Center for Engineering Mechanobiology, University of Pennsylvania, Philadelphia, PA 19104.
Department of Materials Science and Engineering, School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, PA 19104.
Proc Natl Acad Sci U S A. 2019 Apr 2;116(14):6790-6799. doi: 10.1073/pnas.1815659116. Epub 2019 Mar 20.
While cells within tissues generate and sense 3D states of strain, the current understanding of the mechanics of fibrous extracellular matrices (ECMs) stems mainly from uniaxial, biaxial, and shear tests. Here, we demonstrate that the multiaxial deformations of fiber networks in 3D cannot be inferred solely based on these tests. The interdependence of the three principal strains gives rise to anomalous ratios of biaxial to uniaxial stiffness between 8 and 9 and apparent Poisson's ratios larger than 1. These observations are explained using a microstructural network model and a coarse-grained constitutive framework that predicts the network Poisson effect and stress-strain responses in uniaxial, biaxial, and triaxial modes of deformation as a function of the microstructural properties of the network, including fiber mechanics and pore size of the network. Using this theoretical approach, we found that accounting for the Poisson effect leads to a 100-fold increase in the perceived elastic stiffness of thin collagen samples in extension tests, reconciling the seemingly disparate measurements of the stiffness of collagen networks using different methods. We applied our framework to study the formation of fiber tracts induced by cellular forces. In vitro experiments with low-density networks showed that the anomalous Poisson effect facilitates higher densification of fibrous tracts, associated with the invasion of cancerous acinar cells. The approach developed here can be used to model the evolving mechanics of ECM during cancer invasion and fibrosis.
尽管组织内的细胞会产生并感知 3D 应变状态，但目前对纤维细胞外基质（ECM）力学的理解主要源于单轴、双轴和剪切测试。在这里，我们证明了 3D 中纤维网络的多轴变形不能仅基于这些测试来推断。三个主应变的相互依存关系导致双轴与单轴刚度之间的异常比值在 8 到 9 之间，表观泊松比大于 1。这些观察结果可以使用微观结构网络模型和粗粒本构框架来解释，该模型预测了网络泊松效应和在单轴、双轴和三轴变形模式下的应力-应变响应，作为网络微观结构特性的函数，包括纤维力学和网络的孔径。使用这种理论方法，我们发现考虑泊松效应会导致在拉伸测试中，薄胶原蛋白样品的表观弹性刚度增加 100 倍，从而协调了使用不同方法测量胶原蛋白网络的刚度时出现的看似不同的测量值。我们应用该框架研究了细胞力诱导的纤维束形成。在具有低密度网络的体外实验中，异常泊松效应促进了纤维束的更高致密化，这与腺癌细胞的侵袭有关。这里开发的方法可用于模拟癌症侵袭和纤维化过程中 ECM 不断变化的力学特性。
