Ateshian Gerard A, Chahine Nadeen O, Basalo Ines M, Hung Clark T
Departments of Mechanical Engineering and Biomedical Engineering, Columbia University, New York, NY10027, USA.
J Biomech. 2004 Mar;37(3):391-400. doi: 10.1016/s0021-9290(03)00252-5.
Mixture models have been successfully used to describe the response of articular cartilage to various loading conditions. Mow et al. (J. Biomech. Eng. 102 (1980) 73) formulated a biphasic mixture model of articular cartilage where the collagen-proteoglycan matrix is modeled as an intrinsically incompressible porous-permeable solid matrix, and the interstitial fluid is modeled as an incompressible fluid. Lai et al. (J. Biomech. Eng. 113 (1991) 245) proposed a triphasic model of articular cartilage as an extension of their biphasic theory, where negatively charged proteoglycans are modeled to be fixed to the solid matrix, and monovalent ions in the interstitial fluid are modeled as additional fluid phases. Since both models co-exist in the cartilage literature, it is useful to show how the measured properties of articular cartilage (the confined and unconfined compressive and tensile moduli, the compressive and tensile Poisson's ratios, and the shear modulus) relate to both theories. In this study, closed-form expressions are presented that relate biphasic and triphasic material properties in tension, compression and shear. These expressions are then compared to experimental findings in the literature to provide greater insight into the measured properties of articular cartilage as a function of bathing solutions salt concentrations and proteoglycan fixed-charge density.
混合模型已成功用于描述关节软骨对各种加载条件的响应。莫等人（《生物力学工程杂志》102卷（1980年）第73页）建立了关节软骨的双相混合模型，其中胶原-蛋白聚糖基质被建模为本质上不可压缩的多孔渗透固体基质，而组织液被建模为不可压缩流体。赖等人（《生物力学工程杂志》113卷（1991年）第245页）提出了关节软骨的三相模型，作为其双相理论的扩展，其中带负电荷的蛋白聚糖被建模为固定在固体基质上，组织液中的单价离子被建模为额外的流体相。由于这两种模型在软骨文献中都存在，因此说明关节软骨的测量特性（受限和非受限压缩及拉伸模量、压缩和拉伸泊松比以及剪切模量）如何与这两种理论相关是很有用的。在本研究中，给出了双相和三相材料在拉伸、压缩和剪切时材料特性的闭式表达式。然后将这些表达式与文献中的实验结果进行比较，以更深入地了解作为浸泡溶液盐浓度和蛋白聚糖固定电荷密度函数的关节软骨测量特性。
