Hurschler C, Loitz-Ramage B, Vanderby R
Division of Orthopedic Surgery, University of Wisconsin, Madison 53792-3228, USA.
J Biomech Eng. 1997 Nov;119(4):392-9. doi: 10.1115/1.2798284.
We propose a mechanical model for tendon or ligament stress-stretch behavior that includes both microstructural and tissue level aspects of the structural hierarchy in its formulation. At the microstructural scale, a constitutive law for collagen fibers is derived based on a strain-energy formulation. The three-dimensional orientation and deformation of the collagen fibrils that aggregate to form fibers are taken into consideration. Fibril orientation is represented by a probability distribution function that is axisymmetric with respect to the fiber. Fiber deformation is assumed to be incompressible and axisymmetric. The matrix is assumed to contribute to stress only through a constant hydrostatic pressure term. At the tissue level, an average stress versus stretch relation is computed by assuming a statistical distribution for fiber straightening during tissue loading. Fiber straightening stretch is assumed to be distributed according to a Weibull probability distribution function. The resulting comprehensive stress-stretch law includes seven parameters, which represent structural and microstructural organization, fibril elasticity, as well as a failure criterion. The failure criterion is stretch based. It is applied at the fibril level for disorganized tissues but can be applied more simply at a fiber level for well-organized tissues with effectively parallel fibrils. The influence of these seven parameters on tissue stress-stretch response is discussed and a simplified form of the model is shown to characterize the nonlinear experimentally determined response of healing medial collateral ligaments. In addition, microstructural fibril organizational data (Frank et al., 1991, 1992) are used to demonstrate how fibril organization affects material stiffness according to the formulation. A simplified form, assuming a linearly elastic fiber stress versus stretch relationship, is shown to be useful for quantifying experimentally determined nonlinear toe-in and failure behavior of tendons and ligaments. We believe this ligament and tendon stress-stretch law can be useful in the elucidation of the complex relationships between collagen structure, fibril elasticity, and mechanical response.
我们提出了一种用于肌腱或韧带应力-拉伸行为的力学模型，该模型在其公式中纳入了结构层次的微观结构和组织层面的因素。在微观结构尺度上，基于应变能公式推导了胶原纤维的本构定律。考虑了聚集形成纤维的胶原原纤维的三维取向和变形。原纤维取向由相对于纤维轴对称的概率分布函数表示。假定纤维变形不可压缩且轴对称。假定基质仅通过恒定的静水压力项对应力产生贡献。在组织层面，通过假定组织加载过程中纤维伸直的统计分布来计算平均应力与拉伸关系。假定纤维伸直拉伸根据威布尔概率分布函数进行分布。所得的综合应力-拉伸定律包括七个参数，这些参数代表结构和微观结构组织、原纤维弹性以及失效准则。失效准则基于拉伸。它适用于无序组织的原纤维层面，但对于具有有效平行原纤维的有序组织，可更简单地应用于纤维层面。讨论了这七个参数对组织应力-拉伸响应的影响，并展示了该模型的简化形式可表征愈合内侧副韧带的非线性实验测定响应。此外，使用微观结构原纤维组织数据（Frank等人，1991年，1992年）来根据该公式说明原纤维组织如何影响材料刚度。假定纤维应力与拉伸呈线性弹性关系的简化形式被证明可用于量化实验测定的肌腱和韧带的非线性趾部和失效行为。我们相信这种韧带和肌腱应力-拉伸定律有助于阐明胶原结构、原纤维弹性和力学响应之间的复杂关系。
