A mathematical model of the stress induced during avascular tumour growth

Citation
Af. Jones et al., A mathematical model of the stress induced during avascular tumour growth, J MATH BIOL, 40(6), 2000, pp. 473-499
Citations number
36
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Multidisciplinary
Journal title
JOURNAL OF MATHEMATICAL BIOLOGY
ISSN journal
0303-6812 → ACNP
Volume
40
Issue
6
Year of publication
2000
Pages
473 - 499
Database
ISI
SICI code
0303-6812(200006)40:6<473:AMMOTS>2.0.ZU;2-0
Abstract
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.