1. Detecting connectivity: MS lesions, cortical thickness, and the “bubbles” task in the fMRI scanner Keith Worsley, McGill (and Chicago) Nicholas Chamandy, McGill and Google Jonathan Taylor, Université de Montréal and Stanford Robert Adler, Technion Philippe Schyns, Fraser Smith, Glasgow Frédéric Gosselin, Université de Montréal Arnaud Charil, Alan Evans, Montreal Neurological Institute Oury’s course, lecture 2

2. What is ‘bubbles’?

3. Nature (2005)

4. Subject is shown one of 40 faces chosen at random … Happy Sad Fearful Neutral

5. … but face is only revealed through random ‘bubbles’ First trial: “Sad” expression Subject is asked the expression: “Neutral” Response: Incorrect Sad 75 random bubble centres Smoothed by a Gaussian ‘bubble’ What the subject sees

6. Your turn … Trial 2 Subject response: “Fearful” CORRECT

7. Your turn … Trial 3 Subject response: “Happy” INCORRECT (Fearful)

8. Your turn … Trial 4 Subject response: “Happy” CORRECT

9. Your turn … Trial 5 Subject response: “Fearful” CORRECT

10. Your turn … Trial 6 Subject response: “Sad” CORRECT

11. Your turn … Trial 7 Subject response: “Happy” CORRECT

12. Your turn … Trial 8 Subject response: “Neutral” CORRECT

13. Your turn … Trial 9 Subject response: “Happy” CORRECT

14. Your turn … Trial 3000 Subject response: “Happy” INCORRECT (Fearful)

15. 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

16. Results Mask average face But are these features real or just noise? Need statistics … Happy Sad Fearful Neutral

17. Statistical analysis Correlate bubbles with response (correct = 1, incorrect = 0), separately for each expression Equivalent to 2-sample Z-statistic for 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

18. Results Thresholded at Z=1.64 (P=0.05) Multiple comparisons correction? Need random field theory … Average face Happy Sad Fearful Neutral Z~N(0,1) statistic

19. Results, corrected for search Random field theory threshold: Z=3.92 (P=0.05) 3.82 3.80 3.81 3.80 Saddle-point approx (Chamandy, 2007): Z=↑ (P=0.05) Bonferroni: Z=4.87 (P=0.05) – nothing Average face Happy Sad Fearful Neutral Z~N(0,1) statistic

20. Scale Separate analysis of the bubbles at each scale

21. Scale space: smooth Z(s) with range of filter widths w = continuous wavelet transform adds an extra dimension to the random 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)Z(s,w)

22. -2 0 2 4 6 8 10mm and 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 they are detected as a single signal half way between them Matched Filter Theorem (= Gauss-Markov Theorem): “to best detect signal + white noise, filter should match signal” Z(s,w)Z(s,w)

23. -60-40-200204060 0 5 10 8mm and 150mm signals at the same location 5 10 15 20 6.8 15.2 34 76 170 -60-40-20 0 20 40 60 w = FWHM (mm, on log scale) s (mm) Scale space can even separate two signals at the same location! Z(s,w)Z(s,w)

24. Bubbles task in fMRI scanner Correlate bubbles with BOLD at every voxel: Calculate Z for each pair (bubble pixel, fMRI voxel) a 5D “image” of Z statistics … Trial 1 2 3 4 5 6 7 … 3000 fMRI

25. 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) for 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)

26. Generalised linear models? The random response is Y=1 (correct) or 0 (incorrect), or Y=fMRI The regressors are X j =bubble mask at pixel j, j=1 … 240x380=91200 (!) Logistic regression or ordinary regression: logit(E(Y)) or E(Y) = b 0 +X 1 b 1 +…+X 91200 b 91200 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) = b 0 +X j b j However the regressors (bubbles) are random with a simple known distribution, so turn the problem around and condition on Y: E(X j ) = c 0 +Yc j Equivalent to conditional logistic regression (Cox, 1962) which gives exact inference for b 1 conditional on sufficient statistics for b 0 Cox also suggested using saddle-point approximations to improve accuracy of inference … Interactions? logit(E(Y)) or E(Y)=b 0 +X 1 b 1 +…+X 91200 b 91200 +X 1 X 2 b 1,2 + …

27. MS lesions and cortical thickness Idea: MS lesions interrupt neuronal signals, causing thinning in down- stream cortex Data: n = 425 mild MS patients 01020304050607080 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)

28. MS lesions and cortical thickness at all pairs of points Dominated by total lesions and 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 for LD Repeat for all voxels in 3D, nodes in 2D ~1 billion correlations, so thresholding essential! Look for high negative correlations … Threshold: P=0.05, c=0.300, T=6.48

29. 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). Cluster extent rather than peak height (Friston, 1994) Z s t Peak height extent D=1 L D ( c l us t er ) » c Y Â ® k L D ( c l us t er )