The role of acidity in tumour development

Abstract

Acidic pH is a common characteristic of human tumours. It has a significant impact on tumour progression and response to therapies. In this thesis, we utilise mathematical modelling to examine the role of acidosis in the interaction between normal and tumour cell populations. In the first section we investigate the cell–microenvironmental interactions that mediate somatic evolution of cancer cells. The model predicts that selective forces in premalignant lesions act to favour cells whose metabolism is best suited to respond to local changes in oxygen, glucose and pH levels. In particular the emergent cellular phenotype, displaying increased acid production and resistance to acid-induced toxicity, has a significant proliferative advantage because it will consistently acidify the local environment in a way that is toxic to its competitors but harmless to itself. In the second section we analyse the role of acidity in tumour growth. 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. Extensions of the model show that cellular quiescence, or non-proliferation, may provide an explanation for experimentally observed cycles of acidity within tumour tissue. Analysis of both models allows assessment of novel therapies directed towards changing the level of acidity within the tumour. Finally we undertake a comparison between experimental tumour pH images and the models of acid dynamics set out in previous chapters. This analysis will allow us to assess and verify the previous modelling work, giving the mathematics a firm biological foundation. Moreover, it provides a methodology of calculating important diagnostic parameters from pH images