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Modelling the interactions between tumour cells and a blood vessel in a microenvironment within a vascular tumour

Breward, C.J.W., Byrne, H.M. and Lewis, C.E. (2001) Modelling the interactions between tumour cells and a blood vessel in a microenvironment within a vascular tumour. European Journal of Applied Mathematics, 12 (5). pp. 529-556. ISSN 0956-7925


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In this paper, we develop a mathematical model to describe interactions between tumour cells and a compliant blood vessel that supplies oxygen to the region. We assume that, in addition to proliferating, the tumour cells die through apoptosis and necrosis. We also assume that pressure differences within the tumour mass, caused by spatial variations in proliferation and degradation, cause cell motion. We couple the behaviour of the blood vessel into the model for the oxygen tension. The model equations track the evolution of the densities of live and dead cells, the oxygen tension within the tumour, the live and dead cell speeds, the pressure and the width of the blood vessel. We present explicit solutions to the model for certain parameter regimes, and then solve the model numerically for more general parameter regimes. We show how the resulting steady-state behaviour varies as the key model parameters are changed. Finally, we discuss the biological implications of our work.

Item Type: Article
Copyright, Publisher and Additional Information: © 2001 Cambridge University Press. Reproduced in accordance with the publisher's self-archiving policy.
Institution: The University of Sheffield
Academic Units: The University of Sheffield > Faculty of Medicine, Dentistry and Health (Sheffield) > School of Medicine (Sheffield) > Division of Genomic Medicine (Sheffield) > Department of Oncology (Sheffield)
Depositing User: Repository Assistant
Date Deposited: 25 Oct 2006
Last Modified: 05 Jun 2014 15:33
Published Version: http://dx.doi.org/10.1017/S095679250100448X
Status: Published
Publisher: Cambridge University Press
Refereed: Yes
Identification Number: 10.1017/S095679250100448X
URI: http://eprints.whiterose.ac.uk/id/eprint/1563

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