Continuum soft tissue models from upscaling of arrays of hyperelastic cells

Barry, R. G., Hill, N. A. and Stewart, P. S. (2022) Continuum soft tissue models from upscaling of arrays of hyperelastic cells. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 478(2266), 20220065. (doi: 10.1098/rspa.2022.0065)

Abstract

Constitutive models for soft tissue mechanics are typically constructed by fitting phenomenological models to experimental measurements. However, a significant challenge is to rationally construct soft tissue models that encode the properties of the constituent cells and their extracellular matrix. This work presents a framework to derive multiscale soft tissue models that incorporate properties of individual cells without assuming homogeneity or periodicity at the cell level. We consider a viscoelastic model for each cell (which can deform, grow and divide), that we couple to form a network description of a one-dimensional line of cells. We use a discrete-to-continuum approach to form (nonlinear) continuum partial differential equation models for the tissue. These models elucidate the contrasting role of the two forms of dissipation: substrate dissipation localizes the deformation to the neighbourhood of the free boundary and inhibits morphoelastic growth, whereas internal cell dissipation promotes spatial uniformity and does not influence the elongation length. Furthermore, cell division is shown to increase the rate of elongation of the array compared with growth alone, provided the substrate dissipation is proportional to the cell surface area.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Stewart, Professor Peter and Hill, Professor Nicholas and Barry, Ms Roxanna
• Authors: Barry, R. G., Hill, N. A., and Stewart, P. S.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences
• Publisher: The Royal Society
• ISSN: 1364-5021
• ISSN (Online): 1471-2946
• Published Online: 12 October 2022
• Copyright Holders: Copyright © 2022 The Authors
• First Published: First published in Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences 478(2266): 20220065
• Publisher Policy: Reproduced under a Creative Commons License
• Data DOI: 10.5525/gla.researchdata.1008

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
172141		EPSRC Centre for Multiscale soft tissue mechanics with application to heart & cancer	Raymond Ogden	Engineering and Physical Sciences Research Council (EPSRC)	EP/N014642/1	M&S - Mathematics