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A linear-elastic model of anisotropic tumour growth

Published online by Cambridge University Press:  01 September 2004

R. P. ARAUJO  and
D. L. S. McELWAIN
R. P. ARAUJO
Affiliation:
School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane 4001, Queensland, Australia
D. L. S. McELWAIN
Affiliation:
School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane 4001, Queensland, Australia
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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.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 15 , Issue 3 , June 2004 , pp. 365 - 384
Copyright
2004 Cambridge University Press

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