The importance of intercellular adhesion in the development of carcinomas.
When grading and classifying tumours several criteria are taken into consideration. These include the type of cell from which the tumour has arisen, whether it is benign or malignant and its ability to invade the surrounding tissue. In this paper we suggest that the ability with which a tumour invades its host environment can be related to the intercellular adhesion forces which maintain the tumour's structure. We develop a mathematical model to describe the growth of an avascular tumour in response to an externally supplied nutrient. Its development depends on the balance between expansive forces caused by cell proliferation and intercellular adhesion forces which maintain the tumour's compactness. We focus attention on the existence, uniqueness, and stability of steady, radially symmetric solutions to the model. Our analysis shows that as the importance of cell-cell adhesion increases the size of the radially symmetric steady tumour radius diminishes and the number of asymmetric modes to which it is stable increases. Thus we conclude that cell-cell adhesion may provide clinicians with a useful index of the invasive potential of a tumour.