Asymmetric Fiber Trajectory Distribution Estimated Using Streamline Differential Equation

Fiber orientation distribution (FOD) estimation with diffusion magnetic resonance imaging (dMRI) is critical in white matter fiber tractography which is most commonly implemented by tracking the principal direction of the FOD step by step. Ambiguous spatial correspondences between estimated diffusion directions and fiber geometry, such as crossing, fanning or bending, makes tractography challenging. As a consequence, a lot of tracts suggest intertangled connections in unexpected regions of the white matter or actually stop prematurely in the white matter. In this work, we propose a novel fiber distribution function (FDF) defined on neighboring voxels based on the streamline differential equation from fluid mechanics. At a local level, the FDF is a series of curve flows which minimizes the energy function characterizing the relations between fibers and the joint fiber fragments within the same fiber bundle. Experiments were performed on FiberCup phantom data and an artificial phantom brain data for qualitative and quantitative evaluation. The results demonstrate that our approach can reveal continuous asymmetric fiber trajectory distribution details which is potential for robust tractography.