Couple stresses and discrete potentials in the vertex model of cellular monolayers.
Couple stresses and discrete potentials in the vertex model of cellular monolayers.
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DOI：
10.1007/s10237-022-01620-2
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发表时间：
2023-10
影响因子：
3.5
通讯作者：
Revell, Christopher K.
中科院分区：
文献类型：
--
作者：
Jensen, Oliver E.;Revell, Christopher K.
顶点模型广泛用于模拟融合上皮和其他多细胞组织的机械特性。这种固有的离散框架允许柯西应力归因于每个细胞，并且其对称分量已被广泛报道，至少对于平面单层而言。在这里，我们考虑归因于每个三细胞连接的邻域的应力，特别评估其主序反对称分量和相关的耦合应力，其表征单个细胞经历（和抵抗）面内弯曲变形的程度。我们开发了具有无序内部结构的局部单层的离散势理论，并用它来推导 Airy 和 Mindlin 应力函数的类似物。这些标量势通常具有宽带谱，突出了小尺度缺陷和边界层对全局应力模式的贡献。仿射近似将应力耦合归因于共享三结点的单元之间的压力差，但模拟表明非仿射变形还有额外的作用。
The vertex model is widely used to simulate the mechanical properties of confluent epithelia and other multicellular tissues. This inherently discrete framework allows a Cauchy stress to be attributed to each cell, and its symmetric component has been widely reported, at least for planar monolayers. Here, we consider the stress attributed to the neighbourhood of each tricellular junction, evaluating in particular its leading-order antisymmetric component and the associated couple stresses, which characterise the degree to which individual cells experience (and resist) in-plane bending deformations. We develop discrete potential theory for localised monolayers having disordered internal structure and use this to derive the analogues of Airy and Mindlin stress functions. These scalar potentials typically have broad-banded spectra, highlighting the contributions of small-scale defects and boundary layers to global stress patterns. An affine approximation attributes couple stresses to pressure differences between cells sharing a trijunction, but simulations indicate an additional role for non-affine deformations.
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