New approaches to estimation of white matter connectivity in diffusion tensor MRI: Elliptic PDEs and geodesics in a tensor-warped space

Abstract

We investigate new approaches to quantifying the white matter connectivity in the brain using Diffusion Tensor Magnetic Resonance Imaging data. Our first approach finds a steady-state concentration/heat distribution using the three-dimensional tensor field as diffusion/conductivity tensors. Our second approach casts the problem in a Riemannian framework, deriving from each tensor a local warping of space, and finding geodesic paths in the space. Both approaches use the information from the whole tensor, and can provide numerical measures of connectivity.