Upscaling diffusion and reaction processes in multicellular systems considering different cell populations

• A local mass equilibrium model for multicellular systems is derived.
• The effective diffusivity is computed theoretically through a closure problem.
• The effective diffusivity depends on the proportion between living and dead cells.
• Theoretical percent errors are computed when only one type of cell is considered.
• There is a range of parameter values in which the percent errors are at least 10%.

In this work, we derive a mass equilibrium model to describe the diffusion and reaction processes in a cell cluster composed of different cell populations. This study extends previous ones in which the existence of only one type of cell population was considered. The microscopic description is used to derive an upscaled model for diffusion and reaction in multicellular systems using the method of volume averaging. The effective diffusivity coefficient that appears in the upscaled equation is predicted by solving a closure problem in simple 2D unit cells. This effective coefficient depends on the volumetric fraction of the cells, the cell distribution, and the ratios of microscopic diffusivities, permeabilities and solubilities that measure the differences between the physical properties of living cells. It was found that there is a wide range of these parameter values in which the effect of considering different cell populations is important, leading to errors in the predictions of the effective diffusivity with respect to those resulting from assuming that there is only one type of cell population.