THE MATHEMATICAL-MODELING OF TUMOR ANGIOGENESIS AND INVASION

In order to accomplish the transition from avascular to vascular growt h, solid tumours secrete a diffusible substance known as tumour angiog enesis factor (TAF) into the surrounding tissue. Endothelial cells whi ch form the lining of neighbouring blood vessels respond to this chemo tactic stimulus in a well-ordered sequence of events comprising, at mi nimum, of a degradation of their basement membrane, migration and prol iferation. Capillary sprouts are formed which migrate towards the tumo ur eventually penetrating it and permitting vascular growth to take pl ace. It is during this stage of growth that the insidious process of i nvasion of surrounding tissues can and does take place. A model mechan ism for angiogenesis is presented which includes the diffusion of the TAF into the surrounding host tissue and the response of the endotheli al cells to the chemotactic stimulus. Numerical simulations of the mod el are shown to compare very well with experimental observations. The subsequent vascular growth of the tumour is discussed with regard to a classical reaction-diffusion pre-pattern model.