A history of the study of solid tumour growth: The contribution of mathematical modelling
 R. P. Araujo,
 D. L. S. McElwain
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A miscellany of new strategies, experimental techniques and theoretical approaches are emerging in the ongoing battle against cancer. Nevertheless, as new, groundbreaking discoveries relating to many and diverse areas of cancer research are made, scientists often have recourse to mathematical modelling in order to elucidate and interpret these experimental findings. Indeed, experimentalists and clinicians alike are becoming increasingly aware of the possibilities afforded by mathematical 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 anticancer treatments.
Thus, a selection of mathematical publications, including the influential theoretical studies by Burton, Greenspan, Liotta et al., McElwain and coworkers, Adam and Maggelakis, and Byrne and coworkers are juxtaposed with the seminal experimental findings of Gray et al. on oxygenation and radiosensitivity, 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 interactions of these different approaches is illuminated, demonstrating the origins of our current understanding of the disease.
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 Title
 A history of the study of solid tumour growth: The contribution of mathematical modelling
 Journal

Bulletin of Mathematical Biology
Volume 66, Issue 5 , pp 10391091
 Cover Date
 20040901
 DOI
 10.1016/j.bulm.2003.11.002
 Print ISSN
 00928240
 Online ISSN
 15229602
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Industry Sectors
 Authors

 R. P. Araujo ^{(1)}
 D. L. S. McElwain ^{(1)}
 Author Affiliations

 1. School of Mathematical Sciences, Queensland University of Technology, P.O. Box 2434, QLD 4001, Brisbane, Queensland, Australia