Mathematical modelling of vascular tumour growth and implications for therapy

In this chapter we briefly discuss the results of a mathematical model formulated in [22] that incorporates many processes associated with tumour growth. The deterministic model, a system of coupled non-linear partial differential equations, is a combination of two previous models that describe the tumour-host interactions in the initial stages of growth [11] and the tumour angiogenic process [6]. Combining these models enables us to investigate combination therapies that target different aspects of tumour growth. Numerical simulations show that the model captures both the avascular and vascular growth phases. Furthermore, we recover a number of characteristic features of vascular tumour growth such as the rate of growth of the tumour and invasion speed. We also show how our model can be used to investigate the effect of different anti-cancer therapies.