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Ensemble Averages, Soliton Dynamics and Influence of Haptotaxis in a Model of Tumor-Induced Angiogenesis

Department of Materials Science and Engineering, G. Millán Institute for Fluid Dynamics, Nanoscience, and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
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Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editors: Marcel Ausloos and Janusz Miskiewicz
Entropy 2017, 19(5), 209; https://doi.org/10.3390/e19050209
Received: 7 April 2017 / Revised: 27 April 2017 / Accepted: 2 May 2017 / Published: 4 May 2017
(This article belongs to the Special Issue Statistical Mechanics of Complex and Disordered Systems)
In this work, we present a numerical study of the influence of matrix degrading enzyme (MDE) dynamics and haptotaxis on the development of vessel networks in tumor-induced angiogenesis. Avascular tumors produce growth factors that induce nearby blood vessels to emit sprouts formed by endothelial cells. These capillary sprouts advance toward the tumor by chemotaxis (gradients of growth factor) and haptotaxis (adhesion to the tissue matrix outside blood vessels). The motion of the capillaries in this constrained space is modelled by stochastic processes (Langevin equations, branching and merging of sprouts) coupled to continuum equations for concentrations of involved substances. There is a complementary deterministic description in terms of the density of actively moving tips of vessel sprouts. The latter forms a stable soliton-like wave whose motion is influenced by the different taxis mechanisms. We show the delaying effect of haptotaxis on the advance of the angiogenic vessel network by direct numerical simulations of the stochastic process and by a study of the soliton motion. View Full-Text
Keywords: tumor-induced angiogenesis; haptotaxis; chemotaxis; soliton; collective coordinates; ensemble average tumor-induced angiogenesis; haptotaxis; chemotaxis; soliton; collective coordinates; ensemble average
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Bonilla, L.L.; Carretero, M.; Terragni, F. Ensemble Averages, Soliton Dynamics and Influence of Haptotaxis in a Model of Tumor-Induced Angiogenesis. Entropy 2017, 19, 209.

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