A mathematical model of tumour angiogenesis, regulated by vascular endothelial growth factor and the angiopoietins

Angiogenesis—the growth of new blood vessels from existing ones—is a prerequisite for the growth of solid tumours beyond a diameter of approximately 2 mm. In recent years, the angiopoietins have emerged as important regulators of angiogenesis. They mediate a delicate balance between vascular quiescence, regression and new growth, but their mechanism of action is not fully understood. This work attempts to provide a mathematical description of the role of the angiopoietins in angiogenesis. The model is formulated within the framework of reinforced random walks, which allows easy transition between the continuum (macroscopic) and discrete (microscopic) forms. Model predictions are in qualitative agreement with experimental observations, and may have implications for anti-cancer therapies based on the prevention of angiogenesis.