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

BioSystems. 2018. Vol. 173. P. 225-234.
Stein A., Logvenkov S. A., Volodyaev I.

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