Hierarchical statistical analysis of fMRI data across

runs/sessions/subjects/studiesusing BRAINSTAT / FMRISTAT

Jonathan Taylor, StanfordKeith 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

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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:

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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

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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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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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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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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 0.5Speaker 0 -0.5 0.5 -0.5 0.5Interaction 0 1 -1 -1 1

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Magnitude sd (relative to error)

EventBlock

00.20.40.60.8

11.21.41.6

Diff sente Diff speak Interac

Delay sd (seconds)

EventBlock

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

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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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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

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Subj Mixed effects

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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

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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

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P=0.05 threshold for local maxima is +/- 4.3

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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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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

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P=0.05 threshold for local maxima is +/- 5.67

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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

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P=0.05 threshold for local maxima is +/- 4.31

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Subj Mixed effects

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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

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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

31,4

21

3 3 313

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.