Spatial Image Gradient Estimation From the Diffusion MRI Profile

In the course of diffusion, water molecules encounter varying values for the relaxation-time properties of the underlying tissue. This factor, which has rarely been accounted for in diffusion MRI (dMRI), is modeled in this work, allowing for the estimation of the gradient of relaxation-time properties from the dMRI signal.

With the aim of mining the dMRI data for information about spatial variations in tissue relaxation-time properties, a new mathematical relationship between the diffusion signal and the spatial gradient of the image is derived, enabling the estimation of the latter from the former. The hypothesis was validated on human brain dMRI images from three datasets: the public Human Connectome Project Young Adults database, 10 healthy volunteers and 1 ex vivo sample scanned in-house with stimulated-echo diffusion encoding and a long diffusion time of 1 s (which we have made publicly available), and three subjects from the public Multi-TE database. The effects of the confounding factor of "fiber continuity" were furthermore measured.

The spatial image gradient estimated from the diffusion signal was compared to the gold-standard spatial gradient approximated using the finite difference method. The former gradient was significantly related to the latter in all datasets (i.e., with a difference significantly smaller than chance), with an effect distinct from fiber continuity.

The results support the hypothesized relationship between within-voxel dMRI signal and image gradient, with an effect that was not explainable by the confounding factor of fiber continuity.