Extension of the Greenspan model to asymmetric tumour growth

摘要

The Greenspan model is one of the most well defined mathematical approaches to the problem of tumour growth. It is built on principles of Fluid Mechanics and it has been applied to the growth of a spherical tumour. The present report attempts a generalization of the Greenspan model to the evolution of a tumour that has different growth characteristics in different spacial directions. Evidently, this behavior refers to the ellipsoidal geometry which models the anisotropic structure of the Euclidean space. It is of interest to realize that the ellipsoidal model of growth needs some non-trivial physical and mathematical adaptations of the corresponding spherical model, in order to end up with a reasonable and solvable algorithm that describes the evolution of the different tumour phases.