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A two-fluid model for tissue growth within a dynamic flow environment

Published online by Cambridge University Press:  01 December 2008

R. D. O'DEA ,
S. L. WATERS  and
H. M. BYRNE
R. D. O'DEA
Affiliation:
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD email: reuben.odea@nottingham.ac.uk
S. L. WATERS
Affiliation:
Mathematical Institute, 24-29 St Giles', Oxford, OX1 3LB
H. M. BYRNE
Affiliation:
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD email: reuben.odea@nottingham.ac.uk
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Abstract

We study the growth of a tissue construct in a perfusion bioreactor, focussing on its response to the mechanical environment. The bioreactor system is modelled as a two-dimensional channel containing a tissue construct through which a flow of culture medium is driven. We employ a multiphase formulation of the type presented by G. Lemon, J. King, H. Byrne, O. Jensen and K. Shakesheff in their study (Multiphase modelling of tissue growth using the theory of mixtures. J. Math. Biol. 52(2), 2006, 571–594) restricted to two interacting fluid phases, representing a cell population (and attendant extracellular matrix) and a culture medium, and employ the simplifying limit of large interphase viscous drag after S. Franks in her study (Mathematical Modelling of Tumour Growth and Stability. Ph.D. Thesis, University of Nottingham, UK, 2002) and S. Franks and J. King in their study (Interactions between a uniformly proliferating tumour and its surrounding: Uniform material properties. Math. Med. Biol. 20, 2003, 47–89).

The novel aspects of this study are: (i) the investigation of the effect of an imposed flow on the growth of the tissue construct, and (ii) the inclusion of a mechanotransduction mechanism regulating the response of the cells to the local mechanical environment. Specifically, we consider the response of the cells to their local density and the culture medium pressure. As such, this study forms the first step towards a general multiphase formulation that incorporates the effect of mechanotransduction on the growth and morphology of a tissue construct.

The model is analysed using analytic and numerical techniques, the results of which illustrate the potential use of the model to predict the dominant regulatory stimuli in a cell population.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 19 , Issue 6 , December 2008 , pp. 607 - 634
Copyright
Copyright © Cambridge University Press 2008

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