Continuum modeling of mechano-dependent reactions in tissues composed of mechanically active cells

Mechanical forces and interactions participate in ontogenesis at all scale levels: intracellular, cellular, and supra-cellular, the latter including tissue level. This concept, now almost trivial, was finding its way with difficulties, and the works of L.V. Beloussov have played a decisive role in its establishment. The continuum approach presented in this study makes it possible to take at the tissue level into account both relative motion of cells and forces that control this motion. The characteristics which allow us to take into account general active properties of the cell medium are described, possible mechanisms represented by these characteristics are discussed, and a concise review of our results obtained to date is presented. In the strain rate tensor, two separate components are distinguished, one of them being related to deformation of individual cells and the other to cell rearrangement. A separate phase (submedium) that corresponds to active subcellular elements associated with rearrangement-controlling active stresses is also introduced. Within this general approach two specific models are considered. The first made it possible to establish general mechanisms whose account enabled us to satisfactorily describe the experimental results of L.V. Beloussov and collaborators, concerning mechano-dependent reactions of embryonic epithelium explants. On the assumptions that the active stress responds to cell shape deviations and the rearrangement strain rate component depends on the active stresses developed by pseudopodia, the cell shape and tissue stress evolution observed experimentally in stretched explants, as well as their post-release deformation, are reproduced. The second particular model considers self-organization in a conglomerate of loosely connected cells in the presence of a fluid phase. In this case, the active stress was assumed to nonlocally depend on the density of cells and the rearrangement strain rate on the active and passive stresses. Due to loss of stability of the spatially homogeneous state, various structures similar to those observed in embryogenesis develop. In particular, within the conglomerate, a cavity can be formed, a certain level of the fluid pressure being necessary for this.