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Integrodifference master equation describing actively growing blood vessels in angiogenesis

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Modelización, Simulación Numérica y Matemática Industriales
dc.contributor.authorLópez Bonilla, Luis Francisco
dc.contributor.authorCarretero Cerrajero, Manuel
dc.contributor.authorTerragni, Filippo
dc.contributor.funderMinisterio de Ciencia, Innovación y Universidades (España)es
dc.date.accessioned2020-12-17T15:06:19Z
dc.date.available2021-11-18T00:00:05Z
dc.date.issued2020-11-18
dc.description.abstractWe 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.en
dc.description.sponsorshipThis work has been supported by the FEDER/Ministerio de Ciencia, Innovación y Universidades – Agencia Estatal de Investigación grant MTM2017-84446-C2-2-R.en
dc.identifier.bibliographicCitationBonilla, 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.doihttps://doi.org/10.1515/ijnsns-2019-0094
dc.identifier.issn1565-1339
dc.identifier.publicationfirstpage705
dc.identifier.publicationissue7-8
dc.identifier.publicationlastpage713
dc.identifier.publicationtitleInternational Journal of Nonlinear Sciences and Numerical Simulation
dc.identifier.publicationvolume21
dc.identifier.urihttps://hdl.handle.net/10016/31633
dc.identifier.uxxiAR/0000026347
dc.language.isoeng
dc.publisherWalter de Gruyter
dc.relation.projectIDGobierno de España. MTM2017-84446-C2-2-R
dc.rights© 2020 Walter de Gruyter GmbH, Berlin/Boston
dc.rights.accessRightsopen access
dc.subject.ecienciaMatemáticases
dc.titleIntegrodifference master equation describing actively growing blood vessels in angiogenesisen
dc.typeresearch article*
dc.type.hasVersionAM*
dspace.entity.typePublication
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