Nagano Akinori, Komura Taku
Center for BioDynamics, Boston University, Boston, MA, USA.
J Biomech. 2003 Nov;36(11):1675-81. doi: 10.1016/s0021-9290(03)00171-4.
Effects of moment arm length on kinetic outputs of a musculoskeletal system (muscle force development, joint moment development, joint power output and joint work output) were evaluated using computer simulation. A skeletal system of the human ankle joint was constructed: a lower leg segment and a foot segment were connected with a hinge joint. A Hill-type model of the musculus soleus (m. soleus), consisting of a contractile element and a series elastic element, was attached to the skeletal system. The model of the m. soleus was maximally activated, while the ankle joint was plantarflexed/dorsiflexed at a variation of constant angular velocities, simulating isokinetic exercises on a muscle testing machine. Profiles of the kinetic outputs (muscle force development, joint moment development, joint power output and joint work output) were obtained. Thereafter, the location of the insertion of the m. soleus was shifted toward the dorsal/ventral direction by 1cm, which had an effect of lengthening/shortening the moment arm length, respectively. The kinetic outputs of the musculoskeletal system during the simulated isokinetic exercises were evaluated with these longer/shorter moment arm lengths. It was found that longer moment arm resulted in smaller joint moment development, smaller joint power output and smaller joint work output in the larger plantarflexion angular velocity region (>120 degrees/s). This is because larger muscle shortening velocity was required with longer moment arm to achieve a certain joint angular velocity. Larger muscle shortening velocity resulted in smaller muscle force development because of the force-velocity relation of the muscle. It was suggested that this phenomenon should be taken into consideration when investigating the joint moment-joint angle and/or joint moment-joint angular velocity characteristics of experimental data.
利用计算机模拟评估了力臂长度对肌肉骨骼系统动力学输出（肌肉力量发展、关节力矩发展、关节功率输出和关节功输出）的影响。构建了人体踝关节的骨骼系统：小腿段和足部段通过铰链接合。将由收缩元件和串联弹性元件组成的比目鱼肌的希尔型模型附着到骨骼系统上。比目鱼肌模型被最大程度激活，同时踝关节以不同的恒定角速度进行跖屈/背屈，模拟在肌肉测试机上的等速运动。获得了动力学输出（肌肉力量发展、关节力矩发展、关节功率输出和关节功输出）的曲线。此后，比目鱼肌的附着点分别向背侧/腹侧方向移动1cm，这分别产生了延长/缩短力臂长度的效果。用这些更长/更短的力臂长度评估了模拟等速运动期间肌肉骨骼系统的动力学输出。发现在较大的跖屈角速度区域（>120度/秒），更长的力臂会导致更小的关节力矩发展、更小的关节功率输出和更小的关节功输出。这是因为要达到一定的关节角速度，更长的力臂需要更大的肌肉缩短速度。由于肌肉的力-速度关系，更大的肌肉缩短速度会导致更小的肌肉力量发展。建议在研究实验数据的关节力矩-关节角度和/或关节力矩-关节角速度特征时应考虑到这一现象。
