Brain white matter tractography based on riemannian manifold

摘要

Diffusion tensor imaging (DTI) is the only noninvasive technique of analyzing and qualifying water molecule's diffusion anisotropy in brain tissues. This paper presented a novel algorithm to analyze DTI and brain white matter tractography based on Riemannian manifold. Firstly, a 3x3 symmetric positive definite covariant tensor was constructed for each voxel using DTI, so brain white matte can be represented as a tensor field. Secondly, the tensor field was regarded as Riemannian manifold, and the fluid motion in the tensor field was represented by Navier-Stoke equation, so the problem of brain white matter tractography between two voxels can be transformed into the computation of smallest distance between two points in Riemannian manifold. Finally, distances between two points in Riemannian manifold can be represented by geodesic, and the numerical solution was based on Level-Set method, which was the brain white matter tractography. In experiment, this paper compared our method and the traditional algorithm based on a digital DTI phantom. The experiment result showed that our method could accurately retrieve the DTI tractography, and was more robust than traditional algorithm.