During vertebrate embryo elongation, neural and muscular tissues grow in contact while remaining segregated and their live imaging reveals cellular turbulent behavior. To understand such behaviors, we introduce two 2D mechanical models reproducing the evolution of two segregated viscous tissues in contact, and displaying swirling cell motions. Segregation is encoded differently in the two models: by passive or active segregation (based on a mechanical repulsion pressure). We formally compute the incompressible limits of the two models to obtain two geometric descriptions of the tissues. The two models at the limit thus obtained are compared and a well-posedness and regularity analysis is conducted. Thanks to a transmission problem formulation, our analysis revealed two striking features: a ghost effect, and the appearance of pressure jumps at the tissues' boundaries. These results are supported by numerical simulations in 2D and confronted to the biological data.
In the second part of this talk, we introduce an additional model which incorporates an extra term modeling the addition of new cells into the tissues, a phenomena also observed in vivo. We calibrate this model using the biological data at hand, and simulate the elongation of the vertebrate embryo. Interesting biological hypotheses arise from the numerical exploration of the model, which we then confirm experimentally on quail embryos.
