basis set
- Name: be creative
Onset: specify the onsets for this condition
Durations: default for events = 0; single number: SPM assumes that all trails have this duration (block)
for mix of blocks and events: number must match the number of onset times

8. (i) fMRI model specification
Multiple conditions:
load all the conditions defined as *.mat
it contains cell arrays: names, onsets and duration eg. Names{2}=‘finger tapping’, onsets{2}=[ ], duration{2}=[0 0 0]
If you have multiple conditions you can add them by adding a new ‘condition’ branch. But you can also define them as

9. (i) fMRI model specification
Regressors: additional columns in the design matrix that may not be convolved with the HR, eg. movement parameters
Name
Value
Multiple regressors: either *.mat or *.txt file that contains details of the multiple regressors; they will be named: R1, R2 … Rn

10. (i) fMRI model specification
High-pass filter cutoff: default = 128s
slow signal drifts with a period longer than 128 will be removed
removes confounds without estimating their parameters explicitly

11. (i) fMRI model specification
Factorial design: if you have a factorial design SPM automatically generate the contrasts that are necessary to test the main effects of interaction:
F-contrasts: at within-subject level
contrasts for second level analysis
create as many factors as you need – name, levels (for each factor)
for example: ‘Stimulus-Repetition’ – 3 levels

12. (i) fMRI model specification
Basis Functions:
SPM uses basis functions to model the hemodynamic response; either 1 function or a set
Canonical HRF: most common choice, default, easiest way to interpret the data
Model derivatives: = ‘informed’ basis set -> covers variations in subject-to-subject and voxel-to-voxel responses: peak and width

13. (i) fMRI model specification
Model interactions: inputs (RT) convolved with the basis set
Directory: where the SPM.mat file will be written

14. (i) fMRI model specification
Global normalization:
estimating the ‘average within-brain fMRI signal’ (gns) over scans (n) and sessions (s)
‘Scaling’: SPM multiplies each value in scan and session by 100/(gns) eg. scaling over all sessions
‘none’: default, estimation of a ‘session specific grand mean value’ (gs) = fMRI signal over all voxels in a session; each fMRI data point in the session is multiplied by 100/(gs); eg. Session specific scaling

15. (i) fMRI model specification
Explicit masking: only those voxels in the brain mask will be analyzed
speeds up the estimation
restricts SPMs to within-mask voxels
Serial correlations: due to aliased biorhythms and unmodelled neural activity
SPM uses an autoregressive AR(1) model during Classical (ReML) parameter estimation
but they can be ignored (‘none’) - Bayesion estimation
Chose a mask: whole brain or just a region such as the hippocampus, amygdala

16. (i) fMRI model specification
What should be included in the model?
Think about contrast/comparisons before the experiment
The more information you have the better: the model represents the a priori ideas about how the experimental paradigm influences the measured signal

17. (i) Review a specified model

18. (i) Review a specified model
Design matrix:
24 conditions/session
last 2 columns model average activity in each session -> total of 50 regressors
191 fMRI scans/session -> 382 rows and 50 columns

19. (i) Review a specified model
Explore Sessions and regressors:
time domain corresponding to the regressor (4 events)
frequency domain corresponding to the regressor: experimental variance is not removed by high-pass filtering
bottom: basis function = HRF

20. (ii) fMRI model estimation
for which voxel does the model (or a explanatory variable) explain the observed variance??
parameters are estimated for each voxel so that the error is minimized
there are more than 1 variables -> it is unlikely that the betas exactly fit: SPM calculates different parameter-sets
each parameter-set determines a fitted response:
Y = observed data (voxel timecourse of 1 voxel) Y
differs slightly from the observed Yj
the algorithm minimizes the residuals

21. (ii) fMRI model estimation
Fitting X to Y gives you one  (parameter estimate) for each column of X and e. Betas provide information about the fit of the regressor X to the data, Y, in each voxel

22. (ii) fMRI model estimation

23. (ii) fMRI model estimation
Select SPM.mat: -
Method:
“Classical”: applies Restricted Maximum Likelihood (ReML); for spatially smoothed images
after estimation effects of parameters are tested by T and F-statistic -> SPM(T), SPM(F)
“Bayesian 1st-level”: applies Variational Bayes (VB); images do not need to be spatially smoothed; takes long;
results: contrasts identify regions with effects larger than a user-specified size, eg 1% of the global mean signal (Posterior Probability Map – PPM)
3 methods to estimate the data: classica + bayesian 1st level = 1st level analyses, bayesian 2nd level = 2nd level. Run 1 first…

24. (iii) Results Testing hypothesis
T-test: is there a significant increase or is there a significant decrease in a specific contrast (between conditions) – directional
F-test: is there a significant difference between conditions in the contrast - nondirectional

25. (iii) Results Contrast-vector: c‘ = [-1 1 0 0 0 0 ] T-Contrast:
H0: no difference between condition 1 and 2 in the 1st block
H1: there is a difference between condition 2 and 1 in the 1st block (condition 2 > condition 1)
Parameters:
Design matrix:
T-statistics in the usual way: Comparison of betas to variance

26. (iii) Results Contrast-vector: c‘ = [-1 1 -1 1 0 0 ] T-Contrast:
H0: no difference between condition 1 and 2 in the 1st and 2nd block
H1: there is a difference between condition 2 and 1 in the 1st and 2nd block (condition 2 > condition 1)
T-Contrast:
Parameters:
Design matrix:
T-statistics in the usual way: Comparison of betas to variance

27. (iii) Results Contrast-vector: c‘ = [1 0 0 0 0 0 0; F-Contrast:; ; ; ]
H0: the factors 1, 2, 3 and 4 do not explain a significant amount of variance
H1:the factors 1, 2, 3 and 4 do explain a significant amount of variance:
F-Contrast:
Parameters:
Design matrix:

28. (iii) Results Contrast-vector: c‘ = [1 0 0 0 0 0 0; F-Contrast:; ]
H0: the factor 1 does not explain a significant amount of variance
H1:the factor 1 does explain a significant amount of variance:
F-Contrast:
Parameters:
Design matrix:

29. (iii) Results Results: Glas-brain List of activated voxel
(maximum intensity projection (MIP))
List of activated
voxel

30. (iii) Results The multiple comparison problem Results:
Voxel-level P: chance of finding a voxel with this or a greater height (T or Z), corrected or uncorrected for search volume
Uncorrected: Default: > voxels = 50 false positives
FWE: ‘family wise error’ is a false positive anywhere in the SPM
controls any false positives
FDR: ‘false discovery rate’ – controls the expected proportion of false positives among suprathresholded voxels -> it adapts to the amount of signal in the data
Results:
Glas-brain
(maximum intensity projection (MIP))
List of activated
voxel

31. (iii) Results Results: Glas-brain List of activated clusters corrected
(maximum intensity projection (MIP))
List of activated
clusters
corrected
uncorrected

32. (iii) Results
Cluster level (P): chance of finding a cluster with this many (ke) or a greater number of voxel, corrected or uncorrected for search volume
Set-level (P): the chance of finding this (c) or a greater number of clusters in the search volume
Results:
Glas-brain
(maximum intensity projection (MIP))
List of activated
clusters
corrected
uncorrected

33. (iii) Results Plotting responses Estimated effect sizes
Fitted responses

34. (iii) Results
Overlaying the data
Slices
Sections

35. (iii) Results
Overlaying the data
Render

36. Thanks for your attention.

37. (ii) fMRI model estimation
Bayesian 1st-level: applies Variational Bayes (VB); allows to specify spatial priors for regression coefficients and regularised voxel-wise AR(P) modelsfor fMRI noise prcesses
images do not need to be spatially smoothed
takes 5x longer than the classical approach
results: contrasts identify regions with effects larger than a user-specified size, eg 1% of the global mean signal (Posterior Probability Map – PPM)

38. (ii) fMRI model estimation
Matrix design
Graphical design