1. Jonathan Taylor, Stanford Keith Worsley, McGill
Hierarchical statistical analysis of fMRI data across runs/sessions/subjects/studies using BRAINSTAT/FMRISTAT
Jonathan Taylor, Stanford
Keith Worsley, McGill

2. What is BRAINSTAT / FMRISTAT ?
FMRISTAT is a Matlab fMRI stats analysis package
BRAINSTAT is a Python version
Main components:
FMRILM: Linear model, AR(p) errors, bias correction, smoothing of autocorrelation to boost degrees of freedom*
MULTISTAT: Mixed effects linear model, ReML estimation, EM algorithm, smoothing of random/fixed effects sd to boost degrees of freedom*
Key idea: IN: effect, sd, df, fwhm, OUT: effect, sd, df, fwhm
STAT_SUMMARY: best of Bonferroni, non-isotropic random field theory, DLM (Discrete Local Maxima)*
*new theoretical results
Treats magnitudes and delays in the same way

3. FMRILM: smoothing of temporal autocorrelation
Variability in acor lowers df
Df depends
on contrast
Smoothing acor brings df back up:
dfacor = dfresidual( )
acor(contrast of data)2
dfeff dfresidual dfacor
FWHMacor /2
FWHMdata2 =
Hot stimulus
Hot-warm stimulus
FWHMdata = 8.79
Residual df = 110
Residual df = 110
100
100
Target = 100 df
Target = 100 df 50
Contrast of data, acor = 0.61 50
Contrast of data, acor = 0.79
dfeff
dfeff 10 20 30 10 20 30
FWHM = 10.3mm
FWHM = 12.4mm
FWHMacor
FWHMacor

4. MULTISTAT: smoothing of random/fixed FX sd
dfratio = dfrandom( )
dfeff dfratio dffixed
FWHMratio /2
FWHMdata2
e.g. dfrandom = 3,
dffixed = 4  110
= 440,
FWHMdata = 8mm: = 20 40
Infinity
100
200
300
400
fixed effects
analysis,
dfeff = 440
dfeff
FWHM
= 19mm
Target = 100 df
random effects
analysis,
dfeff = 3
FWHMratio

5. High FWHM: use Random Field Theory Low FWHM: use Bonferroni
STAT_SUMMARY
High FWHM: use Random Field Theory
Low FWHM:
use Bonferroni
In between: use Discrete Local Maxima (DLM)
0.12
Gaussian
T, 20 df
T, 10 df
0.1
Bonferroni
Random Field Theory
0.08
DLM
can ½
P-value
when
FWHM
~3 voxels
P-value
0.06
0.04
True
Discrete Local Maxima
0.02
Bonferroni, N=Resels 1 2 3 4 5 6 7 8 9 10
FWHM of smoothing kernel (voxels)

6. High FWHM: use Random Field Theory Low FWHM: use Bonferroni
STAT_SUMMARY
High FWHM: use Random Field Theory
Low FWHM:
use Bonferroni
In between: use Discrete Local Maxima (DLM)
4.7
Bonferroni
4.6
4.5
True
T, 10 df
4.4
Random Field Theory
4.3
T, 20 df
Gaussianized threshold
4.2
Discrete Local Maxima (DLM)
4.1
Gaussian 4
3.9
Bonferroni, N=Resels
3.8
3.7 1 2 3 4 5 6 7 8 9 10
FWHM of smoothing kernel (voxels)

8. STAT_SUMMARY example: single run, hot-warm
Detected by BON and
DLM but not by RFT
Detected by DLM,
but not by BON or RFT

9. Estimating the delay of the response
Delay or latency to the peak of the HRF is approximated by a linear combination of two optimally chosen basis functions:
delay -5 5 10 15 20 25
-0.4
-0.2
0.2
0.4
0.6
t (seconds)
basis1
basis2
HRF
shift
HRF(t + shift) ~ basis1(t) w1(shift) + basis2(t) w2(shift)
Convolve bases with the stimulus, then add to the linear model

10. Example: FIAC data 16 subjects 4 runs per subject 4 conditions
2 runs: event design
2 runs: block design
4 conditions
Same sentence, same speaker
Same sentence, different speaker
Different sentence, same speaker
Different sentence, different speaker
3T, 200 frames, TR=2.5s

11. Response
Events
Blocks
Beginning of block/run

12. Design matrix for block expt
B1, B2 are basis functions for magnitude and delay:

13. 1st level analysis Motion and slice time correction (using FSL)
5 conditions
Smoothing of temporal autocorrelation to control the effective df (new!)
3 contrasts
Beginning of block/run
Same sent, same speak
Same sent, diff speak
Diff sent, same speak
Diff sent, diff speak
Sentence
-0.5
0.5
Speaker
Interaction 1 -1

14. Efficiency
Sd of contrasts (lower is better) for a single run, assuming additivity of responses
For the magnitudes, event and block have similar efficiency
For the delays, event is much better.

15. 2nd level analysis 3rd level analysis
Analyse events and blocks separately
Register contrasts to Talairach (using FSL)
Bad registration on 2 subjects - dropped
Combine 2 runs using fixed FX
Combine remaining 14 subjects using random FX
3 contrasts × event/block × magnitude/delay = 12
Threshold using best of Bonferroni, random field theory, and discrete local maxima (new!)
3rd level analysis

16. Part of slice
z = -2 mm

21. Event
Block
Magnitude
Delay

22. Events vs blocks for delays in different – same sentence
Events: 0.14±0.04s; Blocks: 1.19±0.23s
Both significant, P<0.05 (corrected) (!?!)
Answer: take a look at blocks:
Greater
magnitude
Different sentence
(sustained interest)
Best fitting block
Same sentence
(lose interest)
Greater
delay

23. SPM BRAINSTAT

24. Magnitude increase for
Sentence, Event
Sentence, Block
Sentence, Combined
Speaker, Combined
at (-54,-14,-2)

25. Magnitude decrease for
Sentence, Block
Sentence, Combined
at (-54,-54,40)

26. Delay increase for Sentence, Event at (58,-18,2)
inside the region where all
conditions are activated

27. Conclusions Greater %BOLD response for Greater latency for
different – same sentences (1.08±0.16%)
different – same speaker (0.47±0.0.8%)
Greater latency for
different – same sentences (0.148±0.035 secs)

28. The main effects of sentence repetition (in red) and of speaker repetition (in blue). 1: Meriaux et al, Madic; 2: Goebel et al, Brain voyager; 3: Beckman et al, FSL; 4: Dehaene-Lambertz et al, SPM2.
z=-12
z=2
z=5 3
1,4 2 1
Brainstat:
combined
block and
event,
threshold
at T>5.67,
P<0.05.