Mesoscopic and continuum modelling of angiogenesis

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Mesoscopic and continuum modelling of angiogenesis. / Spill, Fabian; Guerrero, P.; Alarcon, T.; Maini, P. K.; Byrne, H. M.

In: Journal of Mathematical Biology, Vol. 70, No. 3, 11.03.2014, p. 485-532.

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Spill, F, Guerrero, P, Alarcon, T, Maini, PK & Byrne, HM 2014, 'Mesoscopic and continuum modelling of angiogenesis', Journal of Mathematical Biology, vol. 70, no. 3, pp. 485-532. https://doi.org/10.1007/s00285-014-0771-1

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Spill, Fabian ; Guerrero, P. ; Alarcon, T. ; Maini, P. K. ; Byrne, H. M. / Mesoscopic and continuum modelling of angiogenesis. In: Journal of Mathematical Biology. 2014 ; Vol. 70, No. 3. pp. 485-532.

Bibtex

@article{c00e67944a224387b920e9dde2965b08,
title = "Mesoscopic and continuum modelling of angiogenesis",
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.",
keywords = "Angiogenesis, Master equation, Mesoscopic models, Reaction–diffusion system, Stochastic models",
author = "Fabian Spill and P. Guerrero and T. Alarcon and Maini, {P. K.} and Byrne, {H. M.}",
year = "2014",
month = mar,
day = "11",
doi = "10.1007/s00285-014-0771-1",
language = "English",
volume = "70",
pages = "485--532",
journal = "Journal of Mathematical Biology",
issn = "0303-6812",
publisher = "Springer Nature",
number = "3",

}

RIS

TY - JOUR

T1 - Mesoscopic and continuum modelling of angiogenesis

AU - Spill, Fabian

AU - Guerrero, P.

AU - Alarcon, T.

AU - Maini, P. K.

AU - Byrne, H. M.

PY - 2014/3/11

Y1 - 2014/3/11

N2 - 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.

AB - 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.

KW - Angiogenesis

KW - Master equation

KW - Mesoscopic models

KW - Reaction–diffusion system

KW - Stochastic models

UR - http://www.scopus.com/inward/record.url?scp=84923882819&partnerID=8YFLogxK

U2 - 10.1007/s00285-014-0771-1

DO - 10.1007/s00285-014-0771-1

M3 - Article

C2 - 24615007

AN - SCOPUS:84923882819

VL - 70

SP - 485

EP - 532

JO - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

SN - 0303-6812

IS - 3

ER -