On the closure of mass balance models for tumor growth

Mass balance equations typically adopted to describe tumor growth are to be closed by introducing a suitable velocity field. The first part of this paper is devoted to a critical review of some approaches devised to this aim in the relevant literature. In the second part we start from the observation that the phenomenological description of a tumor spheroid suggests to model it as a growing and deformable porous material. The concept of volume fraction and the essentials of the mechanics of multicomponent continua are then introduced and applied to the problem at hand. The system of equations regulating such a system is stated and its validity is then discussed at the light of numerical simulations.