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).

中文翻译：

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由两种不同类型的主动相互作用细胞组成的生物培养基的连续模型

活跃的细胞间相互作用控制细胞相对于彼此的运动，并在生物形态发生和与组织重塑相关的过程中发挥重要作用。开发了由两种不同类型的细胞和细胞外液形成的机械活性生物介质的连续多相模型。该模型包括负责细胞之间主动力相互作用的附加阶段。这种相互作用（同一相内和不同相内的细胞之间）通过在附加相中产生的主动应力进行建模，并取决于（在一般情况下，非局部）细胞相的密度。细胞相的应变率由主动应力决定，也取决于作用在介质中的其他应力。解决了无限平面层中细胞相密度初始均匀分布演化的模型问题。考虑了层边界的固定位置及其在没有外部载荷的情况下可能发生的位移的情况。结果表明，所提出的模型描述了细胞分选现象：一种类型的细胞形成了被另一种类型的细胞包围的紧密团块。解决方案的结果表明，只有在考虑到主动应力对细胞相密度的非局部依赖性时，分类过程才是可能的。所提出的模型通过引入具有不同机械意义的参数和关系（特别是，