doi:10.1016/j.bulm.2003.11.002 Bulletin of Mathematical Biology (2004) 66, 1039–1091 A History of the Study of Solid Tumour Growth: The Contribution of Mathematical Modelling R. P. ARAUJO AND D. L. S. MCELWAIN ∗ School of Mathematical Sciences, Queensland University of Technology, P.O. Box 2434, QLD 4001 Brisbane, Queensland, Australia E-mail: s.mcelwain@qut.edu.au A miscellany of new strategies, experimental techniques and theoretical approaches are emerging in the ongoing battle against cancer. Nevertheless, as new, ground- breaking discoveries relating to many and diverse areas of cancer research are made, scientists often have recourse to mathematical modelling in order to elu- cidate and interpret these experimental findings. Indeed, experimentalists and clin- icians alike are becoming increasingly aware of the possibilities afforded by math- ematical modelling, recognising that current medical techniques and experimental approaches are often unable to distinguish between various possible mechanisms underlying important aspects of tumour development. This short treatise presents a concise history of the study of solid tumour growth, illustrating the development of mathematical approaches from the early decades of the twentieth century to the present time. Most importantly these mathematical investigations are interwoven with the associated experimental work, showing the crucial relationship between experimental and theoretical approaches, which together have moulded our understanding of tumour growth and contributed to current anti-cancer treatments. Thus, a selection of mathematical publications, including the influential the- oretical studies by Burton, Greenspan, Liotta et al., McElwain and co-workers, Adam and Maggelakis, and Byrne and co-workers are juxtaposed with the seminal experimental findings of Gray et al. on oxygenation and radio-sensitivity, Folkman on angiogenesis, Dorie et al. on cell migration and a wide variety of other crucial discoveries. In this way the development of this field of research through the inter- actions of these different approaches is illuminated, demonstrating the origins of our current understanding of the disease. c  2003 Society for Mathematical Biology. Published by Elsevier Ltd. All rights reserved. 1. I NTRODUCTION It has been stated recently that ‘cancer is now poised to overtake heart disease as the major cause of premature death in the Western World’ (Byrne, 1999a). Indeed, ∗ Author to whom correspondence should be addressed. 0092-8240/04/051039 + 53 $30.00/0 c  2003 Society for Mathematical Biology. Published by Elsevier Ltd. All rights reserved.