Keith Worsley

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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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Savic et al. (2005). Brain response to putative
pheromones in homosexual men. Proceedings of the
National Academy of Sciences, 1027356-7361
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fMRI data 120 scans, 3 scans each of hot, rest,
warm, rest, hot, rest,
T (hot warm effect) / S.d. t110 if no
effect
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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
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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
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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
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Matched Filter Theorem ( Gauss-Markov Theorem)
to best detect a signal white noise, filter
should match signal
10mm and 23mm signals
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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
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22.7
6
4
15.2
2
10.2
0
-2
6.8
-60
-40
-20
0
20
40
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t (mm)
But if the signals are too close together they
are detected as a single signal half way between
them
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Scale space can even separate two signals at the
same location!
8mm and 150mm signals at the same location
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5
0
-60
-40
-20
0
20
40
60
170
113.7
20
76
50.8
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S FWHM (mm, on log scale)
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10
22.7
15.2
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10.2
6.8
-60
-40
-20
0
20
40
60
t (mm)
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Expressive or not expressive (EXNEX)?
Male or female (GENDER)?
Correct bubbles
All bubbles
Image masked by bubbles as presented to the
subject
Correct / all bubbles
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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
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threshold
threshold
threshold
threshold
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BrainStat- the details

• Jonathan Taylor, Stanford
• Keith Worsley, McGill

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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

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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)

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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

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Conclusions

• Strong overall BOLD increase of 30.5
• Substantial subject variability (sd ratio 8)
• Evidence for greater BOLD response for different
  sentences (0.50.1)
• Evidence for greater latency for different
  sentences (0.160.04 secs)
• Event design is better for delays
• Block design is better for overall magnitude