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Regular version of the site

Article

Mathematical Model of a Biological Medium with Account for the Active Interactions and Relative Displacements of Cells that Form It

Fluid Dynamics. 2018. Vol. 53. No. 5. P. 583-595.
Logvenkov S. A.

A three-phase continuum model of a biological medium formed by cells, extracellular
fluid, and an additional phase responsible for independently controlled active force interaction
between the cells is obtained. The model describes the reconstruction of biological tissues with
account for the active stresses exerted at intercellular interactions. The constitutive relation for
the active stress tensor takes into account different mechanisms of cell interactions, including the
chaotic and directed cell activities as the active stresses are created, as well as the anisotropy of
their development due to cell density distribution inhomogeneity. On the basis of the model, the
problem of forming a cavity within an initially homogeneous cell spheroid due to the loss of stability
of the homogeneous state is solved. The constitutive relation for the medium strain rate due to cell
rearrangements takes into account two mechanisms of relative cell motion: related to cell adhesion
and cellmotility. The participation of differentmechanisms of cell interaction in the self-organization
of the biological system that consists of mechanically active cells is investigated.