Permeability and surface area of cell membranes from the DWI signal

Introduction: Diffusion of water in living tissues is strongly restricted on the length scale of cell sizes, ~10 μm. The consequence of such a restriction is a ubiquitous non-Gaussian shape of the diffusion-weighted imaging (DWI) signal, log S(b) = -bD + (K/6)(bD) + ..., where b=qt. In particular, the probability distribution function for water molecules is characterized by a noticeable kurtosis K [1]; however, the microscopic origins of this non-Gaussian diffusion are not understood. The restrictions can potentially originate from two sources. The first is the difference in bulk diffusivity D between the extraand intra-cellular compartments. The second is the finite permeability of cell membranes. Here we demonstrate that the presence of membranes alone leads to non-Gaussian diffusion, and suggest a model to determine cell permeability from the DWI signal.