Tensor Distribution Function

Diffusion weighted MR imaging is a powerful tool that can be employed to study white matter microstructure by examing the 3D displacement profile of water molecules in brain tissue. By applying diffusion-sensitizing gradients along a minimum of 6 directions, second-order tensors can be computed to model dominant diffusion processes. However, it has been shown that conventional DTI is not sufficient to resolve crossing fiber tracts. More recently, High Angular Resolution Diffusion Imaging (HARDI) seeks to address this issue by employing more than 6 gradient directions. In this paper, we introduce the Tensor Distribution Function (TDF), a probability function defined on the space of symmetric and positive definite matrices. Here, fiber crossing is modeled as an ensemble of Gaussian diffusion processes with weights specified by the TDF. Once this optimal TDF is determined, ODF can easily be computed by analytic integration of the resulting displacement probability function. Moreover, principal fiber directions can also be directly derived from the TDF.