Mesoscopic and continuum modelling of angiogenesis

Fabian Spill*, P. Guerrero, T. Alarcon, P. K. Maini, H. M. Byrne

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

44 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)485-532
Number of pages48
JournalJournal of Mathematical Biology
Issue number3
Publication statusPublished - 11 Mar 2014


  • Angiogenesis
  • Master equation
  • Mesoscopic models
  • Reaction–diffusion system
  • Stochastic models

ASJC Scopus subject areas

  • Modelling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics


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