Jonathan Taylor, Stanford Keith Worsley, McGill

Hierarchical statistical analysis of fMRI data across

runs/sessions/subjects/studiesusing 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, 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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FWHMacor

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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

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

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FWHMratio

dfeff

random effectsanalysis, dfeff = 3

fixed effects analysis, dfeff = 440

Target = 100 df FWHM = 19mm

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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

In between: use Discrete Local Maxima (DLM)

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FWHM of smoothing kernel (voxels)

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Bonferroni

Random Field Theory

Discrete Local Maxima (DLM)

STAT_SUMMARY High FWHM: use Random Field Theory

Low FWHM: use Bonferroni

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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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

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

Events

Blocks

Response

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Seconds

Beginning of block/run

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:

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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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

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

Part of slice z = -2 mm

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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

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Slice range is -74<x<70mm, -46<y<4mm, z=-2mm; Contour is: magnitude, stimulus average, T statistic > 5


FWHM (mm)


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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

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 forSentence, Eventat (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)

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.

Jonathan Taylor, Stanford Keith Worsley, McGill

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