Collins J J, O'Connor J J
Oxford Orthopaedic Engineering Centre, Nuffield Orthopaedic Engineering Centre.
Proc Inst Mech Eng H. 1991;205(1):11-8. doi: 10.1243/PIME_PROC_1991_205_256_02.
A two-dimensional mathematical model of the knee is used with gait analysis to calculate muscle, cruciate ligament and tibio-femoral contact forces developed at the knee during normal level walking. Ten normal adult subjects--four females and six males--participated. The knee model is based upon a four-bar linkage comprising the femur, tibia and two cruciate ligaments. It takes account of the rolling and sliding of the femur on the tibia during flexion/extension and the changes in direction of the ligaments and muscle tendons. We considered forces transmitted by six elements: quadriceps, hamstrings, gastrocnemius, anterior and posterior cruciate ligaments, and tibio-femoral contact. The equations of mechanics can be used to determine the absolute values of only three of the knee forces simultaneously, so that twenty limiting solutions of three of the six forces were considered. A limiting solution was rejected if any of the three forces were negative, corresponding to compressive muscle or ligament forces, or tensile contact forces. These constraints always reduced and at times removed the redundancy of the knee structures. The high incidence of predicted single muscle activity, supported by electromyography, suggested that the ligaments play a significant role in load transmission during gait. The temporal patterns of muscle and ligament activity and ligament force magnitudes were sensitive to the choice of model parameters. The analysis showed that each of four possible minimum principles of muscle selection--minimal muscle force, muscle stress, ligament force and contact force--was unlikely to be valid throughout the walking cycle.
一个膝关节的二维数学模型与步态分析相结合，用于计算正常水平行走时膝关节处产生的肌肉、交叉韧带和胫股接触力。十名正常成年受试者参与了研究，其中四名女性，六名男性。该膝关节模型基于一个由股骨、胫骨和两条交叉韧带组成的四杆连杆机构。它考虑了屈伸过程中股骨在胫骨上的滚动和滑动以及韧带和肌腱方向的变化。我们考虑了由六个元件传递的力：股四头肌、腘绳肌、腓肠肌、前后交叉韧带以及胫股接触。力学方程只能同时确定三个膝关节力的绝对值，因此考虑了六个力中的三个力的二十种极限解。如果三个力中的任何一个为负，即对应于肌肉或韧带的压缩力或接触拉力，则该极限解被排除。这些约束总是减少，有时甚至消除了膝关节结构的冗余性。预测的单肌肉活动的高发生率得到了肌电图的支持，这表明韧带在步态中的负荷传递中起着重要作用。肌肉和韧带活动的时间模式以及韧带力的大小对模型参数的选择很敏感。分析表明，四种可能的肌肉选择最小原则——最小肌肉力、肌肉应力、韧带力和接触力——在整个步行周期中不太可能都是有效的。
