Dynamics and geometry from high dimensional data

Tumor growth: from agent-based model to free-boundary problem

Sébastien Motsch

Arizona State University

In this talk, we investigate the large time behavior of an agent based model modeling tumor growth. This microscopic model combines short-range repulsion and cell division. We derive the associated macroscopic dynamics leading to a porous media type equation. In order to capture the long-time behavior of the microscopic model, we have to modify the porous media in order to include a density threshold for the repulsion. The main difficulty is then to investigate the limit as the repulsion between cells becomes singular (modeling non-overlapping constraint). We show formally that such asymptotic limit leads to a free-boundary problem (Hele-Shaw type). Numerical results confirm the relevance of such limit.