In this paper we present random walk based solutions to diffusion in semi-permeable layered media with varying diffusivity.
We propose a novel transit model for solving the interaction of random walkers with a membrane. This hybrid model is
based on treating the membrane permeability and the step change in diffusion coefficient as two interactions separated by
an infinitesimally small layer. By conducting an extensive analytical flux analysis, the performance of our hybrid model is
compared with a commonly used membrane transit model (reference model). Numerical simulations demonstrate the limitations
of the reference model in dealing with step changes in diffusivity and show the capability of the hybrid model to overcome
this limitation and to offer substantial gains in computational efficiency. The suitability of both random walk transit models
for the application to simulations of diffusion tensor cardiovascular magnetic resonance (DT-CMR) imaging is assessed in a
histology-based domain relevant to DT-CMR. In order to demonstrate the usefulness of the new hybrid model for other possible
applications, we also consider a larger range of permeabilities beyond those commonly found in biological tissues.