A mathematical model of the stress induced during avascular tumour growth

A. F. Jones, H. M. Byrne, J. S. Gibson, J. W. Dold

    Research output: Contribution to journalArticlepeer-review


    In this paper a mathematical model is developed to describe the effect of nonuniform growth on the mechanical stress experienced by cells within an avascular tumour. The constitutive law combines the stress-strain relation of linear elasticity with a growth term that is derived by analogy with thermal expansion. To accommodate the continuous nature of the growth process, the law relates the rate of change of the stress tensor to the rate of change of the strain (rather than relating the stress to the strain directly). By studying three model problems which differ in detail, certain characteristic features are identified. First, cells near the tumour boundary, where nutrient levels and cell proliferation rates are high, are under compression. By contrast, cells towards the centre of the tumour, where nutrient levels are low and cell death dominant, are under tension. The implications of these results and possible model developments are also discussed. © Springer-Verlag 2000.
    Original languageEnglish
    Pages (from-to)473-499
    Number of pages26
    JournalJournal of Mathematical Biology
    Issue number6
    Publication statusPublished - Jun 2000


    • Elasticity
    • Growth
    • Stress
    • Tumour modelling


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