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.
authors.affiliation: OCCAM, Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK, fabian.spill@gmail.com.
authors.forename: F
authors.initials: F
authors.lastname: Spill
authors.forename: P
authors.initials: P
authors.lastname: Guerrero
authors.forename: T
authors.initials: T
authors.lastname: Alarcon
authors.forename: P K
authors.initials: PK
authors.lastname: Maini
authors.forename: H M
authors.initials: HM
authors.lastname: Byrne
mesh_terms: D000818:Animals; D001163:Arteriovenous Anastomosis / Q000166:cytology; D002465:Cell Movement; D049109:Cell Proliferation; D002633:Chemotaxis; D042783:Endothelial Cells / Q000166:cytology / Q000502:physiology; D006801:Humans; D055641:Mathematical Concepts; D008955:Models, Cardiovascular; D009389:Neovascularization, Pathologic; D018919:Neovascularization, Physiologic; D013269:Stochastic Processes