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The buckling of capillaries in solid tumours

The buckling of capillaries in solid tumours
The buckling of capillaries in solid tumours
We develop a model of the buckling (both planar and axial) of capillaries in cancer tumours, using nonlinear solid mechanics. The compressive stress in the tumour interstitium is modelled as a consequence of the rapid proliferation of the tumour cells, using a multiplicative decomposition of the deformation gradient. In turn, the tumour cell proliferation is determined by the oxygen concentration (which is governed by the diffusion equation) and the solid stress. We apply a linear stability analysis to determine the onset of mechanical instability, and the Liapunov–Schmidt reduction to determine the postbuckling behaviour. We find that planar modes usually go unstable before axial modes, so that our model can explain the buckling of capillaries, but not as easily their tortuosity. We also find that the inclusion of anisotropic growth in our model can substantially affect the onset of buckling. Anisotropic growth also results in a feedback effect that substantially affects the magnitude of the buckle.

nonlinear elasticity, capillary, cancer, buckle
1364-5021
MacLauring, J.
180c62bd-9269-4278-8651-7c8a7e0e4251
Chapman, S.J.
2fb8f0b2-56ab-4ac7-8518-35abf1047cf9
Jones, G.W.
a862c268-9008-45aa-95b4-9b5fd15410a6
Roose, Tiina
3581ab5b-71e1-4897-8d88-59f13f3bccfe
MacLauring, J.
180c62bd-9269-4278-8651-7c8a7e0e4251
Chapman, S.J.
2fb8f0b2-56ab-4ac7-8518-35abf1047cf9
Jones, G.W.
a862c268-9008-45aa-95b4-9b5fd15410a6
Roose, Tiina
3581ab5b-71e1-4897-8d88-59f13f3bccfe

MacLauring, J., Chapman, S.J., Jones, G.W. and Roose, Tiina (2012) The buckling of capillaries in solid tumours. Proceedings of the Royal Society A. (doi:10.1098/rspa.2012.0418).

Record type: Article

Abstract

We develop a model of the buckling (both planar and axial) of capillaries in cancer tumours, using nonlinear solid mechanics. The compressive stress in the tumour interstitium is modelled as a consequence of the rapid proliferation of the tumour cells, using a multiplicative decomposition of the deformation gradient. In turn, the tumour cell proliferation is determined by the oxygen concentration (which is governed by the diffusion equation) and the solid stress. We apply a linear stability analysis to determine the onset of mechanical instability, and the Liapunov–Schmidt reduction to determine the postbuckling behaviour. We find that planar modes usually go unstable before axial modes, so that our model can explain the buckling of capillaries, but not as easily their tortuosity. We also find that the inclusion of anisotropic growth in our model can substantially affect the onset of buckling. Anisotropic growth also results in a feedback effect that substantially affects the magnitude of the buckle.

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More information

Accepted/In Press date: October 2012
e-pub ahead of print date: 15 October 2012
Keywords: nonlinear elasticity, capillary, cancer, buckle
Organisations: Bioengineering Group

Identifiers

Local EPrints ID: 344238
URI: https://eprints.soton.ac.uk/id/eprint/344238
ISSN: 1364-5021
PURE UUID: fac53a69-6f92-4aa2-80e9-62abfe339700
ORCID for Tiina Roose: ORCID iD orcid.org/0000-0001-8710-1063

Catalogue record

Date deposited: 15 Oct 2012 14:58
Last modified: 20 Jul 2019 00:49

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