Dependence of human squat jump performance on the series elastic compliance of the triceps surae: a simulation study

The purposes of this study were to determine the dependence of human squat jump performance on the compliance of series elastic elements (SEEs) of the triceps surae (consisting of the soleus and gastrocnemius) and to explain this dependence. Vertical squat jumps were simulated using an optimal control model of the human musculo-skeletal system. Maximum jump height was found for several values of triceps surae SEE strain at maximum isometric force (epsilon(0)). When epsilon(0) was increased from 1 to 10 %, maximum jump height increased by 8 cm. This was partly due to a higher work output of contractile elements (CEs) of the muscles, primarily of the soleus, and also partly to an increased efficacy of converting muscle work to energy contributing to jump height. The soleus produced more work at epsilon(0)=10 % because, as a result of SEE recoil, the CE covered its shortening range at lower velocity and hence produced more force. Efficacy was higher at epsilon(0)=10 % because a higher vertical velocity at take-off was achieved with a lower rotational energy of the body segments. This apparent discrepancy was explained by increased angular velocities of the shanks and feet, which have small moments of inertia, and decreased angular velocities of the thighs and trunk, which have larger moments of inertia. This redistribution of segmental contributions to the vertical velocity of the centre of mass was possible because the increased compliance of the triceps surae SEE enhanced the energy-buffering capacity of this muscle group and, thereby, allowed for a higher power output at the ankles. It seems that long compliant tendons in the plantar flexors are an elegant solution to the problem of maximizing jumping performance.