Physical modelling and simulations of tumour growth and angiogenesis: predictions and new hypotheses

The initial stages of tumour growth (avascular phase) are characterised by a low nutrient availability, which soon become a limiting factor for the progression of the neoplasm. Normally a transition to a vascular phase occurs, during which cancer cells stimulate the proliferation of endothelial cells belonging to vessels, hence the formation of new capillaries. The newly formed vascular system rapidly approaches the tumour surface and even infiltrates it, providing additional nutrients which allow further growth (angiogenesis). Blocking the process, might induce tumour to latency, with the consequent implications from therapeutical point of view. In the present contribution we will consider angiogenesis as a case study to show how mathematical models help in the interpretation and quantification of the experimental results.