Detecting Connectivity Between Images: MS Lesions,
Cortical Thickness, and the 'Bubbles' Task in an fMRI Experiment
Keith
Worsley
Department of Mathematics and Statistics
McGill University
Thursday,
March 8, 2007
3:30 PM, 115
Ford Hall
Minneapolis, East Bank Campus
Social at 3:00 PM, 300 Ford Hall
We
are interested in the general problem of detecting
connectivity, or high correlation, between pairs of pixels or voxels in
two
sets of images. To do this, we set a
threshold on the correlations that controls the false positive rate,
which we
approximate by the expected Euler characteristic of the excursion set. An exact expression for this is found using
new results in random field theory involving Lipschitz-Killing
curvatures and
Jonathan Taylor's Gaussian Kinematic Formula. The first example is a
data set
on 425 multiple sclerosis patients. Lesion
density was measured at each voxel in
white matter, and cortical thickness was measured at each point on the
cortical
surface. The hypothesis is that
increased lesion density interrupts neuronal activity, provoking
cortical
thinning in those grey matter regions connected through the affected
white
matter regions. The second example is an
fMRI experiment using the 'bubbles' task. In
this experiment, the subject is asked to
discriminate between images that are revealed only through a random set
of
small windows or 'bubbles'. We are
interested in which parts of the image are used in successful
discrimination,
and which parts of the brain are involved in this task.