Lu X Lux, Miller Chester, Chen Faye H, Guo X Edward, Mow Van C
Department of Biomedical Engineering, Columbia University, 351 Engineering Terrace, 500 West 120th Street, New York, NY 10027, USA.
J Biomech. 2007;40(11):2434-41. doi: 10.1016/j.jbiomech.2006.11.015. Epub 2007 Jan 12.
The triphasic mixture theory has been used to describe the mechanical and physicochemical behaviors of articular cartilage under some specialized loading conditions. However, the mathematical complexities of this theory have limited its applications for theoretical analyses of experimental studies and models for predicting cartilage and other biological tissues' deformational behaviors. A generalized correspondence principle has been established in the present study, and this principle shows that the equilibrium deformational behavior of a charged-hydrated material under loading is identical to that of an elastic medium without charge. A set of explicit formulas has been derived to correlate the mechanical properties of an equivalent material with the intrinsic elastic moduli, fixed charge density and free-ion concentration within the cartilage tissue. The validity of these formulas is independent of the deformation state of the elastic solid matrix under an infinitesimal strain. Therefore they can be employed for any loading conditions, such as confined or unconfined compression, tension, and indentation tests, etc. In the current study, the fixed charge density of bovine cartilage is determined from the indentation creep data using this generalized correspondence principle. The proteoglycan content results were then compared with those from biochemical assay, yielding a linear regression slope of 1.034. Additionally a correspondence principle within a framework of cubic symmetry and a bilinear response in tension-compression (the conewise linear elasticity model) has also been developed to demonstrate the potential application of current methodology for inhomogeneous, anisotropic and nonlinear situations.
三相混合理论已被用于描述在某些特定加载条件下关节软骨的力学和物理化学行为。然而，该理论的数学复杂性限制了其在实验研究理论分析以及预测软骨和其他生物组织变形行为模型中的应用。本研究建立了一个广义对应原理，该原理表明加载下带电水合材料的平衡变形行为与不带电弹性介质的平衡变形行为相同。已推导得出一组显式公式，用于将等效材料的力学性能与软骨组织内的固有弹性模量、固定电荷密度和自由离子浓度相关联。这些公式的有效性与无限小应变下弹性固体基质的变形状态无关。因此，它们可用于任何加载条件，如受限或无受限压缩、拉伸和压痕试验等。在当前研究中，利用这一广义对应原理从压痕蠕变数据中确定了牛软骨的固定电荷密度。然后将蛋白聚糖含量结果与生化分析结果进行比较，得到线性回归斜率为1.034。此外，还开发了立方对称框架内的对应原理以及拉伸 - 压缩中的双线性响应（锥形线性弹性模型），以证明当前方法在非均匀、各向异性和非线性情况下的潜在应用。
