CONTINUUM MODELING OF THE BIOLOGICAL MEDIUM COMPOSED OF ACTIVELY INTERACTING CELLS OF TWO DIFFERENT TYPES

Active intercellular interactions control the movement of cells relative to one another and play an important role in biological morphogenesis and processes associated with tissue remodeling. A continuum multiphase model of the mechanically active biological medium formed by two different types of cells and extracellular fluid is developed. The model includes additional phases responsible for active force interactions between cells. Such interactions (between cells both within the same phase and of different phases) are modeled by means of active stresses that develop in additional phases and depend (in the general case, nonlocally) on the densities of cell phases. The strain rates of the cell phases are determined by active stresses and also depend on other stresses acting in the medium. A model problem of the evolution of an initially homogeneous distribution of the densities of cell phases in an infinite plane layer is solved. Cases of a fixed position of the layer boundaries and of their possible displacement in the absence of external loading are considered. It is shown that the proposed model describes the phenomenon of cell sorting: cells of one type form a compact mass surrounded by cells of another type. The results of the solution have shown that the sorting process is possible only when taking into account the nonlocal dependence of active stresses on the densities of cell phases. The proposed model differs from other approaches to the theoretical description of sorting by introducing into consideration the parameters and relationships that have a distinct mechanical meaning (in particular, without using the concept of “surface tension” in the cell medium).