Semiparametric geometric methods for extracting and modeling white matter volumetric structures of the brain

White matter axonal fibers are the long range communications connections between gray matter regions of the brain. Among many others, two questions that anatomists would like to ask about living brains are: Which gray matter regions are directly connected to each other by white matter fibers? Given that a number of white matter fibers start out in one region of gray matter how many end up in another specific region of gray matter? These questions are difficult to answer using current modeling methods. We present a new modeling method called the Semiparametric Geometric Model that addresses these and other questions about white matter. The Semiparametric Geometric Model takes Diffusion Magnetic Resonance Images as input, automatically segments the white matter fiber bundles, and outputs a global nonlinear geometric model of the white matter tracts. Volumes, surfaces and curves are well defined in this model. This allows the fibers to be partitioned into volumes that enable these types of questions to be directly addressed. The model produces a curvilinear coordinate system that allows white matter to be analyzed according its actual structure rather than the arbitrary rectilinear organization of the imaging data. This enables new methods of statistical analysis of the geometry and tissue properties of white matter.