Mathematical modelling of angiogenesis

  • Chaplain M
  • 98


    Mendeley users who have this article in their library.
  • 88


    Citations of this article.


Angiogenesis, the formation of blood vessels from a pre-existing vasculature, is a process whereby capillary sprouts are formed in response to externally supplied chemical stimuli. The sprouts then grow and develop, driven initially by endothelial cell migration, and organize themselves into a branched, connected network. Subsequent cell proliferation near the sprout-tips permits further extension of the capillaries and ultimately completes the process. Angiogenesis occurs during embryogenesis, wound healing, arthritis and during the growth of solid tumours. In this article we first of all present a review of a variety of mathematical models which have been used to describe the formation of capillary networks and then focus on a specific recent model which uses novel mathematical modelling techniques to generate both two- and three-dimensional vascular structures. The modelling focusses on key events of angiogenesis such as the migratory response of endothelial cells to exogenous cytokines (tumour angiogenic factors, TAF) secreted by a solid tumour; endothelial cell proliferation; endothelial cell interactions with extracellular matrix macromolecules such as fibronectin; capillary sprout branching and anastomosis. Numerical simulations of the model, using parameter values based on experimental data, are presented and the theoretical structures generated by the model are compared with the morphology of actual capillary networks observed in in vivo experiments. A final conclusions section discusses the use of the mathematical model as a possible angiogenesis assay.

Author-supplied keywords

  • Angiogenesis
  • Chemotaxis
  • Haptotaxis
  • Mathematical modelling

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document


  • M. A.J. Chaplain

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free