A multiphase multiscale model for nutrient limited tissue growth

Holden, Elizabeth C.; Collis, Joseph; Brook, Bindi S.; O'Dea, Reuben D.

Abstract

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.

Citation

Holden, E. C., Collis, J., Brook, B. S., & O'Dea, R. D. (2017). A multiphase multiscale model for nutrient limited tissue growth. ANZIAM Journal, 59, 499-532. https://doi.org/10.21914/anziamj.v59i0.12240

• Journal Article Type: Article
• Acceptance Date: Jan 25, 2018
• Online Publication Date: May 23, 2018
• Publication Date: 2017
• Deposit Date: Sep 28, 2020
• Journal: ANZIAM Journal
• Print ISSN: 1446-1811
• Publisher: Cambridge University Press
• Peer Reviewed: Peer Reviewed
• Volume: 59
• Pages: 499-532
• DOI: https://doi.org/10.21914/anziamj.v59i0.12240
• Public URL: https://nottingham-repository.worktribe.com/output/4929773