MATHEMATICAL MODELLING OF AVASCULAR AND VASCULAR TUMOUR GROWTH

The most common cause of primary tumours is the genetic mutation of one or more cells resulting in uncontrolled proliferation. The mutated cells have a proliferative advantage over neighbouring healthy cells and are able to form a growing mass. The reason for this advantage is not necessarily an increase in the proliferation rate, but may be a decrease in the cell death rate. If the mutated cells remain contained within a single cluster, with a well defined boundary separating them from neighbouring normal cells, the tumour is said to be benign, and surgical removal will often provide a complete cure. However, if the tumour cells are inter-mixed with normal cells and attempt to invade surrounding tissue, the growth ceases to be contained and the tumour is described as malignant. A tumour may persist in a diffusion limited or avascular state, usually not more than 2mm in diameter, with cell proliferation balanced by cell death for many months or years. It rarely gives rise to significant damage and often goes undetected. A tumour may however emerge from dormancy by inducing the growth of now blood vessels, a process termed angiogenesis, or neovascularisation. This process allows the tumour to progress from the avascular to the vascular state. There are a large number of pro-angiogenic and anti-angiogenic factors. It is a shifting of the balance from the anti-to the pro-angionenic factors (the so-called angiogenic switch)that causes the transition from the dormant to the angiogenic phase. This switch is a highly complex process which is not fully understood, but oxygen deficiency in the tumour is thought, to be an important factor stimulating the production of pro-angiogenic molecules by the tumour cells. In this paper we develop generic models of both avascular and vascular tumour growth. We begin by briefly describing the underlying biochemistry and