From Mutation to Metastasis: The Mathematical Modelling of the Stages of Tumour Development

  • M. A. J. Chaplain
Part of the Modeling and Simulation in Science, Engineering, & Technology book series (MSSET)


Cancer is a complicated multi-stage process beginning at the intra-cellular level of genetic mutation processing to the inter-cellular level and then in some cases the inter-organ level (metastasis). There are three well-recognised carcinogenic agents which are known to directly cause tumour growth in animals or induce cell transformation and purposeless proliferation in vitro-viruses, chemical carcinogens and radiation. The genetic mutations occurring at the single cell level lead among other things to the transformed cells escaping the normal growth control mechanisms. This in turn, coupled with a favourable local environment and adequate nutrient supply, leads to the formation of a rapidly growing mass of tissue — a solid tumour. In the case of a malignant tumour, such as a carcinoma, this early growth remains avascular and limited in size to a few millimeters in diameter (cf. multicellular spheroids). The tumour cells may then secrete certain chemicals (angiogenic factors) which induce neighbouring blood vessels to form a well-organised capillary network which grows toward and connects with the primary tumour. Once supplied with its own micro-circulation invasive growth of the tumour is possible and the tumour cells may then spread to distant parts of the body via the lymph or blood systems. This chapter presents some mathematical models describing avascular tumour growth, angiogenesis and pre-invasive growth.


Necrotic Core Quiescent Cell Endothelial Cell Density Multicellular Spheroid Growth Inhibitory Factor 
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© Springer Science+Business Media New York 1997

Authors and Affiliations

  • M. A. J. Chaplain
    • 1
  1. 1.School of Mathematical SciencesUniversity of BathBathUK

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