Mechanics of human triceps surae muscle in walking, running and jumping.

Length changes of the muscle-tendon complex (MTC) during activity are in part the result of length changes of the active muscle fibres, the contractile component (CC), and also in part the result of stretch of elastic structures [series-elastic component (SEC)]. We used a force platform and kinematic measurements to determine force and length of the human calf muscle during walking, running and squat jumping. The force-length relation of the SEC was determined in dynamometer experiments on the same four subjects. Length of the CC was calculated as total muscle-tendon length minus the force dependent length of the SEC. The measured relations between force and length or velocity were compared with the individually determined force-length and force-velocity relations of the CC. In walking or running the negative work performed in the eccentric phase was completely stored as elastic energy. This elastic energy was released in the concentric phase, at speeds well exceeding the maximum shortening speed predicted by the Hill force-velocity relation. Speed of the CC, in contrast, was positive and low, well within the range predicted by the measured force-velocity properties and compatible with a favourable muscular efficiency. These effects were also present in purely concentric contractions, like the squatted jump. Contractile component length usually started at the far end of the force-length relation. Inter-individual differences in series-elastic stiffness were reflected in the force and length recordings during natural activity.

Predictions of mechanical output of the human M. triceps surae on the basis of electromyographic signals: the role of stimulation dynamics.

In order to assess the significance of the dynamics of neural control signals for the rise time of muscle moment, simulations of isometric and dynamic plantar flexion contractions were performed using electromyographic signals (EMG signals) of m. triceps surae as input. When excitation dynamics of the muscle model was optimized for an M-wave of the medial head of m. gastrocnemius (GM), the model was able to make reasonable predictions of the rise time of muscle moment during voluntary isometric plantar flexion contractions on the basis of voluntary GM EMG signals. The rise time of muscle moment in the model was for the greater part determined by the amplitude of the first EMG burst. For dynamic jumplike movements of the ankle joint, however, no relationship between rise time of muscle moment in the experiment and muscle moment predicted by the model on the basis of GM EMG signals was found. Since rise time of muscle moment varied over a small range for this movement, it cannot be completely excluded that stimulation dynamics plays a role in control of these simple single-joint movements.

Control of maximal and submaximal vertical jumps.

PURPOSE: It was investigated to what extent control signals used by human subjects to perform submaximal vertical jumps are related to control signals used to perform maximal vertical jumps. METHODS: Eight subjects performed both maximal and submaximal height jumps from a static squatting position. Kinematic and kinetic data were recorded as well as electromyographic (EMG) signals from eight leg muscles. Principal component analysis was used analyze the shape of smoothed rectified EMG (SREMG) histories. Jumps were also simulated with a forward dynamic model of the musculoskeletal system, comprising four segments and six muscles. First, a maximal height jump was simulated by finding the optimal stimulation pattern, i.e., the pattern resulting in a maximum height of the mass center of the body. Subsequently, submaximal jumps were simulated by adapting the optimal stimulation pattern using strategies derived from the experimental SREMG histories. RESULTS: SREMG histories of maximal and submaximal jumps revealed only minor differences in relative timing of the muscles between maximal and submaximal jumps, but SREMG amplitude was reduced in the biarticular muscles. The shape of the SREMG recordings was not much different between the two conditions, even for the biarticular muscles. The simulated submaximal jump resembled to some extent the submaximal jumps found in the experiment, suggesting that differences in control signals as inferred from the experimental data could indeed be sufficient to get the observed behavior. CONCLUSIONS: The results fit in with theories on the existence of generalized motor programs within the central nervous system, the output of which is determined by the setting of parameters such as amplitude and relative timing of control signals.

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.

Dynamics of force and muscle stimulation in human vertical jumping.

PURPOSE: The purpose of this study was to gain insight into the importance of stimulation dynamics for force development in human vertical jumping. METHODS: Maximum height squat jumps were performed by 21 male subjects. As a measure of signal dynamics, rise time (RT) was used, i.e., the time taken by the signal to increase from 10% to 90% of its peak value. RT were calculated for time histories of smoothed rectified electromyograms (SREMG) of seven lower extremity muscles, net moments about hip, knee, and ankle joints, and components of the ground reaction force vector. RESULTS: Average RT values were 105-143 ms for SREMG signals, 90-112 ms for joint moments, and 120 ms for the vertical component of the ground reaction force (Fz). A coefficient of linear correlation of 0.88 was found between RT of SREMG of m. gluteus maximus (GLU) and RT of Fz. To explain this correlation, it was speculated that for an effective transfer from joint extensions to vertical motion of the center of mass (CM), the motion of CM needs a forward component during the push-off. Given the starting position, only the hip extensor muscles are able to generate such a forward acceleration of CM. To preserve the forward motion of CM, RT of knee and ankle joint moments need to be adjusted to RT of the hip joint moment. Thus, the greater RT of the hip joint moment and RT of GLU-SREMG, the greater RT of Fz. CONCLUSIONS: Overall, it was concluded that the time it takes to develop muscle stimulation has a substantial effect on the dynamics of force development in vertical jumping, and that this effect should not be neglected in studies of the control of explosive movements.

From twitch to tetanus for human muscle: experimental data and model predictions for m. triceps surae.

In models describing the excitation of muscle by the central nervous system, it is often assumed that excitation during a tetanic contraction can be obtained by the linear summation of responses to individual stimuli, from which the active state of the muscle is calculated. We investigate here the extent to which such a model describes the excitation of human muscle in vivo. For this purpose, experiments were performed on the calf muscles of four healthy subjects. Values of parameters in the model describing the behaviour of the contractile element (CE) and the series elastic element (SEE) of this muscle group were derived on the basis of a set of isokinetic release contractions performed on a special-purpose dynamometer as well as on the basis of morphological data. Parameter values describing the excitation of the calf muscles were optimized such that the model correctly predicted plantar flexion moment histories in an isometric twitch, elicited by stimulation of the tibial nerve. For all subjects, the model using these muscle parameters was able to make reasonable predictions of isometric moment histories at higher stimulation frequencies. These results suggest that the linear summation of responses to individual stimuli can indeed give an adequate description of the process of human muscle excitation in vivo.

Evaluation of a self-consistent method for calculating muscle parameters from a set of isokinetic releases.

A new method for calculating parameters describing the force-velocity relationship of the contractile element and the force-extension relationship of the series elastic element of skeletal muscle from a set of isokinetic release contractions is evaluated using experimental and numerical techniques. The method calculates from the set of isokinetic releases those force-velocity and force-extension relationships that give a self-consistent description of the data set. The self-consistent calculation method is applied to data obtained from the gastrocnemius medialis muscle of the rat, since for such an animal model both relationships can be independently derived from a set of isotonic release contractions. For the two animals studied, the force-velocity and force-extension relationships calculated by the self-consistent method were in good agreement with the ones derived from isotonic releases performed on the same muscle. The statistical properties of the estimates obtained by the calculation method were investigated using a Monte Carlo technique. The method was found to yield results which were biased by less than 2% and which possessed a coefficient of variation smaller than 5%. These findings indicate that the proposed calculation method can be a useful tool for determining the contractile properties of skeletal muscle as reflected in the force-velocity and force-extension relationships.

On the effectiveness of force application in guided leg movements.

In guided leg movements (e.g., in cycling or wheelchair propulsion), the kinematics of a limb are determined by the object on which a force is applied. As a consequence, the force direction can vary and may deviate from the movement direction, that is, the effective direction. In the present study, the relation of effective force application and maximal power output was examined. Subjects (n = 5) performed guided leg tasks on a special dynamometer. They were instructed to exert a maximal force against a moving forceplate in the direction of the movement, as if they were pushing the plate away. Three different movement directions were tested: perpendicular to the horizontal, rotated 30 degrees backward, and rotated 30 degrees forward. For each trial, force and position data were recorded. The results of the experiments showed that in the extreme movement directions (both 30 degrees conditions), the force vector deviated significantly from the direction of the movement. Apparently, maximal power output was achieved with a low force effectiveness in these tasks. The background of this phenomenon was revealed by using the kinematics of one of these tasks in a simulation model. The stimulation level of 6 leg muscles was optimized toward a maximal effective force component (a) without a constraint on the direction of the total force or (b) with a constraint on the force component perpendicular to the effective force. The muscle stimulation pattern that resulted in the highest effective force coincided with a low force effectiveness. Apparently, this is a prerequisite for maximal power transfer from the muscles to the plate in these guided movements.

From twitch to tetanus: performance of excitation dynamics optimized for a twitch in predicting tetanic muscle forces.

In models of the excitation of muscles it is often assumed that excitation during a tetanic contraction can be obtained by the linear summation of responses to individual stimuli from which the active state of the muscle is calculated. The purpose of this study was to investigate whether such a model adequately describes the process of excitation of muscle. Parameters describing the contraction dynamics of the muscle model used were derived from physiological and morphological measurements made on the gastrocnemius medialis muscle of three adult Wistar rats. Parameters pertaining to the excitation dynamics were optimized such that the muscle model correctly predicted force histories recorded during an isometric twitch. When a relationship between intracellular calcium and active state from literature on rat muscle was used, the muscle model was capable of generating force histories at stimulation frequencies of 20, 40, 60 and 80 Hz and other muscle-tendon complex lengths which closely matched those measured experimentally - albeit forces were underestimated slightly in all cases. Differences in responses to higher stimulation frequencies between animals could be traced back to differences in twitch dynamics between the animals and adequate predictions of muscle forces were obtained for all animals. These results suggest that the linear summation of responses to individual stimuli indeed gives an adequate description of the excitation of muscle.