On the Asymptotic Theory From Microscopic to Macroscopic Growing Tissue Models: An Overview With Perspectives

This paper proposes a review and critical analysis of the asymptotic limit methods focused on the derivation of macroscopic equations for a class of equations modeling complex multicellular systems by methods of the kinetic theory for active particles. Cellular interactions generate both modification of biological functions and proliferative/destructive events. The asymptotic analysis deals with suitable parabolic, hyperbolic, and mixed limits. The review includes the derivation of the classical Keller–Segel model and flux limited models that prevent non-physical blow up of solutions.