A method to predict muscle control in the kinematically and mechanically indeterminate human masticatory system

A method is proposed to generate muscle activation patterns for goal-directed movements of the human masticatory system. This system is special because apart from a larger amount of muscles than degrees of freedom its joints do not restrict its movements a priori. Therefore, each muscle is able to influence all six degrees of freedom which makes the system kinematically and mechanically indeterminate. Furthermore, its working space is principally determined by the dynamical properties of its muscles and not by passive constraints.The presented method determines the contribution of each degree of freedom to a movement of a reference point on the mandible. It avails of straightforward mathematical techniques like Linear Programming. It does not require a separate trajectory planning step. It was applied in a six degrees of freedom dynamical mathematical model of the human masticatory system. This model which was based upon rigid-body dynamics incorporating skull morphology and muscle architecture including dynamical properties. Movements were exclusively defined by a goal position of the mandibular reference point.The method proved to be robust in generating muscle activation patterns for both feasible and infeasible movement tasks. Generally, they were accomplished faster than habitually observed. If the task was infeasible the movement stopped at the outer boundary of the working space at the side of the unreachable goal. The method, therefore, enables to explore the working space of the mandible and the factors that are relevant for its boundaries.     

Analysis of an optimal control model of multi-joint arm movements

 In this paper, we propose a model of biological motor control for generation of goal-directed multi-joint arm movements, and study the formation of muscle control inputs and invariant kinematic features of movements. The model has a hierarchical structure that can determine the control inputs for a set of redundant muscles without any inverse computation. Calculation of motor commands is divided into two stages, each of which performs a transformation of motor commands from one coordinate system to another. At the first level, a central controller in the brain accepts instructions from higher centers, which represent the motor goal in the Cartesian space. The controller computes joint equilibrium trajectories and excitation signals according to a minimum effort criterion. At the second level, a neural network in the spinal cord translates the excitation signals and equilibrium trajectories into control commands to three pairs of antagonist muscles which are redundant for a two-joint arm. No inverse computation is required in the determination of individual muscle commands. The minimum effort controller can produce arm movements whose dynamic and kinematic features are similar to those of voluntary arm movements. For fast movements, the hand approaches a target position along a near-straight path with a smooth bell-shaped velocity. The equilibrium trajectories in X and Y show an ‘N’ shape, but the end-point equilibrium path zigzags around the hand path. Joint movements are not always smooth. Joint reversal is found in movements in some directions. The excitation signals have a triphasic (or biphasic) pulse pattern, which leads to stereotyped triphasic (or biphasic) bursts in muscle control inputs, and a dynamically modulated joint stiffness. There is a fixed sequence of muscle activation from proximal muscles to distal muscles. The order is preserved in all movements. For slow movements, it is shown that a constant joint stiffness is necessary to produce a smooth movement with a bell-shaped velocity. Scaled movements can be reproduced by varying the constraints on the maximal level of excitation signals according to the speed of movement. When the inertial parameters of the arm are altered, movement trajectories can be kept invariant by adjusting the pulse height values, showing the ability to adapt to load changes. These results agree with a wide range of experimental observations on human voluntary movements. Received: 4 December 1995 / Accepted in revised form: 17 September 1996     

Concurrent adaptation of force and impedance in the redundant muscle system

This article examines the validity of a model to explain how humans learn to perform movements in environments with novel dynamics, including unstable dynamics typical of tool use. In this model, a simple rule specifies how the activation of each muscle is adapted from one movement to the next. Simulations of multijoint arm movements with a neuromuscular plant that incorporates neural delays, reflexes, and signal-dependent noise, demonstrate that the controller is able to compensate for changing internal or environment dynamics and noise properties. The computational model adapts by learning both the appropriate forces and required limb impedance to compensate precisely for forces and instabilities in arbitrary directions with patterns similar to those observed in motor learning experiments. It learns to regulate reciprocal activation and co-activation in a redundant muscle system during repeated movements without requiring any explicit transformation from hand to muscle space. Independent error-driven change in the activation of each muscle results in a coordinated control of the redundant muscle system and in a behavior that reduces instability, systematic error, and energy.     

Impedance characteristics of a neuromusculoskeletal model of the human arm II. Movement control

The modulation of neuromusculoskeletal impedance during movements is analysed using a motor control model of the human arm. The motor control system combines feedback and feedforward control and both control modes are determined in one optimization process. In the model, the stiffness varies at the double movement frequency for 2-Hz oscillatory elbow movements and has high values at the movement reversals. During goal-directed two-degrees-of-freedom arm movements, the stiffness is decreased during the movement and may be increased in the initial and final phases, depending on the movement velocity. The stiffness has a considerable curl during the movement, as was also observed in experimental data. The dynamic stiffness patterns of the model can be explained basically by the α−γ coactivation scheme where feedback gains covary with motor control signals. In addition to the modulation of the gain factors, it is argued that the variation of the intrinsic stiffness has a considerable effect on movement control, especially during fast movements. Received: 14 October 1997 / Accepted in revised form: 18 May 1999     

Trunk Muscle Activation at the Initiation and Braking of Bilateral Shoulder Flexion Movements of Different Amplitudes

The aim of this study was to investigate if trunk muscle activation patterns during rapid bilateral shoulder flexions are affected by movement amplitude. Eleven healthy males performed shoulder flexion movements starting from a position with arms along sides (0°) to either 45°, 90° or 180°. EMG was measured bilaterally from transversus abdominis (TrA), obliquus internus (OI) with intra-muscular electrodes, and from rectus abdominis (RA), erector spinae (ES) and deltoideus with surface electrodes. 3D kinematics was recorded and inverse dynamics was used to calculate the reactive linear forces and torque about the shoulders and the linear and angular impulses. The sequencing of trunk muscle onsets at the initiation of arm movements was the same across movement amplitudes with ES as the first muscle activated, followed by TrA, RA and OI. All arm movements induced a flexion angular impulse about the shoulders during acceleration that was reversed during deceleration. Increased movement amplitude led to shortened onset latencies of the abdominal muscles and increased level of activation in TrA and ES. The activation magnitude of TrA was similar in acceleration and deceleration where the other muscles were specific to acceleration or deceleration. The findings show that arm movements need to be standardized when used as a method to evaluate trunk muscle activation patterns and that inclusion of the deceleration of the arms in the analysis allow the study of the relationship between trunk muscle activation and direction of perturbing torque during one and the same arm movement.     

Modeling inter-human movement coordination: synchronization governs joint task dynamics

Human interaction partners tend to synchronize their movements during repetitive actions such as walking. Research of inter-human coordination in purely rhythmic action tasks reveals that the observed patterns of interaction are dominated by synchronization effects. Initiated by our finding that human dyads synchronize their arm movements even in a goal-directed action task, we present a step-wise approach to a model of inter-human movement coordination. In an experiment, the hand trajectories of ten human dyads are recorded. Governed by a dynamical process of phase synchronization, the participants establish in-phase as well as anti-phase relations. The emerging relations are successfully reproduced by the attractor dynamics of coupled phase oscillators inspired by the Kuramoto model. Three different methods on transforming the motion trajectories into instantaneous phases are investigated and their influence on the model fit to the experimental data is evaluated. System identification technique allows us to estimate the model parameters, which are the coupling strength and the frequency detuning among the dyad. The stability properties of the identified model match the relations observed in the experimental data. In short, our model predicts the dynamics of inter-human movement coordination. It can directly be implemented to enrich human-robot interaction.     

Analysis of muscle movement during frequency-modulated activation of efferents

The basic principles governing trajectories of change in muscle length (henceforth referred to as "movement") were analyzed at varying rates of distributed afferent stimulation during experiments on the soleus and plantaris muscles in unanesthetized cats. The theoretical possibility of describing evoked movements within the context of a model having nonlinear hysteresis properties and dependence of dynamic parameters on direction of movement were demonstrated. A difference in static transitions between muscle contraction and lengthening was found and vice versa and retardation of movement at the start of lengthening reaction (induced by a reduced efferent stimulation rate) was more pronounced. Interaction was discovered between two disruptive influences: changes in the rate of efferent stimulation and external load, mainly due to hysteresis effects of muscle contraction. The trajectory of movement produced by alteration in one of the inputs at work (external load or afferent stimulation) is associated with the lead-up to the muscle motion, irrespective of the reason inducing the foregoing movement. Functional implications of the nonlinear dynamics of muscular contraction are discussed.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 21, No. 4, pp. 443–450, July–August, 1989.     

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.     

Influence of gravity compensation on muscle activity during reach and retrieval in healthy elderly

IntroductionArm support like gravity compensation may improve arm movements during stroke rehabilitation. It is unknown how gravity compensation affects muscle activation patterns during reach and retrieval movements. Since muscle activity during reach is represented by a component varying with movement velocity and a component supposedly counteracting gravity, we hypothesized that gravity compensation decreases the amplitude of muscle activity, but does not affect the pattern. To examine this, we compared muscle activity during well defined movements with and without gravity compensation in healthy elderly.MethodsTen subjects performed reach and retrieval movements with and without gravity compensation. Muscle activity of biceps, triceps, anterior, middle and posterior parts of deltoid and upper trapezius was compared between the two conditions.ResultsThe level of muscle activity was lower with gravity compensation in all muscles, reaching significance in biceps, anterior deltoid and trapezius (p ? 0.026). The muscle activation pattern did not differ between movements with and without gravity compensation (p ? 0.662).DiscussionGravity compensation only influenced the level of muscle activity but not the muscle activation pattern in terms of timing. Future studies should examine if the influence of gravity compensation is comparable for stroke patients. This may stimulate early and intensive training during rehabilitation.     

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.     

Analysis of a muscular control system in human movements

In this work, we have studied a muscular control system under experimental conditions for analyzing the dynamic behavior of individual muscles and theoretical considerations for elucidating its control strategy. Movement of human limbs is achieved by joint torques and each torque is specified as the sum of torques generated by muscle forces. The behavior of individual muscles is controlled by the neural input which is estimated by means of an electromyogram (EMG). In this study, the EMGs for a flexor and an extensor are measured in elbow joint movements and the dynamic behavior of individual muscles is analyzed. As a result, it is verified that both a flexor and an extensor are activated throughout the entire movement and that the activation of muscles is controlled above a specific limit independent of the hand-held load. Subsequently, a system model for simulating elbow joint movements is developed which includes the muscle dynamic relationship between the neural input and the isometric force. The minimum limit of muscle activation that has been confirmed in experiments is provided as a constraint of the neural input and the criterion is defined by a derivative of the isometric force of individual muscles. The optimal trajectories formulated under these conditions are quantitatively compared with the experimentally observed trajectories, and the control strategy of a muscular control system is studied. Finally, a muscular control system in multi-joint arm movements is discussed with regard to the comparative analysis between observed and optimal trajectories. Received: 7 April 1999 / Accepted in revised form: 27 July 1999     

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.     

Similar movements are associated with drastically different muscle contraction velocities

We investigated how kinematic redundancy interacts with the neurophysiological control mechanisms required for smooth and accurate, rapid limb movements. Biomechanically speaking, tendon excursions are over-determined because the rotation of few joints determines the lengths and velocities of many muscles. But how different are the muscle velocity profiles induced by various, equally valid hand trajectories? We used an 18-muscle sagittal-plane arm model to calculate 100,000 feasible shoulder, elbow, and wrist joint rotations that produced valid basketball free throws with different hand trajectories, but identical initial and final hand positions and velocities. We found large differences in the eccentric and concentric muscle velocity profiles across many trajectories; even among similar trajectories. These differences have important consequences to their neural control because each trajectory will require unique, time-sensitive reflex modulation strategies. As Sherrington mentioned a century ago, failure to appropriately silence the stretch reflex of any one eccentrically contracting muscle will disrupt movement. Thus, trajectories that produce faster or more variable eccentric contractions will require more precise timing of reflex modulation across motoneuron pools; resulting in higher sensitivity to time delays, muscle mechanics, excitation/contraction dynamics, noise, errors and perturbations. By combining fundamental concepts of biomechanics and neuroscience, we propose that kinematic and muscle redundancy are, in fact, severely limited by the need to regulate reflex mechanisms in a task-specific and time-critical way. This in turn has important consequences to the learning and execution of accurate, smooth and repeatable movements—and to the rehabilitation of everyday limb movements in developmental and neurological conditions, and stroke.     

Pattern generating and reflex-like processes controlling aiming movements in the presence of inertia,damping and gravity

A model is proposed, in which goal-directed movements of the forearm are controlled by a central pattern generator (CPG) initiated for exactly one period, and by reflex-analogous processes. Movement width is proportional to the amplitude factor of the CPG's output, and to the square of the CPG's period length. The period duration can be freely selected, thus enabling the CPG to accommodate its time scale to the period of others CPG's. Parameters which influence movement accuracy can be adjusted by means of closed control loop, which are discrete with respect to time: The time unit corresponds to the period of the CPG. For instance, momentum adjustment balances the CPG in such a manner that the velocity of the arm becomes zero on termination of the period, while gain adjustment serves to attain a correct movement length in the presence of an inertial load. Friction, stiffness and gravitational force are neutralized by additional reflex-type processes, interpretable as positive feedback loops with adjustable gain factors, using position and velocity signals.     

Mutual influences of upper and lower extrimities during cyclic movements

The possibility of muscle activation of passive arm during its cyclic movements, imposed by active movements of contralateral arm or by experimenter was studied, as well as the influence of lower extremities cyclic movements onto arm muscles activity. In addition to that the activity of legs muscles was estimated in dependence on motor task condition for arms. Ten healthy supine subjects carried out opposite movements of arms with and without stepping-like movements of both legs. The experiment included three conditions for arm movements: 1) the active movements of both arms; 2) the active movements of one arm, when other entirely passive arm participated in the movement by force; 3) passive arm movement caused by experimenter. In the condition 2) additional load on active arm was applied (30 N and 60 N). In all three conditions the experiment was carried out with arms movements only or together with legs movements. The capability of passive moving arm muscles activation depended on increasing afferent inflow from muscles of contralateral arm was demonstrated. Emerging electrical activity was modulated in the arms movements cycle and depended on the degree of active arm loading. During combined active movements of arms and legs the reduction of activity in the flexor muscles of shoulder and forearm was observed. Concomitant arms movements increased the magnitude ofelectromiographic bursts during passive stepping-like movements in the most of recorded muscles, and the same increasing was only observed in biceps femoris and tibialis anterior muscles during active legs movement. The increasing of loading of one arm caused essential augmentation of EMG-activity in the majority of recording legs muscles. The data obtained are the additional proof of existence of functionally significant neuronal interaction both between arms and between upper and lower extremities, which is evidently depend on the intraspinal neuronal connections.     

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.     

Biomechanics of a muscular hydrostat: a model of lapping by a reptilian tongue

We have developed a quantitative model of an example of a muscular hydrostat, a reptilian tongue, and have used this model to study a functional movement, protrusion and retrusion, a form of lapping. The model tongue consists of a longitudinal muscle that shortens the tongue when it contracts, and a circumferential muscle wrapped around the longitudinal muscle that lengthens the tongue when it contracts. The anatomy of the model tongue and the pattern of activation of its muscles are based on studies of the tongue of the lizard Tupinambis nigropunctatus (Smith 1984). The mechanics of pressure vessels were used to derive a relationship between the forces in the two muscles. Muscle force production was modelled as the product of length/tension properties, force/velocity properties, and activation due to neural inputs (incorporating both recruitment and firing period). Passive forces were modeled as a force in parallel with the longitudinal muscle. Muscle activation dynamics were modeled as a first order low pass filter. When the model tongue is short, the two muscles can lengthen or shorten it with comparable forces, but as it lengthens, the force that the circumferential muscle can exert drops precipitously. When the tongue is long, it can neither be very stiff, nor can it generate much force. The model also reproduces the kinematics of lapping movements actually observed in Tupinambis.     

Effect of Tendon Vibration on Hemiparetic Arm Stability in Unstable Workspaces

Sensory stimulation of wrist musculature can enhance stability in the proximal arm and may be a useful therapy aimed at improving arm control post-stroke. Specifically, our prior research indicates tendon vibration can enhance stability during point-to-point arm movements and in tracking tasks. The goal of the present study was to investigate the influence of forearm tendon vibration on endpoint stability, measured at the hand, immediately following forward arm movements in an unstable environment. Both proximal and distal workspaces were tested. Ten hemiparetic stroke subjects and 5 healthy controls made forward arm movements while grasping the handle of a two-joint robotic arm. At the end of each movement, the robot applied destabilizing forces. During some trials, 70 Hz vibration was applied to the forearm flexor muscle tendons. 70 Hz was used as the stimulus frequency as it lies within the range of optimal frequencies that activate the muscle spindles at the highest response rate. Endpoint position, velocity, muscle activity and grip force data were compared before, during and after vibration. Stability at the endpoint was quantified as the magnitude of oscillation about the target position, calculated from the power of the tangential velocity data. Prior to vibration, subjects produced unstable, oscillating hand movements about the target location due to the applied force field. Stability increased during vibration, as evidenced by decreased oscillation in hand tangential velocity.     

Abnormalities of mutual influences of the upper and lower limbs after a stroke

The common pattern of muscle activation and specifics of interlimb neuronal connections during the performance of rhythmic separate and simultaneous arm and leg movements in the lying position in healthy subjects, which reflected functionally significant interlimb neuronal interactions, were shown. The study was designed to investigate these mutual influences of the upper and lower limbs during the performance of similar motor tasks by stroke patients. Sixteen poststroke patients with different degrees of hemiparesis performed active and passive arm movements simultaneously with stepping leg movements or without them while lying supine. It was demonstrated that the patients had a disordered common pattern of distribution of muscle activity when they performed voluntary cyclic movements with both arms. Passive movements of both paretic and nonparetic arms led to different degrees of activation of their muscles, depending on the degree of paresis: in patients with mild paresis, muscle activation was similar to that in healthy subjects; in patients with severe paresis, it was insignificant. The loading of the nonparetic arm resulted in an increase in the activity in the paretic arm shoulder flexor muscles in patients with mild paresis (which was typical of healthy subjects), while loading did not influence significantly patients with severe paresis. The combination of cyclic arm movements and stepping leg movements in diagonal synergy decreased the activity in the proximal muscles of both arms, irrespective of the degree of paresis, as it was observed in healthy subjects. Simultaneous arm and leg movements did not change the muscle activity in nonparetic legs in either groups of patients, but the activity in the paretic leg muscles even decreased. The results obtained revealed important features of poststroke motor disturbances, which caused changes in interlimb interactions and largely depended on the degree of paresis. The data could be useful for developing new methods for the performance of rehabilitative procedures in poststroke patients.     

Virtual musculo-skeletal model for the biomechanical analysis of the upper limb

In this paper, a musculo-skeletal model of the upper limb is presented. The limb is modelled as a three-dimensional 7 degrees-of-freedom system, linked to the shoulder, which has been considered as frame. The upper limb model is made up of four links corresponding to the most important body segments: the humerus, the ulna, the radius and the hand, considered as a single rigid body. Particular attention has been paid to the modelling of joints in order to mimic all the possible arm and forearm movements (including prono-supination). The model also includes 24 muscles. The mathematical model used to describe the muscles is that proposed by Zajac in 1989, modified by the authors. The kinematic analysis has been performed including an ergonomics index to take into account the posture and joint physical limits. Moreover an optimization criterion based on minimum activation pattern has been included in order to find muscular activation coefficients. The results of the proposed methodology concerning muscular activations have been compared to those coming from processed EMG signals, which have been acquired during experimental tests.