Growth of necrotic tumors in the presence and absence of inhibitors

H. M. Byrne, M. A. J. Chaplain

    Research output: Contribution to journalArticlepeer-review

    214 Citations (Scopus)

    Abstract

    A mathematical model is presented for the growth of a multicellular spheroid that comprises a central core of necrotic cells surrounded by an outer annulus of proliferating cells. The model distinguishes two mechanisms for cell loss: apoptosis and necrosis. Cell loss due to apoptosis is defined to be programmed cell death, occurring, for example, when a cell exceeds its natural lifespan, whereas cell death due to necrosis is induced by changes in the cell's microenvironment, occurring, for example, in nutrient-depleted regions. Mathematically, the problem involves tracking two free boundaries, one for the outer tumor radius, the other for the inner necrotic radius. Numerical simulations of the model are presented in an inhibitor-free setting and an inhibitor-present setting for various parameter values. The effects of nutrients and inhibitors on the existence and stability of the time-independent solutions of the model are studied using a combination of numerical and asymptotic techniques.
    Original languageEnglish
    Pages (from-to)187-216
    Number of pages30
    JournalMathematical Biosciences
    Volume135
    Issue number2
    DOIs
    Publication statusPublished - 1996

    Keywords

    • Multicell spheroids
    • Necrosis
    • Apoptosis
    • Inhibitors

    Fingerprint

    Dive into the research topics of 'Growth of necrotic tumors in the presence and absence of inhibitors'. Together they form a unique fingerprint.

    Cite this