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Mathematical modelling of fibre-enhanced perfusion inside a tissue-engineering bioreactor |
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| Authors: | Robert J. Whittaker Richard Booth Clare Bailey Shailesh Naire Zimei Rong Linda J. Cummings Lina Mawasse Marianne J. Ellis Nicola J. Kuiper |
| Affiliation: | a Mathematical Institute, University of Oxford, OX1 3LB, UK b Centre for Plant Integrative Biology, University of Nottingham, LE12 5RD, UK c School of Mathematical Sciences, University of Nottingham, NG7 2RD, UK d Department of Civil and Building Engineering, Loughborough University, LE11 3TU, UK e Complex Systems Research Center, University of New Hampshire, NH 03824, USA f School of Computing and Mathematics, University of Keele, ST5 5BG, UK g Department of Bioengineering, Imperial College London, SW7 2AZ, UK h Interdisciplinary Research Centre in Biomedical Materials, Queen Mary University of London, E1 4NS, UK i Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, NJ 07102-1982, USA j Department of Chemical Engineering, Centre for Regenerative Medicine, University of Bath, BA2 7AY, UK k Institute of Science and Technology, University of Keele, ST4 7QB, UK |
| Abstract: | We develop a simple mathematical model for forced flow of culture medium through a porous scaffold in a tissue-engineering bioreactor. Porous-walled hollow fibres penetrate the scaffold and act as additional sources of culture medium. The model, based on Darcy's law, is used to examine the nutrient and shear-stress distributions throughout the scaffold. We consider several configurations of fibres and inlet and outlet pipes. Compared with a numerical solution of the full Navier-Stokes equations within the complex scaffold geometry, the modelling approach is cheap, and does not require knowledge of the detailed microstructure of the particular scaffold being used. The potential of this approach is demonstrated through quantification of the effect the additional flow from the fibres has on the nutrient and shear-stress distribution. |
| Keywords: | Tissue engineering Bioreactor Darcy flow Mathematical modelling |
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