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A Multiphase Multiscale Model for Nutrient-limited Tissue Growth, Part II : A Simplified Description

In this paper, we revisit our previous work in which we derive 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 linearization of the underlying multiphase model (whose nonlinearity poses a significant challenge for such analyses), we obtain, by means of multiple-scale homogenization, 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 parameterize 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.

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Judul Seri

THE ANZIAM JOURNAL : THE AUSTRALIAN AND NEW ZEALAND INDUSTRIAL AND APPLIED MATHEMATICS JOURNAL; Vol.61 Issue 4 October 2019

No. Panggil

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Penerbit

: .,

Deskripsi Fisik

p. 368 - 381

Bahasa

English

ISBN/ISSN

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Klasifikasi

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Tipe Isi

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Tipe Media

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Tipe Pembawa

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Edisi

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Subjek

MIXTURE THEORY
TISSUE GROWTH
TISSUE ENGINEERING
POROUS FLOW
MULTISCALE HOMOGENIZATION

Info Detail Spesifik

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Pernyataan Tanggungjawab

Elizabeth C. Holden, S. Jonathan Chapman, Bindi S. Brook, Reuben D. O'Dea

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