Two-dimensional models of tumour angiogenesis and anti-angiogenesis strategies

M. E. Orme, M. A. J. Chaplain

    Research output: Contribution to journalArticle

    81 Citations (Scopus)

    Abstract

    There is a very strong link between the vascularization of a tumour and the spread of the disease, both locally and to distant sites (Gimbrone et al., 1974, J. Natl. Cancer Inst. 52, 413–27; Muthukkaruppan et al, 1982, J. Natl. Cancer Inst. 69, 699–704; Ellis & Fiddler, 1995, Lancet 346, 388–9). A tumour becomes vascularized by a process known as angiogenesis. Tumour angiogenesis is initiated by the release of diffusible substances by the tumour, whereby neighbouring capillary vessels are stimulated to grow and eventually penetrate the tumour. Anti-angiogenesis has been proposed as a potential strategy for the treatment of cancer (Folkman, 1995, Nature Med. 1, 21–31; Harris et al, 1996, Breast Cancer Res. Treat. 38, 97–108). In this paper, a mathematical model of the development of the tumour vasculature is presented. By suitable manipulation of the model parameters, we simulate various anti-angiogenesis strategies and we examine the roles that haptotaxis and chemotaxis may play during the growth of the neovasculature. The model is simulated in two space dimensions (on a square domain) so that it is, in theory, experimentally reproducible and any predictions of the model can therefore be tested.
    Original languageEnglish
    Pages (from-to)189-205
    Number of pages17
    JournalIMA Journal of Mathematics Applied in Medicine and Biology
    Volume14
    Issue number3
    DOIs
    Publication statusPublished - Sep 1997

    Fingerprint

    Angiogenesis
    angiogenesis
    Tumor
    neoplasms
    Neoplasms
    Cancer
    Haptotaxis
    Model
    Chemotaxis
    Breast Cancer
    Vessel
    Strategy
    Manipulation
    chemotaxis
    Mathematical Model
    breast neoplasms
    Prediction
    Theoretical Models
    mathematical models
    Breast Neoplasms

    Keywords

    • Tumour angiogenesis
    • Chemotaxis
    • Haptotaxis
    • Anti-angiogenesis

    Cite this

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    abstract = "There is a very strong link between the vascularization of a tumour and the spread of the disease, both locally and to distant sites (Gimbrone et al., 1974, J. Natl. Cancer Inst. 52, 413–27; Muthukkaruppan et al, 1982, J. Natl. Cancer Inst. 69, 699–704; Ellis & Fiddler, 1995, Lancet 346, 388–9). A tumour becomes vascularized by a process known as angiogenesis. Tumour angiogenesis is initiated by the release of diffusible substances by the tumour, whereby neighbouring capillary vessels are stimulated to grow and eventually penetrate the tumour. Anti-angiogenesis has been proposed as a potential strategy for the treatment of cancer (Folkman, 1995, Nature Med. 1, 21–31; Harris et al, 1996, Breast Cancer Res. Treat. 38, 97–108). In this paper, a mathematical model of the development of the tumour vasculature is presented. By suitable manipulation of the model parameters, we simulate various anti-angiogenesis strategies and we examine the roles that haptotaxis and chemotaxis may play during the growth of the neovasculature. The model is simulated in two space dimensions (on a square domain) so that it is, in theory, experimentally reproducible and any predictions of the model can therefore be tested.",
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    Two-dimensional models of tumour angiogenesis and anti-angiogenesis strategies. / Orme, M. E.; Chaplain, M. A. J.

    In: IMA Journal of Mathematics Applied in Medicine and Biology, Vol. 14, No. 3, 09.1997, p. 189-205.

    Research output: Contribution to journalArticle

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