Probabilistic Cortical and Myocardial Fiber Tracking in Diffusion Tensor Imaging

This thesis involves the tracking of white matter and heart fibers, using diffusion tensor imaging data and high resolution MR scans. Dynamic programming is employed to generate fibers linking regions of interest in the brain and heart with paths that minimize an energy constraint. From the diffusion tensor data it is possible to determine the probability that a fiber passing through a particular voxel is oriented in a particular direction. One can define the energy associated with a path connecting a given voxel to one of its neighboring voxels as the inverse of the probability of a fiber being oriented in the direction of this neighbor. In addition assume this energy is additive. Thus the energy associated with a path between two voxels and passing through a third voxel, is the equal to the sum of the energies associated with the path from the starting voxel to the intermediate voxel and the path from the intermediate voxel to the ending voxel. Thus to determine the optimal path between a start and an end voxel, we search over all paths connecting the two voxels and choose the path in which the total energy is minimized. In order for this search to be performed more efficiently, dynamic programming is used to reduce the complexity of the problem. In addition a technique to extend the dynamic programming algorithm is presented to take into account not only the diffusion tensor information, but also accomodate any prior information about the Frenet characteristics of cortical and myocardial fibers. Properties of average curvature and average torsion of the fibers are incorporated into the cost function of the dynamic programming algorithm, so as to better model fibers.