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Hierarchical statistical analysis of fMRI data across
runs/sessions/subjects/studiesusing BRAINSTAT/FMRISTAT
Jonathan Taylor, Stanford
Keith Worsley, McGill
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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
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0 10 20 30
0
50
100
FWHMacor
0 10 20 300
50
100
FWHMacor
FMRILM: smoothing of temporal autocorrelation
Hot stimulus Hot-warm stimulus
Target = 100 df
Residual df = 110
Target = 100 df
Residual df = 110
FWHM = 10.3mm FWHM = 12.4mm
dfacor = dfresidual(2 + 1) 1 1 2 acor(contrast of data)2
dfeff dfresidual dfacor
FWHMacor2 3/2
FWHMdata2
= +
• Variability in acor lowers df• Df depends on contrast • Smoothing acor brings df back up:
Contrast of data, acor = 0.79Contrast of data, acor = 0.61
FWHMdata = 8.79
dfeff dfeff
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dfratio = dfrandom(2 + 1)1 1 1
dfeff dfratio dffixed
MULTISTAT: smoothing of random/fixed FX sd
FWHMratio2 3/2
FWHMdata2
= +e.g. dfrandom = 3, dffixed = 4 110 = 440, FWHMdata = 8mm:
0 20 40 Infinity0
100
200
300
400
FWHMratio
dfeff
random effectsanalysis, dfeff = 3
fixed effects analysis, dfeff = 440
Target = 100 df FWHM = 19mm
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0 1 2 3 4 5 6 7 8 9 100
0.02
0.04
0.06
0.08
0.1
0.12
Gaussian T, 20 df T, 10 df
Bonferroni, N=Resels
P-v
alue
FWHM of smoothing kernel (voxels)
True
Bonferroni Random Field Theory
Discrete Local Maxima
In between: use Discrete Local Maxima (DLM)
STAT_SUMMARY High FWHM: use Random Field Theory
Low FWHM: use Bonferroni
DLMcan ½
P-valuewhen
FWHM~3 voxels
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In between: use Discrete Local Maxima (DLM)
0 1 2 3 4 5 6 7 8 9 10
3.7
3.8
3.9
4
4.1
4.2
4.3
4.4
4.5
4.6
4.7
Bonferroni, N
=Resels
Gaussian
T, 20 df
T, 10 df
Gau
ssia
niz
ed
thre
sho
ld
FWHM of smoothing kernel (voxels)
True
Bonferroni
Random Field Theory
Discrete Local Maxima (DLM)
STAT_SUMMARY High FWHM: use Random Field Theory
Low FWHM: use Bonferroni
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STAT_SUMMARY example: single run, hot-warm
Detected by DLM,but not by BON or RFT
Detected by BON andDLM but not by RFT
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-5 0 5 10 15 20 25-0.4
-0.2
0
0.2
0.4
0.6
t (seconds)
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:
HRF(t + shift) ~ basis1(t) w1(shift) + basis2(t) w2(shift)
• Convolve bases with the stimulus, then add to the linear model
basis1 basis2HRF
shift
delay
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Example: FIAC data 16 subjects 4 runs per subject
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
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Events
Blocks
Response
0 50 100 150 200 250 300 350 400 450 500-0.2
0
0.2
0.4
0 50 100 150 200 250 300 350 400 450 500-0.2
0
0.2
0.4
Seconds
Beginning of block/run
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1st snt in blockS snt, S spk, B1S snt, S spk, B2S snt, D spk, B1S snt, D spk, B2D snt, S spk, B1D snt, S spk, B2D snt, D spk, B1D snt, D spk, B2 Constant Linear Quadratic Cubic Spline Whole brain avg
Design matrix for block expt
B1, B2 are basis functions for magnitude and delay:
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Motion and slice time correction (using FSL) 5 conditions
Smoothing of temporal autocorrelation to control the effective df (new!)
1st level analysis
3 contrasts Beginning of block/run
Same sent, same speak
Same sent, diff speak
Diff sent, same speak
Diff sent, diff speak
Sentence 0 -0.5 -0.5 0.5 0.5
Speaker 0 -0.5 0.5 -0.5 0.5
Interaction 0 1 -1 -1 1
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0
0.5
1
1.5
2
Diff sente Diff speak Interac
Magnitude sd (relative to error)
Event
Block
00.20.40.60.8
11.21.41.6
Diff sente Diff speak Interac
Delay sd (seconds)
Event
Block
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.
Efficiency
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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
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
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Part of slice z = -2 mm
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-2
-1
0
1
2
0
0.5
1
-5
0
5
Left Right Left R
ight Left Right P
ost.
Ant.
0
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Subj Mixed effects
Ef
Sd
T
df
Magnitude (%BOLD), diff - same sentence, event experiment
Slice range is -74<x<70mm, -46<y<4mm, z=-2mm; Contour is: min fMRI > 6214
Random /fixed effects sdsmoothed 7.0105mm
FWHM (mm)
P=0.05 threshold for local maxima is +/- 5.68
0.5
1
1.5
0
5
10
15
y (mm)
x
(mm
)
-40-20 0
-50
0
50
0
5
10
15
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-2
-1
0
1
2
0
0.5
1
-5
0
5
Left Right Left R
ight Left Right P
ost.
Ant.
0
202
1
202
3
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205
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204
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203
8
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9
202
10
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11
206
12
205
13
202
14
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15
200 40
Subj Mixed effects
Ef
Sd
T
df
Magnitude (%BOLD), diff - same sentence, block experiment
Slice range is -74<x<70mm, -46<y<4mm, z=-2mm; Contour is: min fMRI > 5904
Random /fixed effects sdsmoothed 7.103mm
FWHM (mm)
P=0.05 threshold for local maxima is +/- 5.67
0.5
1
1.5
0
5
10
15
y (mm)
x
(mm
)
-40-20 0
-50
0
50
0
5
10
15
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-0.2
-0.1
0
0.1
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0
0.2
0.4
-2
0
2
Left Right Left R
ight Left Right P
ost.
Ant.
0
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271
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Subj Mixed effects
Ef
Sd
T
df
Delay shift (secs), diff - same sentence, event experiment
Slice range is -74<x<70mm, -46<y<4mm, z=-2mm; Contour is: magnitude, stimulus average, T statistic > 5
Random /fixed effects sdsmoothed 10.6778mm
FWHM (mm)
P=0.05 threshold for local maxima is +/- 4.31
0.5
1
1.5
0
5
10
15
y (mm)
x
(mm
)
-40-20 0
-50
0
50
0
5
10
15
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-1
-0.5
0
0.5
1
0
0.5
1
1.5
2
-2
0
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Left Right Left R
ight Left Right P
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Ant.
0
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202
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Subj Mixed effects
Ef
Sd
T
df
Delay shift (secs), diff - same sentence, block experiment
Slice range is -74<x<70mm, -46<y<4mm, z=-2mm; Contour is: magnitude, stimulus average, T statistic > 5
Random /fixed effects sdsmoothed 8.8952mm
FWHM (mm)
P=0.05 threshold for local maxima is +/- 4.3
0.5
1
1.5
0
5
10
15
y (mm)
x
(mm
)
-40-20 0
-50
0
50
0
5
10
15
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Mag
nitu
deEvent Block
Del
ay
-2
-1
0
1
2
0
0.5
1
-5
0
5
Left Right Left R
ight Left Right P
ost.
Ant.
0
271
1
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271
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9
275
10
269
11
274
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248
13
256
14
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278 40
Subj Mixed effects
Ef
Sd
T
df
Magnitude (%BOLD), diff - same sentence, event experiment
Slice range is -74<x<70mm, -46<y<4mm, z=-2mm; Contour is: min fMRI > 6214
Random /fixed effects sdsmoothed 7.0105mm
FWHM (mm)
P=0.05 threshold for local maxima is +/- 5.68
0.5
1
1.5
0
5
10
15
y (mm)
x
(mm
)
-40-20 0
-50
0
50
0
5
10
15
-2
-1
0
1
2
0
0.5
1
-5
0
5
Left Right Left R
ight Left Right P
ost.
Ant.
0
202
1
202
3
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6
204
7
203
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9
202
10
200
11
206
12
205
13
202
14
204
15
200 40
Subj Mixed effects
Ef
Sd
T
df
Magnitude (%BOLD), diff - same sentence, block experiment
Slice range is -74<x<70mm, -46<y<4mm, z=-2mm; Contour is: min fMRI > 5904
Random /fixed effects sdsmoothed 7.103mm
FWHM (mm)
P=0.05 threshold for local maxima is +/- 5.67
0.5
1
1.5
0
5
10
15
y (mm)
x
(mm
)
-40-20 0
-50
0
50
0
5
10
15
-0.2
-0.1
0
0.1
0.2
0
0.2
0.4
-2
0
2
Left Right Left R
ight Left Right P
ost.
Ant.
0
271
1
272
3
271
4
265
6
264
7
132
8
270
9
275
10
269
11
274
12
248
13
256
14
264
15
278 40
Subj Mixed effects
Ef
Sd
T
df
Delay shift (secs), diff - same sentence, event experiment
Slice range is -74<x<70mm, -46<y<4mm, z=-2mm; Contour is: magnitude, stimulus average, T statistic > 5
Random /fixed effects sdsmoothed 10.6778mm
FWHM (mm)
P=0.05 threshold for local maxima is +/- 4.31
0.5
1
1.5
0
5
10
15
y (mm)
x
(mm
)
-40-20 0
-50
0
50
0
5
10
15
-1
-0.5
0
0.5
1
0
0.5
1
1.5
2
-2
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Left Right Left R
ight Left Right P
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Ant.
0
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1
202
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4
205
6
204
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203
8
201
9
202
10
200
11
206
12
205
13
202
14
204
15
200 40
Subj Mixed effects
Ef
Sd
T
df
Delay shift (secs), diff - same sentence, block experiment
Slice range is -74<x<70mm, -46<y<4mm, z=-2mm; Contour is: magnitude, stimulus average, T statistic > 5
Random /fixed effects sdsmoothed 8.8952mm
FWHM (mm)
P=0.05 threshold for local maxima is +/- 4.3
0.5
1
1.5
0
5
10
15
y (mm)
x
(mm
)
-40-20 0
-50
0
50
0
5
10
15
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Events: 0.14±0.04s; Blocks: 1.19±0.23s Both significant, P<0.05 (corrected) (!?!) Answer: take a look at blocks:
Events vs blocks for delaysin different – same sentence
Different sentence(sustained interest)
Same sentence (lose interest)
Best fitting block
Greatermagnitude
Greater delay
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SPM BRAINSTAT
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Magnitude increase for Sentence, Event Sentence, Block Sentence, Combined Speaker, Combined at (-54,-14,-2)
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Magnitude decrease for
Sentence, Block Sentence, Combined
at (-54,-54,40)
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Delay increase forSentence, Eventat (58,-18,2)inside the region where all conditions are activated
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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)
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z=-12 z=2 z=5
3
1,4
21
3 3 31
3
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.
Brainstat:combinedblock andevent, threshold at T>5.67, P<0.05.