A linear-elastic model of anisotropic tumour growth

Araujo, Robyn P. & McElwain, Donald (2004) A linear-elastic model of anisotropic tumour growth. European Journal of Applied Mathematics, 15(3), pp. 365-384.

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Abstract

This paper examines the effect of anisotropic growth on the evolution of mechanical stresses in a linear-elastic model of a growing, avascular tumour. This represents an important improvement on previous linear-elastic models of tissue growth since it has been shown recently that spatially-varying isotropic growth of linear-elastic tissues does not afford the necessary stress-relaxation for a steady-state stress distribution upon reaching a nutrient-regulated equilibrium size. Time-dependent numerical solutions are developed using a Lax-Wendroff scheme, which show the evolution of the tissue stress distributions over a period of growth until a steady-state is reached. These results are compared with the steady-state solutions predicted by the model equations, and key parameters influencing these steady-state distributions are identified. Recommendations for further extensions and applications of this model are proposed.

Impact and interest:

16 citations in Scopus
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19 citations in Web of Science®

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ID Code: 74329
Item Type: Journal Article
Refereed: Yes
DOI: 10.1017/S0956792504005406
ISSN: 1469-4425
Divisions: Current > Institutes > Institute of Health and Biomedical Innovation
Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Deposited On: 24 Jul 2014 01:01
Last Modified: 28 Jul 2014 00:43

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