Generalized Diffusion Tensor Imaging (GDTI): A Method for Characterizing and Imaging Diffusion Anisotropy Caused by Non‐Gaussian Diffusion

Abstract

AbstractFor non‐Gaussian distributed random displacement, which is common in restricted diffusion, a second‐order diffusion tensor is incapable of fully characterizing the diffusion process. The insufficiency of a second‐order tensor is evident in the limited capability of diffusion tensor imaging (DTI) in resolving multiple fiber orientations within one voxel of human white matter. A generalized diffusion tensor imaging (GDTI) method was recently proposed to solve this problem by generalizing Fick's law to a higher‐order partial differential equation (PDE). The relationship between the higher‐order tensor coefficients of the PDE and the higher‐order cumulants of the random displacement can be derived. The statistical property of the diffusion process was fully characterized via the higher‐order tensor coefficients by reconstructing the probability density function (PDF) of the molecular random displacement. Those higher‐order tensor coefficients can be measured using conventional diffusion‐weighted imaging or spectroscopy techniques. Simulations demonstrated that this method was capable of quantitatively characterizing non‐Gaussian diffusion and accurately resolving multiple fiber orientations. It can be shown that this method is consistent with the q‐space approach. The second‐order approximation of GDTI was shown to be DTI.