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

Handle URI:
http://hdl.handle.net/10754/597325
Title:
A multiscale analysis of nutrient transport and biological tissue growth in vitro
Authors:
O'Dea, R. D.; Nelson, M. R.; El Haj, A. J.; Waters, S. L.; Byrne, H. M.
Abstract:
© The authors 2014. In this paper, we consider the derivation of macroscopic equations appropriate to describe the growth of biological tissue, employing a multiple-scale homogenization 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, characterized 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 to correctly determine flow dynamics and nutrient delivery in tissue engineering applications.
Citation:
O’Dea RD, Nelson MR, El Haj AJ, Waters SL, Byrne HM (2014) A multiscale analysis of nutrient transport and biological tissue growth in vitro . Mathematical Medicine and Biology 32: 345–366. Available: http://dx.doi.org/10.1093/imammb/dqu015.
Publisher:
Oxford University Press (OUP)
Journal:
Mathematical Medicine and Biology
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
15-Oct-2014
DOI:
10.1093/imammb/dqu015
PubMed ID:
25323738
Type:
Article
ISSN:
1477-8599; 1477-8602
Sponsors:
This publication was based on work supported in part by Award No. KUK-C1-013-04, made by KingAbdullah University of Science and Technology (KAUST).We thank E. Baas (ISTM, Keele University)for the provision of experimental data. We acknowledge helpful contributions from J.R. King, and alsothank R. Penta, R.J. Shipley and D. Ambrosi. Lastly, we thank the anonymous reviewers for their helpfulsuggestions.
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Full metadata record

DC FieldValue Language
dc.contributor.authorO'Dea, R. D.en
dc.contributor.authorNelson, M. R.en
dc.contributor.authorEl Haj, A. J.en
dc.contributor.authorWaters, S. L.en
dc.contributor.authorByrne, H. M.en
dc.date.accessioned2016-02-25T12:30:43Zen
dc.date.available2016-02-25T12:30:43Zen
dc.date.issued2014-10-15en
dc.identifier.citationO’Dea RD, Nelson MR, El Haj AJ, Waters SL, Byrne HM (2014) A multiscale analysis of nutrient transport and biological tissue growth in vitro . Mathematical Medicine and Biology 32: 345–366. Available: http://dx.doi.org/10.1093/imammb/dqu015.en
dc.identifier.issn1477-8599en
dc.identifier.issn1477-8602en
dc.identifier.pmid25323738en
dc.identifier.doi10.1093/imammb/dqu015en
dc.identifier.urihttp://hdl.handle.net/10754/597325en
dc.description.abstract© The authors 2014. In this paper, we consider the derivation of macroscopic equations appropriate to describe the growth of biological tissue, employing a multiple-scale homogenization 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, characterized 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 to correctly determine flow dynamics and nutrient delivery in tissue engineering applications.en
dc.description.sponsorshipThis publication was based on work supported in part by Award No. KUK-C1-013-04, made by KingAbdullah University of Science and Technology (KAUST).We thank E. Baas (ISTM, Keele University)for the provision of experimental data. We acknowledge helpful contributions from J.R. King, and alsothank R. Penta, R.J. Shipley and D. Ambrosi. Lastly, we thank the anonymous reviewers for their helpfulsuggestions.en
dc.publisherOxford University Press (OUP)en
dc.subjectMultiscale homogenizationen
dc.subjectPorous flowen
dc.subjectTissue engineeringen
dc.titleA multiscale analysis of nutrient transport and biological tissue growth in vitroen
dc.typeArticleen
dc.identifier.journalMathematical Medicine and Biologyen
dc.contributor.institutionUniversity of Nottingham, Nottingham, United Kingdomen
dc.contributor.institutionNG11 8NS, Nottingham, United Kingdomen
dc.contributor.institutionKeele University, Keele, United Kingdomen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en

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