Random walk diffusion simulations in semi-permeable layered media with varying diffusivity

TL;DR

This paper introduces a new hybrid random walk model for simulating diffusion in semi-permeable layered media with varying diffusivity, outperforming traditional models and applicable to biological and other complex systems.

Contribution

A novel hybrid random walk transit model that separately treats membrane permeability and diffusivity changes, improving simulation accuracy over existing models.

Findings

The hybrid model overcomes limitations of the reference model.

Numerical demonstrations show improved flux accuracy.

Model applicability extends to DT-CMR and other fields.

Abstract

In this paper we present analytical and random walk based solutions to diffusion in semi-permeable layered media with varying diffusivity. We propose a new random walk transit model (hybrid model) based on treating the membrane permeability and the change in diffusion as two infinitesimal separate phenomena. By conducting an extensive analytical flux analysis, the performance of our hybrid model is compared with a commonly used membrane model (reference model). We numerically demonstrate the limitations of the reference model and show the capability of our new model to overcome these restrictions. The suitability of both random walk transit models for the application to simulations of the diffusion tensor cardiovascular magnetic resonance (DT-CMR) is assessed in a histology-based domain. We consider a larger range of permeabilities to show the potential of our model to other possible applications beyond biological tissue.