Modelling aspects of cancer growth: insight from mathematical and numerical analysis and computational simulation

Mark A. J. Chaplain

    Research output: Chapter in Book/Report/Conference proceedingChapter

    28 Citations (Scopus)

    Abstract

    In this chapter we present a variety of reaction-diffusion-taxis(i.e. macroscopic) models of several key stages of solid tumour growth - avascular growth, the immune response to solid tumours and invasive growth. The basis for all of the models is deriving the continuum PDE using a conservation of mass argument. In the model for avascular growth we examine the potential role prepattern theory (diffusion-driven instability `a la Turing) may play in the generation of spatio-temporal heterogeneity of mitotic activity on the surface of multicell spheroids. In the model for the immune response to cancer, working from an initial“microscale” cell interaction scheme, we derive a system of PDEs which are used to predict the capacity of the immune system to eradicate cancer (or not). In the final model of cancer invasion, once again we initially focus on “microscale” activity of matrix degrading enzymes and their binding to cell-surface receptors to derive a PDE model of the process of cancer invasion of the local tissue. For each system, we carry out mathematical and numerical analyses of the model and perform computational simulations and attempt to draw relevant biological conclusions and make experimentally-testable predictions from the results.
    Original languageEnglish
    Title of host publicationMultiscale problems in the life sciences
    Subtitle of host publicationfrom microscopic to macroscopic
    EditorsVincenzo Capasso, Miroslaw Lachowicz
    Place of PublicationBerlin
    PublisherSpringer
    Pages147-200
    Number of pages54
    Volume19405
    ISBN (Electronic)9783540783626
    ISBN (Print)9783540783602
    DOIs
    Publication statusPublished - 2008
    EventBanach Center and CIME Joint Summer School From a Microscopic to a Macroscopic Description of Complex Systems - Bedlewo, Poland
    Duration: 4 Sep 20069 Sep 2006

    Publication series

    NameLecture notes in mathematics
    PublisherSpringer
    Number1940
    ISSN (Print)0075-8434
    ISSN (Electronic)1617-9692

    Conference

    ConferenceBanach Center and CIME Joint Summer School From a Microscopic to a Macroscopic Description of Complex Systems
    Country/TerritoryPoland
    CityBedlewo
    Period4/09/069/09/06

    Keywords

    • Necrosis factor-alpha
    • Plasminogen activation system
    • Traveling waves solutions
    • Gastric cacinoma cells
    • Pattern formation
    • Tumor growth
    • TGF-Beta
    • Multicellular spheroids
    • Autocrine growth
    • Breast cancer

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