Estimation of the Spatial Gradient of the MR Image from the Diffusion Profile

In the course of diffusion, water molecules experience varying values for the relaxation-time property of the underlying tissue, a factor that has not been accounted for in diffusion MRI (dMRI) modeling. Accordingly, we derive a relationship between the diffusion profile measured by dMRI and the spatial gradient of the image, and subsequently estimate the latter from the former. We test our hypothesized relationship via dMRI of the human brain (a public in vivo image and an acquired ex vivo stimulated-echo image), showing statistically significant results that may be due to our model and/or the confounding factor of "fiber continuity".