title: Mathematical modelling of fibre-enhanced perfusion inside a tissue-engineering bioreactor.
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.
authors.affiliation: Mathematical Institute, University of Oxford, OX13LB, UK.
authors.forename: Robert J
authors.initials: RJ
authors.lastname: Whittaker
authors.forename: Richard
authors.initials: R
authors.lastname: Booth
authors.forename: Rosemary
authors.initials: R
authors.lastname: Dyson
authors.forename: Clare
authors.initials: C
authors.lastname: Bailey
authors.forename: Louise
authors.initials: L
authors.lastname: Parsons Chini
authors.forename: Shailesh
authors.initials: S
authors.lastname: Naire
authors.forename: Sevil
authors.initials: S
authors.lastname: Payvandi
authors.forename: Zimei
authors.initials: Z
authors.lastname: Rong
authors.forename: Hannah
authors.initials: H
authors.lastname: Woollard
authors.forename: Linda J
authors.initials: LJ
authors.lastname: Cummings
authors.forename: Sarah L
authors.initials: SL
authors.lastname: Waters
authors.forename: Lina
authors.initials: L
authors.lastname: Mawasse
authors.forename: Julian B
authors.initials: JB
authors.lastname: Chaudhuri
authors.forename: Marianne J
authors.initials: MJ
authors.lastname: Ellis
authors.forename: Vipin
authors.initials: V
authors.lastname: Michael
authors.forename: Nicola J
authors.initials: NJ
authors.lastname: Kuiper
authors.forename: Sarah
authors.initials: S
authors.lastname: Cartmell
mesh_terms: D019149:Bioreactors; D003470:Culture Media; D006801:Humans; D008954:Models, Biological; D010477:Perfusion; D016062:Porosity; D012212:Rheology; D013314:Stress, Mechanical; D023822:Tissue Engineering / Q000295:instrumentation / Q000379:methods*
chemical_list: D003470:Culture Media