  The coordinated behaviors of epithelial cells are widely observed in tissue
development, such as re-epithelialization, tumor growth, and morphogenesis. In
these processes, cells either migrate collectively or organize themselves into
specific structures to serve certain purposes. In this work, we study a
spreading epithelial monolayer whose migrating front encloses a circular gap in
the monolayer center. Such tissue is usually used to mimic the wound healing
process in Virto. We model the epithelial sheet as a layer of active viscous
polar fluid. With an axisymmetric assumption, the model can be analytically
solved under two special conditions, suggesting two possible spreading modes
for the epithelial monolayer. Based on these two sets of analytical solutions,
we assess the velocity of the spreading front affected by the gap size, the
active intercellular contractility, and the purse-string contraction acting on
the spreading edge. Several critical values exist in the model parameters for
the initiation of the gap closure process, and the purse-string contraction
plays a vital role in governing the gap closure kinetics. Finally, the
instability of the morphology of the spreading front was studied. Numerical
calculations show how the perturbated velocities and the growth rates vary with
respect to different model parameters.
