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

Research output: Contribution to journalArticlepeer-review

292 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)765-798
Number of pages34
JournalJournal of Mathematical Biology
Issue number4-5
Publication statusPublished - Apr 2009


  • Solid tumour
  • Avascular growth
  • Angiogenesis
  • Vascular growth
  • Multiscale mathematical model
  • Cell migration speed
  • Induced angiogenesis
  • Structural adaptation
  • Mathematical model
  • Multicellular spheroids
  • Microvascular networks
  • Clinical implications
  • Glioma growth
  • Blood flow
  • Set method


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