Estimating Crossing Fibers: A Tensor Decomposition Approach

Abstract

Diffusion weighted magnetic resonance imaging is a unique tool for non-invasive investigation of major nerve fiber tracts. Since the popular diffusion tensor (DT-MRI) model is limited to voxels with a single fiber direction, a number of high angular resolution techniques have been proposed to provide information about more diverse fiber distributions. Two such approaches are Q-Ball imaging and spherical deconvolution, which produce orientation distribution functions (ODFs) on the sphere. For analysis and visualization, the maxima of these functions have been used as principal directions, even though the results are known to be biased in case of crossing fiber tracts. In this paper, we present a more reliable technique for extracting discrete orientations from continuous ODFs, which is based on decomposing their higher-order tensor representation into an isotropic component, several rank-1 terms, and a small residual. Comparing to ground truth in synthetic data shows that the novel method reduces bias and reliably reconstructs crossing fibers which are not resolved as individual maxima in the ODF. We present results on both Q-Ball and spherical deconvolution data and demonstrate that the estimated directions allow for plausible fiber tracking in a real data set.