The Mathematical Institute, University of Oxford, Eprints Archive

A general reaction-diffusion model of acidity in cancer invasion

Mcgillen, J B and Gaffney, E. A. and Martin, N K and Maini, P. K. (2014) A general reaction-diffusion model of acidity in cancer invasion. Journal of Mathematical Biology, 68 (5). pp. 1199-1224.



We model the metabolism and behaviour of a developing cancer tumour in the context of its microenvironment, with the aim of elucidating the consequences of altered energy metabolism. Of particular interest is the Warburg Effect, a widespread preference in tumours for cytosolic glycolysis rather than oxidative phosphorylation for glucose breakdown, as yet incompletely understood. We examine a candidate explanation for the prevalence of the Warburg Effect in tumours, the acid-mediated invasion hypothesis, by generalising a canonical non-linear reaction–diffusion model of acid-mediated tumour invasion to consider additional biological features of potential importance. We apply both numerical methods and a non-standard asymptotic analysis in a travelling wave framework to obtain an explicit understanding of the range of tumour behaviours produced by the model and how fundamental parameters govern the speed and shape of invading tumour waves. Comparison with conclusions drawn under the original system—a special case of our generalised system—allows us to comment on the structural stability and predictive power of the modelling framework.

Item Type:Article
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:1818
Deposited By: Philip Maini
Deposited On:12 Mar 2014 08:45
Last Modified:29 May 2015 19:30

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