A hybrid discrete-continuum model of tumour induced angiogenesis

Angiogenesis, the formation of new blood vessels, is a crucial step in solid tumour development, as it links the relatively harmless avascular and the potentially fatal vascular phases of tumour growth. Tumour induced angiogenesis follows a specific sequence of events that are initiated by the tumour secreting angiogenic factors into the surrounding tissue; upon contact with nearby blood vessels these angiogenic factors induce the endothelial cells lining the vessels to degrade their basement lamina. Endothelial cells then degrade the surrounding tissue, migrate towards the tumour and proliferate, in so doing they generate new vessels which can branch and link with one another to form loops (anastomosis). As soon as the first anastomosis forms, blood begins to flow and then all subsequent growth evolves in response to the combined effects of migratory cues within the tumour microenvironment and haemodynamic forces produced by the vasculature. In this chapter, we first present a brief review of previous models of angiogenesis and then focus our attention on the original hybrid discrete-continuum model of tumour induced angiogenesis. This model has been extensively cited and developed in a multitude of ways, specifically via the incorporation of blood flow and as a component of larger multiscale models of cancer development. Some of that work is discussed in subsequent chapters of this book, however, our primary focus here is on the details of the original no-flow model and its implementation.