A model of the human triceps surae muscle-tendon complex applied to jumping

The purpose of this study was to gain more insight into the behavior of the muscle-tendon complex of human m. triceps surae in jumping. During one-legged vertical jumps of ten subjects ground reaction forces as well as cinematographic data were registered, and electromyograms were recorded from m. soleus and m. gastrocnemius. A model was developed of m. triceps surae, incorporating assumptions concerning dimensions, architecture, force-length and force-velocity relationships of muscle fibers, as well as assumptions concerning dimensions and elastic behavior of tendinous tissue in series with the muscle fibers. The velocity with which origin approaches insertion (V OI) was calculated for m. soleus and m. gastrocnemius using cine film data, and served as input of the model. During the last part of the push-off phase EMG-levels were found to be more or less constant, V OI of m. soleus and m. gastrocnemius rapidly increased, and the plantar flexing moment obtained by solving equations concerning a free body diagram of the foot rapidly declined. A similar decline was observed in the plantar flexing moment obtained by multiplying force calculated with help of the model by estimated moment arm at the ankle. As a result of the decline of exerted force tendon length decreases. According to the model the shortening velocity of tendon reaches higher values than that of muscle fibers. The results of a kinetic analysis demonstrate that during the last part of the push-off phase a combination of high angular velocities with relatively large plantar flexing moments is required. It is concluded that without a compliant tendon m. triceps surae would not be able to satisfy this requirement.