Mathematical Modelling of Macrophage Dynamics in Tumours

Macrophages form an important part of the immune response to cancer. In this paper, we present a mathematical model of reaction–diffusion form, which represents the influx of macrophages into a small avascular tumour, and their dynamics within the tumour as it grows. The model predicts that, despite their ability to selectively kill tumour cells, macrophages are unable to prevent tumour growth. However, significant effects on the form of the tumour are predicted, including in particular the formation of spatial patterns. When the model is extended to include macrophage chemotaxis, these patterns can in some cases bifurcate to give irregular spatiotemporal oscillations, and the authors present a detailed numerical bifurcation study which suggests a novel dynamical origin for these oscillations. Finally, we present results of model simulations in two spatial dimensions.