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REGULAR ARTICLE A Model for Short-and Long-range Interactions

A Model for Short- and Long-range Interactions
of Migrating Tumour Cell
M. Aubert M. Badoual B. Grammaticos
Received: 6 February 2008 / Accepted: 22 September 2008 / Published online: 9 October 2008
Springer Science+Business Media B.V. 2008
Abstract We examine the consequences of long-range effects on tumour cell
migration. Our starting point are previous results of ours where we have shown that
the migration patterns of glioma cells are best interpreted if one assumes attractive
interactions between cells. Here we complement the cellular automaton model
previously introduced by the assumption of the existence of a chemorepellent
produced by the main bulk of large spheroids (in the hypoxic/necrotic areas).
Visible effects due to the presence of such a substance can be found in the density
profiles of cells migrating out of a single spheroid as well as in the angular distri-
bution of cells coming from two close-lying spheroids. These effects depend
crucially on the diffusion speed of the chemorepellent. A comparison of the sim-
ulation results to experimental data of Werbowetski et al. allows to draw (tentative)
conclusions on the existence of a chemorepellent and its properties.
Keywords Glioblastoma Invasion Cellular automaton Interactions
Repulsion Secreted factor


Source: Aubert, Marine - Department of Mathematics, University of Dundee


Collections: Mathematics