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Acidic pH is a common characteristic of human tumours. It has a significant impact on tumour progression and response to therapies. In this paper, we develop a simple model of three-dimensional tumour growth to examine the role of acidosis in the interaction between normal and tumour cell populations. Both vascular and avascular tumour dynamics are investigated, and a number of different behaviours are observed. Whilst an avascular tumour always proceeds to a benign steady state, a vascular tumour may display either benign or invasive dynamics, depending on the value of a critical parameter. Analysis of the model allows us to assess novel therapies directed towards changing the level of acidity within the tumour.

Original publication




Journal article


J Theor Biol

Publication Date





476 - 484


Cell Proliferation, Disease Progression, Humans, Hydrogen-Ion Concentration, Models, Biological, Necrosis, Neoplasm Invasiveness, Neoplasms, Neovascularization, Pathologic