Action of body forces in tumor growth

In the present work two mathematical models are proposed to investigate tumor growth within the framework of continuum mechanics. In particular, the tumor is modeled as an ideal saturated mixture, where the mechanical description is based on both the mixtures theory and the notion of multiple natural configurations. The mixture is considered as a porous material composed by a hyperelastic compressible solid and an incompressible viscous fluid. In addition, the growth of a tumor considered as a single hyperelastic solid material is also studied as a particular case. Then, a general mathematical model is formulated using particular constitutive laws for each component involved. The resulting constitutive equation is used to describe the isotropic inhomogeneous growth of an encapsulated spherical solid tumor. During that process, the mixture is assumed to be isothermal. Furthermore, growth is understood as a change in the body mass of the constituents supplemented with diffusion of nutrients. The mechanical modulation of growth by body forces is then illustrated and analyzed by means of computer numerical simulations. To that end, the material parameter values considered were taken from experimental data, and model results describe realistic tumor growth dynamics.