Analysis of Fiber Reconstruction Accuracy in High Angular Resolution Diffusion Images (HARDI)

Introduction: High angular resolution diffusion imaging (HARDI) is a powerful extension of MRI that maps the directional diffusion of water in the brain. With more diffusion gradients and directions, fiber directions may be tracked with greater angular precision, fiber crossings can be resolved, and anisotropy measures can be derived from the full fiber orientation density function. To better reconstruct HARDI, we recently introduced the tensor distribution function (TDF), which models multidirectional diffusion as a probabilistic mixture of all symmetric positive definite tensors [1]. The TDF overcomes limitations of several HARDI reconstruction methods (e.g., q-ball imaging, DOT, PAS) which restrict all component fibers in a voxel to have the same anisotropy profile. The TDF models the HARDI signal more flexibly, as a unit-mass probability density on the 6D manifold of symmetric positive definite tensors, yielding a TDF, or continuous mixture of tensors, at each point in the brain. From the TDF, one can derive analytic formulae for the orientation distribution function (ODF), tensor orientation density (TOD), and their corresponding anisotropy measures. Because this model can accurately resolve sharp signal peaks in angular space where fibers cross, we studied how many gradients are required in practice to compute accurate orientation density functions, as more gradients require longer scanning times. In simulated two-fiber systems with varying Rician noise, we assessed how many diffusionsensitized gradients were sufficient for (1) accurately resolving the diffusion profile, and (2) measuring the exponential isotropy (EI), a TDF-derived measure of fiber integrity that exploits the full multidirectional HARDI signal.