O'Connell Grace D, Guerin Heather L, Elliott Dawn M
Department of Orthopaedic Surgery, University of Pennsylvania, Philadelphia, 19104-6081, USA.
J Biomech Eng. 2009 Nov;131(11):111007. doi: 10.1115/1.3212104.
The highly organized structure and composition of the annulus fibrosus provides the tissue with mechanical behaviors that include anisotropy and nonlinearity. Mathematical models are necessary to interpret and elucidate the meaning of directly measured mechanical properties and to understand the structure-function relationships of the tissue components, namely, the fibers and extrafibrillar matrix. This study models the annulus fibrosus as a combination of strain energy functions describing the fibers, matrix, and their interactions. The objective was to quantify the behavior of both nondegenerate and degenerate annulus fibrosus tissue using uniaxial tensile experimental data. Mechanical testing was performed with samples oriented along the circumferential, axial, and radial directions. For samples oriented along the radial direction, the toe-region modulus was 2x stiffer with degeneration. However, no other differences in measured mechanical properties were observed with degeneration. The constitutive model fit well to samples oriented along the radial and circumferential directions (R(2)> or =0.97). The fibers supported the highest proportion of stress for circumferential loading at 60%. There was a 70% decrease in the matrix contribution to stress from the toe-region to the linear-region of both the nondegenerate and degenerate tissue. The shear fiber-matrix interaction (FMI) contribution increased by 80% with degeneration in the linear-region. Samples oriented along the radial and axial direction behaved similarly under uniaxial tension (modulus=0.32 MPa versus 0.37 MPa), suggesting that uniaxial testing in the axial direction is not appropriate for quantifying the mechanics of a fiber reinforcement in the annulus. In conclusion, the structurally motivated nonlinear anisotropic hyperelastic constitutive model helps to further understand the effect of microstructural changes with degeneration, suggesting that remodeling in the subcomponents (i.e., the collagen fiber, matrix and FMI) may minimize the overall effects on mechanical function of the bulk material with degeneration.
纤维环高度有序的结构和组成赋予该组织包括各向异性和非线性在内的力学特性。数学模型对于解释和阐明直接测量的力学性能的意义以及理解组织成分（即纤维和纤维外基质）的结构 - 功能关系是必要的。本研究将纤维环建模为描述纤维、基质及其相互作用的应变能函数的组合。目的是使用单轴拉伸实验数据量化非退变和退变纤维环组织的行为。对沿圆周、轴向和径向取向的样本进行力学测试。对于沿径向取向的样本，退变时趾区模量增加了两倍。然而，退变时未观察到其他测量力学性能的差异。本构模型与沿径向和圆周方向取向的样本拟合良好（R²≥0.97）。在圆周加载时，纤维承受的应力比例最高，为60%。从非退变和退变组织的趾区到线性区，基质对应力的贡献降低了70%。在两个区域中，线性区内剪切纤维 - 基质相互作用（FMI）的贡献随着退变增加了80%。沿径向和轴向取向的样本在单轴拉伸下表现相似（模量分别为0.32MPa和0.37MPa），这表明在轴向进行单轴测试不适用于量化纤维环中纤维增强的力学性能。总之，基于结构的非线性各向异性超弹性本构模型有助于进一步理解退变引起的微观结构变化的影响，这表明亚成分（即胶原纤维、基质和FMI）的重塑可能会最小化退变对整体材料力学功能的影响。
