Integrodifference master equation describing actively growing blood vessels in 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 2020-12-17T15:06:19Z
dc.date.issued 2020-11-18
dc.identifier.bibliographicCitation Bonilla, L. L., Carretero, M., & Terragni, F. (2020). Integrodifference master equation describing actively growing blood vessels in angiogenesis, International Journal of Nonlinear Sciences and Numerical Simulation, 21(7-8), 705-713
dc.identifier.issn 1565-1339
dc.identifier.uri http://hdl.handle.net/10016/31633
dc.description.abstract We study a system of particles in a two-dimensional geometry that move according to a reinforced random walk with transition probabilities dependent on the solutions of reaction-diffusion equations (RDEs) for the underlying fields. A birth process and a history-dependent killing process are also considered. This system models tumor-induced angiogenesis, the process of formation of blood vessels induced by a growth factor (GF) released by a tumor. Particles represent vessel tip cells, whose trajectories constitute the growing vessel network. New vessels appear and may fuse with existing ones during their evolution. Thus, the system is described by tracking the density of active tips, calculated as an ensemble average over many realizations of the stochastic process. Such density satisfies a novel discrete master equation with source and sink terms. The sink term is proportional to a space-dependent and suitably fitted killing coefficient. Results are illustrated studying two influential angiogenesis models.
dc.description.sponsorship This work has been supported by the FEDER/Ministerio de Ciencia, Innovación y Universidades – Agencia Estatal de Investigación grant MTM2017-84446-C2-2-R.
dc.language.iso eng
dc.publisher Walter de Gruyter
dc.rights © 2020 Walter de Gruyter GmbH, Berlin/Boston
dc.title Integrodifference master equation describing actively growing blood vessels in angiogenesis
dc.type article
dc.subject.eciencia Matemáticas
dc.identifier.doi https://doi.org/10.1515/ijnsns-2019-0094
dc.rights.accessRights embargoedAccess
dc.relation.projectID Gobierno de España. MTM2017-84446-C2-2-R
dc.type.version acceptedVersion
dc.identifier.publicationfirstpage 705
dc.identifier.publicationissue 7-8
dc.identifier.publicationlastpage 713
dc.identifier.publicationtitle International Journal of Nonlinear Sciences and Numerical Simulation
dc.identifier.publicationvolume 21
dc.identifier.uxxi AR/0000026347
carlosiii.embargo.liftdate 2021-11-18
carlosiii.embargo.terms 2021-11-18
dc.contributor.funder Ministerio de Ciencia, Innovación y Universidades (España)
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