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A multiscale analysis of nutrient transport and biological tissue growth in vitro

O'Dea, Reuben D.; Nelson, Martin, R.; El Haj, A.; Waters, Sarah L.; Byrne, Helen M.

Authors

Martin, R. Nelson

A. El Haj

Sarah L. Waters

Helen M. Byrne



Abstract

In this paper, we consider the derivation of macroscopic equations appropriate to describe the growth of biological tissue, employing a multiple-scale homogenisation method to accommodate explicitly the influence of the underlying microscale structure of the material, and its evolution, on the macroscale dynamics. Such methods have been widely used to study porous and poroelastic materials; however, a distinguishing feature of biological tissue is its ability to remodel continuously in response to local environmental cues. Here, we present the derivation of a model broadly applicable to tissue engineering applications, characterised by cell proliferation and extracellular matrix deposition in porous scaffolds used within tissue culture systems, which we use to study coupling between fluid flow, nutrient transport and microscale tissue growth. Attention is restricted to surface accretion within a rigid porous medium saturated with a Newtonian fluid; coupling between the various dynamics is achieved by specifying the rate of microscale growth to be dependent upon the uptake of a generic diffusible nutrient. The resulting macroscale model comprises a Darcy-type equation governing fluid flow, with flow characteristics dictated by the assumed periodic microstructure and surface growth rate of the porous medium, coupled to an advection--reaction equation specifying the nutrient concentration. Illustrative numerical simulations are presented to indicate the influence of microscale growth on macroscale dynamics, and to highlight the importance of including experimentally-relevant microstructural information in order to correctly determine flow dynamics and nutrient delivery in tissue engineering applications.

Journal Article Type Article
Publication Date Oct 15, 2014
Journal Mathematical Medicine and Biology
Print ISSN 1477-8599
Electronic ISSN 1477-8599
Publisher Oxford University Press (OUP)
Peer Reviewed Peer Reviewed
APA6 Citation O'Dea, R. D., Nelson, M. R., El Haj, A., Waters, S. L., & Byrne, H. M. (2014). A multiscale analysis of nutrient transport and biological tissue growth in vitro. Mathematical Medicine and Biology, doi:10.1093/imammb/dqu015
DOI https://doi.org/10.1093/imammb/dqu015
Keywords multiscale homogenization; porous flow; tissue engineering
Publisher URL http://imammb.oxfordjournals.org/content/early/2014/10/15/imammb.dqu015.short
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
Additional Information This is a pre-copyedited, author-produced PDF of an article accepted for publication in Mathematical Medicine and Biology following peer review. The version of record is available online at: http://imammb.oxfordjou.../15/imammb.dqu015.short

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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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