Mathematical models for tumour invasion

Mathematical modelling of tumour invasion and cancer development has grown dramatically in recent years, with mathematics being applied to understand more complex and specific tumour mechanisms such as angiogenesis and metastasis. One such mechanism that has gained attention is aerobic glycolysis due to the association of this mechanism with increased tissue invasion, increases in angiogenesis and metastasis and some evidence suggesting it causes an increase in chemoresistance. Aerobic glycolysis is an altered metabolism that results in the extracellular tumour environment becoming acidic. This acidity has been hypothesised to be a mechanism for invasion termed the acid-mediation hypothesis. This is the hypothesis that the acidification of the tumour and surrounding microenvironment causes destruction of normal tissue ahead of the tumour-host interface, removing competitive forces and allowing the tumour to invade. This thesis looks to develop mathematical models and methods for examining tumour invasion with these models and methods being applied to the acid-meditation hypothesis. Through the examination we hope to gain a better understanding of the implications of the acid-mediation hypothesis and potential methods that can be used to counteract this invasion. Our analysis will also provide a greater insight in to certain models for invasion and their limitations, as well as providing methods for the analysis of similar models.