Diffusion in Cellular Systems
Prof. Brian D. Wood (Oregon State University)
Thursday 16th June, 2016 14:00-15:00 Maths 326
Diffusion of chemical species in cellular systems has relevance to a wide variety of biological applications, from understanding biofilm growth to modeling processes in oncogenesis. In this talk, I will discuss one route to deriving the effective diffusion coefficient (or tensor) for a cellular system consisting of (1) cells, (2) an extracellular matrix, and (3) a cell wall separating the two regions of the system. The process for developing the effective description of the diffusion process will be upscaling via the method of volume averaging. In this process, a set of microscale balance equations are proposed. Then, by applying appropriately weighted spatial averages over a representative volume of the system, a set of balance equations which apply at the macroscale (i.e., the support scale of the weighting functions) are developed. These macroscale equations necessarily include unclosed terms involving integrals of the microscale concentration. The formal approach for closing the problem is presented in some detail, and methods for developing both analytical and numerical solutions are described. Analytical and numerical solutions for (roughly) isotropic cellular systems is described for two cases: (1) the case where the solute is excluded from the cell, and (2) the case where the solute is actively transported across the cell wall. Comparisons of these solutions are made with experimental data for the diffusion coefficient collected from a number of studies reported in the literature. The treatment of anisotropic systems is discussed with particular relevance to its use in medical imaging studies.