Journal Article

A continuum model of cell proliferation and nutrient transport in a perfusion bioreactor

Muhammad Shakeel, Paul C. Matthews, Richard S. Graham and Sarah L. Waters

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 30, issue 1, pages 21-44
Published in print March 2013 | ISSN: 1477-8599
Published online October 2011 | e-ISSN: 1477-8602 | DOI:
A continuum model of cell proliferation and nutrient transport in a perfusion bioreactor

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  • Applied Mathematics
  • Biomathematics and Statistics


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Tissue engineering aims to regenerate, repair or replace organs or defective tissues. This tissue regeneration often occurs in a bioreactor. Important challenges in tissue engineering include ensuring adequate nutrient supply, maintaining the desired cell distribution and achieving sufficiently high cell yield. To put laboratory experiments into a theoretical framework, mathematical modelling of the physical and biochemical processes involved in tissue growth is a useful tool. In this work, we derive and solve a model for a cell-seeded porous scaffold placed in a perfusion bioreactor in which fluid delivers nutrients to the cells. The model describes the key features, including fluid flow, nutrient delivery, cell proliferation and consequent variation of scaffold porosity. Fluid flow through the porous scaffold is modelled by Darcy's law, and nutrient delivery is described by a reaction–advection–diffusion equation. A reaction–diffusion equation describes the evolution of cell density, in which cell proliferation is modelled via logistic growth and cell spreading via non-linear diffusion, which depends on cell density. The effect of shear stress on nutrient consumption and cell proliferation is also included in the model. COMSOL (a commercial finite element solver) is used to solve the model numerically. The results reveal the dependence of the cell distribution and total cell yield on the initial cell density and scaffold porosity. We suggest various seeding strategies and scaffold designs to improve the cell distribution and total cell yield in the engineered tissue construct.

Keywords: in vitro tissue engineering; mathematical model; fluid flow; nutrient transport; cell proliferation

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

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