Mathematical modelling of fibre-enhanced perfusion inside a tissue-engineering bioreactor

Robert J. Whittaker, Richard Booth, Rosemary Dyson, Clare Bailey, Louise Parsons Chini, Shailesh Naire, Sevil Payvandi, Zimei Rong, Hannah Woollard, Linda J. Cummings, Sarah L. Waters, Lina Mawasse, Julian B. Chaudhuri, Marianne J. Ellis, Vipin Michael, Nicola J. Kuiper, Sarah Cartmell

Research output: Contribution to journalArticlepeer-review

42 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)533-546
Number of pages14
JournalJournal of Theoretical Biology
Issue number4
StatePublished - Feb 21 2009

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • General Biochemistry, Genetics and Molecular Biology
  • General Immunology and Microbiology
  • General Agricultural and Biological Sciences
  • Applied Mathematics


  • Bioreactor
  • Darcy flow
  • Mathematical modelling
  • Tissue engineering


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