A ray tracing method for geodesic based tractography in diffusion tensor images

We present multi-valued solution algorithm for geodesic-based fiber tracking in a tensor-warped space given by diffusion tensor imaging data. This technique is based on solving ordinary differential equations describing geodesics by a ray tracing algorithm. The algorithm can capture all possible geodesics connecting two given points instead of a single geodesic captured by Hamilton-Jacobi based algorithms. Once the geodesics have been computed, using suitable connectivity measures, we can choose among all solutions the most likely connection pathways which correspond best to the underlying real fibrous structures. In comparison with other approaches, our algorithm gives the possibility of applying different cost functions in a fast post-processing. Moreover, the algorithm can be used for capturing possible multi-path connections between two points that can happen when, e.g., pathologies are presented. Synthetic second order diffusion tensor data in a two dimensional space are employed to illustrate the potential applications of the algorithm to fiber tracking.