  This paper deals with the analysis of the asymptotic limit toward the
derivation of macroscopic equations for a class of equations modeling complex
multicellular systems by methods of the kinetic theory. After having chosen an
appropriate scaling of time and space, a Chapman-Enskog expansion is combined
with a closed, by minimization, technique to derive hyperbolic models at the
macroscopic level. The resulting macroscopic equations show how the macroscopic
tissue behavior can be described by hyperbolic systems which seem the most
natural in this context. We propose also an asymptotic-preserving well-balanced
scheme for the one-dimensional hyperbolic model, in the two dimensional case,
we consider a time splitting method between the conservative part and the
source term where the conservative equation is approximated by the
Lax-Friedrichs scheme.
