Modelling of fluid flow and protein transport in hollow-fibre bioreactors
Creators: name: Labecki, Marek
Publisher: name: University of British Columbia
Year: 2009

description: A mathematical model (the Porous Medium Model, PMM) was developed to predict the fluid flow and solute transport in hollow-fibre devices, with a particular emphasis on hollowfibre bioreactors (HFBRs). In the PMM, both the extracapillary space (ECS) and the lumen side are treated as interpenetrating porous regions with a continuous source or sink of fluid. The hydrodynamic equations of the PMM are based on Darcy's law and continuity considerations while the transport of the ECS protein is described by the time-dependent convective-diffusion equation. Compared to the earlier Krogh Cylinder Model (KCM), in which the fluid flow and protein transport are assumed to be the same for each fibre, the PMM represents an improved approach in which the spatial domain corresponds to the real dimensions of the hollow-fibre module. Thus, it can be applied to operating conditions where macroscopic radial pressure and concentration gradients exist, such as in open-shell operations. It was demonstrated that, in the absence of radial gradients, the PMM becomes mathematically equivalent to the one-dimensional KCM. The PMM also takes into account the osmotic pressure dependence on the ECS protein concentration, which causes a coupling of the hydrodynamic and protein transport equations. The Porous Medium Model was tested by applying it to one- and two-dimensional closed-shell operations. Both confirmed that a significant polarization of the ECS protein occurs in the direction of the existing pressure gradients under dominant convective transport conditions. The downstream polarization of protein affects HFBR hydrodynamics by virtually shutting down the flow in a significant portion of the ECS due to locally high osmotic pressures. It can also facilitate harvesting of the product protein by increasing its concentration near the downstream ECS port. Modelling studies of the hydrodynamics of hollow-fibre devices in the partial and full filtration modes of operation were carried out for a wide range of membrane permeabilities (10"14&lt;LP&lt; 10-7 m). It was demonstrated using the PMM that, for membranes with permeabilities below about 10"13 m, practically all of the pressure drop between the inlet lumen and outlet ECS ports is due to the hydraulic resistance of the membrane. If the Lp value is increased above approximately 10'12 m, this assumption, commonly made in order to experimentally determine membrane permeabilities, begins to break down. Also, for membrane permeabilities exceeding this value, the ECS and lumen flow rates predicted by the PMM and KCM for the partial filtration mode become significantly different. Modelling of the inoculation phase of HFBR operation is used as another example application of the Porous Medium Model. PMM simulations of the inoculation phase showed that, in the case of a Gambro HFBR with a membrane permeability of the order of 10"15 m, the protein concentration distribution at the end of the inoculation period is very non-uniform and most of the shell side remains free of protein. Using a lower-concentration inoculum solution partially alleviates this problem. Alternatively, a relaxation phase with all ports closed can be applied after inoculation to help homogenize the contents of the ECS by diffusion and osmotically-driven convection. However, this process may be fairly time-consuming and may pose the risk of cell starvation due to oxygen limitations. It is suggested that introduction of the inoculum through both ECS ports simultaneously or periodic changes of the flow direction may be more efficient ways of carrying out the inoculation process. The cell-packed conditions, which exist in the ECS during the production and harvesting phases of HFBR operation, can significantly decrease the ECS hydraulic conductivity and, to a lesser extent, the effective protein diffusivity due to a decrease in the ECS porosity. The ECS permeability value affects the magnitude of convective transport in the shell side and hence the rate of protein removal from the ECS and the product concentration in the harvested solution, thereby influencing the overall efficiency of the process. High-cell-density conditions in the ECS might not allow achievement of high product removal rates and product harvest concentrations. Two modes of harvesting, the closed-lumen mode (with only the two ECS ports open) and the standard mode (with only the downstream ECS port and both lumen ports open), were compared and showed no significant differences in their efficiencies. It was found that the downstream polarization of the ECS protein prior to harvesting can considerably improve the efficiency of this process.