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

O'Dea, Reuben D.; Waters, Sarah L.; Byrne, Helen M.

Authors

Reuben D. O'Dea reuben.odea@nottingham.ac.uk

Sarah L. Waters

Helen M. Byrne



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 chanotransduction 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.

Journal Article Type Article
Publication Date Aug 1, 2008
Journal European Journal of Applied Mathematics
Print ISSN 0956-7925
Electronic ISSN 0956-7925
Publisher Cambridge University Press (CUP)
Peer Reviewed Peer Reviewed
Volume 19
APA6 Citation O'Dea, R. D., Waters, S. L., & Byrne, H. M. (2008). A two-fluid model for tissue growth within a dynamic flow environment. European Journal of Applied Mathematics, 19, doi:10.1017/S0956792508007687
DOI https://doi.org/10.1017/S0956792508007687
Publisher URL http://journals.cambridge.org/action/displayJournal?jid=EJM
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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