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

FWHM acor FWHM acor FMRILM: smoothing of temporal autocorrelation Hot stimulus Hot-warm stimulus Target = 100 df Residual df = 110 Target = 100 df Residual df = 110 FWHM = 10.3mmFWHM = 12.4mm df acor = df residual ( ) acor(contrast of data) 2 df eff df residual df acor FWHM acor 2 3/2 FWHM data 2 = + Variability in acor lowers df Df depends on contrast Smoothing acor brings df back up: Contrast of data, acor = 0.79 Contrast of data, acor = 0.61 FWHM data = 8.79 df eff

df ratio = df random ( ) df eff df ratio df fixed MULTISTAT: smoothing of random/fixed FX sd FWHM ratio 2 3/2 FWHM data 2 = + e.g. df random = 3, df fixed = 4  110 = 440, FWHM data = 8mm: 02040Infinity FWHM ratio df eff random effects analysis, df eff = 3 fixed effects analysis, df eff = 440 Target = 100 df FWHM = 19mm

GaussianT, 20 dfT, 10 df Bonferroni, N=Resels P-value 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 DLM can ½ P-value when FWHM ~3 voxels

In between: use Discrete Local Maxima (DLM) Bonferroni, N=Resels Gaussian T, 20 df T, 10 df Gaussianized threshold 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

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

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) ~ basis 1 (t) w 1 (shift) + basis 2 (t) w 2 (shift) Convolve bases with the stimulus, then add to the linear model basis 1 basis 2 HRF 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 Beginning of block/run

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!) 1 st 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 Speaker Interaction01 1

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

2 nd 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!) 3 rd level analysis

Part of slice z = -2 mm

Magnitude EventBlock Delay

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 delays in different – same sentence Different sentence (sustained interest) Same sentence (lose interest) Best fitting block Greater magnitude 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 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)

z=-12z=2z=5 3 1, 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: combined block and event, threshold at T>5.67, P<0.05.