  Tissue dynamics and collective cell motion are crucial biological processes.
Their biological machinery is mostly known, and simulation models such as the
"active vertex model" (AVM) exist and yield reasonable agreement with
experimental observations like tissue fluidization or fingering. However, a
good and well-founded continuum description for tissues remains to be
developed. In this work we derive a macroscopic description for a
two-dimensional cell monolayer by coarse-graining the vertex model through the
Poisson bracket approach. We obtain equations for cell density, velocity and
the cellular shape tensor. We then study the homogeneous steady states, their
stability (which coincides with thermodynamic stability), and especially their
behavior under an externally applied shear. Our results contribute to elucidate
the interplay between flow and cellular shape. The obtained macroscopic
equations present a good starting point for adding cell motion, morphogenetic
and other biologically relevant processes.
