DWI signal from a medium with heterogeneous diffusivity

Introduction: In the context of diffusion in tissues, one can think of the two broad classes of restrictions to molecular motion: (i) surface restrictions (membranes), and (ii) diffusivity heterogeneity in the bulk of the tissue. The latter class encompasses variation of diffusion properties on a finite length scale, such as diffusivity contrast between cells, or between the intraand extracellular space, or between clusters of cells of different types within a voxel. Any tissue generally possesses both classes of restrictions. To assess their relative contributions and importance, it is useful to understand them separately. The case (i) of membrane restrictions has been recently considered [1]. The present work deals with the effect (ii) of the heterogeneous diffusivity using the effective-medium framework [2,3].