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The foundations of a unified approach to mathematical modelling of angiogenesis

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Abstract

It is well known that avascular tumours only grow to a limited size before metabolic demands are impeded due to the diffusion limit of oxygen and other nutrients. For continued growth the tumour switches to an angiogenic phenotype that induces sprouting of new blood vessels from the surrounding medium. Sprouting angiogenesis is the most widely studied aspect of neovascular growth and has been modelled from several mathematical points of view. In this paper we propose a new underlying theme, which unifies a number of the existing techniques employed to model angiogenesis. The basic formulation is in terms of stochastic differential equations. The ideas discussed have wide application, particularly in the validation of models of vessel cooption, vasculogenic mimicry and lymphangiogenesis.

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Authors and Affiliations

  1. Department of Computer Science, University of Leeds, Leeds, UK

    Matthew Hubbard

  2. Leeds Institute of Molecular Medicine, University of Leeds, Section of Molecular Gastroenterology, Wellcome Trust Brenner Building, St. James’s University Hospital, Leeds, Leeds, UK

    Pamela F. Jones

  3. School of Mathematics, University of Leeds, Leeds, UK

    Brian D. Sleeman

Authors
  1. Matthew Hubbard
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  2. Pamela F. Jones
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  3. Brian D. Sleeman
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Correspondence to Matthew Hubbard.

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Hubbard, M., Jones, P.F. & Sleeman, B.D. The foundations of a unified approach to mathematical modelling of angiogenesis. Int J Adv Eng Sci Appl Math 1, 43–52 (2009). https://doi.org/10.1007/s12572-009-0004-9

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  • DOI: https://doi.org/10.1007/s12572-009-0004-9

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