Spatially regularized low-rank tensor approximation for accurate and fast tractography.

Tractography based on diffusion Magnetic Resonance Imaging (dMRI) is the prevalent approach to the in vivo delineation of white matter tracts in the human brain. Many tractography methods rely on models of multiple fiber compartments, but the local dMRI information is not always sufficient to reliably estimate the directions of secondary fibers. Therefore, we introduce two novel approaches that use spatial regularization to make multi-fiber tractography more stable. Both represent the fiber Orientation Distribution Function (fODF) as a symmetric fourth-order tensor, and recover multiple fiber orientations via low-rank approximation. Our first approach computes a joint approximation over suitably weighted local neighborhoods with an efficient alternating optimization. The second approach integrates the low-rank approximation into a current state-of-the-art tractography algorithm based on the unscented Kalman filter (UKF). These methods were applied in three different scenarios. First, we demonstrate that they improve tractography even in high-quality data from the Human Connectome Project, and that they maintain useful results with a small fraction of the measurements. Second, on the 2015 ISMRM tractography challenge, they increase overlap, while reducing overreach, compared to low-rank approximation without joint optimization or the traditional UKF, respectively. Finally, our methods permit a more comprehensive reconstruction of tracts surrounding a tumor in a clinical dataset. Overall, both approaches improve reconstruction quality. At the same time, our modified UKF significantly reduces the computational effort compared to its traditional counterpart, and to our joint approximation. However, when used with ROI-based seeding, joint approximation more fully recovers fiber spread.