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A MULTIPHASE MULTISCALE MODEL FOR NUTRIENT LIMITED TISSUE GROWTH

Part of: Mathematical biology in general

Published online by Cambridge University Press:  23 May 2018

E. C. HOLDEN Open the ORCID record for E. C. HOLDEN [Opens in a new window] ,
J. COLLIS Open the ORCID record for J. COLLIS [Opens in a new window] ,
B. S. BROOK Open the ORCID record for B. S. BROOK [Opens in a new window]  and
R. D. O’DEA Open the ORCID record for R. D. O’DEA [Opens in a new window]
E. C. HOLDEN
Affiliation:
CMMB, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, UK email elizabeth.holden@nottingham.ac.uk, bindi.brook@nottingham.ac.uk, reuben.odea@nottingham.ac.uk
J. COLLIS
Affiliation:
CMMB, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, UK email elizabeth.holden@nottingham.ac.uk, bindi.brook@nottingham.ac.uk, reuben.odea@nottingham.ac.uk
B. S. BROOK
Affiliation:
CMMB, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, UK email elizabeth.holden@nottingham.ac.uk, bindi.brook@nottingham.ac.uk, reuben.odea@nottingham.ac.uk
R. D. O’DEA*
Affiliation:
CMMB, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, UK email elizabeth.holden@nottingham.ac.uk, bindi.brook@nottingham.ac.uk, reuben.odea@nottingham.ac.uk
*
✉reuben.odea@nottingham.ac.uk
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Abstract

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We derive an effective macroscale description for the growth of tissue on a porous scaffold. A multiphase model is employed to describe the tissue dynamics; linearisation to facilitate a multiple-scale homogenisation provides an effective macroscale description, which incorporates dependence on the microscale structure and dynamics. In particular, the resulting description admits both interstitial growth and active cell motion. This model comprises Darcy flow, and differential equations for the volume fraction of cells within the scaffold and the concentration of nutrient, required for growth. These are coupled with Stokes-type cell problems on the microscale, incorporating dependence on active cell motion and pore scale structure. The cell problems provide the permeability tensors with which the macroscale flow is parameterised. A subset of solutions is illustrated by numerical simulations.

Keywords

multiscale homogenisationmixture theorytissue growthtissue engineeringporous flow

MSC classification

Primary: 92B05: General biology and biomathematics
Type
Research Article
Information
The ANZIAM Journal , Volume 59 , Issue 4 , April 2018 , pp. 499 - 532
Copyright
© 2018 Australian Mathematical Society 

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