Modelling metabolite transport in hollow fibre membrane bioreactors #

George Booth, Mohit Dalwadi, Pierre-Alexis Mouthuy, Hua Ye, Sarah Waters

12:10 Monday in 4Q56.

Part of the Physiological flows and transport session.

Abstract #

To engineer functional tissue, we need to provide appropriate biomechanical and biochemical cues to promote cell proliferation and differentiation. Mathematical modelling aims to provide a mechanistic understanding of cell growth, fluid flow and nutrient and waste transport in these systems to inform experimental design. Our experimental collaborators have developed a bio-compatible electrospun hollow fibre membrane. Cells are seeded on the outer surface of these fibres which are then cultured in a bioreactor. Nutrients and growth factors are delivered to the system via flow into the fibre lumen, and they transport to the cells by advection and diffusion through the porous membrane wall.

We develop an axisymmetric transport model to describe nutrient delivery to cells, and waste metabolite removal. We first consider steady Stokes flow in and around the membrane, and derive a reduced model by exploiting the small aspect ratio of bioreactor radius to length. To model nutrient transport, we make a coordinate transformation of our advection-diffusion-reaction equations into a streamfunction-arclength formulation. This reduces our governing equations to a coupled system of effective 1D heat equations with non-constant coefficients. These equations can be coupled to the fluid flow model and solved using the Method of Lines to reveal how nutrient delivery to cells depends on membrane permeability. We then determine how spatial variations in scaffold permeability can be established to tune nutrient delivery to the cells, and consider the trade-off between maximising nutrient delivery and minimising local mechanical disruption to the cell.