A qualitative analysis of some models of tissue growth

N. F. Britton, M. A. J. Chaplain

    Research output: Contribution to journalArticle

    37 Citations (Scopus)

    Abstract

    Using maximum principles for parabolic and elliptic operators, we examine, in a general way, some models of tissue growth. These typically consist of a model mechanism for the diffusion of a mitotic inhibitor (growth inhibitory factor, GIF) throughout the tissue. Central to the modeling is the inclusion of a source function that models the production of GIF throughout the tissue. We examine the effect this term has on the resulting distribution of GIF in the tissue and comment on the appropriateness of different source functions, in particular a uniform production rate or a nonuniform production rate of inhibitor. Given that it is more appropriate to infer from the patterns of mitosis that are observed experimentally in various tissues the GIF concentration profile rather than the source function profile, it may be more appropriate to use these types of models to determine the qualitative form of the source term rather than proposing this function a priori.
    Original languageEnglish
    Pages (from-to)77-89
    Number of pages13
    JournalMathematical Biosciences
    Volume113
    Issue number1
    DOIs
    Publication statusPublished - Jan 1993

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