Formulation and Efficient Computation of l1 - and Smoothness Penalized Estimates for Microstructure-Informed Tractography.

Fiber tractography based on diffusion-weighted magnetic resonance imaging is to date the only method for the three-dimensional visualization of nerve fiber bundles in the living human brain noninvasively. However, various existing methods suffer from reconstructing anatomically implausible fiber tracks due to exclusive local treatment of the input data. A method that seeks to filter out invalid tracks in a postprocessing step by solving a convex optimization problem with l1 -norm regularization was recently introduced in the work by Daducci et al. In this paper, we derive an improved version of this method by adding Sobolev-norm regularization terms. Furthermore, we present a robust and efficient strategy using the alternating direction method of multipliers and dimension reduction using truncated singular value decomposition to solve the resulting optimization problem. The qualitative results show the applicability of the algorithm to large in vivo data sets. The quantitative results and numerical experiments for diffusion phantom data with known ground truth show the benefits of the proposed method.

Semi-local tractography strategies using neighborhood information.

Fiber tractography based on Diffusion MRI measurements is a valuable tool for the detection and visual representation of neural pathways in vivo. We present a novel fiber orientation distribution function (ODF) based streamline tractography approach which incorporates information of neighboring regions derived from a Bayesian model. In each iteration step, the proposed algorithm defines a set of candidate fiber fragments continuing the already tracked path and assigns an a-posteriori probability. We compute the posterior as the normalized product of a likelihood function based on the given ODF-field and a prior distribution representing anatomical plausibility of a candidate fiber fragment with respect to tract curvature derived from the previously tracked fiber path by an extrapolation strategy. We derive both a deterministic tractography algorithm obtaining in each iteration a tracking direction by maximum a-posteriori estimation, as well as a probabilistic version drawing a direction from the marginalized posterior distribution. Compared to fiber tracking methods that rely only on the local ODF, the proposed algorithm proves more robust in the presence of noise and partial volume effects. We demonstrate the effectiveness of both our deterministic and probabilistic method on simulated, phantom, and in vivo data.