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

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.