Shelburne K B, Pandy M G
Department of Mechanical Engineering, University of Texas at Austin 78712, USA.
J Biomech. 1997 Feb;30(2):163-76. doi: 10.1016/s0021-9290(96)00119-4.
A model of the knee in the sagittal plane was developed to study the forces in the ligaments induced by isometric contractions of the extensor and flexor muscles. The geometry of the distal femur was obtained from cadaver data. The tibial plateau and patellar facet were modeled as flat surfaces. Eleven elastic elements were used to describe the mechanical behavior of the anterior and posterior cruciate ligaments (ACL and PCL), the medial and lateral collateral ligaments (MCL and LCL), and the posterior capsule. The model knee was actuated by 11 musculotendinous units, each muscle represented by a Hill-type contractile element, a series-elastic element, and a parallel-elastic element. Tendon was assumed to be elastic. The response of the model to anterior-posterior drawer suggests that the geometrical and mechanical properties of the model ligaments approximate the behavior of real ligaments in the intact knee. Calculations for a simulated quadriceps leg raise indicate further that the two-dimensional model reproduces the response of the three-dimensional knee under similar conditions of loading and constraint. During maximum isometric contractions of the quadriceps, the model ACL is loaded from full extension to 80 degrees C of flexion; the model PCL is loaded at 70 degrees of flexion and greater. For maximum isometric extension, ACL forces in the range 0-20 degrees of flexion depend most heavily upon the force-length properties of the quadriceps. At flexion angles greater than 20 degrees, cruciate ligament forces are determined by the geometry of the articulating surfaces of the bones. During isolated contractions of the hamstrings and gastrocnemius muscles, the model ACL is loaded from full extension to 10 degrees of flexion; the model PCL is loaded at all flexion angles greater than 10 degrees. Isolated contractions of the flexor muscles cannot unload the ACL near full extension, as the behavior of the ACL in this region is governed by the shapes of the bones. At 10 degrees of flexion or greater, the overall pattern of PCL force is explained by the force length properties of the hamstrings and by the geometrical arrangement of the flexor muscles about the knee.
建立了矢状面膝关节模型，以研究伸肌和屈肌等长收缩引起的韧带受力情况。股骨远端的几何形状取自尸体数据。胫骨平台和髌面被建模为平面。使用11个弹性元件来描述前交叉韧带和后交叉韧带（ACL和PCL）、内侧和外侧副韧带（MCL和LCL）以及后关节囊的力学行为。模型膝关节由11个肌肉肌腱单元驱动，每块肌肉由一个希尔型收缩元件、一个串联弹性元件和平行弹性元件表示。肌腱被假定为弹性的。模型对前后抽屉试验的反应表明，模型韧带的几何和力学特性近似于完整膝关节中真实韧带的行为。对模拟股四头肌抬腿的计算进一步表明，二维模型在相似的加载和约束条件下再现了三维膝关节的反应。在股四头肌最大等长收缩期间，模型ACL从完全伸展加载到屈曲80摄氏度；模型PCL在屈曲70度及更大角度时加载。对于最大等长伸展，屈曲0至20度范围内的ACL力最主要取决于股四头肌的力-长度特性。在屈曲角度大于20度时，交叉韧带力由骨骼关节面的几何形状决定。在腘绳肌和腓肠肌单独收缩期间，模型ACL从完全伸展加载到屈曲10度；模型PCL在所有大于10度的屈曲角度时加载。屈肌单独收缩不能在接近完全伸展时卸载ACL，因为该区域ACL的行为受骨骼形状支配。在屈曲10度或更大角度时，PCL力的总体模式由腘绳肌的力-长度特性以及屈肌围绕膝关节的几何排列来解释。
