Stamenović Dimitrije
Department of Biomedical Engineering and Division of Materials Science & Engineering, Boston University, 44 Cummington Mall, Boston, MA, 02215, USA.
Biomech Model Mechanobiol. 2025 Feb;24(1):1-15. doi: 10.1007/s10237-024-01894-8. Epub 2024 Oct 15.
We reviewed two microstructural models, cellular solid models and prestressed affine network models, that have been used previously in studies of elastic behavior of soft biological materials. These models provide simple and mathematically transparent equations that can be used to interpret experimental data and to obtain quantitative predictions of the elastic properties of biological structures. In both models, volumetric density and elastic properties of the microstructure are key determinants of the macroscopic elastic properties. In the prestressed network model, geometrical rearrangement of the microstructure (kinematic stiffness) is also important. As examples of application of these models, we considered the shear behavior of the cytoskeleton of adherent cells, of the collagen network of articular cartilage, and of the lung parenchymal network since their ability to resist shear is important for their normal biological and physiological functions. All three networks carry a pre-existing stress (prestress). We predicted their shear moduli using the microstructural models and compared those predictions with existing experimental data. Prestressed network models of the cytoskeleton and of the lung parenchyma provided a better correspondence to experimental data than cellular solid models. Both cellular solid and prestressed network models of the cartilage collagen network provided reasonable agreements with experimental values. These findings suggested that the kinematic stiffness and material stiffness of microstructural elements were both important determinants of the shear modulus of the cytoskeleton and of the lung parenchyma, whereas elasticity of collagen fibrils had a predominant role in the cartilage shear behavior.
我们回顾了两种微观结构模型，即细胞固体模型和预应力仿射网络模型，它们此前已被用于软生物材料弹性行为的研究。这些模型提供了简单且数学上透明的方程，可用于解释实验数据并获得生物结构弹性特性的定量预测。在这两种模型中，微观结构的体积密度和弹性特性都是宏观弹性特性的关键决定因素。在预应力网络模型中，微观结构的几何重排（运动学刚度）也很重要。作为这些模型应用的示例，我们考虑了贴壁细胞的细胞骨架、关节软骨的胶原网络以及肺实质网络的剪切行为，因为它们抵抗剪切的能力对其正常生物学和生理功能很重要。所有这三种网络都承受着预先存在的应力（预应力）。我们使用微观结构模型预测了它们的剪切模量，并将这些预测与现有的实验数据进行了比较。细胞骨架和肺实质的预应力网络模型与实验数据的对应性比细胞固体模型更好。软骨胶原网络的细胞固体模型和预应力网络模型与实验值都有合理的一致性。这些发现表明，微观结构元件的运动学刚度和材料刚度都是细胞骨架和肺实质剪切模量的重要决定因素，而胶原纤维的弹性在软骨剪切行为中起主要作用。
