Hierarchical statistical analysis of
fMRI data across
runs/sessions/subjects/studies
using BRAINSTAT / FMRISTAT
Jonathan Taylor, Stanford
Keith Worsley, McGill
What is
BRAINSTAT / FMRISTAT ?



FMRISTAT is a Matlab fMRI stats analysis package
BRAINSTAT is a Python version
Main components:



FMRILM: Linear model for %BOLD, AR(p) errors, bias correction,
smoothing of autocorrelation to boost degrees of freedom (df)*
MULTISTAT: Mixed effects linear model for contrasts from
previous level in hierarchy, using ReML estimation, EM algorithm,
smoothing of random/fixed effects sd to boost df*
 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 (T, W, et al., 2002, 2005, 2006)

Treats magnitudes (%BOLD) and delays (sec) identically
FMRILM: smoothing of temporal autocorrelation
• Variability in
2
3/2
FWHM
acor
acor lowers df
dfacor = dfresidual 2
+1
2
FWHMdata
• Df depends
2
1
1
2
acor(contrast
of
data)
on contrast
= df
+
df
dfacor
• Smoothing acor
eff
residual
brings df back up:
Hot-warm stimulus
Hot stimulus
FWHM = 8.79
(
)
data
Residual df = 110
Residual df = 110
100
Target = 100 df
Contrast of data, acor = 0.61
50
dfeff
0
100
Target = 100 df
0
10
20
FWHM = 10.3mm
Contrast of data, acor = 0.79
50
dfeff
30
FWHMacor
0
0
10
20
FWHM = 12.4mm
30
FWHMacor
MULTISTAT: smoothing of random/fixed FX sd
(
dfratio = dfrandom
FWHMratio2
2
+1
2
FWHMdata
)
1
1
1
=
+
dfeff dfratio dffixed
3/2
e.g. dfrandom = 3,
dffixed = 4  110
= 440,
FWHMdata = 8mm:
fixed effects
analysis,
dfeff = 440
400
300
dfeff
Target = 100 df
random effects
analysis,
dfeff = 3
200
FWHM
= 19mm
100
0
0
20
40
FWHMratio
Infinity
STAT_SUMMARY
Low FWHM:
In between: use Discrete
use Bonferroni
Local Maxima (DLM)
High FWHM:
use Random
Field Theory
0.12
Gaussian
T, 20 df
T, 10 df
0.1
Random Field Theory
Bonferroni
P-value
0.08
DLM
can ½
P-value
when
FWHM
~3 voxels
0.06
0.04
True
Discrete Local Maxima
0.02
Bonferroni, N=Resels
0
0
1
2
3
4
5
6
7
FWHM of smoothing kernel (voxels)
8
9
10
STAT_SUMMARY
Low FWHM:
In between: use Discrete
use Bonferroni
Local Maxima (DLM)
High FWHM:
use Random
Field Theory
Bonferroni
4.7
4.6
Gaussianized threshold
4.5
True
4.4
T, 10 df
Random Field Theory
4.3
T, 20 df
Discrete Local Maxima (DLM)
4.2
4.1
Gaussian
4
3.9
3.8
3.7
0
1
2
3
4
5
6
7
FWHM of smoothing kernel (voxels)
8
9
10
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
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
0.6
0.4
basis1
0.2
HRF
basis2
0
-0.2
-0.4
-5
0
shift
5
10
t (seconds)
15
20
25
HRF(t + shift) ~ basis1(t) w1(shift) + basis2(t) w2(shift)
• Convolve bases with the stimulus, then add to the linear model
Example: FIAC data


16 subjects
4 runs per subject



4 conditions





2 runs: event design
2 runs: block design
Same sentence, same speaker
Same sentence, different speaker
Different sentence, same speaker
Different sentence, different speaker
3T, 200 frames, TR=2.5s
Response

Events
0.4
0.2
0
-0.2
0
50
100
150
200
250
300
350
400
450
500
350
400
450
500
Beginning of block/run

Blocks
0.4
0.2
0
-0.2
0
50
100
150
200
250
Seconds
300
Design matrix for block expt

B1, B2 are basis functions for magnitude and delay:
1st snt in block
S snt, S spk, B1
S snt, S spk, B2
S snt, D spk, B1
S snt, D spk, B2
D snt, S spk, B1
D snt, S spk, B2
D snt, D spk, B1
D snt, D spk, B2
Constant
Linear
Quadratic
Cubic
Spline
Whole brain avg
1st level analysis


Motion and slice time correction (using FSL)
5 conditions
3 contrasts
Beginning
of block/run
Same sent, Same sent,
same speak diff speak
Diff sent,
same speak
Diff sent,
diff speak
Sentence
Speaker
0
0
-0.5
-0.5
-0.5
0.5
0.5
-0.5
0.5
0.5
1
-1
-1
1
Interaction 0

Smoothing of temporal autocorrelation to
control the effective df (new!)
Magnitude sd (relative to error)
Efficiency
2
1.5
Sd of contrasts (lower is
better) for a single run,
assuming additivity of
responses
Event
Block
1
0.5
0
Diff sente Diff speak
• For the magnitudes,
event and block have
similar efficiency
• For the delays, event is
much better.
Interac
Delay sd (seconds)
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
Event
Block
Diff sente Diff speak
Interac
2nd 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
3rd level analysis

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!)
Part of slice
z = -2 mm
Magnitude (%BOLD), diff - same sentence, event experiment
Subj 0
1
3
4
6
7
8
9
10
11
12
13
14
Mixed
effects
15
Left
2
1
0
Ef
Right
-1
Random
/fixed
effects sd
smoothed
7.0105mm
1.5
-2
Slice range is -74<x<70mm, -46<y<4mm, z=-2mm; Contour is: min fMRI > 6214
1
Left
Sd
Right
271
272
271
265
264
132
270
275
269
274
248
256
264
278
1
0
0.5
5
FWHM (mm)
15
40
Left
-50
T
0
x (mm)
df
0.5
10
0
5
50
Ant.
Post.
Right
P=0.05 threshold for local maxima is +/- 5.68
-5
-40-20 0
y (mm)
0
Magnitude (%BOLD), diff - same sentence, block experiment
Subj 0
1
3
4
6
7
8
9
10
11
12
13
14
Mixed
effects
15
Left
2
1
0
Ef
Right
-1
Random
/fixed
effects sd
smoothed
7.103mm
1.5
-2
Slice range is -74<x<70mm, -46<y<4mm, z=-2mm; Contour is: min fMRI > 5904
1
Left
Sd
Right
202
202
204
205
204
203
201
202
200
206
205
202
204
200
1
0
0.5
5
FWHM (mm)
15
40
Left
-50
T
0
x (mm)
df
0.5
10
0
5
50
Ant.
Post.
Right
P=0.05 threshold for local maxima is +/- 5.67
-5
-40-20 0
y (mm)
0
Delay shift (secs), diff - same sentence, event experiment
Subj 0
1
3
4
6
7
8
9
10
11
12
13
14
Mixed
effects
15
Left
0.2
0.1
0
-0.1
-0.2
Ef
Right
Random
/fixed
effects sd
smoothed
10.6778mm
1.5
Slice range is -74<x<70mm, -46<y<4mm, z=-2mm; Contour is: magnitude, stimulus average, T statistic > 5
Left
0.4
Sd
1
0.2
Right
df
271
272
271
265
264
132
270
275
269
274
248
256
264
278
0
0.5
40
FWHM (mm)
15
T
0
-2
Ant.
Post.
Right
P=0.05 threshold for local maxima is +/- 4.31
-50
x (mm)
Left
2
10
0
5
50
-40-20 0
y (mm)
0
Delay shift (secs), diff - same sentence, block experiment
Subj 0
1
3
4
6
7
8
9
10
11
12
13
14
Mixed
effects
15
Left
1
0.5
0
Ef
Right
-0.5
Random
/fixed
effects sd
smoothed
8.8952mm
1.5
-1
Slice range is -74<x<70mm, -46<y<4mm, z=-2mm; Contour is: magnitude, stimulus average, T statistic > 5
2
Left
1.5
Sd
1
1
0.5
Right
df
202
202
204
205
204
203
201
202
200
206
205
202
204
200
0
0.5
40
FWHM (mm)
15
T
0
-2
Ant.
Post.
Right
P=0.05 threshold for local maxima is +/- 4.3
-50
x (mm)
Left
2
10
0
5
50
-40-20 0
y (mm)
0
Event
Block
Subj 0
1
3
4
6
7
8
9
10
11
12
13
14
Magnitude (%BOLD), diff - same sentence, block experiment
Mixed
effects
15
1
3
4
6
7
8
9
10
11
12
13
14
Left
Left
0
0
Random
/fixed
effects sd
smoothed
7.0105mm
1.5
-2
1
1
Left
271
265
264
132
270
275
269
274
248
256
264
278
Sd
0.5
1
0
0.5
40
Right
Right
272
Random
/fixed
effects sd
smoothed
7.103mm
1.5
-2
Slice range is -74<x<70mm, -46<y<4mm, z=-2mm; Contour is: min fMRI > 5904
Left
Sd
271
-1
Right
Right
-1
2
1
Ef
Slice range is -74<x<70mm, -46<y<4mm, z=-2mm; Contour is: min fMRI > 6214
df
Mixed
effects
15
1
Ef
Magnitude
Subj 0
2
df
202
202
204
205
204
203
201
202
200
206
205
202
204
200
x (mm)
10
FWHM (mm)
15
-50
T
0
0.5
Left
Left
0
0
5
-50
T
1
40
FWHM (mm)
15
5
0.5
0
5
x (mm)
Magnitude (%BOLD), diff - same sentence, event experiment
50
1
3
4
6
7
8
9
10
11
12
13
14
-40-20 0
y (mm)
P=0.05 threshold for local maxima is +/- 5.67
Delay shift (secs), diff - same sentence, block experiment
Mixed
effects
15
Subj 0
1
3
4
6
7
8
9
10
11
12
13
14
Mixed
effects
15
Left
Left
0.2
0.1
0
-0.1
-0.2
Ef
-0.5
2
1.5
Sd
1
0.2
271
272
271
265
264
132
270
275
269
274
248
256
264
278
1
0.5
0
Right
Right
df
Random
/fixed
effects sd
smoothed
8.8952mm
1.5
-1
Left
Left
1
0.5
40
df
202
202
204
205
204
203
201
202
200
206
205
202
204
200
0
0.5
40
-2
10
T
0
2
-50
0
5
50
0
P=0.05 threshold for local maxima is +/- 4.3
Ant.
-40-20 0
y (mm)
-2
Post.
Right
Ant.
Post.
Right
P=0.05 threshold for local maxima is +/- 4.31
x (mm)
0
-50
Left
Left
T
FWHM (mm)
15
x (mm)
FWHM (mm)
15
2
0
1
Slice range is -74<x<70mm, -46<y<4mm, z=-2mm; Contour is: magnitude, stimulus average, T statistic > 5
0.4
Sd
-40-20 0
y (mm)
0
Right
Right
Random
/fixed
effects sd
smoothed
10.6778mm
1.5
-5
0.5
Ef
Slice range is -74<x<70mm, -46<y<4mm, z=-2mm; Contour is: magnitude, stimulus average, T statistic > 5
Delay
0
Ant.
Subj 0
5
50
Post.
Right
Delay shift (secs), diff - same sentence, event experiment
-5
Ant.
Post.
Right
P=0.05 threshold for local maxima is +/- 5.68
10
0
10
0
5
50
-40-20 0
y (mm)
0
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
Best fitting block
Greater
delay
Different sentence
(sustained interest)
Same sentence
(lose interest)
SPM
BRAINSTAT
Magnitude increase for
 Sentence, Event
 Sentence, Block
 Sentence, Combined
 Speaker, Combined
at (-54,-14,-2)
Magnitude decrease for
 Sentence, Block
 Sentence, Combined
at (-54,-54,40)
Delay increase for
Sentence, Event
at (58,-18,2)
inside the region where all
conditions are activated
Conclusions

Greater %BOLD response 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)
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
2
3
z=5
1
1,4
3
Brainstat:
combined
block and
event,
threshold
at T>5.67,
P<0.05.
3
3
1
3