A multiphase multiscale model for nutrient limited tissue growth

Holden, Elizabeth and Collis, Joe and Brook, Bindi S. and O'Dea, Reuben D. (2018) A multiphase multiscale model for nutrient limited tissue growth. ANZIAM Journal, 59 (4). pp. 499-532. ISSN 1446-8735

[img] PDF - Repository staff only until 23 November 2018. - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (7MB)

Abstract

In this work, an effective macroscale description is derived 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 to underlying Stokes-type cell problems that provide permeability tensors, with multiscale dependence incorporating active cell motion, with which to parameterise the macroscale flow. A subset of solutions are illustrated by numerical simulations.

Item Type: Article
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1017/S1446181118000044
Depositing User: Holden, Elizabeth
Date Deposited: 26 Jan 2018 13:46
Last Modified: 16 Jul 2018 13:45
URI: http://eprints.nottingham.ac.uk/id/eprint/49326

Actions (Archive Staff Only)

Edit View Edit View