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

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dc.contributor.author López Bonilla, Luis Francisco
dc.contributor.author Carretero Cerrajero, Manuel
dc.contributor.author Terragni, Filippo
dc.date.accessioned 2019-01-11T12:29:06Z
dc.date.available 2019-01-11T12:29:06Z
dc.date.issued 2017-05-04
dc.identifier.bibliographicCitation Bonilla,L.L., Carretero,M., Terragni,F.(2017).Ensemble Averages, Soliton Dynamics and Influence of Haptotaxis in a Model of Tumor-Induced Angiogenesis. Entropy, 19(5), 209.
dc.identifier.issn 1099-4300
dc.identifier.uri http://hdl.handle.net/10016/27872
dc.description.abstract 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.
dc.description.sponsorship We thank Vincenzo Capasso, Bjorn Birnir and Boris Malomed for fruitful discussions. This work has been supported by the Ministerio de Economía y Competitividad grant MTM2014-56948-C2-2-P.
dc.format.extent 15
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher MDPI
dc.rights © 2017 by the authors. Licensee MDPI, Basel, Switzerland.
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject.other tumor-induced angiogenesis
dc.subject.other haptotaxis
dc.subject.other chemotaxis
dc.subject.other soliton
dc.subject.other collective coordinates
dc.subject.other ensemble average
dc.title Ensemble Averages, Soliton Dynamics and Influence of Haptotaxis in a Model of Tumor-Induced Angiogenesis
dc.type article
dc.subject.eciencia Matemáticas
dc.identifier.doi https://doi.org/10.3390/e19050209
dc.relation.projectID Gobierno de España. MTM2014-56948-C2-2-P
dc.type.version publishedVersion
dc.identifier.publicationissue 5
dc.identifier.publicationtitle Entropy
dc.identifier.publicationvolume 19
dc.identifier.uxxi AR/0000020297
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