Multiscale simulation of nutrient transport in hollow fibre membrane bioreactor for growing bone tissue: Sub-cellular scale and beyond

Abstract

Recent experimental studies suggest that hollow fibre membrane bioreactors (HFMBs) may be used to grow 3-D bone tissues in the laboratory, which may then be implanted into patients to repair skeletal defects. The HFMBs mimic the capillary network that exists in bones and are very effective in supplying nutrients to cells (to maintain cell metabolism) and removing waste products (e.g., excreta from micro-organisms, etc.). In order to guide the design of HFMBs for bone tissue engineering, it is necessary to elucidate the quantitative relationships between the cell environment and tissue behaviour in HFMBs and their relationship with nutrient supply. However, the nutrient transport processes in these bioreactors depend on several scales: from the scale of the individual cell to the scale of the bioreactors (laboratory scale). Further, the significance of the mass transfer processes is different from one scale to another. At the sub-cellular scale (i.e., within individual cell), the transport processes are dominated by diffusive-reaction mechanisms. At the extracellular matrix, these processes are primarily diffusion dominated. The transport of nutrients in the capillary network is convection dominated. At the scale of the laboratory device, the transport behaviour is governed by non-linear coupled convection–diffusion and reaction processes. Therefore, to characterise the ‘overall’ nutrient transfer processes and function of the HFMB, one needs an understanding of the processes at the smaller scale (e.g., sub-cellular scale) and their manifestation at larger scale, such as the bioreactor. This paper presents an approach for modelling and simulating nutrient transport in HFMB for growing bone tissues where the separations of scales from individual cell to the scales of bioreactor are considered. We use direct numerical simulation (finite element method) instead of more tedious applied mathematics based upscaling theorems for modelling nutrient transport in HFMB. The advantage of this approach is that it does not rely on the determination of averaged transport properties (e.g., diffusion coefficient) that appear in averaged transport equations which are often difficult to measure experimentally or may not have significant physical meaning. In this paper, the developed computational framework is used to upscale the mass transfer processes at sub-cellular scale to the scale of HFMB (laboratory scale). The developed framework is then employed to carry out a systematic analysis of the influence of various process parameters of HFMB (e.g., fluid velocity, cell density, cellular size, etc.) on the nutrient transport behaviour. It is envisaged that the developed multiscale tool will provide better understanding of the functioning of HFMB for the purposes discussed above.