Mathematical Modelling of Tumour-induced Angiogenesis: Network Growth and Structure

  • Mark Chaplain
  • Alexander Anderson
Part of the Cancer Treatment and Research book series (CTAR, volume 117)


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 alI present a review of a variety of mathematical models which have been used to describe the formation of apillary 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 celIs 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.


mathematical modelling endothelial cell migration angiogenesis chemotaxis haptotaxis 


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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Mark Chaplain
    • 1
  • Alexander Anderson
    • 1
  1. 1.Division of MathematicsThe SIMBIOS Centre ,University of DundeeDundeeUK

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