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An Age and Spatially Structured Model of Tumor Invasion with Haptotaxis II

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  • JANET DYSON
  • ROSANNA VILLELLA-BRESSAN
  • GLENN WEBB
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    Abstract

    An analysis of a model of tumor growth into surrounding tissue is continued from an earlier treatment, in which the global existence of unique solutions to the model was established. The model consists of a system of nonlinear partial differential equations for the population densities of tumor cells, extracellular matrix macromolecules, oxygen concentration, and extracellular matrix degradative enzyme concentration. The spatial growth of the tumor involves the directed movement of tumor cells toward the extracellular matrix through haptotaxis. Cell age is used to track progression of cells through the cell cycle. Regularity, positivity, and global bounds of the solutions of the model are proved.

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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Mathematical Population Studies.

    Volume (Year): 15 (2008)
    Issue (Month): 2 ()
    Pages: 73-95

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    Handle: RePEc:taf:mpopst:v:15:y:2008:i:2:p:73-95

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    Related research

    Keywords: analytic semigroup; cell proliferation; degradation enzyme; diffusion; extracellular matrix; fractional power; haptotaxis; tumor cells;

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