A mathematical analysis of a model for tumour angiogenesis

M. A. J. Chaplain, Suan M. Giles, B. D. Sleeman, R. J. Jarvis

Research output: Contribution to journalArticlepeer-review

55 Citations (Scopus)

Abstract

In order to accomplish the transition from avascular to vascular growth, solid tumours secrete a diffusible substance known as tumour angiogenesis factor (TAF) into the surrounding tissue. Neighbouring endothelial cells respond to this chemotactic stimulus in a well-ordered sequence of events comprising, at minimum, of a degradation of their basement membrane, migration and proliferation. A mathematical model is presented which takes into account two of the most important events associated with the endothelial cells as they form capillary sprouts and make their way towards the tumour i.e. cell migration and proliferation. The numerical simulations of the model compare very well with the actual experimental observations. We subsequently investigate the model analytically by making some relevant biological simplifications. The mathematical analysis helps to clarify the particular contributions to the model of the two independent processes of endothelial cell migration and proliferation.
Original languageEnglish
Pages (from-to)744-770
Number of pages27
JournalJournal of Mathematical Biology
Volume33
Issue number7
DOIs
Publication statusPublished - 1995

Keywords

  • Tumour angiogenesis
  • Mathematical modelling
  • Endothelial cells

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