Pandy MARCUS G., Sasaki KOTARO
Department of Kinesiology and Department of Mechanical Engineering, University of Texas at Austin, Austin, Texas 78712, U.S.A.
Comput Methods Biomech Biomed Engin. 1998;1(4):265-283. doi: 10.1080/01495739808936707.
A three-dimensional model of the knee is used to study ligament function during anterior-posterior (a-p) draw, axial rotation, and isometric contractions of the extensor and flexor muscles. The geometry of the model bones is based on cadaver data. The contacting surfaces of the femur and tibia are modeled as deformable; those of the femur and patella are assumed to be rigid. Twelve elastic elements are used to describe the geometry and mechanical properties of the cruciate ligaments, the collateral ligaments, and the posterior capsule. The model is actuated by thirteen musculotendinous units, each unit represented as a three-element muscle in series with tendon. The calculations show that the forces applied during a-p draw are substantially different from those applied by the muscles during activity. Principles of knee-ligament function based on the results of in vitro experiments may therefore be overstated. Knee-ligament forces during straight a-p draw are determined solely by the changing geometry of the ligaments relative to the bones: ACL force decreases with increasing flexion during anterior draw because the angle between the ACL and the tibial plateau decreases as knee flexion increases; PCL force increases with increasing flexion during posterior draw because the angle between the PCL and the tibial plateau increases. The pattern of ligament loading during activity is governed by the geometry of the muscles spanning the knee: the resultant force in the ACL during isometric knee extension is determined mainly by the changing orientation of the patellar tendon relative to the tibia in the sagittal plane; the resultant force in the PCL during isometric knee flexion is dominated by the angle at which the hamstrings meet the tibia in the sagittal plane.
利用膝关节的三维模型来研究前后（a-p）拉伸、轴向旋转以及伸肌和屈肌等长收缩过程中的韧带功能。模型骨骼的几何形状基于尸体数据。股骨和胫骨的接触表面被建模为可变形的；股骨和髌骨的接触表面则假定为刚性的。使用十二个弹性元件来描述交叉韧带、侧副韧带和后关节囊的几何形状和力学性能。该模型由十三个肌肉肌腱单元驱动，每个单元表示为与肌腱串联的三元件肌肉。计算结果表明，a-p拉伸过程中施加的力与活动期间肌肉施加的力有很大不同。因此，基于体外实验结果得出的膝关节韧带功能原理可能被夸大了。直线a-p拉伸过程中膝关节韧带的力仅由韧带相对于骨骼的几何形状变化决定：前拉过程中，随着膝关节屈曲增加，前交叉韧带（ACL）的力减小，因为随着膝关节屈曲增加，ACL与胫骨平台之间的角度减小；后拉过程中，随着膝关节屈曲增加，后交叉韧带（PCL）的力增加，因为PCL与胫骨平台之间的角度增加。活动期间韧带加载模式由跨越膝关节的肌肉几何形状决定：等长膝关节伸展过程中ACL的合力主要由髌腱在矢状面相对于胫骨的方向变化决定；等长膝关节屈曲过程中PCL的合力主要由腘绳肌在矢状面与胫骨相交的角度决定。
