Degree Name

Doctor of Philosophy


School of Mathematics and Applied Sciences


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.


Holder, Andrew Brett, Mathematical models for tumour invasion, Doctor of Philosophy thesis, School of Mathematics and Applied Sciences, University of Wollongong, 2015.

FoR codes (2008)

010201 Approximation Theory and Asymptotic Methods, 010202 Biological Mathematics, 010204 Dynamical Systems in Applications



Unless otherwise indicated, the views expressed in this thesis are those of the author and do not necessarily represent the views of the University of Wollongong.