Modelling the role of cell-cell adhesion in the growth and development of carcinomas

摘要: In this paper, a mathematical model is presented to describe the evolution of an avascular solid tumour in response externally-supplied nutrient. The growth depends on balance between expansive forces caused by cell proliferation and cell-cell adhesion which exist maintain tumour's compactness. Cell-cell incorporated into using Gibbs-Thomson relation relates change nutrient concentration across boundary local curvature, energy being used preserve forces. Our analysis focuses existence uniqueness steady, radially-symmetric solutions model, also their stability time-dependent asymmetric perturbations. particular, our suggests that if needed bonds large then configuration stable with respect all perturbations, maintains structure-this corresponds benign tumour. As compactness diminishes so number modes underlying solution unstable increases-this invasive carcinoma. strength may at some stage provide clinicians useful index potential