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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.

Original publication

DOI

10.1007/s00285-013-0665-7

Type

Journal article

Journal

J Math Biol

Publication Date

04/2014

Volume

68

Pages

1199 - 1224

Keywords

Computer Simulation, Energy Metabolism, Glycolysis, Humans, Hydrogen-Ion Concentration, Models, Biological, Neoplasms