Interactive Visualization of Volumetric White Matter Connectivity in DT-MRI Using a Parallel-Hardware Hamilton-Jacobi Solver

In this paper we present a method to compute and visualize volumetric white matter connectivity in diffusion tensor magnetic resonance imaging (DT-MRI) using a Hamilton-Jacobi (H-J) solver on the GPU (Graphics Processing Unit). Paths through the volume are assigned costs that are lower if they are consistent with the preferred diffusion directions. The proposed method finds a set of voxels in the DTI volume that contain paths between two regions whose costs are within a threshold of the optimal path. The result is a volumetric optimal path analysis, which is driven by clinical and scientific questions relating to the connectivity between various known anatomical regions of the brain. To solve the minimal path problem quickly, we introduce a novel numerical algorithm for solving H-J equations, which we call the Fast Iterative Method (FIM). This algorithm is well-adapted to parallel architectures, and we present a GPU-based implementation, which runs roughly 50-100 times faster than traditional CPU-based solvers for anisotropic H-J equations. The proposed system allows users to freely change the endpoints of interesting pathways and to visualize the optimal volumetric path between them at an interactive rate. We demonstrate the proposed method on some synthetic and real DT-MRI datasets and compare the performance with existing methods.