A multiphase multiscale model for nutrient limited tissue growth

Authors

DOI:

https://doi.org/10.21914/anziamj.v59i0.12240

Keywords:

multiscale homogenisation, mixture theory, tissue growth, tissue engineering, porous flow.

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. doi:10.1017/S1446181118000044

Author Biographies

Elizabeth C. Holden, University of Nottingham

CMMB, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham.

Joseph Collis

CMMB, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham.

Bindi S. Brook, University of Nottingham

CMMB, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham.

Reuben D. O'Dea, University of Nottingham

CMMB, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham.

Published

2018-08-09

Issue

Section

Special Issues on Mathematical Biology