Department of Orthopaedic Surgery, University of Pennsylvania, 424 Stemmler Hall, Philadelphia, PA 19104-6081, USA.
Biomech Model Mechanobiol. 2012 Jan;11(1-2):197-205. doi: 10.1007/s10237-011-0303-5. Epub 2011 Apr 3.
Structural constitutive modeling approaches are often based on the assumption of affine fiber kinematics, even though this assumption has rarely been evaluated experimentally. We are interested in applying mathematical models to understand the mechanisms responsible for the inhomogeneous, anisotropic, and non-linear properties of human supraspinatus tendon (SST); however, the relationship between macroscopic and fiber-level deformation in this tendon remains unknown and current methods for making this assessment are inadequate. Therefore, the purpose of this study was to develop an improved method for quantitatively assessing agreement between two distributions and to examine the affine assumption in SST by comparing experimental fiber alignment to affine model predictions using this analysis approach. Measured fiber angle values of SST samples in uniaxial tensile tests were compared with predictions of affine fiber deformation using modified projection plots, which provide a method for qualitative and quantitative comparisons of two distributions. The projection plot metrics of offset and range, which were developed in this study, are of particular benefit by providing a quantitative representation of agreement that can be subjected to statistical comparisons. For SST, offset and range values varied by tendon location and test orientation, with more affine deformation evidenced for tendon regions of higher alignment. Results suggest that non-affine fiber behavior is dependent on specific tissue, orientation of the applied stretch relative to the fiber organization, and length scale of the observation. In addition, this study has established a method for evaluating the affine assumption in other tissues.
结构本构建模方法通常基于仿射纤维运动学的假设，尽管这一假设很少通过实验进行评估。我们有兴趣应用数学模型来理解导致人肩袖上肌腱（SST）不均匀、各向异性和非线性特性的机制；然而，在这种肌腱中宏观和纤维水平变形之间的关系尚不清楚，目前用于进行这种评估的方法还不够充分。因此，本研究的目的是开发一种改进的方法来定量评估两个分布之间的一致性，并通过使用该分析方法比较实验纤维排列与仿射模型预测来检查 SST 中的仿射假设。使用改良的投影图比较单轴拉伸试验中 SST 样本的测量纤维角度值与仿射纤维变形的预测值，该分析方法提供了两种分布定性和定量比较的方法。本研究中开发的偏移和范围的投影图指标特别有益，因为它们提供了一种可以进行统计比较的一致性的定量表示。对于 SST，偏移和范围值因肌腱位置和测试方向而异，在纤维排列较高的肌腱区域表现出更多的仿射变形。结果表明，非仿射纤维行为取决于特定的组织、施加的拉伸相对于纤维组织的方向以及观察的长度尺度。此外，本研究还建立了一种在其他组织中评估仿射假设的方法。
