2-DIMENSIONAL MODELS OF TUMOR ANGIOGENESIS AND ANTI-ANGIOGENESIS STRATEGIES

There is a very strong link between the vascularization of a tumour an d the spread of the disease, both locally and to distant sites (Gimbro ne et al., 1974, J. Natl. Cancer Inst. 52, 413-27; Muthukkaruppan et a t, 1982, J. Natl. Cancer Inst. 69, 699-704; Ellis & Fiddler, 1995, Lan cet 346, 388-9). A tumour becomes vascularized by a process known as a ngiogenesis. Tumour angiogenesis is initiated by the release of diffus ible substances by the tumour, whereby neighbouring capillary vessels are stimulated to grow and eventually penetrate the tumour. Anti-angio genesis has been proposed as a potential strategy for the treatment of cancer (Folkman, 1995, Nature Med. 1, 21-31; Harris et al., 1996, Bre ast Cancer Res. Treat. 38, 97-108). In this paper, a mathematical mode l of the development of the tumour vasculature is presented. By suitab le manipulation of the model parameters, we simulate various anti-angi ogenesis strategies and we examine the roles that haptotaxis and chemo taxis may play during the growth of the neovasculature. The model is s imulated in two space dimensions (on a square domain) so that it is, i n theory, experimentally reproducible and any predictions of the model can therefore be tested.