A linearized formulation of triphasic mixture theory for articular cartilage, and its application to indentation analysis
A linearized formulation of triphasic mixture theory for articular cartilage, and its application to indentation analysis
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DOI：
10.1016/j.jbiomech.2009.10.026
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发表时间：
2010-03-03
影响因子：
2.4
通讯作者：
Mow, Van C.
中科院分区：
文献类型：
--
作者：
Lu, Xin L.;Wan, Leo Q.;Mow, Van C.
蛋白多糖表面的负电荷对关节软骨的力学行为有显著影响。混合物理论，如三相理论，可以定量地描述这种带电性质如何有助于这种组织的机械电化学行为。然而，该理论的数学复杂性阻碍了其应用于复杂的负载分布，例如，压痕或其它多维结构。在这项研究中，三相混合物理论的软组织的控制方程进行了线性化，并显着简化，通过使用一个规则的摄动方法和使用两个潜在的功能。我们表明，这种新的制定可用于任何轴对称问题，如有约束或无约束压缩，液压灌注，压痕。进一步编制了有限差分数值计算程序，计算了压痕作用下关节软骨内部的变形、电学和流动特性。计算的组织响应与压痕实验（我们自己的和文献中报道的）的数据高度一致。结果发现，蛋白聚糖的带电性质可以增加固体基质的表观刚度，并减少由流体流动引入的粘性效应。压头尖端的几何和物理特性，软骨厚度，以及软骨的电化学特性对整个组织的变形和流体压力场的影响也进行了研究和介绍。这些结果对研究不同软骨区的软骨细胞力学转导以及组织工程设计或体内软骨修复具有意义。(C)2009爱思唯尔有限公司保留所有权利。
The negative charges on proteoglycans significantly affect the mechanical behaviors of articular cartilage. Mixture theories, such as the triphasic theory, can describe quantitatively how this charged nature contributes to the mechano-electrochemical behaviors of such tissue. However, the mathematical complexity of the theory has hindered its application to complicated loading profiles, e.g., indentation or other multi-dimensional configurations. In this study, the governing equations of triphasic mixture theory for soft tissue were linearized and dramatically simplified by using a regular perturbation method and the use of two potential functions. We showed that this new formulation can be used for any axisymmetric problem, such as confined or unconfined compressions, hydraulic perfusion, and indentation. A finite difference numerical program was further developed to calculate the deformational, electrical, and flow behaviors inside the articular cartilage under indentation. The calculated tissue response was highly consistent with the data from indentation experiments (our own and those reported in the literature). It was found that the charged nature of proteoglycans can increase the apparent stiffness of the solid matrix and lessen the viscous effect introduced by fluid flow. The effects of geometric and physical properties of indenter tip, cartilage thickness, and that of the electrochemical properties of cartilage on the resulting deformation and fluid pressure fields across the tissue were also investigated and presented. These results have implications for studying chondrocyte mechanotransduction in different cartilage zones and for tissue engineering designs or in vivo cartilage repair. (C) 2009 Elsevier Ltd. All rights reserved.