Abdel-Rahman E M, Hefzy M S
Department of Mechanical, Industrial and Manufacturing Engineering, The University of Toledo, OH 43606, USA.
Med Eng Phys. 1998 Jun;20(4):276-90. doi: 10.1016/s1350-4533(98)00010-1.
The objective of this study is to determine the three-dimensional dynamic response of the human knee joint. A three-dimensional anatomical dynamic model was thus developed and consists of two body segments in contact (the femur and tibia) executing a general three-dimensional dynamic motion within the constraints of the different ligamentous structures. Each of the articular surfaces at the tibio-femoral joint was represented mathematically by a separate mathematical function. The joint ligaments were modelled as nonlinear elastic springs. The six-degrees-of-freedom joint motions were characterized by using six kinematic parameters, and ligamentous forces were expressed in terms of these six parameters. Knee response was studied by considering sudden external forcing pulse loads applied to the tibia. Model equations consist of nonlinear second-order ordinary differential equations coupled with nonlinear algebraic constraint conditions. Constraint equations were written to maintain at least one-point contact throughout motion; one- and two-point contact versions of the model were developed. This Differential-Algebraic Equations (DAE) system was solved by employing a DAE solver: the Differential/Algebraic System Solver (DASSL) developed at Lawrence Livermore National Laboratory. A solution representing the response of this three-dimensional dynamic system was thus obtained for the first time. Earlier attempts to determine the system's response were unsuccessful owing to the inherent numerical instabilities in the system and the limitations of the solution techniques. Under the conditions tested, evidence of "femoral roll back" on both medial and lateral tibial plateaus was not observed from the model predictions. In the range of 20 degrees to 66 degrees of knee flexion, the lateral tibial contact point moved posteriorly while the medial tibial contact point moved anteriorly. In the range of 66 degrees to 90 degrees of knee flexion, contact was maintained only on the medial side and the tibial contact point (on the medial side) continued to move anteriorly. It was further found that increasing pulse amplitude and/or duration caused a decrease in the magnitude of the tibio-femoral contact force at a given flexion angle. These results suggest that increasing load level caused a decrease in joint stiffness. The results of this study also show that the anterior fibres of the posterior cruciate and the medial collateral ligaments are the primary restraints for a posterior forcing pulse in the range of 20 degrees to 90 degrees of knee flexion; this explains why most isolated posterior cruciate ligament injuries and combined injuries to the posterior cruciate and the medial collateral result from a posterior impact on a flexed knee.
本研究的目的是确定人体膝关节的三维动态响应。因此开发了一个三维解剖动态模型，该模型由两个相互接触的身体部分（股骨和胫骨）组成，它们在不同韧带结构的约束下执行一般的三维动态运动。胫股关节的每个关节面都由一个单独的数学函数进行数学表示。关节韧带被建模为非线性弹性弹簧。通过使用六个运动学参数来表征六自由度的关节运动，韧带力用这六个参数来表示。通过考虑施加在胫骨上的突然外部强迫脉冲载荷来研究膝关节的响应。模型方程由非线性二阶常微分方程和非线性代数约束条件组成。编写约束方程以在整个运动过程中保持至少一点接触；开发了模型的一点接触和两点接触版本。该微分代数方程（DAE）系统通过使用DAE求解器来求解：劳伦斯利弗莫尔国家实验室开发的微分/代数系统求解器（DASSL）。从而首次获得了代表该三维动态系统响应的解。早期确定系统响应的尝试由于系统固有的数值不稳定性和求解技术的局限性而未成功。在所测试的条件下，从模型预测中未观察到内侧和外侧胫骨平台上“股骨后滚”的证据。在膝关节屈曲20度至66度的范围内，外侧胫骨接触点向后移动，而内侧胫骨接触点向前移动。在膝关节屈曲66度至90度的范围内，仅在内侧保持接触，并且胫骨接触点（在内侧）继续向前移动。进一步发现，增加脉冲幅度和/或持续时间会导致在给定屈曲角度下胫股接触力的大小减小。这些结果表明，增加负荷水平会导致关节刚度降低。本研究的结果还表明，在膝关节屈曲20度至90度的范围内，后交叉韧带和内侧副韧带的前部纤维是后向强迫脉冲的主要约束；这解释了为什么大多数孤立的后交叉韧带损伤以及后交叉韧带和内侧副韧带的联合损伤是由对屈曲膝关节的后向撞击引起的。
