Protein transport in packed-bed ultrafiltration hollow-fibre bioreactors

Abstract

A mathematical model was developed to describe the coupled hydrodynamics and high molecular weight protein transport in cell-filled ultrafiltration hollow-fibre bioreactors (HFBRs). The multi-fibre reactor was represented by a single, straight fibre surrounded by a symmetry envelope containing a homogeneous packed bed of cells. The low Reynolds number flow in this cell-packed extracapillary space (ECS) was described by Darcy's law. Since the protein transport and HFBR hydrodynamics were coupled, numerical methods were required to solve the governing equations of both the two-dimensional (axial and radial) and one-dimensional (axial) models developed to predict the redistribution of proteins retained in the ECS. Because of the large length/radius ratio of the representative fibre unit, the two-dimensional model predictions were closely duplicated by the simpler one-dimensional model over a wide range of operating conditions. An HFBR filled with mammalian cells was simulated experimentally by filling the ECS of a hollow-fibre module with an agarose/protein solution to form a porous medium with uniform initial protein concentration. All of the ECS protein distributions, measured after 5–16 days of lumen flow, were adequately described by the model if an effective ECS conductivity of 5 × 10 −15 m 2 was assumed. The model was then used to predict transient and steady-state protein distributions in HFBRs under various packed-bed conditions. It was shown that, for low ECS conductivities typical of values measured for mammalian tissues, diffusion begins to compete effectively with convection as an important mechanism of axial protein transport. Also, the rate and extent of protein polarization in these cases was greatly reduced compared to the predictions obtained for a cell-free HFBR. The implications of these findings, particularly for product protein harvesting from a cell-packed ECS, were discussed.