Dependence of human maximum jump height on moment arms of the bi-articular m. gastrocnemius; a simulation study

In this study the dependence of maximum jump height on moment arms of m. gastrocnemius at the knee and ankle joint was investigated, using a forward dynamic simulation model of the human musculoskeletal system. Input of the model was the stimulation of six muscles of the lower extremity as a function of time, output was the movement of body segments. For many different combinations of moment arms, maximum jump heigt was determined by optimizing muscle stimulation. It was found that (1) maximum jump height depends on the combination of moment arms of m. gastrocnemius at the knee and ankle, (2) at a given moment arm at the ankle there is an optimal moment arm at the knee joint, and (3) this moment arm differs from zero, i.e. there is an advantage in the bi-articularity of m. gastrocnemius. This advantage, which amounted to less than 2 cm, was explained as follows. When m. gastrocnemius is bi-articular, it causes a particular combination of net joint moments at the knee and ankle joint during the last part of the push-off. This combination is such that the acceleration of the body's mass centre remains vertical, even at maximal stimulation of all muscles. Such a profitable situation cannot be achieved when m. gastrocnemius is mono-articular. Finally, it was shown that moment arm values derived from cadaver data reported in the literature were close to the optimal values determined for the model.