Viscoelastic approach to cell migration in epiboly

In this work a viscoelastic model that couples enveloping cell layer velocities and tensions is built including the geometric corrections on the sphere surface, showing that stress anisotropy increases in the layer as a function of the polar coordinate. This trend is enforced as the enveloping cell front advances, which rules the mitotic spindle and contributes to tissue propagation. The theory is general and applicable to gastrulation phases in different vertebrates. Cell speeds and stresses obtained from the leading order of this theory are in good agreement with previous formulations, and an exact approach containing these results generalizes the theoretical model and includes inertial and advective terms, allowing to perform simulations of the enveloping cell layer during epiboly and at following stages such as disperse and reaggregation phases.