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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.

Authors

E.C. Holden

S.J. Chapman



Abstract

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.

Journal Article Type Article
Publication Date 2019-10
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
APA6 Citation 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. https://doi.org/10.1017/S1446181119000130
DOI https://doi.org/10.1017/S1446181119000130
Publisher URL https://www.cambridge.org/core/journals/anziam-journal/article/multiphase-multiscale-model-for-nutrientlimited-tissue-growth-part-ii-a-simplified-description/CA0DA4642716CBAD894AA4D715527243

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