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

Abstract

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. Math. Models Methods Appl. Sci. 2012.22. Downloaded from www.worldscientific.com by ROYAL INSTITUTE OF TECHNOLOGY on 02/05/15. For personal use only. Asymptotic Theory from Microscopic to Macroscopic Tissue Models(v) The biological systems are complex, and the mathematical models are obtained by approaches that attempt to reduce their complexity.

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