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

  • Chapter
Angiogenesis in Brain Tumors

Part of the book series: Cancer Treatment and Research ((CTAR,volume 117))

Abstract

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.

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Authors and Affiliations

  1. Division of Mathematics, The SIMBIOS Centre ,University of Dundee, Dundee, DD1 4HN, UK

    Mark Chaplain & Alexander Anderson

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  1. Mark Chaplain
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  2. Alexander Anderson
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Editors and Affiliations

  1. Neurosurgery Carl Gustav Carus Hospital, Technical University of Dresden, Dresden, Germany

    Matthias Kirsch

  2. Neurosurgery Children’s Hospital Brigham and Women’s Hospital, Harvard Medical School, Boston, MA, USA

    Peter McL. Black

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Chaplain, M., Anderson, A. (2004). Mathematical Modelling of Tumour-induced Angiogenesis: Network Growth and Structure. In: Kirsch, M., Black, P.M. (eds) Angiogenesis in Brain Tumors. Cancer Treatment and Research, vol 117. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-8871-3_3

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  • DOI: https://doi.org/10.1007/978-1-4419-8871-3_3

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-4699-9

  • Online ISBN: 978-1-4419-8871-3

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