  In developing organisms, internal cellular processes generate mechanical
stresses at the tissue scale. The resulting deformations depend on the material
properties of the tissue, which can exhibit long-ranged orientational order and
topological defects. It remains a challenge to determine these properties on
the time scales relevant for developmental processes. Here, we build on the
physics of liquid crystals to determine material parameters of cell monolayers.
Specifically, we use a hydrodynamic description to characterize the stationary
states of compressible active polar fluids around defects. We illustrate our
approach by analyzing monolayers of C2C12 cells in small circular confinements,
where they form a single topological defect with integer charge. We find that
such monolayers exert compressive stresses at the defect centers, where
localized cell differentiation and formation of three-dimensional shapes is
observed.
