Development of Finite Element Analysis for Articular Cartilage considering Electrochemical

关节软骨由间质液、胶原蛋白和蛋白多糖聚集体组成，这些聚集体被固定的硫酸化糖胺聚糖带负电荷。由于负电荷引起的渗透压引起肿胀并影响软骨的粘弹性行为。另一方面，由于软骨表面上的接触载荷引起的软骨变形又影响固定负电荷密度，从而改变软骨中的电化学ee。本研究的目的是发展一种有限元分析方法来分析这种机械-电化学耦合现象。2002年，描述机械电化学现象的三相理论被重新表述为适用于大变形问题。有限元公式实现了一个原型程序。2003年，在有限元分析中考虑了变形依赖的固定电荷密度和软骨渗透性的非线性， ...更多信息 裂解，并开发了一个程序，比较完整。数值结果表明，在软骨等三相结构中，固体基质对间质流体流动的阻力是影响粘性的主要因素。由于压缩引起的间质液的流出引起固定电荷密度的增加，从而增加软骨的刚度以及电势和离子浓度。并对软骨自由膨胀进行了模拟，模拟结果与实验结果吻合较好。另一方面，通过引入Gregory曲面光滑算法，避免了离散接触面不连续引起的不稳定性，建立了大滑动接触问题的有限元分析方法。最后，通过对关节软骨的机械电化学行为的实验测量，包括电化学效应的关节软骨接触问题的分析成为可能，关节软骨的机械电化学行为正在发展中，因此三相理论的材料常数在当前阶段还没有揭示，通过将软骨处理为单相超弹性固体进行分析以获得临床信息，Rivlin本构关系少

Articular cartilage consists of interstitial fluid, collagen and proteoglycan aggregates which are negatively charged by fixed sulfated glycosaminoglycans. The osmotic pressure due to the negative charges induces swelling and affects the viscoelastic behavior of cartilages. On the other hand, the deformation of the cartilage due to the contact load on the cartilage surface affects in turn the fixed negative charge density to change the eledctrochemical ee in the cartilage. The purpose of this research is to develop finite element analysis approach for such mechanical electrochemical coupling phenomena. In 2002, the triphasic theory describing the mechanical electrochemical phenomena was reformulated to be applicable for the problems with large deformation. The finite element formulation was implemented to a prototype program. In 2003, the nonlinearities of the deformation dependent fixed charge density and permeability of the cartilage were taken in to account in the finite element ana … More lysis and a program was developed with fairly completion. The numerical results show that the dominant factor of viscosity in triphasic structure such as cartilage is the resistance of solid matrix to the interstitial fluid flow. The out flow of interstitial fluid due to the compression induces increase of the fixed charge density and thus increases the stiffness of the cartilage and also the electrical potential and the concentration o ions. Furthermore, the simulation of the cartilage free swelling was carried out to get the results in good agreement with the experimental results. On the other hand, a finite element analysis procedure for contact problems with large sliding was developed by in introducing Gregory patch smoothing algorithm to get off the instability due to the discontinuity of discretized contact surfaces. Finally, the analysis of contact problems for articular cartilage including electrochemical effects becomes possible by experimental measurements of the mechanical electrochemical behaviors of articular cartilages are under development and thus the material constants of the triphasic theory are not revealed in the current stage, the analysis was carried out to get clinical information by treating the cartilage as a single phase of hyperelastic solid which obey the Mooney-Rivlin constitutive relations. Less