Department of Engineering Mechanics, State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi'an Jiaotong University, Xi'an 710049, China.
Soft Matter. 2018 Sep 19;14(36):7534-7541. doi: 10.1039/c8sm01216d.
Atomic force microscopy (AFM) has become the most commonly used tool to measure the mechanical properties of biological cells. In AFM indentation experiments, the Hertz and Sneddon models of contact mechanics are usually adopted to extract the elastic modulus by analyzing the load-indent depth curves for spherical and conical tips, respectively. However, the effects of surface tension, neglected in existing contact models, become more significant in indentation responses due to the lower elastic moduli of living cells. Here, we present two simple yet robust relations between load and indent depth considering surface tension effects for spherical and conical indentations, through dimensional analysis and finite element simulations. When the indent depth is smaller than the intrinsic length defined as the ratio of surface tension to elastic modulus, the elastic modulus obtained by classical contact mechanics theories would be overestimated. Contrary to the majority of reported results, we find that the elastic modulus of a cell could be independent of indent depths if surface tension is taken into account. Our model seems to be in agreement with experimental data available. A comprehensive comparison will be done in the future.
原子力显微镜（AFM）已成为测量生物细胞机械性能最常用的工具。在 AFM 压痕实验中，通常采用 Hertz 和 Sneddon 接触力学模型，通过分析球形和锥形针尖的载荷-压痕深度曲线，分别提取弹性模量。然而，由于活细胞的弹性模量较低，在现有的接触模型中被忽略的表面张力效应在压痕响应中变得更加显著。在这里，我们通过尺寸分析和有限元模拟，为球形和锥形压痕提出了两个简单而稳健的考虑表面张力效应的载荷与压痕深度之间的关系。当压痕深度小于由表面张力与弹性模量之比定义的固有长度时，通过经典接触力学理论获得的弹性模量将被高估。与大多数报道的结果相反，如果考虑表面张力，细胞的弹性模量似乎可以不依赖于压痕深度。我们的模型似乎与现有的实验数据一致。未来将进行更全面的比较。
