Estimation of dynamic joint torques and trajectory formation from surface electromyography signals using a neural network model

In this study, human arm movement was re-constructed from electromyography (EMG) signals using a forward dynamics model acquired by an artificial neural network within a modular architecture. Dynamic joint torques at the elbow and shoulder were estimated for movements in the horizontal plane from the surface EMG signals of 10 flexor and extensor muscles. Using only the initial conditions of the arm and the EMG time course as input, the network reliably reconstructed a variety of movement trajectories. The results demonstrate that posture maintenance and multijoint movements, entailing complex via-point specification and co-contraction of muscles, can be accurately computed from multiple surface EMG signals. In addition to the model's empirical uses, such as calculation of arm stiffness during motion, it allows evaluation of hypothesized computational mechanisms of the central nervous system such as virtual trajectory control and optimal trajectory planning.     

Optimal control of antagonistic muscle stiffness during voluntary movements

This paper presents a study on the control of antagonist muscle stiffness during single-joint arm movements by optimal control theory with a minimal effort criterion. A hierarchical model is developed based on the physiology of the neuromuscular control system and the equilibrium point hypothesis. For point-to-point movements, the model provides predictions on (1) movement trajectory, (2) equilibrium trajectory, (3) muscle control inputs, and (4) antagonist muscle stiffness, as well as other variables. We compared these model predictions to the behavior observed in normal human subjects. The optimal movements capture the major invariant characteristics of voluntary movements, such as a sigmoidal movement trajectory with a bell-shaped velocity profile, an N-shaped equilibrium trajectory, a triphasic burst pattern of muscle control inputs, and a dynamically modulated joint stiffness. The joint stiffness is found to increase in the middle of the movement as a consequence of the triphasic muscle activities. We have also investigated the effects of changes in model parameters on movement control. We found that the movement kinematics and muscle control inputs are strongly influenced by the upper bound of the descending excitation signal that activates motoneuron pools in the spinal cord. Furthermore, a class of movements with scaled velocity profiles can be achieved by tuning the amplitude and duration of this excitation signal. These model predictions agree with a wide body of experimental data obtained from normal human subjects. The results suggest that the control of fast arm movements involves explicit planning for both the equilibrium trajectory and joint stiffness, and that the minimal effort criterion best characterizes the objective of movement planning and control.     

Velocity-Based Planning of Rapid Elbow Movements Expands the Control Scheme of the Equilibrium Point Hypothesis

According to the equilibrium point hypothesis of voluntary motor control, control action of muscles is not explicitly computed, but rather arises as a consequence of interaction between moving equilibrium position, current kinematics and stiffness of the joint. This approach is attractive as it obviates the need to explicitly specify the forces controlling limb movements. However, many debatable aspects of this hypothesis remain in the manner of specification of the equilibrium point trajectory and muscle activation (or its stiffness), which elicits a restoring force toward the planned equilibrium trajectory. In this study, we expanded the framework of this hypothesis by assuming that the control system uses the velocity measure as the origin of subordinate variables scaling descending commands. The velocity command is translated into muscle control inputs by second order pattern generators, which yield reciprocal command and coactivation commands, and create alternating activation of the antagonistic muscles during movement and coactivation in the post-movement phase, respectively. The velocity command is also integrated to give a position command specifying a moving equilibrium point. This model is purely kinematics-dependent, since the descending commands needed to modulate the visco-elasticity of muscles are implicitly given by simple parametric specifications of the velocity command alone. The simulated movements of fast elbow single-joint movements corresponded well with measured data performed over a wide range of movement distances, in terms of both muscle excitations and kinematics. Our proposal on a synthesis for the equilibrium point approach and velocity command, may offer some insights into the control scheme of the single-joint arm movements.     

Kinematic invariants during cyclical arm movements

It has been observed that the motion of the arm end-point (the hand, fingertip or the tip of a pen) is characterized by a number of regularities (kinematic invariants). Trajectory is usually straight, and the velocity profile has a bell shape during point-to-point movements. During drawing movements, a two-thirds power law predicts the dependence of the end-point velocity on the trajectory curvature. Although various principles of movement organization have been discussed as possible origins of these kinematic invariants, the nature of these movement trajectory characteristics remains an open question. A kinematic model of cyclical arm movements derived in the present study analytically demonstrates that all three kinematic invariants can be predicted from a two-joint approximation of the kinematic structure of the arm and from sinusoidal joint motions. With this approach, explicit expressions for two kinematic invariants, the two-thirds power law during drawing movements and the velocity profile during point-to-point movements are obtained as functions of arm segment lengths and joint motion parameters. Additionally, less recognized kinematic invariants are also derived from the model. The obtained analytical expressions are further validated with experimental data. The high accuracy of the predictions confirms practical utility of the model, showing that the model is relevant to human performance over a wide range of movements. The results create a basis for the consolidation of various existing interpretations of kinematic invariants. In particular, optimal control is discussed as a plausible source of invariant characteristics of joint motions and movement trajectories.     

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.     

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.     

Description of electromyograms using a mathematical model of single joint movement

A mathematical model for motor control over one-joint fast and slow movements is proposed based on the equilibrium point (EP) hypothesis. Equations describing a reaction of the muscle with its servo to an EP shift are presented. EMG level is estimated as a function of kinematic and control variables. Voluntary movements are performed by a ramp EP shift for the muscles subserving a given joint. EMG patterns obtained by a computer simulation are in good agreement with the experimental data.     

Multijoint Control Strategies Transfer Between Tasks

In this paper, the hypothesis that multijoint control strategies are transferred between similar tasks was tested. To test this hypothesis, we studied the take-off phase of two types of backward somersault dives: one while translating backwards (Back), the other while translating forward (Reverse). An experimentally based dynamic model of the musculoskeletal system was employed to simulate the measured kinematics and reaction force data and to study the sensitivity of take-off performance to initial kinematic conditions. It was found that the horizontal velocity of the total body center of mass (CM) was most sensitive to modifications in the initial shank conditions. Consequently, the initial shank kinematics of the Back dive was modified in the optimization procedure while maintaining the joint coordination of the Back in order to generate the CM trajectory and reaction forces of a Reverse. Similarly, the initial shank kinematics of the Reverse dive was modified to simulate the CM trajectory and reaction force of the Back. It was found that small modifications in the initial shank kinematics led to change in direction of horizontal CM velocity at take-off; resulting in a switch from Back to Reverse and vice versa. In both cases, the simulated momentum conditions at departure and the bimodal shape of the reaction force-time curve were consistent with those experimentally observed. The results of this study support the hypothesis that transfer of control strategies between similar tasks is a viable option in multijoint control. This transfer of control strategy is explained using a hierarchical model of the motion control system.     

Feasibility of using EMG driven neuromusculoskeletal model for prediction of dynamic movement of the elbow.

Neuromusculoskeletal (NMS) modeling is a valuable tool in orthopaedic biomechanics and motor control research. To evaluate the feasibility of using electromyographic (EMG) signals with NMS modeling to estimate individual muscle force during dynamic movement, an EMG driven NMS model of the elbow was developed. The model incorporates dynamical equation of motion of the forearm, musculoskeletal geometry and musculotendon modeling of four prime elbow flexors and three prime elbow extensors. It was first calibrated to two normal subjects by determining the subject-specific musculotendon parameters using computational optimization to minimize the root mean square difference between the predicted and measured maximum isometric flexion and extension torque at nine elbow positions (0-120 degrees of flexion with an increment of 15 degrees ). Once calibrated, the model was used to predict the elbow joint trajectories for three flexion/extension tasks by processing the EMG signals picked up by both surface and fine electrodes using two different EMG-to-activation processing schemes reported in the literature without involving any trajectory fitting procedures. It appeared that both schemes interpreted the EMG somewhat consistently but their prediction accuracy varied among testing protocols. In general, the model succeeded in predicting the elbow flexion trajectory in the moderate loading condition but over-drove the flexion trajectory under unloaded condition. The predicted trajectories of the elbow extension were noted to be continuous but the general shape did not fit very well with the measured one. Estimation of muscle activation based on EMG was believed to be the major source of uncertainty within the EMG driven model. It was especially so apparently when fine wire EMG signal is involved primarily. In spite of such limitation, we demonstrated the potential of using EMG driven neuromusculoskeletal modeling for non-invasive prediction of individual muscle forces during dynamic movement under certain conditions.     

Inverse dynamic investigation of voluntary trunk movements in weightlessness: a new microgravity-specific strategy

Present investigation faces the question of quantitative assessment of exchanged forces and torques at the restraints during whole body posture exercises in long-term microgravity. Inverse dynamic modelling and total angular momentum at the ankle joint were used in order to reconstruct movement dynamics at the restraining point, represented by the ankle joint. The hypothesis is that the minimisation of the torques at the interface point assumes a key role in movement planning in 0 g. This hypothesis would respond to an optimisation of muscles activity, a minimisation of energy expenditure and therefore an accurate control of body movement. Results show that the 0 g movement strategy adopted ensures that the integral of the net ankle moment between the beginning and the end of the movement is zero. This expected mechanical constraint is not satisfied when 0 g movement dynamics is simulated using terrestrial kinematics. This accounts for a significant imposed change of movement strategy. Particularly, the efficient compensation of the inertial effects of the segments in terms of total angular momentum at the ankle joint was evidenced. These results explain the exaggerated axial synergies, observed on kinematics and which moved centre of mass (CM) backward from its already backward initial positioning, as a tool for enhancing the compensation and achieving the desired minimisation of the torques exchanges at the restraints.     

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.     

1998 ISEK Congress Keynote Lecture: Multi-muscle control in human movements

It has been suggested that the coordination of the activity of multiple muscles results from the comparison of the actual configuration of the body with a referent configuration specified by the nervous system so that the recruitment and gradation of the activity of each skeletal muscle depend on the difference between these two configurations. Active movements may be produced by the modification of the referent configuration. The hypothesis predicts the existence of a global minimum in electromyographic (EMG) activity of multiple muscles during movements involving reversals in direction. This prediction was tested in five subjects by analysing movements resembling the act of reaching for an object placed beyond one's reach from a sitting position. In such movements, initially sitting subjects raise their body to a semi-standing position and then return to sitting. Consistent with the hypothesis is the observation of a global minimum in the surface EMG activity of 16 muscles of the arm, trunk and leg at a specific phase of the movement. When the minimum occurred, EMG activity of each muscle did not exceed 2–7% of its maximal activity during the movement. As predicted, global EMG minima occurred at the phase corresponding to the reversal in movement direction, that is, during the transition from raising to lowering of the body. The global EMG minimum may represent the point at which temporal matching occurs between the actual and the referent body configurations. This study implies a specific link between motor behavior and the geometric shape of the body modified by the brain according to the desired action.     

Trajectory formation and speed-accuracy trade-off in aiming movements

The trade-off between speed and accuracy and the patterning of movement kinematics have been central issues for theories of human movement for almost a century. In the present contribution experimentally obtained kinematics of reciprocal aiming movements, performed under different task conditions, are modelled as resulting from a single non-linear dynamical system whose parameters vary so as to respond to the task demands. Providing a unified account of speed-accuracy trade-off and trajectory formation phenomena, the model offers a theoretical framework in which both discrete and continuous movements, performed along one or more dimensions can be understood.     

Analysis of kinematic invariances of multijoint reaching movement

 There is a no unique relationship between the trajectory of the hand, represented in cartesian or extrinsic space, and its trajectory in joint angle or intrinsic space in the general condition of joint redundancy. The goal of this work is to analyze the relation between planning the trajectory of a multijoint movement in these two coordinate systems. We show that the cartesian trajectory can be planned based on the task parameters (target coordinates, etc.) prior to and independently of angular trajectories. Angular time profiles are calculated from the cartesian trajectory to serve as a basis for muscle control commands. A unified differential equation that allows planning trajectories in cartesian and angular spaces simultaneously is proposed. Due to joint redundancy, each cartesian trajectory corresponds to a family of angular trajectories which can account for the substantial variability of the latter. A set of strategies for multijoint motor control following from this model is considered; one of them coincides with the frog wiping reflex model and resolves the kinematic inverse problem without inversion. The model trajectories exhibit certain properties observed in human multijoint reaching movements such as movement equifinality, straight end-point paths, bell-shaped tangential velocity profiles, speed-sensitive and speed-insensitive movement strategies, peculiarities of the response to double-step targets, and variations of angular trajectory without variations of the limb end-point trajectory in cartesian space. In humans, those properties are almost independent of limb configuration, target location, movement duration, and load. In the model, these properties are invariant to an affine transform of cartesian space. This implies that these properties are not a special goal of the motor control system but emerge from movement kinematics that reflect limb geometry, dynamics, and elementary principles of motor control used in planning. All the results are given analytically and, in order to compare the model with experimental results, by computer simulations. Received: 6 April 1994/Accepted in revised form: 25 April 1995     

How does microgravity affect the muscular and kinematic synergies in a complex movement?

The planning and the execution of voluntary movement relies on sensorimotor transformations in which representations of the external environment are integrated into motor programs. We studied executions of Whole Body Pointing movements, in normal and in transient microgravity (parabolic flights) conditions. Three processes could lead to adaptation to the new environmental condition: a radical change of terrestrial synergies, their partial modification or preservation. By applying a multivariate analysis on kinematic and electromyographic (EMG) data and by comparing the 1g and 0g conditions, our findings hint the hypothesis the descending information from vestibular system may be directed to change the synergies' modulation. An analogous analysis was performed on the kinematics: the invariance of intersegmental coordination among the segments' elevation angles suggests that these kinematic waveforms are used as reference signals to determine the appropriate muscle synergies in a subordinate and flexible manner in order to adapt to the novel mechanical constraints.     

Hybrid neuromusculoskeletal modeling to best track joint moments using a balance between muscle excitations derived from electromyograms and optimization

Current electromyography (EMG)-driven musculoskeletal models are used to estimate joint moments measured from an individual?s extremities during dynamic movement with varying levels of accuracy. The main benefit is the underlying musculoskeletal dynamics is simulated as a function of realistic, subject-specific, neural-excitation patterns provided by the EMG data. The main disadvantage is surface EMG cannot provide information on deeply located muscles. Furthermore, EMG data may be affected by cross-talk, recording and post-processing artifacts that could adversely influence the EMG?s information content. This limits the EMG-driven model?s ability to calculate the multi-muscle dynamics and the resulting joint moments about multiple degrees of freedom. We present a hybrid neuromusculoskeletal model that combines calibration, subject-specificity, EMG-driven and static optimization methods together. In this, the joint moment tracking errors are minimized by balancing the information content extracted from the experimental EMG data and from that generated by a static optimization method. Using movement data from five healthy male subjects during walking and running we explored the hybrid model?s best configuration to minimally adjust recorded EMGs and predict missing EMGs while attaining the best tracking of joint moments. Minimally adjusted and predicted excitations substantially improved the experimental joint moment tracking accuracy than current EMG-driven models. The ability of the hybrid model to predict missing muscle EMGs was also examined. The proposed hybrid model enables muscle-driven simulations of human movement while enforcing physiological constraints on muscle excitation patterns. This might have important implications for studying pathological movement for which EMG recordings are limited.     

Examination of the λ equilibrium point hypothesis when applied to single degree of freedom movements performed with different inertial loads

 One of the theories of human motor control is the λ Equilibrium Point Hypothesis. It is an attractive theory since it offers an easy control scheme where the planned trajectory shifts monotionically from an initial to a final equilibrium state. The feasibility of this model was tested by reconstructing the virtual trajectory and the stiffness profiles for movements performed with different inertial loads and examining them. Three types of movements were tested: passive movements, targeted movements, and repetitive movements. Each of the movements was performed with five different inertial loads. Plausible virtual trajectories and stiffness profiles were reconstructed based on the λ Equilibrium Point Hypothesis for the three different types of movements performed with different inertial loads. However, the simple control strategy supported by the model, where the planned trajectory shifts monotonically from an initial to a final equilibrium state, could not be supported for targeted movements performed with added inertial load. To test the feasibility of the model further we must examine the probability that the human motor control system would choose a trajectory more complicated than the actual trajectory to control. Received: 20 June 1995 / Accepted in revised form: 6 August 1996     

A general-purpose framework to simulate musculoskeletal system of human body: using a motion tracking approach*

Computation of muscle force patterns that produce specified movements of muscle-actuated dynamic models is an important and challenging problem. This problem is an undetermined one, and then a proper optimization is required to calculate muscle forces. The purpose of this paper is to develop a general model for calculating all muscle activation and force patterns in an arbitrary human body movement. For this aim, the equations of a multibody system forward dynamics, which is considered for skeletal system of the human body model, is derived using Lagrange–Euler formulation. Next, muscle contraction dynamics is added to this model and forward dynamics of an arbitrary musculoskeletal system is obtained. For optimization purpose, the obtained model is used in computed muscle control algorithm, and a closed-loop system for tracking desired motions is derived. Finally, a popular sport exercise, biceps curl, is simulated by using this algorithm and the validity of the obtained results is evaluated via EMG signals.     

Positioning of the Human Forearm in Tracking Movements and Their Reproduction under Conditions of Limited Visual Control

In 14 healthy persons, we studied movements of the forearm with its positioning on a target level. A double trapezium was used as the command trajectory (flexion in the elbow joint from the state of full extension, 0°, with positioning on the level of 50 or 60° and further flexion to the 100° angle, and a similar reverse movement). We compared (i) tracking movements, when the subject tried to adequately reproduce the movement of the target along the command trajectory visualized on the monitor screen and obtained visual information about the performed movement (shifts of the second light point in time/joint angle coordinates), and (ii) reproduction of these movements under conditions of limitation of the visual feedback (when there was no information about the performed movement). Parameters of the tracking movements and of their reproductions (delays of initiation of the movement phases as compared with the command signal, durations of these phases, and angle velocities of the forearm movement), as well as the quality of positioning after oppositely directed movements, were compared. Positioning on the target level performed under proprioceptive control (when visual control was limited) was accompanied by systematic errors, whose sign in most test series performed by most subjects coincided with the direction of the preceding movement phase. The pattern of signs of systematic positioning errors after movements of opposite directions was quite individual (typical of a given subject) and demonstrated no dependence on the value of the extensor loading. Averaged intragroup systematic errors of positioning after movement phase 1 (flexion to the target level) and phase 3 (extension to the same level) under conditions of a minimum extensor loading (0.5-1.0 N · m) were 2.57° and 2.52°, respectively. When the loading was substantial (3.6-6.0 N · m), the respective errors were 3.85° and 3.48°. The nonlinear properties of muscle stretch receptors in the elbow flexors and extensors (responsible for the significant dependence of the parameters of afferent signals produced in these receptors on the movement prehistory) are considered the primary reason for systematic errors when positioning is performed exclusively under proprioceptive control. The influence of alpha-gamma co-activation in active muscles on the characteristics of the above signals is discussed.