Sensitivity of vertical jumping performance to changes in muscle stimulation onset times: a simulation study

The effect of muscle stimulation dynamics on the sensitivity of jumping achievement to variations in timing of muscle stimulation onsets was investigated. Vertical squat jumps were simulated using a forward dynamic model of the human musculoskeletal system. The model calculates the motion of body segments corresponding to STIM(t) of six major muscle groups of the lower extremity, where STIM is muscle stimulation level. For each muscle, STIM was allowed to switch "on" only once. The subsequent rise of STIM to its maximum was described using a sigmoidal curve, the dynamics of which was expressed as rise time (RT). For different values of stimulation RT, the optimal set of onset times was determined using dynamic optimization with height reached by the center of mass as performance criterion. Subsequently, 200 jumps were simulated in which the optimal muscle stimulation onset times were perturbed by adding to each a small number taken from a Gaussian-distributed set of pseudo-random numbers. The distribution of heights achieved in these perturbed jumps was used to quantify the sensitivity of jump height to variations in timing of muscle stimulation onsets. It was found that with increasing RT, the sensitivity of jump height to timing of stimulation onset times decreased. To try and understand this finding, a post-hoc analysis was performed on the perturbed jumps. Jump height was most sensitive to errors in the delay between stimulation onset times of proximal muscles and stimulation onset times of plantar flexors. It is explained how errors in this delay cause aberrations in the configuration of the system, which are regenerative and lead to relatively large jump height deficits. With increasing RT, the initial aberrations due to erroneous timing of muscle stimulation are smaller, and the regeneration is less pronounced. Finally, it is speculated that human subjects decrease or increase RT depending on the relative importance of different performance criteria.