On the Problem of Diffusivity in Heterogeneous Biological Materials with Random Structure

Abstract

Biological tissues are multicompartmental heterogeneous media composed of cellular and subcellular domains. Randomly walking water molecules may have different diffusion coefficients and densities (concentrations) in different domains, namely within cells and within the outer medium. Results of the proposed effective media scale-averaging iterative scheme are used to explore the effects of a large range of microstructural and compositional parameters on the apparent (effective) diffusion coefficient. A self-consistent modelling framework for predicting the steady-state effective diffusion coefficient is presented; the framework reveals the strong dependence of the apparent diffusion coefficient on the ratio of the microscopic diffusion coefficients of the comprising phases, permeability of the cells, and their volume fractions.