Diffusion propagators for hindered diffusion in open geometries

Abstract

The diffusion of spin‐bearing particles around simple geometrical objects like cylinders and spheres abides by the form of the diffusion propagator that specifies the probability of a particle to diffuse from one position to another within a specific time span. While diffusion propagators for diffusion inside a cylinder or sphere are well‐analyzed, diffusion propagators for hindered diffusion around these open geometries are rarely discussed in MR literature. Knowledge of such diffusion propagators for hindered diffusion allows quantifying the influence of diffusion processes on the MR signal around single vessels or blood residues and ultra‐small iron‐oxide particles, respectively, when there is no outer boundary present. In this work, analytical expressions for the diffusion propagator for hindered diffusion in one, two and three dimensions as well as the resulting correlation functions for diffusion in a dipole field around cylinders and spheres are derived. © 2015 Wiley Periodicals, Inc. Concepts Magn Reson Part A 44A: 150–159, 2015.