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

doi:10.1016/j.jtbi.2008.10.013

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

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

42 Scopus citations

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.

Original language	English (US)
Pages (from-to)	533-546
Number of pages	14
Journal	Journal of Theoretical Biology
Volume	256
Issue number	4
DOIs	https://doi.org/10.1016/j.jtbi.2008.10.013
State	Published - 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

Keywords

Bioreactor
Darcy flow
Mathematical modelling
Tissue engineering

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10.1016/j.jtbi.2008.10.013

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Whittaker, R. J., Booth, R., Dyson, R., Bailey, C., Parsons Chini, L., Naire, S., Payvandi, S., Rong, Z., Woollard, H., Cummings, L. J., Waters, S. L., Mawasse, L., Chaudhuri, J. B., Ellis, M. J., Michael, V., Kuiper, N. J., & Cartmell, S. (2009). Mathematical modelling of fibre-enhanced perfusion inside a tissue-engineering bioreactor. Journal of Theoretical Biology, 256(4), 533-546. https://doi.org/10.1016/j.jtbi.2008.10.013

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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.",

keywords = "Bioreactor, Darcy flow, Mathematical modelling, Tissue engineering",

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

note = "Funding Information: Dr. Cartmell and Dr. Kuiper wish to acknowledge the financial support of a private local charity. Dr Waters is grateful to the EPSRC for funding in the form of an Advanced Research Fellowship. Dr. Cummings wishes to thank the City College of New York's Department of Chemical Engineering and Levich Institute for hospitality during a stay as a visiting professor. ",

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doi = "10.1016/j.jtbi.2008.10.013",

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Whittaker, RJ, Booth, R, Dyson, R, Bailey, C, Parsons Chini, L, Naire, S, Payvandi, S, Rong, Z, Woollard, H, Cummings, LJ, Waters, SL, Mawasse, L, Chaudhuri, JB, Ellis, MJ, Michael, V, Kuiper, NJ & Cartmell, S 2009, 'Mathematical modelling of fibre-enhanced perfusion inside a tissue-engineering bioreactor', Journal of Theoretical Biology, vol. 256, no. 4, pp. 533-546. https://doi.org/10.1016/j.jtbi.2008.10.013

TY - JOUR

T1 - Mathematical modelling of fibre-enhanced perfusion inside a tissue-engineering bioreactor

AU - Whittaker, Robert J.

AU - Booth, Richard

AU - Dyson, Rosemary

AU - Bailey, Clare

AU - Parsons Chini, Louise

AU - Naire, Shailesh

AU - Payvandi, Sevil

AU - Rong, Zimei

AU - Woollard, Hannah

AU - Cummings, Linda J.

AU - Waters, Sarah L.

AU - Mawasse, Lina

AU - Chaudhuri, Julian B.

AU - Ellis, Marianne J.

AU - Michael, Vipin

AU - Kuiper, Nicola J.

AU - Cartmell, Sarah

N1 - Funding Information: Dr. Cartmell and Dr. Kuiper wish to acknowledge the financial support of a private local charity. Dr Waters is grateful to the EPSRC for funding in the form of an Advanced Research Fellowship. Dr. Cummings wishes to thank the City College of New York's Department of Chemical Engineering and Levich Institute for hospitality during a stay as a visiting professor.

PY - 2009/2/21

Y1 - 2009/2/21

N2 - 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.

AB - 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.

KW - Bioreactor

KW - Darcy flow

KW - Mathematical modelling

KW - Tissue engineering

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AN - SCOPUS:58749086882

SN - 0022-5193

VL - 256

SP - 533

EP - 546

JO - Journal of Theoretical Biology

JF - Journal of Theoretical Biology

IS - 4

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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