Handle URI:
http://hdl.handle.net/10754/598806
Title:
Mesoscopic and continuum modelling of angiogenesis
Authors:
Spill, F.; Guerrero, P.; Alarcon, T.; Maini, P. K.; Byrne, H. M.
Abstract:
Angiogenesis is the formation of new blood vessels from pre-existing ones in response to chemical signals secreted by, for example, a wound or a tumour. In this paper, we propose a mesoscopic lattice-based model of angiogenesis, in which processes that include proliferation and cell movement are considered as stochastic events. By studying the dependence of the model on the lattice spacing and the number of cells involved, we are able to derive the deterministic continuum limit of our equations and compare it to similar existing models of angiogenesis. We further identify conditions under which the use of continuum models is justified, and others for which stochastic or discrete effects dominate. We also compare different stochastic models for the movement of endothelial tip cells which have the same macroscopic, deterministic behaviour, but lead to markedly different behaviour in terms of production of new vessel cells. © 2014 Springer-Verlag Berlin Heidelberg.
Citation:
Spill F, Guerrero P, Alarcon T, Maini PK, Byrne HM (2014) Mesoscopic and continuum modelling of angiogenesis. Journal of Mathematical Biology 70: 485–532. Available: http://dx.doi.org/10.1007/s00285-014-0771-1.
Publisher:
Springer Nature
Journal:
Journal of Mathematical Biology
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
11-Mar-2014
DOI:
10.1007/s00285-014-0771-1
PubMed ID:
24615007
Type:
Article
ISSN:
0303-6812; 1432-1416
Sponsors:
This publication was based on work supported in part by Award No KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). TA and PG gratefully acknowledge the Spanish Ministry for Science and Innovation (MICINN) for funding under grant MTM2011-29342 and Generalitat de Catalunya for funding under grant 2009SGR345. PKM was partially supported by the National Cancer Institute, National Institutes of Health grant U54CA143970.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorSpill, F.en
dc.contributor.authorGuerrero, P.en
dc.contributor.authorAlarcon, T.en
dc.contributor.authorMaini, P. K.en
dc.contributor.authorByrne, H. M.en
dc.date.accessioned2016-02-25T13:41:35Zen
dc.date.available2016-02-25T13:41:35Zen
dc.date.issued2014-03-11en
dc.identifier.citationSpill F, Guerrero P, Alarcon T, Maini PK, Byrne HM (2014) Mesoscopic and continuum modelling of angiogenesis. Journal of Mathematical Biology 70: 485–532. Available: http://dx.doi.org/10.1007/s00285-014-0771-1.en
dc.identifier.issn0303-6812en
dc.identifier.issn1432-1416en
dc.identifier.pmid24615007en
dc.identifier.doi10.1007/s00285-014-0771-1en
dc.identifier.urihttp://hdl.handle.net/10754/598806en
dc.description.abstractAngiogenesis is the formation of new blood vessels from pre-existing ones in response to chemical signals secreted by, for example, a wound or a tumour. In this paper, we propose a mesoscopic lattice-based model of angiogenesis, in which processes that include proliferation and cell movement are considered as stochastic events. By studying the dependence of the model on the lattice spacing and the number of cells involved, we are able to derive the deterministic continuum limit of our equations and compare it to similar existing models of angiogenesis. We further identify conditions under which the use of continuum models is justified, and others for which stochastic or discrete effects dominate. We also compare different stochastic models for the movement of endothelial tip cells which have the same macroscopic, deterministic behaviour, but lead to markedly different behaviour in terms of production of new vessel cells. © 2014 Springer-Verlag Berlin Heidelberg.en
dc.description.sponsorshipThis publication was based on work supported in part by Award No KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). TA and PG gratefully acknowledge the Spanish Ministry for Science and Innovation (MICINN) for funding under grant MTM2011-29342 and Generalitat de Catalunya for funding under grant 2009SGR345. PKM was partially supported by the National Cancer Institute, National Institutes of Health grant U54CA143970.en
dc.publisherSpringer Natureen
dc.subjectAngiogenesisen
dc.subjectMaster equationen
dc.subjectMesoscopic modelsen
dc.subjectReaction-diffusion systemen
dc.subjectStochastic modelsen
dc.titleMesoscopic and continuum modelling of angiogenesisen
dc.typeArticleen
dc.identifier.journalJournal of Mathematical Biologyen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
dc.contributor.institutionCentre de Recerca Matematica, Cerdanyola del Valles, Spainen
dc.contributor.institutionUCL, London, United Kingdomen
dc.contributor.institutionUniversitat Autbnoma de Barcelona, Cerdanyola del Valles, Spainen
kaust.grant.numberKUK-C1-013-04en

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