MODELING THE GROWTH OF SOLID TUMORS AND INCORPORATING A METHOD FOR THEIR CLASSIFICATION USING NONLINEAR ELASTICITY THEORY

Medically, tumours are classified into two important classes - benign and malignant. Generally speaking, the two classes display different b ehaviour with regard to their rate and manner of growth and subsequent possible spread. In this paper, we formulate a new approach to tumour growth using results and techniques from nonlinear elasticity theory. A mathematical model is given for the growth of a solid tumour using membrane and thick-shell theory. A central feature of the model is the characterisation of the material composition of the model through the use of a strain-energy function, thus permitting a mathematical descr iption of the degree of differentiation of the tumour explicitly in th e model. Conditions are given in terms of the strain-energy function f or the processes of invasion and metastasis occurring in a tumour, bei ng interpreted as the bifurcation modes of the spherical shell which t he tumour is essentially modelled as. Our results are compared with ac tual experimental results and with the general behaviour shown by beni gn and malignant tumours. Finally, we use these results in conjunction with aspects of surface morphogenesis of tumours (in particular, the Gaussian and mean curvatures of the surface of a solid tumour) in an a ttempt to produce a mathematical formulation and description of the im portant medical processes of staging and grading cancers. We hope that this approach may form the basis of a practical application.