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

For 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.