Department of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, UK.
Wellcome Trust Centre for Cell-Matrix Research, University of Manchester, Oxford Road, Manchester, M13 9PL, UK.
Biomech Model Mechanobiol. 2023 Oct;22(5):1465-1486. doi: 10.1007/s10237-022-01620-2. Epub 2022 Oct 6.
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.
顶点模型被广泛用于模拟融合上皮和其他多细胞组织的力学特性。这种固有的离散框架允许为每个细胞分配一个柯西应力，并且其对称分量已经被广泛报道，至少对于平面单层是这样。在这里，我们考虑分配给每个三叉结附近的应力，特别是评估其领先阶反对称分量和相关的偶应力，它们表征了单个细胞经历（和抵抗）面内弯曲变形的程度。我们为具有无序内部结构的局部单层开发离散位势理论，并利用该理论推导出类似于艾里和明德尔应力函数的量。这些标量势通常具有宽频带谱，突出了小尺度缺陷和边界层对整体应力模式的贡献。仿射逼近将偶应力归因于共享三叉结的细胞之间的压力差，但模拟表明非仿射变形起着额外的作用。
