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A multiphase multiscale model for nutrient limited tissue growth, Part II: A simplified description

Holden, E.C.; Chapman, S.J.; Brook, B.S.; O'Dea, R.D.


E.C. Holden

S.J. Chapman

Professor of Mathematical Medicine and Biology


In this paper, we revisit and extend our recent work (Holden et al. (2018) A multiphase multiscale model for nutrient limited tissue growth, The ANZIAM Journal, 59(4), 499-532), that considers the derivation of an effective macroscale description suitable to describe the growth of biological tissue within a porous tissue-engineering scaffold. The underlying tissue dynamics is described as a multiphase mixture, thereby naturally accommodating features such as interstitial growth and active cell motion. Via a linearisation of the underlying multiphase model (whose nonlinearity poses significant challenge for such analyses), we obtain, by means of multiple-scales homogenisation, a simplified macroscale model that nevertheless retains explicit dependence on both the microscale scaffold structure and the tissue dynamics, via so-called unit cell problems that provide permeability tensors to parameterise the macroscale description. In our previous work, the cell problems retain macroscale dependence, posing significant challenges for computational implementation of the eventual macroscopic model; here, we obtain a decoupled system whereby the quasi-steady cell-problems may be solved separately from the macroscale description. Moreover, we indicate how the formulation is influenced by a set of alternative microscale boundary conditions.


Holden, E., Chapman, S., Brook, B., & O'Dea, R. (2019). A multiphase multiscale model for nutrient limited tissue growth, Part II: A simplified description. ANZIAM Journal, 61(4), 368-381.

Journal Article Type Article
Acceptance Date Jul 7, 2019
Online Publication Date Sep 18, 2019
Publication Date 2019-10
Deposit Date Jul 11, 2019
Publicly Available Date Mar 19, 2020
Journal ANZIAM Journal
Print ISSN 1446-1811
Electronic ISSN 1446-8735
Publisher Cambridge University Press (CUP)
Peer Reviewed Peer Reviewed
Volume 61
Issue 4
Pages 368-381
Public URL
Publisher URL


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