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Keith Worsley Department of Mathematics and Statistics, and McConnell Brain Imaging Centre,

Correlation random fields, brain connectivity, and cosmology. Keith Worsley Department of Mathematics and Statistics, and McConnell Brain Imaging Centre, Montreal Neurological Institute, McGill University.

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Keith Worsley Department of Mathematics and Statistics, and McConnell Brain Imaging Centre,

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  1. Correlation random fields, brain connectivity, and cosmology Keith Worsley Department of Mathematics and Statistics, and McConnell Brain Imaging Centre, Montreal Neurological Institute, McGill University

  2. Savic et al. (2005). Brain response to putative pheromones in homosexual men. Proceedings of the National Academy of Sciences, 102:7356-7361

  3. First scan of fMRI data Highly significant effect, T=6.59 1000 hot 890 rest 880 870 warm 500 0 100 200 300 No significant effect, T=-0.74 820 hot 0 rest 800 T statistic for hot - warm effect warm 5 0 100 200 300 Drift 810 0 800 790 -5 0 100 200 300 Time, seconds fMRI data: 120 scans, 3 scans each of hot, rest, warm, rest, hot, rest, … T = (hot – warm effect) / S.d. ~ t110 if no effect

  4. Scale space: smooth X(t) with a range of filter widths, s = continuous wavelet transform adds an extra dimension to the random field: X(t, s) Scale space, no signal 34 8 22.7 6 4 15.2 2 10.2 0 -2 6.8 -60 -40 -20 0 20 40 60 S = FWHM (mm, on log scale) One 15mm signal 34 8 22.7 6 4 15.2 2 10.2 0 -2 6.8 -60 -40 -20 0 20 40 60 t (mm) 15mm signal best detected with a ~15mm smoothing filter

  5. Matched Filter Theorem (= Gauss-Markov Theorem): “to best detect a signal + white noise, filter should match signal” 10mm and 23mm signals 34 8 22.7 6 4 15.2 2 10.2 0 -2 6.8 -60 -40 -20 0 20 40 60 S = FWHM (mm, on log scale) Two 10mm signals 20mm apart 34 8 22.7 6 4 15.2 2 10.2 0 -2 6.8 -60 -40 -20 0 20 40 60 t (mm) But if the signals are too close together they are detected as a single signal half way between them

  6. Scale space can even separate two signals at the same location! 8mm and 150mm signals at the same location 10 5 0 -60 -40 -20 0 20 40 60 170 113.7 20 76 50.8 15 S = FWHM (mm, on log scale) 34 10 22.7 15.2 5 10.2 6.8 -60 -40 -20 0 20 40 60 t (mm)

  7. Male or female (GENDER)? Expressive or not expressive (EXNEX)? Correct bubbles All bubbles Image masked by bubbles as presented to the subject Correct / all bubbles

  8. Fig. 1. Results of Experiment 1. (a) the raw classification images, (b) the classification images filtered with a smooth low-pass (Butterworth) filter with a cutoff at 3 cycles per letter, and (c) the best matches between the filtered classification images and 11,284 letters, each resized and cut to fill a square window in the two possible ways. For (b), we squeezed pixel intensities within 2 standard deviations from the mean. Subject 1 Subject 2 Subject 3

  9. n=425 subjects, correlation = -0.56826 5.5 5 4.5 4 Average cortical thickness 3.5 3 2.5 2 1.5 0 10 20 30 40 50 60 70 80 Average lesion volume

  10. threshold threshold threshold threshold

  11. BrainStat- the details Jonathan Taylor, Stanford Keith Worsley, McGill

  12. What is BrainStat? • Based on FMRISTAT (Matlab) • Written in Python (open source) • Part of BrainPy (Poster 763 T-AM) • Concentrates on statistics • Analyses both magnitudes and delays (latencies) • P-values for peaks and clusters uses latest random field theory

  13. Details • Input data is motion corrected and preferably slice timing corrected • Output is complete hierarchical mixed effects ReML analysis (local AR(p) errors at first stage) • Spatial regularization of (co)variance ratios chosen to target 100 df (Poster 610 M-PM) • P-values for peaks and clusters are best of • Bonferroni • random field theory • discrete local maxima (Poster 539 T-AM)

  14. Methods • Slice timing and motion correction by FSL • AR(1) errors on each run • For each subject, 2 runs combined using fixed effects analysis • Spatial registration to 152 MNI by FSL • Subjects combined using mixed effects analysis • Repeated for all contrasts of both magnitudes and delays

  15. Magnitude (%BOLD), diff - same sentence Subject id, block experiment Mixed 0 1 3 4 6 7 8 9 10 11 12 13 14 15 effects 2 1 Ef 0 -1 Random /fixed -2 effects sd smoothed Contour is: average anatomy > 2000 11.5625mm 1 1.5 Sd 0.5 1 0 0.5 df 205 206 203 206 206 204 203 201 205 200 200 201 201 205 100 FWHM (mm) 5 20 20 -50 15 15 x (mm) T 0 0 10 10 5 5 50 -5 0 0 -60 -40 -20 0 P=0.05 threshold for peaks is +/- 5.1375 y (mm)

  16. Delay shift (secs), diff - same sentence Subject id, block experiment Mixed 0 1 3 4 6 7 8 9 10 11 12 13 14 15 effects 2 1 Ef 0 -1 Random /fixed -2 effects sd smoothed Contour is: magnitude, stimulus average, T statistic > 5 14.3802mm 2 1.5 1.5 Sd 1 1 0.5 0 0.5 df 205 206 203 206 206 204 203 201 205 200 200 201 201 205 100 FWHM (mm) 4 20 20 -50 2 15 15 x (mm) T 0 0 10 10 -2 5 5 50 -4 0 0 -60 -40 -20 0 P=0.05 threshold for peaks is +/- 4.0888 y (mm)

  17. Conclusions • Strong overall %BOLD increase of 3±0.5% • Substantial subject variability (sd ratio ~8) • Evidence for greater %BOLD response for different sentences (0.5±0.1%) • Evidence for greater latency for different sentences (0.16±0.04 secs) • Event design is better for delays • Block design is better for overall magnitude

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