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Journal of Mathematical Biology

, Volume 58, Issue 4–5, pp 765–798 | Cite as

Multiscale modelling and nonlinear simulation of vascular tumour growth

  • Paul Macklin
  • Steven McDougall
  • Alexander R. A. Anderson
  • Mark A. J. Chaplain
  • Vittorio Cristini
  • John Lowengrub
Article

Abstract

In this article, we present a new multiscale mathematical model for solid tumour growth which couples an improved model of tumour invasion with a model of tumour-induced angiogenesis. We perform nonlinear simulations of the ulti-scale model that demonstrate the importance of the coupling between the development and remodeling of the vascular network, the blood flow through the network and the tumour progression. Consistent with clinical observations, the hydrostatic stress generated by tumour cell proliferation shuts down large portions of the vascular network dramatically affecting the flow, the subsequent network remodeling, the delivery of nutrients to the tumour and the subsequent tumour progression. In addition, extracellular matrix degradation by tumour cells is seen to have a dramatic affect on both the development of the vascular network and the growth response of the tumour. In particular, the newly developing vessels tend to encapsulate, rather than penetrate, the tumour and are thus less effective in delivering nutrients.

Keywords

Solid tumour Avascular growth Angiogenesis Vascular growth Multiscale mathematical model 

Mathematics Subject Classification (2000)

62P10 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Paul Macklin
    • 1
  • Steven McDougall
    • 2
  • Alexander R. A. Anderson
    • 3
  • Mark A. J. Chaplain
    • 3
  • Vittorio Cristini
    • 1
    • 4
  • John Lowengrub
    • 5
  1. 1.School of Health Information SciencesUniversity of Texas Health Science CenterHoustonUSA
  2. 2.Institute of Petroleum EngineeringHeriot-Watt UniversityEdinburghScotland, UK
  3. 3.Division of MathematicsUniversity of DundeeDundeeScotland, UK
  4. 4.M.D. Anderson Cancer CenterHoustonUSA
  5. 5.Mathematics DepartmentUniversity of CaliforniaIrvineUSA

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