Tumor growth and immune response: On the impact of the space-structuration of the tumor microenvironment

We use a model inspired from mixture theory to describe tumor growth, its interaction with the environment, its needs of nutrients and oxygen supply, and the effects of the immune response. The latter might have a dual nature, since the expected antitumor mechanisms can be perverted at the tumor advantage. The PDE system brings out crucial features of the space organization in shaping tumor expansion or the efficiency of the immune response. In particular, our two-dimensional numerical experiments exhibit equilibrium phases, with a residual tumor kept under control by the immune system. They also show possible displacement of the tumor core, where small volume fractions are able to find an environment favorable to tumor expansion.