Asymmetric fiber trajectory distribution estimation using streamline differential equation.

Abstract

Fiber orientation distribution estimation with diffusion magnetic resonance imaging (dMRI) is critical in white matter fiber tractography which is most commonly based on symmetric crossing structures. Ambiguous spatial correspondence between estimated diffusion directions and fiber geometry, such as asymmetric crossing, bending, fanning, or kissing, makes tractography challenging. Consequently, numerous tracts suggest intertwined connections in unexpected regions of the white matter or actually stop prematurely in the white matter. In this work, we propose a novel asymmetric fiber trajectory distribution (FTD) function defined on neighboring voxels based on a streamline differential equation from fluid mechanics. The spatial consistency with intra- and inter-voxel constraints is derived for FTD estimation by introducing the concept of divergence. At a local level, the FTD is a series of curve flows that minimize the energy function, characterizes the relations between fibers and joint fiber fragments within the same fiber bundle. Experiments are performed on FiberCup phantom, ISMRM 2015 Tractography challenge data, and in vivo brain dMRI data for qualitative and quantitative evaluations. Results show that our approach can reveal continuous asymmetric FTD details that are potentially useful for robust tractography.