Pattern formation and Spatiotemporal
Irregularity in a model for
Macrophage--Tumour Interactions
AUTHORS:
Markus R. Owen & Jonathan A. Sherratt
Nonlinear Systems Laboratory, Mathematics Institute,
University of Warwick, Coventry CV4 7AL, UK.
ABSTRACT:
Solid tumours do not develop as a homogeneous mass of mutant cells,
rather, they grow in tandem with normal tissue cells initially present,
and may also recruit other cell types including lymphatic and endothelial
cells. Many solid tumours contain a high proportion of macrophages,
a type of white blood cell which can have a variety of effects upon the
tumour, leading to a delicate balance between growth promotion and
inhibition. In this paper we present a brief review of the main properties
and interactions of such tumour-associated macrophages, leading to a
description of a mathematical model for the spatial interactions of
macrophages, tumour cells and normal tissue cells, focusing on the
ability of macrophages to kill mutant cells. Analysis of the
homogeneous steady states shows that, for this model, normal tissue is
unstable to the introduction of mutant cells despite such an immune
response, but that the composition of the resulting tumour can be
significantly altered.
Including random cell movement and chemical diffusion, we
demonstrate the existence of travelling wave solutions connecting the
normal tissue and tumour steady states, corresponding to a growing tumour,
and of the development of a spatial instability
behind the wave front. Numerical solutions are illustrated in one and two
dimensions. We go on to estimate macrophage motility parameters using data
from Boyden chamber experiments.
We then extend our model to include macrophage chemotaxis, that is,
their directed movement in response to gradients of chemicals secreted by
tumours.
Solutions in one dimension indicate the possibility of spatiotemporal
irregularities within the growing tumour, which are deduced to be
the result of a series of bifurcations as the effective domain length
increases, leading to a permanently transient solution.
These results suggest that tumour heterogeneity may arise in part as a
natural consequence of the macrophage infiltration. Recent experiments
suggest that macrophages may indeed be involved in
spatiotemporal variations within some human tumours.
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