A Novel Algorithm for Region-to-Region Tractography in Diffusion Tensor Imaging

Geodesic tractography is an elegant, though typically time consuming method for finding connections or ‘tracks’ between given endpoints from diffusion-weighted MRI images, which can be representative of brain white matter fibers. In this work we consider the problem of constructing bundles of tracks between seed and target regions in the most efficient way. In contrast to streamline based methods, a naive region-to-region geodesic approach for finding the true bundle requires connecting all pairs of voxels in seed and target regions and then selecting the appropriate tracks. The running time of this approach is quadratic in the number of voxels, which is prohibitively long for clinical use. Moreover, matching full seed and target regions may include voxels that are not part of the target bundle, e.g. due to segmentation inaccuracies. In order to bring geodesic tractography closer to clinical applicability, we present a novel, efficient algorithm for region-to-region geodesic tractography which extends existing point-to-point algorithms and incorporates anatomical knowledge by assuming a topographic organization of fibers. The proposed method connects only seed and target voxels that belong to the target bundle, based on iterative refinement of a Delaunay tessellation of sample points. In addition, it can be used in combination with any point-to-point tractography algorithm. A theoretical analysis shows that, under reasonable assumptions, our algorithm is significantly more efficient than the quadratic-time solution. This is also confirmed by the experiments, which reveal a reduction in computation time of up to three orders of magnitude.