Geodesic ray-tracing in white matter fiber crossing region using decomposition of 4th order tensor

Abstract

The streamline methods in Diffusion tensor imaging (DTI) use principal eigenvectors for tracking white matter fibers. In comparison, the geodesics in a multivalued ray-tracing method are closer to the actual underlying white matter fibers. This method provides multiple solutions in the form of geodesics in a Riemannian space. These geodesics are robust in tracking high curvature structures in the presence of noise. In the DTI modality, the 2nd order tensor fails to model the heterogeneous regions, e.g., crossing/merging fibers. Therefore, the ray-tracing method is limited to guide the geodesics in these regions. This work, as a first step, utilizes 4th order tensor approximation for the white matter regions. Subsequently, a non-linear optimization is performed to decompose 4th order tensors into multiple 2nd order tensors keeping their symmetric positive definite property. We are using the initial fiber directions from the diagonal components of the 4th order tensor and use the 4th order tensor decomposition for fiber tracking. The experimental results on synthetic images show that geodesics can traverse in heterogeneous and high curvature structures.