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## Detecting connectivity: MS lesions, cortical thickness, in addition to the bubbles task i

Thompson, Clive, Contributing Editor has reference to this Academic Journal, PHwiki organized this Journal Detecting connectivity: MS lesions, cortical thickness, in addition to the bubbles task in the fMRI scanner Keith Worsley, McGill ( in addition to Chicago) Nicholas Cham in addition to y, McGill in addition to Google Jonathan Taylor, Université de Montréal in addition to Stan as long as d Robert Adler, Technion Philippe Schyns, Fraser Smith, Glasgow Frédéric Gosselin, Université de Montréal Arnaud Charil, Alan Evans, Montreal Neurological Institute Ourys course, lecture 2 What is bubbles Nature (2005)

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Subject is shown one of 40 faces chosen at r in addition to om Happy Sad Fearful Neutral but face is only revealed through r in addition to om bubbles First trial: Sad expression Subject is asked the expression: Neutral Response: Incorrect Sad 75 r in addition to om bubble centres Smoothed by a Gaussian bubble What the subject sees Your turn Trial 2 Subject response: Fearful CORRECT

Your turn Trial 3 Subject response: Happy INCORRECT (Fearful) Your turn Trial 4 Subject response: Happy CORRECT Your turn Trial 5 Subject response: Fearful CORRECT

Your turn Trial 6 Subject response: Sad CORRECT Your turn Trial 7 Subject response: Happy CORRECT Your turn Trial 8 Subject response: Neutral CORRECT

Your turn Trial 9 Subject response: Happy CORRECT Your turn Trial 3000 Subject response: Happy INCORRECT (Fearful) Bubbles analysis E.g. Fearful (3000/4=750 trials): Trial 1 + 2 + 3 + 4 + 5 + 6 + 7 + + 750 = Sum Correct trials Proportion of correct bubbles =(sum correct bubbles) /(sum all bubbles) Thresholded at proportion of correct trials=0.68, scaled to [0,1] Use this as a bubble mask

Results Mask average face But are these features real or just noise Need statistics Happy Sad Fearful Neutral Statistical analysis Correlate bubbles with response (correct = 1, incorrect = 0), separately as long as each expression Equivalent to 2-sample Z-statistic as long as correct vs. incorrect bubbles, e.g. Fearful: Very similar to the proportion of correct bubbles: Response 0 1 1 0 1 1 1 1 Trial 1 2 3 4 5 6 7 750 Z~N(0,1) statistic Results Thresholded at Z=1.64 (P=0.05) Multiple comparisons correction Need r in addition to om field theory Average face Happy Sad Fearful Neutral Z~N(0,1) statistic

Results, corrected as long as search R in addition to om field theory threshold: Z=3.92 (P=0.05) 3.82 3.80 3.81 3.80 Saddle-point approx (Cham in addition to y, 2007): Z= (P=0.05) Bonferroni: Z=4.87 (P=0.05) nothing Average face Happy Sad Fearful Neutral Z~N(0,1) statistic Scale Separate analysis of the bubbles at each scale Scale space: smooth Z(s) with range of filter widths w = continuous wavelet trans as long as m adds an extra dimension to the r in addition to om field: Z(s,w) 15mm signal is best detected with a 15mm smoothing filter -2 0 2 4 6 8 Scale space, no signal 6.8 10.2 15.2 22.7 34 -60 -40 -20 0 20 40 60 -2 0 2 4 6 8 One 15mm signal 6.8 10.2 15.2 22.7 34 -60 -40 -20 0 20 40 60 w = FWHM (mm, on log scale) s (mm) Z(s,w)

-2 0 2 4 6 8 10mm in addition to 23mm signals 6.8 10.2 15.2 22.7 34 -60 -40 -20 0 20 40 60 -2 0 2 4 6 8 Two 10mm signals 20mm apart 6.8 10.2 15.2 22.7 34 -60 -40 -20 0 20 40 60 w = FWHM (mm, on log scale) s (mm) But if the signals are too close together t

Thresholding Thresholding in advance is vital, since we cannot store all the ~1 billion 5D Z values Resels = (image resels = 146.2) × (fMRI resels = 1057.2) as long as P=0.05, threshold is Z = 6.22 (approx) Only keep 5D local maxima Z(pixel, voxel) > Z(pixel, 6 neighbours of voxel) > Z(4 neighbours of pixel, voxel) Generalised linear models The r in addition to om response is Y=1 (correct) or 0 (incorrect), or Y=fMRI The regressors are Xj=bubble mask at pixel j, j=1 240×380=91200 (!) Logistic regression or ordinary regression: logit(E(Y)) or E(Y) = b0+X1b1+ +X91200b91200 But there are only n=3000 observations (trials) Instead, since regressors are independent, fit them one at a time: logit(E(Y)) or E(Y) = b0+Xjbj However the regressors (bubbles) are r in addition to om with a simple known distribution, so turn the problem around in addition to condition on Y: E(Xj) = c0+Ycj Equivalent to conditional logistic regression (Cox, 1962) which gives exact inference as long as b1 conditional on sufficient statistics as long as b0 Cox also suggested using saddle-point approximations to improve accuracy of inference Interactions logit(E(Y)) or E(Y)=b0+X1b1+ +X91200b91200+X1X2b1,2+ MS lesions in addition to cortical thickness Idea: MS lesions interrupt neuronal signals, causing thinning in down-stream cortex Data: n = 425 mild MS patients 0 10 20 30 40 50 60 70 80 1.5 2 2.5 3 3.5 4 4.5 5 5.5 Average cortical thickness (mm) Total lesion volume (cc) Correlation = -0.568, T = -14.20 (423 df)

MS lesions in addition to cortical thickness at all pairs of points Dominated by total lesions in addition to average cortical thickness, so remove these effects as follows: CT = cortical thickness, smoothed 20mm ACT = average cortical thickness LD = lesion density, smoothed 10mm TLV = total lesion volume Find partial correlation(LD, CT-ACT) removing TLV via linear model: CT-ACT ~ 1 + TLV + LD test as long as LD Repeat as long as all voxels in 3D, nodes in 2D ~1 billion correlations, so thresholding essential! Look as long as high negative correlations Threshold: P=0.05, c=0.300, T=6.48 Cluster extent rather than peak height (Friston, 1994) Choose a lower level, e.g. t=3.11 (P=0.001) Find clusters i.e. connected components of excursion set Measure cluster extent by resels Distribution: fit a quadratic to the peak: Distribution of maximum cluster extent: Bonferroni on N = clusters ~ E(EC). Z s t Peak height extent D=1

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