Modelling nutrient transport in hollow fibre membrane bioreactors for growing three-dimensional bone tissue

Recent experimental studies suggest that hollow fibre membrane bioreactors (HFMBs) may be used to grow three-dimensional (3D) bone tissue, which may then be implanted into patients to repair skeletal defects. It has become necessary to develop a theoretical framework that elucidates the quantitative relationships between the cell environment and tissue behaviour in HFMBs in order to guide the design of effective bone tissue engineering protocols. Online measurements of the important flow and transport properties in HFMBs do not provide a very practical solution because of the very small size of the laboratory scale devices. To circumvent these difficulties and to direct further experimental investigations, a mathematical modelling framework has been developed in this study based on the Krogh cylinder assumption. The model has been developed to describe mass transfer and nutrient distribution profiles in HFMB. The governing model equations have been solved using the commercially available software, FEMLAB. FEMLAB is a MATLAB-based platform and uses the finite element method (FEM) to solve the governing equations. With the developed modelling tool, the influences of some important operating parameters, such as cell density, medium flowrate, cellular matrix thickness and hindering factors, on the nutrient concentration distribution in HFMB has been analysed. The simulated results confirm the experimental evidence that suggest that sufficiently high nutrient concentration can be maintained in HFMB to grow 3D bone tissues.