On the organizing role of nonmuscular forces during performance of a giant circle in gymnastics

Five elite gymnasts performed giant circles on the high bar under different conditions of loading (without and with 6-kg loads attached to the shoulders, waist or ankles). Comparing the gymnasts' kinematic pattern of movement with that of a triple-pendulum moving under the sole influence of nonmuscular forces revealed qualitative similarities, including the adoption of an arched position during the downswing and a piked position during the upswing. The structuring role of nonmuscular forces in the organization of movement was further reinforced by the results of an inverse dynamics analysis, assessing the contributions of gravitational, inertial and muscular components to the net joint torques. Adding loads at the level of the shoulders, waist or ankles systematically influenced movement kinematics and net joint torques. However, with the loads attached at the level of the shoulders or waist, the load-induced changes in gravitational and inertial torques provided the required increase in net joint torque, thereby allowing the muscular torques to remain unchanged. With the loads attached at the level of the ankles, this was no longer the case and the gymnasts increased the muscular torques at the shoulder and hip joints. Together, these results demonstrate that expert gymnasts skillfully exploit the operative nonmuscular forces, employing muscle force only in the capacity of complementary forces needed to perform the task.     

Dynamic interactions between limb segments during planar arm movement

Movement of multiple segment limbs requires generation of appropriate joint torques which include terms arising from dynamic interactions among the moving segments as well as from such external forces as gravity. The interaction torques, arising from inertial, centripetal, and Coriolis forces, are not present for single joint movements. The significance of the individual interaction forces during reaching movements in a horizontal plane involving only the shoulder and elbow joints has been assessed for different movement paths and movement speeds. Trajectory formation strategies which simplify the dynamics computation are presented.     

Which data should be tracked in forward-dynamic optimisation to best predict muscle forces in a pathological co-contraction case?

The choice of the cost-function for predicting muscle forces during a movement remains a challenge, especially in patients with neuromuscular disorders. Forward dynamics-based optimisations mainly track joint kinematics or torques, combined with a least-excitation criterion. Tracking marker trajectories and/or electromyography (EMG) has rarely been proposed. Our objective was to determine the best tracking objective-function to accurately predict the upper-limb muscle forces. A musculoskeletal model was created and EMG was simulated to obtain a reference movement – a shoulder abduction. A Gaussian noise (mean = 0; standard deviation = 15%) was added to the simulated EMG. Another noise – corresponding to the actual soft tissue artefacts (STA) of experimental shoulder abduction movements – was added to the trajectories of the markers placed on the model. Muscle forces were estimated from these noisy data, using forward dynamics assisted by six non-linear least-squared objective-functions. These functions involved the tracking of marker trajectories, joint angles or torques, with and without EMG-tracking. All six approaches used the same musculoskeletal model and were solved using a direct multiple shooting algorithm. Finally, the predicted joint angles, muscle forces and activations were compared to the reference values, using root-mean-square errors (RMSe) and biases. The force RMSe of the approach tracking both marker trajectories and EMG (18.45 ± 12.60 N) was almost five times lower than the one of the approach tracking only joint angles (82.37 ± 66.26 N) or torques (85.10 ± 116.40 N). Therefore, using EMG as a complementary tracking-data in forward dynamics seems to be promising for the estimation of muscle forces.     

Evidence of residual force enhancement for multi-joint leg extension

Force enhancement is a well accepted property of skeletal muscle and has been observed at all structural levels ranging from single myofibrils to voluntarily activated m. quadriceps femoris in vivo. However, force enhancement has not been studied for multi-joint movements like human leg extension; therefore knowledge about its relevance in daily living remains limited. The purpose of this study was to determine whether there is force enhancement during maximal voluntary multi-joint leg extension. Human leg extension was studied (n=22) on a motor driven leg press dynamometer where external reaction forces under the feet as well as activity of 8 lower extremity muscles were measured. In addition, torque in the ankle and knee joints was calculated using inverse dynamics. The steady-state isometric force, joint torques, and muscle activation after active stretch (20° stretch amplitude at 60°/s) were compared with the corresponding values obtained during isometric reference contractions. There was consistent force enhancement during and following stretch for both forces and joint torques. Potentiation during stretch reached values between 26% and 30%, while a significant force enhancement of 10.5–12.3% and 4.3–7.4% remained 0.5–1 and 2.5–3 s after stretch, respectively. During stretch, EMG signals of m. gastrocnemius medialis and lateralis were significantly increased, while following stretch all analyzed muscles showed the same activity as during the reference contractions. We conclude from these results that force enhancement exists in everyday movements and should be accounted for when analyzing or modelling human movement.     

The envelope of passive knee joint motion

The purpose of this study is to create an accurate experimental database for the passive (in vitro) freedom-of-motion characteristics of the human knee joint on a subject to subject basis, suitable for the verification and enhancement of mathematical knee-joint models. Knee-joint specimens in a six degree-of-freedom motion rig are moved through flexion under several combinations of external loads, including tibial torques, axial forces and AP-forces. Euler rotation angles and translation vectors, describing the relative, spatial motions of the joint are measured using an accurate Roentgen Stereo Photogrammetric system. Conceptually the joint is considered as a two degrees-of-freedom of motion mechanism (flexion-tibial rotation), whereby the limits of internal and external tibial rotation are defined at torques of +/- 3 Nm. The motion pathways along these limits are defined as the envelopes of passive knee joint motion. It is found that these envelope pathways are consistent and hardly influenced by additional axial forces up to 300 N and AP-forces of 30 N. Within the envelope of motion, however, the motion patterns are highly susceptible to small changes in the external load configuration. It is shown that the external tibial rotation during extension ('screw-home mechanism') is not an obligatory effect of the passive joint characteristics, but a direct result of the external loads. Anatomical differences notwithstanding, the inter-individual discrepancies in the motion patterns of the four specimens tested, showed to be relatively small in a qualitative sense. Quantitative differences can be explained by small differences in the alignment of the coordinate systems relative to the joint anatomy and by differences in rotatory laxity.     

The linear co-variance between joint muscle torques is not a generalized principle

In 1996, Gottlieb et al. [Gottlieb GL, Song Q, Hong D, Almeida GL, Corcos DM. Coordinating movement at two joints: A principle of linear covariance. J Neurophysiol 1996;75(4):1760–4] identified a linear co-variance between the joint muscle torques generated at two connected joints. The joint muscle torques changed directions and magnitudes in a synchronized and linear fashion and called it the principle of linear co-variance. Here we showed that this principle cannot hold for some class of movements. Neurologically normal subjects performed multijoint movements involving elbow and shoulder with reversal towards three targets in the sagittal plane without any constraints. The movement kinematics was calculated using the X and Y coordinates of the markers positioned over the joints. Inverse dynamics was used to calculate the joint muscle, interaction and net torques. We found that for the class of voluntary movements analyzed, the joint muscle torques of the elbow and the shoulder were not linearly correlated. The same was observed for the interaction torques. But, the net torques at both joints, i.e., the sum of the interaction and the joint muscle torques were linearly correlated. We showed that by decoupling the joint muscle torques, but keeping the net torques linearly correlated, the CNS was able to generate fast and accurate movements with straight fingertip paths. The movement paths were typical of the ones in which the joint muscle torques were linearly correlated.     

Segment interactions within the swing leg during unloaded and loaded running

In this study, designed to determine the effect of lower extremity inertia manipulation on joint kinetics and segment energetics during the swing phase, 15 male distance runners were filmed as they performed treadmill running (3.35 m s-1) under five load conditions: no added load and loads of 0.25 kg and 0.50 kg added to each thigh or each foot. Results of this study demonstrated that the energetics of the lower extremity movements during the swing phase of the running cycle were dominated by mechanical energy transfers between adjacent segments attributed to the joint reaction forces, which acted to redistribute mechanical energy within the system. These contributions were considerably greater than those of the net joint moments, which primarily reflected muscular generation and dissipation of mechanical energy. Lower extremity loading caused little change in the movement pattern of the swing leg. However, increases in the joint reaction forces and net moments and in the amount of work done and the energy transfer attributed to the reaction forces and moments were observed, but were limited to the joints proximal to the location of the added load. These results were consistent with the increased aerobic demand associated with increases in lower extremity inertia that have been reported elsewhere and also have implications for the manner in which the neuromuscular system controls the motion of the legs during running.     

Lower extremity control and dynamics during backward angular impulse generation in forward translating tasks

Observation of complex whole body movements suggests that the nervous system coordinates multiple operational subsystems using some type of hierarchical control. When comparing two forward translating tasks performed with and without backward angular impulse, we have learned that both trunk-leg coordination and reaction force-time characteristics are significantly different between tasks. This led us to hypothesize that differences in trunk-leg coordination and reaction force generation would induce between-task differences in the control of the lower extremity joints during impulse generation phase of the tasks. Eight highly skilled performers executed a series of forward jumps with and without backward rotation (reverse somersault and reverse timer, respectively). Sagittal plane kinematics, reaction forces, and electromyograms of lower extremity muscles were acquired during the take-off phase of both tasks. Lower extremity joint kinetics were calculated using inverse dynamics. The results demonstrated between-task differences in the relative angles between the lower extremity segments and the net joint forces/reaction force and the joint angular velocity profiles. Significantly less knee extensor net joint moments and net joint moment work and greater hip extensor net joint moments and net joint moment work were observed during the push interval of the reverse somersault as compared to the reverse timer. Between-task differences in lower extremity joint kinetics were regulated by selectively activating the bi-articular muscles crossing the knee and hip. These results indicate that between-task differences in the control of the center of mass relative to the reaction force alters control and dynamics of the multijoint lower extremity subsystem.     

Optimization and evaluation of a proportional derivative controller for planar arm movement

In most clinical applications of functional electrical stimulation (FES), the timing and amplitude of electrical stimuli have been controlled by open-loop pattern generators. The control of upper extremity reaching movements, however, will require feedback control to achieve the required precision. Here we present three controllers using proportional derivative (PD) feedback to stimulate six arm muscles, using two joint angle sensors. Controllers were first optimized and then evaluated on a computational arm model that includes musculoskeletal dynamics. Feedback gains were optimized by minimizing a weighted sum of position errors and muscle forces. Generalizability of the controllers was evaluated by performing movements for which the controller was not optimized, and robustness was tested via model simulations with randomly weakened muscles. Robustness was further evaluated by adding joint friction and doubling the arm mass. After optimization with a properly weighted cost function, all PD controllers performed fast, accurate, and robust reaching movements in simulation. Oscillatory behavior was seen after improper tuning. Performance improved slightly as the complexity of the feedback gain matrix increased.     

An upper extremity kinematic model for evaluation of hemiparetic stroke

Quantification of rehabilitation progress is necessary for accurately assessing clinical treatments. A three-dimension (3D) upper extremity (UE) kinematic model was developed to obtain joint angles of the trunk, shoulder and elbow using a Vicon motion analysis system. Strict evaluation confirmed the system's accuracy and precision. As an example of application, the model was used to evaluate the upper extremity movement of eight hemiparetic stroke patients with spasticity, while completing a set of reaching tasks. Main outcome measures include kinematic variables of movement time, range of motion, peak angular velocity, and percentage of reach where peak velocity occurs. The model computed motion patterns in the affected and unaffected arms. The unaffected arm showed a larger range of motion and higher angular velocity than the affected arm. Frequency analysis (power spectrum) demonstrated lower frequency content for elbow angle and angular velocity in the affected limb when compared to the unaffected limb. The model can accurately quantify UE arm motion, which may aid in the assessment and planning of stroke rehabilitation, and help to shorten recovery time.     

Effect of pre-impact movement strategies on the impact forces resulting from a lateral fall

Approximately 90% of hip fractures in older adults result from falls, mostly from landing on or near the hip. A three-dimensional, 11-segment, forward dynamic biomechanical model was developed to investigate whether segment movement strategies prior to impact can affect the impact forces resulting from a lateral fall. Four different pre-impact movement strategies, with and without using the ipsilateral arm to break the fall, were implemented using paired actuators representing the agonist and antagonist muscles acting about each joint. Proportional-derivative feedback controller controlled joint angles and velocities so as to minimize risk of fracture at any of the impact sites. It was hypothesized that (a) the use of active knee, hip and arm joint torques during the pre-contact phase affects neither the whole body kinetic energy at impact nor the peak impact forces on the knee, hip or shoulder and (b) muscle strength and reaction time do not substantially affect peak impact forces. The results demonstrate that, compared with falling laterally as a rigid body, an arrest strategy that combines flexion of the lower extremities, ground contact with the side of the lower leg along with an axial rotation to progressively present the posterolateral aspects of the thigh, pelvis and then torso, can reduce the peak hip impact force by up to 56%. A 30% decline in muscle strength did not markedly affect the effectiveness of that fall strategy. However, a 300-ms delay in implementing the movement strategy inevitably caused hip impact forces consistent with fracture unless the arm was used to break the fall prior to the hip impact.     

The contribution of the wrist, elbow and shoulder joints to single-finger tapping

We aimed to determine the role of the wrist, elbow and shoulder joints to single-finger tapping. Six human subjects tapped with their index finger at a rate of 3 taps/s on a keyswitch across five conditions, one freestyle (FS) and four instructed tapping strategies. The four instructed conditions were to tap on a keyswitch using the finger joint only (FO), the wrist joint only (WO), the elbow joint only (EO), and the shoulder joint only (SO). A single-axis force plate measured the fingertip force. An infra-red active-marker three-dimensional motion analysis system measured the movement of the fingertip, hand, forearm, upper arm and trunk. Inverse dynamics estimated joint torques for the metacarpal-phalangeal (MCP), wrist, elbow, and shoulder joints. For FS tapping 27%, 56%, and 18% of the vertical fingertip movement were a result of flexion of the MCP joint and wrist joint and extension of the elbow joint, respectively. During the FS movements the net joint powers between the MCP, wrist and elbow were positively correlated (correlation coefficients between 0.46 and 0.76) suggesting synergistic efforts. For the instructed tapping strategies (FO, WO, EO, and SO), correlations decreased to values below 0.35 suggesting relatively independent control of the different joints. For FS tapping, the kinematic and kinetic data indicate that the wrist and elbow contribute significantly, working in synergy with the finger joints to create the fingertip tapping task.     

Optimal trajectory formation of constrained human arm reaching movements

Opening a door, turning a steering wheel, and rotating a coffee mill are typical examples of human movements that are constrained by the physical environment. The constraints decrease the mobility of the human arm and lead to redundancy in the distribution of actuator forces (either joint torques or muscle forces). Due to this actuator redundancy, there is an infinite number of ways to form a specific arm trajectory. However, humans form trajectories in a unique way. How do humans resolve the redundancy of the constrained motions and specify the hand trajectory? To investigate this problem, we examine human arm movements in a crank-rotation task. To explain the trajectory formation in constrained point-to-point motions, we propose a combined criterion minimizing the hand contact force change and the actuating force change over the course of movement. Our experiments show a close matching between predicted and experimental data.     

Synergic analysis of upper limb target-reaching movements

The topological invariance and synergies of human movements are discussed through the analysis and comparison of upper-limb target-reaching tasks. Five subjects were asked to perform different target-reaching tasks with different indices of difficulty, and the movements were captured using a Vicon 3D motion analysis system.Topological invariance was observed in the trajectories of different task performances. After normalization, the trajectories of the arm tips had very close patterns for different target-reaching tasks. Synergy in the target-reaching movements of the upper limbs was also found among the different joint angles. The joint angles can be fitted using the same format of functions proposed in this study. The parameters in the function can be taken as a characteristic feature of target-reaching movement patterns. A target-reaching movement can be determined by these parameters and the start and end positions.     

Three-dimensional model to predict muscle forces and their relation to motor variances in reaching arm movements

A three-dimensional (3-D) arm movement model is presented to simulate kinematic properties and muscle forces in reaching arm movements. Healthy subjects performed reaching movements repetitively either with or without a load in the hand. Joint coordinates were measured. Muscle moment arms, 3-D angular acceleration, and moment of inertias of arm segments were calculated to determine 3-D joint torques. Variances of hand position, arm configuration, and muscle activities were calculated. Ratios of movement variances observed in the two conditions (load versus without load) showed no differences for hand position and arm configuration variances. Virtual muscle force variances for all muscles except deltoid posterior and EMG variances for four muscles increased significantly by moving with the load. The greatly increased variances in muscle activity did not imply equally high increments in kinematic variances. We conclude that enhanced muscle cooperation through synergies helps to stabilize movement at the kinematic level when a load is added.     

A Neuro-Muscular Elasto-Dynamic Model of the Human Arm Part 2: Musculotendon Dynamics and Related Stress Effects

In this paper we develop an elasto-dynamic model of the human arm that includes effects of neuro-muscular control uponelastic deformation in the limb.The elasto-dynamic model of the arm is based on hybrid parameter multiple body systemvariational projection principles presented in the companion paper.Though the technique is suitable for detailed bone and jointmodeling,we present simulations for simplified geometry of the bones,discretized as Rayleigh beams with elongation,whileallowing for large deflections.Motion of the upper extremity is simulated by incorporating muscle forces derived from aHill-type model of musculotendon dynamics.The effects of muscle force are modeled in two ways.In one approach,aneffective joint torque is calculated by multiplying the muscle force by a joint moment ann.A second approach models themuscle as acting along a straight line between the origin and insertion sites of the tendon.Simple arm motion is simulated byutilizing neural feedback and feedforward control.Simulations illustrate the combined effects of neural control strategies,models of muscle force inclusion,and elastic assumptions on joint trajectories and stress and strain development in the bone andtendon.     

Comparison of global and joint-to-joint methods for estimating the hip joint load and the muscle forces during walking

A three-dimensional musculoskeletal model of the lower limb was developed to study the influence of biarticular muscles on the muscle force distribution and joint loads during walking. A complete walking cycle was recorded for 9 healthy subjects using the standard optoelectronic motion tracking system. Ground contact forces were also measured using a 6-axes force plate. Inverse dynamics was used to compute net joint reactions (forces and torques) in the lower limb. A static optimization method was then used to estimate muscle forces. Two different approaches were used: in the first one named global method, the biarticular muscles exerted a torque on the two joints they spanned at the same time, and in the second one called joint-by-joint method, these biarticular muscles were divided into two mono-articular muscles with geometrical (insertion, origin, via points) and physiological properties remained unchanged. The hip joint load during the gait cycle was then calculated taking into account the effect of muscle contractions. The two approaches resulted in different muscle force repartition: the biarticular muscles were favoured over any set of single-joint muscles with the same physiological function when using the global method. While the two approaches yielded only little difference in the resultant hip load, the examination of muscle power showed that biarticular muscles could produce positive work at one joint and negative work at the other, transferring energy between body segments and thus decreasing the metabolic cost of movement.     

Principles for learning horizontal-planar arm movements with reversal

PurposeThis study tested the hypothesis that muscle and interaction torques can be altered independently in order to improve in specific kinematics performance observed following practice. We also tested the hypothesis that a simple set of rules of EMG-control and kinetic-control models could explain the EMG and kinetic changes due to practice of movements with reversal.ScopeKinematics of the upper arm with reversal, performed over three distances, was reconstructed using motion analysis. The muscle and interaction torques were calculated using inverse-dynamics. EMG activities of the major arm muscles were also recorded. The results demonstrate that improved performance is facilitated by an increase in muscle torque (and therefore acceleration) at the proximal joint (shoulder) and by an increase in the interaction torque at the distal joint (elbow). No changes were observed in the amount of muscle activity underlying these kinetic modifications, except for a decrease in the shoulder antagonist latency.ConclusionThe results confirm Bernstein’s idea that the central nervous system takes advantage of the passive-interactive properties of the moving system. Also the modulation of the EMG patterns should be explained taking in account the reactive forces and the dual functions (maintenance of posture and generation of movement) of the muscles.     

A neuromusculoskeletal tracking method for estimating individual muscle forces in human movement

A neuromusculoskeletal tracking (NMT) method was developed to estimate muscle forces from observed motion data. The NMT method combines skeletal motion tracking and optimal neuromuscular tracking to produce forward simulations of human movement quickly and accurately. The skeletal motion tracker calculates the joint torques needed to actuate a skeletal model and track observed segment angles and ground forces in a forward simulation of the motor task. The optimal neuromuscular tracker resolves the muscle redundancy problem dynamically and finds the muscle excitations (and muscle forces) needed to produce the joint torques calculated by the skeletal motion tracker. To evaluate the accuracy of the NMT method, kinematics and ground forces obtained from an optimal control (parameter optimization) solution for maximum-height jumping were contaminated with both random and systematic noise. These data served as input observations to the NMT method as well as an inverse dynamics analysis. The NMT solution was compared to the input observations, the original optimal solution, and a simulation driven by the inverse dynamics torques. The results show that, in contrast to inverse dynamics, the NMT method is able to produce an accurate forward simulation consistent with the optimal control solution. The NMT method also requires 3 orders-of-magnitude less CPU time than parameter optimization. The speed and accuracy of the NMT method make it a promising new tool for estimating muscle forces using experimentally obtained kinematics and ground force data.