Mathematical modeling of cancer cell invasion of tissue

biological insight from mathematical analysis and computational simulation

Vivi Andasari, Alf Gerisch, Georgios Lolas, Andrew P. South, Mark A. J. Chaplain

    Research output: Contribution to journalArticle

    75 Citations (Scopus)

    Abstract

    The ability of cancer cells to break out of tissue compartments and invade locally gives solid tumours a defining deadly characteristic. One of the first steps of invasion is the remodelling of the surrounding tissue or extracellular matrix (ECM) and a major part of this process is the over-expression of proteolytic enzymes, such as the urokinase-type plasminogen activator (uPA) and matrix metalloproteinases (MMPs), by the cancer cells to break down ECM proteins. Degradation of the matrix enables the cancer cells to migrate through the tissue and subsequently to spread to secondary sites in the body, a process known as metastasis. In this paper we undertake an analysis of a mathematical model of cancer cell invasion of tissue, or ECM, which focuses on the role of the urokinase plasminogen activation system. The model consists of a system of five reaction-diffusion-taxis partial differential equations describing the interactions between cancer cells, uPA, uPA inhibitors, plasmin and the host tissue. Cancer cells react chemotactically and haptotactically to the spatio-temporal effects of the uPA system. The results obtained from computational simulations carried out on the model equations produce dynamic heterogeneous spatio-temporal solutions and using linear stability analysis we show that this is caused by a taxis-driven instability of a spatially homogeneous steady-state. Finally we consider the biological implications of the model results, draw parallels with clinical samples and laboratory based models of cancer cell invasion using three-dimensional invasion assay, and go on to discuss future development of the model.

    Original languageEnglish
    Pages (from-to)141-171
    Number of pages31
    JournalJournal of Mathematical Biology
    Volume63
    Issue number1
    DOIs
    Publication statusPublished - Jul 2011

    Keywords

    • Cancer invasion
    • uPA system
    • Haptotaxis
    • Spatio-temporal heterogeneity
    • Organotypic culture
    • Invasion index
    • PLASMINOGEN ACTIVATION SYSTEM
    • EXTRACELLULAR-MATRIX
    • TUMOR-GROWTH
    • SOLID TUMOR
    • CHEMOTAXIS
    • ADHESION
    • HETEROGENEITY
    • ANGIOGENESIS
    • METASTASIS
    • MICROENVIRONMENT

    Cite this

    Andasari, Vivi ; Gerisch, Alf ; Lolas, Georgios ; South, Andrew P. ; Chaplain, Mark A. J. / Mathematical modeling of cancer cell invasion of tissue : biological insight from mathematical analysis and computational simulation. In: Journal of Mathematical Biology. 2011 ; Vol. 63, No. 1. pp. 141-171.
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    abstract = "The ability of cancer cells to break out of tissue compartments and invade locally gives solid tumours a defining deadly characteristic. One of the first steps of invasion is the remodelling of the surrounding tissue or extracellular matrix (ECM) and a major part of this process is the over-expression of proteolytic enzymes, such as the urokinase-type plasminogen activator (uPA) and matrix metalloproteinases (MMPs), by the cancer cells to break down ECM proteins. Degradation of the matrix enables the cancer cells to migrate through the tissue and subsequently to spread to secondary sites in the body, a process known as metastasis. In this paper we undertake an analysis of a mathematical model of cancer cell invasion of tissue, or ECM, which focuses on the role of the urokinase plasminogen activation system. The model consists of a system of five reaction-diffusion-taxis partial differential equations describing the interactions between cancer cells, uPA, uPA inhibitors, plasmin and the host tissue. Cancer cells react chemotactically and haptotactically to the spatio-temporal effects of the uPA system. The results obtained from computational simulations carried out on the model equations produce dynamic heterogeneous spatio-temporal solutions and using linear stability analysis we show that this is caused by a taxis-driven instability of a spatially homogeneous steady-state. Finally we consider the biological implications of the model results, draw parallels with clinical samples and laboratory based models of cancer cell invasion using three-dimensional invasion assay, and go on to discuss future development of the model.",
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    Mathematical modeling of cancer cell invasion of tissue : biological insight from mathematical analysis and computational simulation. / Andasari, Vivi; Gerisch, Alf; Lolas, Georgios; South, Andrew P.; Chaplain, Mark A. J.

    In: Journal of Mathematical Biology, Vol. 63, No. 1, 07.2011, p. 141-171.

    Research output: Contribution to journalArticle

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    T2 - biological insight from mathematical analysis and computational simulation

    AU - Andasari, Vivi

    AU - Gerisch, Alf

    AU - Lolas, Georgios

    AU - South, Andrew P.

    AU - Chaplain, Mark A. J.

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    AB - The ability of cancer cells to break out of tissue compartments and invade locally gives solid tumours a defining deadly characteristic. One of the first steps of invasion is the remodelling of the surrounding tissue or extracellular matrix (ECM) and a major part of this process is the over-expression of proteolytic enzymes, such as the urokinase-type plasminogen activator (uPA) and matrix metalloproteinases (MMPs), by the cancer cells to break down ECM proteins. Degradation of the matrix enables the cancer cells to migrate through the tissue and subsequently to spread to secondary sites in the body, a process known as metastasis. In this paper we undertake an analysis of a mathematical model of cancer cell invasion of tissue, or ECM, which focuses on the role of the urokinase plasminogen activation system. The model consists of a system of five reaction-diffusion-taxis partial differential equations describing the interactions between cancer cells, uPA, uPA inhibitors, plasmin and the host tissue. Cancer cells react chemotactically and haptotactically to the spatio-temporal effects of the uPA system. The results obtained from computational simulations carried out on the model equations produce dynamic heterogeneous spatio-temporal solutions and using linear stability analysis we show that this is caused by a taxis-driven instability of a spatially homogeneous steady-state. Finally we consider the biological implications of the model results, draw parallels with clinical samples and laboratory based models of cancer cell invasion using three-dimensional invasion assay, and go on to discuss future development of the model.

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    KW - ADHESION

    KW - HETEROGENEITY

    KW - ANGIOGENESIS

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    U2 - 10.1007/s00285-010-0369-1

    DO - 10.1007/s00285-010-0369-1

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