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A multiphase multiscale model for nutrient limited tissue growth

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


Elizabeth Holden

Joe Collis

Professor of Mathematical Medicine and Biology


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.


Holden, E., Collis, J., Brook, B. S., & O'Dea, R. D. (2018). A multiphase multiscale model for nutrient limited tissue growth. ANZIAM Journal, 59(4),

Journal Article Type Article
Acceptance Date Jan 25, 2018
Publication Date May 23, 2018
Deposit Date Jan 26, 2018
Publicly Available Date Nov 24, 2018
Journal ANZIAM Journal
Print ISSN 1446-1811
Electronic ISSN 1446-8735
Publisher Cambridge University Press
Peer Reviewed Peer Reviewed
Volume 59
Issue 4
Public URL
Publisher URL


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