  In this manuscript, we are concerned with data generated from a diffusion
tensor imaging (DTI) experiment. The goal is to parameterize manifold-like
white matter tracts, such as the corpus callosum, using principal surfaces. We
approach the problem by finding a geometrically motivated surface-based
representation of the corpus callosum and visualize the fractional anisotropy
(FA) values projected onto the surface; the method applies to any other
diffusion summary as well as to other white matter tracts. We provide an
algorithm that 1) constructs the principal surface of a corpus callosum; 2)
flattens the surface into a parametric 2D map; 3) projects associated FA values
on the map. The algorithm was applied to a longitudinal study containing 466
diffusion tensor images of 176 multiple sclerosis (MS) patients observed at
multiple visits. For each subject and visit the study contains a registered DTI
scan of the corpus callosum at roughly 20,000 voxels. Extensive simulation
studies demonstrate fast convergence and robust performance of the algorithm
under a variety of challenging scenarios.
