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 journalArticle

    46 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

    Fingerprint Dive into the research topics of 'A mathematical analysis of a model for tumour angiogenesis'. Together they form a unique fingerprint.

  • Cite this

    Chaplain, M. A. J., Giles, S. M., Sleeman, B. D., & Jarvis, R. J. (1995). A mathematical analysis of a model for tumour angiogenesis. Journal of Mathematical Biology, 33(7), 744-770. https://doi.org/10.1007/BF00184647