Unless connected to a circulating blood supply, a solid tumour is relatively harmless, remaining localised and receiving vital nutrients a via diffusion. By contrast, a tumour which is linked to the host's blood supply is life-threatening since it has a practically inexhaustible nutrient supply and a transport route to other parts of the body where, under favourable conditions, secondary tumours or metastases may develop. The subject of this talk is angiogenesis, the process by which a solid tumour acquires a blood supply. An accurate description of tumour angiogenesis is particularly important since it may help with the design of therapeutic strategies capable of arresting angiogenesis and thereby limiting tumour growth and invasion. In this presentation existing mathematical models of tumour angiogenesis will be reviewed and their relative merits compared. Possible directions for future work in this important area will also be discussed.

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1998-1999 Mathematics in Biology