A cell-based constitutive model for embryonic epithelia and other planar aggregates of biological cells

Embryonic epithelia are shown to have in common with plastic materials a number of key characteristics, including fabric evolution, “yielding”, “particle” (cell) rearrangement, energy dissipation, dependence of stress on fabric and irreversibility of deformation. The strains apparent at the tissue level can be large (several hundred percent over the course of 5–10 h), and are possible because of in-plane cell rearrangement. We propose a cell-based constitutive model, the first of its kind, to relate in-plane stresses, tissue deformations, evolution of cellular fabric (cell size, shape and orientation), mitosis and cell rearrangement. The governing equations are based on results from finite element models, statistical mechanics analyses and experiments. The constitutive model overcomes drawbacks of existing finite element models where cells are modeled using multiple elements, and it confirms that tissue fabric is a primary determinant of stress and deformation. Fabric predictions made using the model are as good as the available data, even when strain histories are complex or multiple biological processes are active simultaneously. The model provides insights into the mechanics of embryonic epithelia and other labile biological tissues, and it sets the stage for future computational studies of whole embryos.