A commonly used assay for studying cell - matrix interactions is the free-floating fibroblast populated collagen lattice, which was introduced in 1979. Briefly, fibroblasts are seeded within an initially thin, amorphous, untethered, circular gel consisting of reconstituted fibrillar collagen. Although the gel remains traction free and circular, the cells typically contract the gel to less than 50% of its original diameter within hours to days. Cellular mechanotransduction mechanisms are fundamental to this contraction, but there has not been a careful study of the associated mechanics. In this paper, we model the initial contraction of a circular gel by assuming a homogeneous, axisymmetric finite deformation while allowing possible radial variations in material properties, including material symmetry. We show that trivial solutions alone (i.e., no deformation, no contraction) are admitted by equilibrium and boundary conditions unless radial variations exist in the material behavior, including cell contraction. Although more complete data are needed to model better this initial-boundary value problem, the present results are consistent with both the salient features of the gel assay and recent observations reported in the literature that cells often introduce regional variations in tissue properties in vivo in an attempt to achieve, maintain, or restore mechanical homeostasis.

中文翻译：

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关于自由浮动工程组织中一类可接受的本构行为。

研究细胞-基质相互作用的常用方法是 1979 年推出的自由漂浮的成纤维细胞填充的胶原晶格。简而言之，成纤维细胞被接种在最初由重建的纤维状胶原组成的薄的、无定形的、不受束缚的圆形凝胶中。尽管凝胶保持无牵引和圆形，但细胞通常会在数小时至数天内将凝胶收缩至其原始直径的 50% 以下。细胞机械转导机制是这种收缩的基础，但尚未对相关力学进行仔细研究。在本文中，我们通过假设均匀的轴对称有限变形来模拟圆形凝胶的初始收缩，同时允许材料特性（包括材料对称性）可能发生径向变化。我们证明单独的微不足道的解决方案（即，没有变形，没有收缩）被平衡和边界条件允许，除非材料行为中存在径向变化，包括单元收缩。虽然需要更完整的数据来更好地模拟这个初始边界值问题，但目前的结果与凝胶测定的显着特征和文献中报道的最近观察结果一致，即细胞经常在体内引入组织特性的区域变化。尝试实现、维持或恢复机械稳态。