Yamaguchi G T, Zajac F E
Department of Mechanical Engineering, Stanford University, CA 94305.
J Biomech. 1989;22(1):1-10. doi: 10.1016/0021-9290(89)90179-6.
A simple planar static model of the knee joint was developed to calculate effective moment arms for the quadriceps muscle. A pathway for the instantaneous center of rotation was chosen that gives realistic orientations of the femur relative to the tibia. Using the model, nonlinear force and moment equilibrium equations were solved at one degree increments for knee flexion angles from 0 (full extension) to 90 degrees, yielding patellar orientation, patellofemoral contact force and patellar ligament force and direction with respect to both the tibial insertion point and the tibiofemoral contact point. The computer-derived results from this two-dimensional model agree with results from more complex models developed previously from experimentally obtained data. Due to our model's simplicity, however, the operation of the patellar mechanism as a lever as well as a spacer is clearly illustrated. Specifically, the thickness of the patella was found to increase the effective moment arm significantly only at flexions below 35 degrees even though the actual moment arm exhibited an increase throughout the flexion range. Lengthening either the patella or the patellar ligament altered the force transmitted from the quadriceps to the patellar ligament, significantly increasing the effective moment arm at flexions greater than 25 degrees. We conclude that the levering action of the patella is an essential mechanism of knee joint operation at moderate to high flexion angles.
开发了一种简单的膝关节平面静态模型，以计算股四头肌的有效力臂。选择了一条瞬时旋转中心路径，该路径给出了股骨相对于胫骨的实际方向。使用该模型，以1度的增量求解膝关节屈曲角度从0（完全伸展）到90度时的非线性力和力矩平衡方程，得出髌骨方向、髌股接触力以及髌韧带相对于胫骨插入点和胫股接触点的力和方向。该二维模型通过计算机得出的结果与先前根据实验获得的数据开发的更复杂模型的结果一致。然而，由于我们模型的简单性，髌骨机制作为杠杆以及间隔物的运作得到了清晰的说明。具体而言，发现髌骨厚度仅在低于35度的屈曲时才会显著增加有效力臂，尽管实际力臂在整个屈曲范围内都有所增加。延长髌骨或髌韧带会改变从股四头肌传递到髌韧带的力，在大于25度的屈曲时显著增加有效力臂。我们得出结论，髌骨的杠杆作用是膝关节在中高屈曲角度运作的基本机制。
