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 journalArticle

    201 Citations (Scopus)

    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.

    Original languageEnglish
    Pages (from-to)765-798
    Number of pages34
    JournalJournal of Mathematical Biology
    Volume58
    Issue number4-5
    DOIs
    Publication statusPublished - Apr 2009

    Fingerprint

    Multiscale Modeling
    Tumor Growth
    blood vessels
    Blood Vessels
    Tumors
    Tumor
    neoplasms
    Growth
    Neoplasms
    Simulation
    Remodeling
    Nutrients
    Progression
    Angiogenesis
    nutrients
    Multiscale Model
    Cell Proliferation
    Hydrostatics
    Food
    angiogenesis

    Keywords

    • 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

    Cite this

    Macklin, P., McDougall, S., Anderson, A. R. A., Chaplain, M. A. J., Cristini, V., & Lowengrub, J. (2009). Multiscale modelling and nonlinear simulation of vascular tumour growth. Journal of Mathematical Biology, 58(4-5), 765-798. https://doi.org/10.1007/s00285-008-0216-9
    Macklin, Paul ; McDougall, Steven ; Anderson, Alexander R. A. ; Chaplain, Mark A. J. ; Cristini, Vittorio ; Lowengrub, John. / Multiscale modelling and nonlinear simulation of vascular tumour growth. In: Journal of Mathematical Biology. 2009 ; Vol. 58, No. 4-5. pp. 765-798.
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    title = "Multiscale modelling and nonlinear simulation of vascular tumour growth",
    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.",
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    Macklin, P, McDougall, S, Anderson, ARA, Chaplain, MAJ, Cristini, V & Lowengrub, J 2009, 'Multiscale modelling and nonlinear simulation of vascular tumour growth', Journal of Mathematical Biology, vol. 58, no. 4-5, pp. 765-798. https://doi.org/10.1007/s00285-008-0216-9

    Multiscale modelling and nonlinear simulation of vascular tumour growth. / Macklin, Paul; McDougall, Steven; Anderson, Alexander R. A.; Chaplain, Mark A. J.; Cristini, Vittorio; Lowengrub, John.

    In: Journal of Mathematical Biology, Vol. 58, No. 4-5, 04.2009, p. 765-798.

    Research output: Contribution to journalArticle

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    Macklin P, McDougall S, Anderson ARA, Chaplain MAJ, Cristini V, Lowengrub J. Multiscale modelling and nonlinear simulation of vascular tumour growth. Journal of Mathematical Biology. 2009 Apr;58(4-5):765-798. https://doi.org/10.1007/s00285-008-0216-9