On the derivation of macroscopic tissue equations from hybrid models of the kinetic theory of multicellular growing systems — The effect of global equilibrium

This paper deals with a new approach to the development of asymptotic methods for the derivation of biological tissue equations from the underlying description offered by models of the kinetic theory for active particles developed for multicellular systems. The basic nonlinear model is linked to a linear stochastic velocity-jump process used to describe the dynamics of velocity variations. Specifically, the method takes into account the effect of global equilibrium configurations on the derivation and structure of macroscopic, tissue level equations, and leads to the final objective reducing the a priori assumptions used in previous papers.