Multivalued Geodesic Ray-Tracing for Computing Brain Connections Using Diffusion Tensor Imaging

In this paper, we propose a new geodesic based algorithm for diffusion tensor fiber tracking. This technique is based on computing multi-valued solutions from the Euler-Lagrange form of the geodesic equations. Compared to other geodesic based approaches, multi-valued solutions at each grid point have been considered other than just computing the viscosity solution. This allows us to compute fibers in a region with sharp orientation, or when the correct physical solution is not the fiber computed from the first arrival time. Compared to the classical stream-line approach, our approach is less sensitive to noise, since the complete tensor is used. We also compare our algorithm with the PDE approach, using the Hamilton-Jacobi equation. We show that in the cases where the U-shaped bundles appear, our algorithm can capture the underlying fiber structure while other approaches may fail. The results for a realistic synthetic data field is shown for both methods.