Breward, C. J. W. and Byrne, H. M. and Lewis, C. E. (2003) A multiphase model describing vascular tumour growth. Bulletin of Mathematical Biology, 65 . pp. 609640.

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Abstract
In this paper we present a new model framework for studying vascular tumour growth, in which the blood vessel density is explicitly considered. Our continuum model comprises conservation of mass and momentum equations for the volume fractions of tumour cells, extracellular material and blood vessels. We include the physical mechanisms that we believe to be dominant, namely birth and death of tumour cells, supply and removal of extracellular fluid via the blood and lymph drainage vessels, angiogenesis and blood vessel occlusion. We suppose that the tumour cells move in order to relieve the increase in mechanical stress caused by their proliferation. We show how to reduce the model to a system of coupled partial differential equations for the volume fraction of tumour cells and blood vessels and the phase averaged velocity of the mixture. We consider possible parameter regimes of the resulting model. We solve the equations numerically in these cases, and discuss the resulting behaviour. The model is able to reproduce tumour structure that is found `in vivo' in certain cases. Our framework can be easily modified to incorporate the effect of other phases, or to include the effect of drugs.
Item Type:  Article 

Subjects:  A  C > Biology and other natural sciences 
Research Groups:  Oxford Centre for Industrial and Applied Mathematics Centre for Mathematical Biology 
ID Code:  121 
Deposited By:  Chris J.W. Breward 
Deposited On:  01 Sep 2004 
Last Modified:  29 May 2015 18:16 
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