Effects of restricted diffusion on MR signal formation.

Numerous functional MRI (fMRI) and diffusion MR studies have recently boosted interest in the theory of MR signal formation in biological systems in the presence of mesoscopic magnetic field in homogeneities. Herein we report an exact solution to the problem of free induction decay (FID) and spin echo (SE) signal formation in the presence of a constant field gradient in three models of one-, two-, and three-dimensional restricted diffusion. We demonstrate the transition with increasing diffusion coefficient from the oscillating FID signal behavior in the static dephasing regime to a monotonic exponential behavior in the motional narrowing regime. Quantitative criteria are presented for applicability of the Gaussian approximation for the description of the MR signal. The spatial distribution of signal density and the edge enhancement effect are analyzed. We also demonstrate that the presence of restrictive barriers in a one-compartment model can lead to a quasi-two-compartment behavior of the MR signal. This result suggests a simple rationale for the experimental findings of biexponential echo attenuation curves in MR diffusion experiments with tissue systems.