Mathematical modeling of tumour-induced angiogenesis: network growth and structure: Angiogenesis in brain tumors

Mark Chaplain, Alexander Anderson

Research output: Chapter in Book/Report/Conference proceedingChapter


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 organise 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 chapter 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 2 and 3 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; matrix degradation; 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 section discusses the use of the mathematical model as a possible angiogenesis assay and implications for chemotherapy regimes.
Original languageEnglish
Title of host publicationAngiogenesis in brain tumors
EditorsPeter McL. Black
Place of PublicationBoston ; London
PublisherKluwer Academic Publishers
Number of pages25
ISBN (Print)9781402077043
Publication statusPublished - 2004

Publication series

NameCancer treatment and research


  • Mathematical modelling
  • Endothelial cell migration
  • Angiogenesis
  • Chemotaxis
  • Haptotaxis


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