Diffusion in compartmental systems. I. A comparison of an analytical model with simulations

This article examines the way in which microscopic tissue parameters affect the signal attenuation of diffusion-weighted MR experiments. The influence of transmembrane water flux on the signal decay is emphasized using the Kärger equations, which are modified with respect to the cellular boundary restrictions for intra- and extracellular diffusion. This analytical approach is extensively compared to Monte-Carlo simulations for a tissue model consisting of two compartments. It is shown that diffusion-weighted MR methods provide a unique tool for estimation of the intracellular exchange time. Restrictions of applicability to in vivo data are examined. It is shown that the intracellular exchange time strongly depends on the size of a cell, leading to an apparent diffusion time dependence for in vivo data. Hence, an analytical model of a two-compartment system with an averaged exchange time is inadequate for the interpretation of signal curves measured in vivo over large ranges of b-values. Furthermore, differences of multiexponential signal curves, as obtained by different methods of diffusion weighting, can be explained by the influence of transmembrane water flux.