Mathematical Modelling of Macrophage
Dynamics in Tumours
AUTHORS:
Markus R. Owen & Jonathan A. Sherratt
Nonlinear Systems Laboratory, Mathematics Institute,
University of Warwick, Coventry CV4 7AL, UK.
ABSTRACT:
Macrophages form an important part of the immune response to cancer.
In this paper, the authors 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, the authors present results of model simulations in two spatial
dimensions.
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