Modeling diffusion in white matter in the brain: a composite porous medium

We model diffusion in white matter fascicles as a problem of diffusion in an array of identical thick-walled cylindrical tubes immersed in an outer medium and arranged periodically in a regular lattice. The diffusing molecules have different diffusion coefficients and concentrations (or densities) within the tubes' inner core, membrane, myelin sheath, and within the outer medium. For an impermeable myelin sheath, diffusing molecules within the inner core are completely restricted, while molecules in the outer medium are hindered due to the tortuosity of the array of impenetrable tubes.