Validating the Tensor Distribution Function for Fiber Reconstruction in HARDI (High-Angular Resolution Diffusion Imaging)

Abstract

Introduction: Diffusion tensor imaging (DTI) reveals white matter microstructure and fiber pathways in the living brain by examining the 3D diffusion profile of water molecules in brain tissue. Even so, DTI-derived measures will be incorrect where fibers cross or mix, as the single tensor model cannot resolve these more complicated white matter configurations. High-angular resolution diffusion imaging (HARDI) addresses this problem by applying more than 6 independent diffusion-sensitized gradients. Many HARDI reconstruction methods (e.g., q-ball imaging, DOT, PAS) impose restrictive assumptions on fibers, e.g., all fiber tracts must have the same anisotropy profile. Here we model the HARDI signal more flexibly, as in [1], as a unit-mass probability density on the 6D manifold of symmetric positive definite tensors, yielding a Tensor Distribution Function (TDF), or continuous mixture of tensors, at each point in the brain. The TDF can model fiber crossing and non-Gaussian diffusion. From the TDF, one can derive analytic formulae for the water displacement probability function, orientation distribution function (ODF), tensor orientation distribution function (TOD), and their corresponding anisotropy measures. Here we further develop the TDF framework, verifying its accuracy in revealing fiber crossings in human brain HARDI data.