Linear viscoelastic response of the vertex model with internal and external dissipation: Normal modes analysis
Linear viscoelastic response of the vertex model with internal and external dissipation: Normal modes analysis
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DOI：
10.1103/physrevresearch.5.013143
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发表时间：
2022-02
影响因子：
4.2
通讯作者：
Sijie Tong;R. Sknepnek;A. Košmrlj
中科院分区：
文献类型：
--
作者：
Sijie Tong;R. Sknepnek;A. Košmrlj
我们使用简正模态形式来研究过阻尼线性响应状态下上皮组织力学顶点模型的剪切流变学。我们考虑具有外部（例如，细胞-基质）和内部（例如，细胞-细胞）耗散机制的系统，并推导由于机械力和耗散力而对细胞产生的应力的表达式。然而，这里开发的半解析方法是通用的，可以直接应用于研究具有内部和外部耗散的一大类软物质系统的线性响应。它涉及简正模分解来计算系统的线性损耗和存储模量。具体而言，沿每个简正模态的位移会因弹性变形和内部耗散而产生应力，这些应力与外部耗散引起的载荷保持力平衡。每个简正模态都以特征松弛时标响应，其流变行为可以描述为由弹性应力引起的标准线性实体单元和由内部耗散应力引起的 Jeffreys 模型单元的组合。然后，通过并联连接与各个简正模态相对应的所有粘弹性元件来完全确定系统的总响应。这样可以全面表征系统在所有驱动频率下潜在复杂的线性流变响应，并识别集体激励。我们表明，由于杰弗里斯元素的存在或不存在，内部和外部耗散机制会导致性质不同的流变行为，这在高驱动频率下尤其明显。因此，我们的研究结果强调了微观耗散机制在理解软材料和组织的流变行为方面的重要性。
We use the normal mode formalism to study the shear rheology of the vertex model for epithelial tissue mechanics in the overdamped linear response regime. We consider systems with external (e.g., cell-substrate) and internal (e.g., cell-cell) dissipation mechanisms, and derive expressions for stresses on cells due to mechanical and dissipative forces. The semi-analytical method developed here is, however, general and can be directly applied to study the linear response of a broad class of soft matter systems with internal and external dissipation. It involves normal mode decomposition to calculate linear loss and storage moduli of the system. Specifically, displacements along each normal mode produce stresses due to elastic deformation and internal dissipation, which are in force balance with loads due to external dissipation. Each normal mode responds with a characteristic relaxation timescale, and its rheological behavior can be described as a combination of a standard linear solid element due to elastic stresses and a Jeffreys model element due to the internal dissipative stresses. The total response of the system is then fully determined by connecting in parallel all the viscoelastic elements corresponding to individual normal modes. This allows full characterization of the potentially complex linear rheological response of the system at all driving frequencies and identification of collective excitations. We show that internal and external dissipation mechanisms lead to qualitatively different rheological behaviors due to the presence or absence of Jeffreys elements, which is particularly pronounced at high driving frequencies. Our findings, therefore, underscore the importance of microscopic dissipation mechanisms in understanding the rheological behavior of soft materials and tissues, in particular.