Multiphase modelling of the influence of fluid flow and chemical concentration on tissue growth in a hollow fibre membrane bioreactor

A model is developed for fluid flow, mass transport and cell distribution in a hollow-fibre membrane bioreactor. Cells are seeded throughout the extracapillary space (ECS), and fluid pumped through the bioreactor via the lumen inlet. In the lumen and porous membrane, flow is described using Stokes and Darcy governing equations respectively, whilst in the ECS porous mixture theory is used to track the volume fractions of the cells, culture medium and scaffold and to describe interactions between each phase. Reaction-advection-diffusion equations govern the concentration of a solute of interest in each region. The model equations are reduced by simplifying the geometry, and exploiting the small aspect ratio of the bioreactor as well as the dominance of cell-scaffold drag over the remaining drag components. This yields a coupled system for the cell volume fraction and solute concentration which is solved numerically for a variety of experimentally-relevant case studies. The model is used to identify different regimes of cell behaviour, and results indicate how the flow rate can be controlled experimentally to generate a uniform cell distribution.