A mathematical model of the stress induced during avascular tumour growth

In this paper a mathematical model is developed to describe the effect of n onuniform growth on the mechanical stress experienced by cells within an av ascular tumour. The constitutive law combines the stress-strain relation of linear elasticity with a growth term that is derived by analogy with therm al expansion. To accommodate the continuous nature of the growth process, t he law relates the rate of change of the stress tensor to the rate of chang e of the strain (rather than relating the stress to the strain directly). B y studying three model problems which differ in detail, certain characteris tic features are identified. First, cells near the tumour boundary, where n utrient levels and cell proliferation rates are high, are under compression . By contrast, cells towards the centre of the tumour, where nutrient level s are low and cell death dominant, are under tension. The implications of t hese results and possible model developments are also discussed.