ANISOTROPHY AND NONLINEARITY OF CARTILAGE MECHANICS

关节软骨是腹泻性关节的承载材料。它的主要机械功能是以最小的摩擦和磨损将大量的载荷传递到关节的关节表面；在正常情况下，软骨可以将这一功能保持七八十年。从工程角度来看，软骨的力学性能被认为是任何传统工程轴承材料所无法比拟的。然而，尽管几十年来对软骨进行了复杂的生物力学研究，但由于其显著的多功能性和复杂性，对软骨力学的准确理解仍然是难以捉摸的。研究表明，关节软骨的力学响应随时间和载荷或变形速率的变化而变化，即软骨表现出粘弹性。此外，还表明，当测试平行和垂直于分割线方向的组织时，软骨的拉伸刚度不同，即表现出各向异性。研究还证实，软骨在压缩状态下的刚度可能比在拉伸状态下的刚度小一到两个数量级，即表现出拉伸-压缩非线性。各种研究也证实，这些测量的特性从软骨的浅层到深层可能不同，即组织表现出随深度变化的不均质性。到目前为止，还没有一个单一的关节软骨本构模型能够描述其在文献中描述的各种测试条件下的力学响应。这一建议的假设是：(1)软骨是正交各向异性的，需要比迄今测量的更多的材料常数来描述其力学响应；(2)软骨的拉伸-压缩非线性要求部分但不是所有这些常数在拉伸和压缩中具有不同的值；以及(3)使用混合理论，包括软骨的正交各向异性和拉伸-压缩非线性的理论框架可以为所有测试构型提供理论和实验之间的一致性；当在分析中考虑组织的不均质性时，这一一致性得到改善。因此，这项建议的具体目的是测试人的髌骨软骨样本，沿着三个相互垂直的方向测试拉伸、压缩、剪切和渗透，这三个方向被假设为表征材料对称性的平面，例如从实验上确定软骨的一整套弹性和渗透常数；确定这些常数是否真的描述了正交异性材料；实验评估软骨的深度依赖的不均质性；以及比较新提出的具有深度依赖的非均匀属性的双相、八向正交、共斜线性弹性模型对相应预测的瞬时和平衡实验响应。为了实现这些目标，建议使用最新的技术来测量组织的力学特性。

Articular cartilage is the bearing material of diarthrodial joints. Its primary mechanical function is to transmit large loads across the articular surfaces of joints with minimal friction and wear; under normal conditions, cartilage can maintain this function for seven to eight decades. From an engineering perspective, the mechanical behavior of cartilage is considered to be remarkable, unmatched by any traditional engineering bearing material. However, despite several decades of sophisticated biomechanical studies of cartilage, an accurate understanding of cartilage mechanics remains elusive due to its remarkable versatility and complexity. Studies have demonstrated that the mechanical response of articular cartilage may vary as a function of duration and rate of loading or deformation, i.e., cartilage exhibits viscoelasticity. Furthermore, it has been shown that the tensile stiffness of cartilage differs when testing the tissue parallel and perpendicular to the split line directions, i.e., it exhibits anisotropy. It has also been established that the stiffness of cartilage in compression may be one to two orders of magnitude smaller than in tension, i.e., it exhibits tension-compression nonlinearity. Various studies have also confirmed that these measured properties may vary from the superficial to the deep zone of cartilage, i.e., the tissue exhibits depth-dependent inhomogeneity. To date, no single constitutive model of articular cartilage has been able to describe its mechanical response under the various testing conditions described in the literature. The hypotheses of this proposal are that (1) cartilage is orthotropic, requiring more material constants than have been measured to date to describe its mechanical response; (2) the tension-compression nonlinearity of cartilage requires that some, but not all of these constants have different values in tension and compression; and (3) that a theoretical framework encompassing cartilage orthotropy and tension-compression nonlinearity, using mixture theory, can provide agreement between theory and experiment for all testing configurations; this agreement improves when incorporating tissue inhomogeneity in the analysis. Therefore, the specific aims of this proposal are to test human patellar cartilage samples in tension, compression, shear and permeation, along the three mutually perpendicular directions which are hypothesized to characterize the planes of material symmetry, such as to determine experimentally a complete set of elastic and permeability constants of cartilage; to determine whether these constants indeed describe an orthotropic material; to experimentally assess the depth-dependent inhomogeneity of cartilage; and to compare transient and equilibrium experimental responses to corresponding predictions from a newly proposed biphasic, octantwise orthotropic, conewise linear elasticity model with depth-dependent inhomogenous properties. To achieve these aims, it is proposed to use the most current techniques for measurement of tissue mechanical properties.