Abstract—

The problem of the evolution of a cavity formed at the initial moment of time in the central part of a spherical cellular aggregate is solved. The earlier-developed model of a biological medium formed by cells displaying mechanical activity and an extracellular fluid is used in studying the influence of different mechanisms of active intercellular interactions (chaotic and directed nonlocal) on the propagation of a front separating the cellular medium and the fluid. Numerical solutions show that in certain cases characterized by the fluid pressure and the density of the initial cell distribution the chaotical activity of the cells alone is sufficient for increasing the radius of the internal cavity. In other cases, the cavity development is impossible without the participation of the nonlocal mechanism of active interactions between the cells and the outer boundary. In the absence of the interaction between the cells and the outer boundary the nonlocal mechanism of active intercellular interactions does not lead to the cavity growth for any its initial dimensions. The formulation and solution of the problem describe more completely the possible scenarios of the morhogenesis at one of the earlier stages of the embryonic development.

中文翻译：

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取决于主动的细胞间相互作用的细胞球体腔发展的调查。

摘要-

解决了在球形蜂窝状聚集体的中心部分的初始时刻形成的空腔的演化问题。由显示机械活性的细胞和细胞外液形成的生物培养基的较早开发模型用于研究活跃的细胞间相互作用的不同机制（混沌和定向的非局部）对分离细胞培养基和细胞的前缘的繁殖的影响。体液。数值解表明，在某些情况下，以流体压力和初始细胞分布的密度为特征，仅细胞的混沌活动就足以增加内腔的半径。在其他情况下，没有细胞与外边界之间的主动相互作用的非局部机制的参与，空腔的发展是不可能的。在细胞与外边界之间不存在相互作用的情况下，主动细胞间相互作用的非局部机制在任何初始尺寸下均不会导致空腔生长。问题的表述和解决方案更完整地描述了在胚胎发育早期阶段之一中发生致畸的可能情况。