Abstract

The mechanical modeling of living tissues has attracted much attention in the last decade. Applications include tissue repair and growth models of solid tumors. In this latter case, these models are calibrated on medical images and help to predict the evolution of the disease, to decide of treatment scheduling and of the optimal therapy. They are also used to understand the biological effects that permit tumor growth.

These models contain several levels of complexity, both in terms of the biological and mechanical effects, and therefore in their mathematical description. The number of scales, from molecules to the organ and entire body, explains partly this complexity. Here, the analysis of the incompressible limit, and the associated free boundary problem, is mathematically challenging.

In this talk I shall give a general presentation of the field. Departing from the simplest (and irrealistic) model of cell division moving by pressure forces, I will include several additional biological effects and explain the consequences in terms of qualitative behavior of solutions.