MODELING THE ROLE OF CELL-CELL ADHESION IN THE GROWTH AND DEVELOPMENTOF CARCINOMA

In this paper, a mathematical model is presented to describe the evolu tion of an avascular solid tumour in response to an externally-supplie d nutrient. The growth of the tumour depends on the balance between ex pansive forces caused by cell proliferation and cell-cell adhesion for ces which exist to maintain the tumour's compactness. Cell-cell adhesi on is incorporated into the model using the Gibbs-Thomson relation whi ch relates the change in nutrient concentration across the tumour boun dary to the local curvature, this energy being used to preserve the ce ll-cell adhesion forces. Our analysis focuses on the existence and uni queness of steady, radially-symmetric solutions to the model, and also their stability to time-dependent and asymmetric perturbations. In pa rticular, our analysis suggests that if the energy needed to preserve the bonds of adhesion is large then the radially-symmetric configurati on is stable with respect to all asymmetric perturbations, and the tum our maintains a radially-symmetric structure-this corresponds to the g rowth of a benign tumour. As the energy needed to maintain the tumour' s compactness diminishes so the number of modes to which the underlyin g radially-symmetric solution is unstable increases-this corresponds t o the invasive growth of a carcinoma. The strength of the cell-cell bo nds of adhesion may at some stage provide clinicians with a useful ind ex of the invasive potential of a tumour.