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Residual stress generation and necrosis formation in multi-cell tumour spheroids

Residual stress generation and necrosis formation in multi-cell tumour spheroids
Residual stress generation and necrosis formation in multi-cell tumour spheroids
We consider how cell proliferation and death generate residual stresses within a multi-cell tumour spheroid (MCTS). Previous work by Jones and co-workers [8] has shown that isotropic growth in a purely elastic MCTS produces growth induced stresses which eventually become unbounded, and hence are physically unrealistic. Since viscoelastic materials show stress relaxation under a fixed deformation we consider the effect of the addition of a small amount of viscosity to the elastic system by examining formation of equilibrium stress profiles within a Maxwell type viscoelastic MCTS. A model of necrosis formation based upon that proposed by Please and co-workers (see [16] [17] [18]) is then presented in which necrosis forms under conditions of adverse mechanical stress rather than in regions of extreme chemical stress as is usually assumed. The influence of rheology on necrosis formation is then investigated, and it is shown that the excessive stress generated in the purely elastic tumour can be relieved either by the addition of some viscosity to the system or by accounting for an inner necrotic interface with an appropriate stress boundary condition.
growth induced stress, necrosis, multi-cell tumour spheroid, continuum mechanics
0303-6812
537-552
MacArthur, Ben D.
2c0476e7-5d3e-4064-81bb-104e8e88bb6b
Please, Colin P.
118dffe7-4b38-4787-a972-9feec535839e
MacArthur, Ben D.
2c0476e7-5d3e-4064-81bb-104e8e88bb6b
Please, Colin P.
118dffe7-4b38-4787-a972-9feec535839e

MacArthur, Ben D. and Please, Colin P. (2004) Residual stress generation and necrosis formation in multi-cell tumour spheroids. Journal of Mathematical Biology, 49 (6), 537-552. (doi:10.1007/s00285-004-0265-7).

Record type: Article

Abstract

We consider how cell proliferation and death generate residual stresses within a multi-cell tumour spheroid (MCTS). Previous work by Jones and co-workers [8] has shown that isotropic growth in a purely elastic MCTS produces growth induced stresses which eventually become unbounded, and hence are physically unrealistic. Since viscoelastic materials show stress relaxation under a fixed deformation we consider the effect of the addition of a small amount of viscosity to the elastic system by examining formation of equilibrium stress profiles within a Maxwell type viscoelastic MCTS. A model of necrosis formation based upon that proposed by Please and co-workers (see [16] [17] [18]) is then presented in which necrosis forms under conditions of adverse mechanical stress rather than in regions of extreme chemical stress as is usually assumed. The influence of rheology on necrosis formation is then investigated, and it is shown that the excessive stress generated in the purely elastic tumour can be relieved either by the addition of some viscosity to the system or by accounting for an inner necrotic interface with an appropriate stress boundary condition.

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Published date: 2004
Keywords: growth induced stress, necrosis, multi-cell tumour spheroid, continuum mechanics

Identifiers

Local EPrints ID: 29262
URI: http://eprints.soton.ac.uk/id/eprint/29262
ISSN: 0303-6812
PURE UUID: 70422866-b1ae-4a8b-b9d8-4cd6c8d0c504

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Date deposited: 11 May 2006
Last modified: 07 Jan 2022 22:22

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Author: Colin P. Please

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