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

Abstract

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.