An equilibrium-point model for fast, single-joint movement: I. Emergence of strategy-dependent EMG patterns

We describe a model for the regulation of fast, single-joint movements, based on the equilibrium-point hypothesis. Limb movement follows constant rate shifts of independently regulated neuromuscular variables. The independently regulated variables are tentatively identified as thresholds of a length sensitive reflex for each of the participating muscles. We use the model to predict EMG patterns associated with changes in the conditions of movement execution, specifically, changes in movement times, velocities, amplitudes, and moments of limb inertia. The approach provides a theoretical neural framework for the dual-strategy hypothesis, which considers certain movements to be results of one of two basic, speed-sensitive or speed-insensitive strategies. This model is advanced as an alternative to pattern-imposing models based on explicit regulation of timing and amplitudes of signals that are explicitly manifest in the EMG patterns.     

Control of Trajectory Modifications in Target-Directed Reaching

Human reaching movements to fixed and displaced visual targets were recorded and compared with simulated movements generated by using a two-joint arm model based on the equilibrium-point (EP) hypothesis (lambda model) of motor control (Feldman, 1986). The aim was to investigate the form of central control signals underlying these movements. According to this hypothesis, movements result from changes in control variables that shift the equilibrium position (EP) of the arm. At any time, muscle activations and forces will depend on the difference between the arm's EP and its actual position and on the limb's velocity. In this article, we suggest that the direction of EP shift in reaching is specified at the hand level, whereas the rate of EP shift may be specified at the hand or joint level. A common mechanism underlying reaching to fixed and displaced targets is proposed whereby the EP of the hand shifts in a straight line toward the present target. After the target is displaced, the direction of the hand EP shift is modified toward the second target. The results suggest that the rate of shift of the hand EP may be modified for movements in different parts of the work space. The model, with control signals that vary in a simple fashion over time, is able to generate the kinematic patterns observed empirically.     

Control of Trajectory Modifications in Target-Directed Reaching

Human reaching movements to fixed and displaced visual targets were recorded and compared with simulated movements generated by using a two-joint arm model based on the equilibrium-point (EP) hypothesis (λ model) of motor control (Feldman, 1986). The aim was to investigate the form of central control signals underlying these movements. According to this hypothesis, movements result from changes in control variables that shift the equilibrium position (EP) of the arm. At any time, muscle activations and forces will depend on the difference between the arm's EP and its actual position and on the limb's velocity. In this article, we suggest that the direction of EP shift in reaching is specified at the hand level, whereas the rate of EP shift may be specified at the hand or joint level. A common mechanism underlying reaching to fixed and displaced targets is proposed whereby the EP of the hand shifts in a straight line toward the present target. After the target is displaced, the direction of the hand EP shift is modified toward the second target. The results suggest that the rate of shift of the hand EP may be modified for movements in different parts of the work space. The model, with control signals that vary in a simple fashion over time, is able to generate the kinematic patterns observed empirically.     

Changes in Movement Symmetry Associated With Strengthening and Fatigue of Agonist and Antagonist Muscles

The hypothesis that strengthening or fatiguing procedures applied on active muscles can affect the symmetry of rapid, discrete movements was tested. Subjects (N = 12) performed rapid, consecutive elbow flexions and extensions between 2 targets before and after (a) applying a strength training program, (b) fatiguing elbow flexors, and (c) fatiguing elbow extensors. The results demonstrated that an increase in strength of elbow extensors caused by applied strength training is associated with an increase in the symmetry ratio (i.e., acceleration time divided by deceleration time) of elbow flexion movements. The symmetry ratio also increased and decreased in movements when agonists and antagonists were fatigued, respectively. Because the strength training and fatiguing procedures are both known to affect muscle force, the data are interpreted as changes in muscles' ability to exert the force while acting as agonists or antagonists. Namely, muscles need equal impulses of force (torque multiplied by time) to accelerate and, thereafter, to decelerate the limb while performing a rapid, discrete movement. The symmetry ratio may therefore be changed so that more time will be provided for muscles that become relatively weaker (compared with their antagonists) because a strengthening or fatiguing procedure has been applied, whereas a shorter time period should be sufficient for action of their stronger antagonists. Although, in the literature, the studied phenomenon has been discussed as a predominantly motor control phenomenon, the present data suggest that the movement symmetry could also be related to agonists' and antagonists' ability to exert force, particularly while performing rapid, discrete movements.     

Changes in movement symmetry associated with strengthening and fatigue of agonist and antagonist muscles

The hypothesis that strengthening or fatiguing procedures applied on active muscles can affect the symmetry of rapid, discrete movements was tested. Subjects (N = 12) performed rapid, consecutive elbow flexions and extensions between 2 targets before and after (a) applying a strength training program, (b) fatiguing elbow flexors, and (c) fatiguing elbow extensors. The results demonstrated that an increase in strength of elbow extensors caused by applied strength training is associated with an increase in the symmetry ratio (i.e., acceleration time divided by deceleration time) of elbow flexion movements. The symmetry ratio also increased and decreased in movements when agonists and antagonists were fatigued, respectively. Because the strength training and fatiguing procedures are both known to affect muscle force, the data are interpreted as changes in muscles' ability to exert the force while acting as agonists or antagonists. Namely, muscles need equal impulses of force (torque multiplied by time) to accelerate and, thereafter, to decelerate the limb while performing a rapid, discrete movement. The symmetry ratio may therefore be changed so that more time will be provided for muscles that become relatively weaker (compared with their antagonists) because a strengthening or fatiguing procedure has been applied, whereas a shorter time period should be sufficient for action of their stronger antagonists. Although, in the literature, the studied phenomenon has been discussed as a predominantly motor control phenomenon, the present data suggest that the movement symmetry could also be related to agonists' and antagonists' ability to exert force, particularly while performing rapid, discrete movements.     

The effects of viscous loading of the human forearm flexors on the stability of coordination

This experiment investigated whether the stability of rhythmic unimanual movements is primarily a function of perceptual/spatial orientation or neuro-mechanical in nature. Eight participants performed rhythmic flexion and extension movements of the left wrist for 30s at a frequency of 2.25 Hz paced by an auditory metronome. Each participant performed 8 flex-on-the-beat trials and 8 extend-on-the-beat trials in one of two load conditions, loaded and unload. In the loaded condition, a servo-controlled torque motor was used to apply a small viscous load that resisted the flexion phase of the movement only. Both the amplitude and frequency of the movement generated in the loaded and unloaded conditions were statistically equivalent. However, in the loaded condition movements in which participants were required to flex-on-the-beat became less stable (more variable) while extend-on-the-beat movements remained unchanged compared with the unload condition. The small alteration in required muscle force was sufficient to result in reliable changes in movement stability even a situation where the movement kinematics were identical. These findings support the notion that muscular constraints, independent of spatial dependencies, can be sufficiently strong to reliably influence coordination in a simple unimanual task.     

An Impulse-Timing Theory for Reciprocal Control of Muscular Activity in Rapid,Discrete Movements

Much remains to be learned about how agonist and antagonist muscles are controlled during the production of rapid, voluntary movements. In an effort to summarize a wide body of existing knowledge and stimulate future research on this subject, an impulse-timing theory is presented which attempts to predict the activity of reciprocal muscles based on certain characteristics of a movement. The basic tenet of the theory is that variables of movement time, movement distance, and inertial load have fairly predictable effects on the underlying muscular activity of the agonist and antagonist muscles during the production of rapid and discrete, voluntary movements. The theory is derived from the kinematic work of Schmidt, Zelaznik, Hawkins, Frank, and Quinn (1979) and supporting evidence from studies which have used electromyographic (EMG) recordings of agonist and antagonist muscles during rapid movements. Issues related to synergistic muscle control, central and peripheral control of reciprocal muscle activity, muscle control, and neurological disorder and the relationship between impulse-timing and mass-spring control are discussed in the final section.     

An impulse-timing theory for reciprocal control of muscular activity in rapid, discrete movements

Much remains to be learned about how agonist and antagonist muscles are controlled during the production of rapid, voluntary movements. In an effort to summarize a wide body of existing knowledge and stimulate future research on this subject, an impulse-timing theory is presented which attempts to predict the activity of reciprocal muscles based on certain characteristics of a movement. The basic tenet of the theory is that variables of movement time, movement distance and inertial load have fairly predictable effects on the underlying muscular activity of the agonist and antagonist muscles during the production of rapid and discrete, voluntary movements. The theory is derived from the kinematic work of Schmidt, Zelaznik, Hawkins, Frank and Quinn (1979) and supporting evidence from studies which have used electromyographic (EMG) recordings of agonist and antagonist muscles during rapid movements. Issues related to synergistic muscle control, central and peripheral control of reciprocal muscle activity, muscle control, and neurological disorder and the relationship between impulse-timing and mass-spring control are discussed in the final section.     

Anxiety-induced changes in movement behaviour during the execution of a complex whole-body task.

We investigated the impact of anxiety on movement behaviour during the execution of a complex perceptual-motor task. Masters' (1992) conscious processing hypothesis suggests that under pressure an inward focus of attention occurs, resulting in more conscious control of the movement execution of well-learned skills. The conscious processes interfere with automatic task execution hereby inducing performance decrements. Recent empirical support for the hypothesis has focused on the effects of pressure on end performance. It has not been tested so far whether the changes in performance are also accompanied by changes in movement execution that would be expected following Masters' hypothesis. In the current study we tested the effects of anxiety on climbing movements on a climbing wall. Two identical traverses at different heights on a climbing wall provided different anxiety conditions. In line with the conscious processing hypothesis we found that anxiety had a significant effect on participants' movement behaviour evidenced by increases in climbing time and the number of explorative movements (Experiments 1 and 2) and by longer grasping of the holds and slower movements (Experiment 2). These results provide additional support for the conscious processing hypothesis and insight into the relation between anxiety, performance, and movement behaviour.     

Servo Hypotheses for the Biological Control of Movement

An analysis is made of equilibrium-point models for motor control, describing these models in the context of servo control mechanisms. We considered issues of speed and stiffness scaling that are incompatible with current formulations of the equilibrium-point models. A modification of the equilibrium-point models is proposed in which the central nervous system controls velocity as well as positions during the course of fast 1imb movements. Numerical simulations are presented that verify that such a servo control mechanism could successfully produce fast limb movements, as observed in human subjects     

Task dynamics and resource dynamics in the assembly of a coordinated rhythmic activity.

Task dynamics corresponding to rhythmic movements emerge from interactions among dynamical resources composed of the musculature, the link segments, and the nervous and circulatory systems. This article investigated whether perturbations of interlimb coordination might be effect over circulatory and nervous elements. Stiffness of wrist-pendulums oscillated at a common tempo and at 180 degrees relative phase was perturbed through the use of tonic activity about an ankle. Left and right stiffnesses, the common period, and the phase relation all changed. Stiffnesses increased with ankle torque in proportion to the wrist's inertial load. Despite different changes in stiffness at the two wrists, isochrony was preserved. The stability was shown to be consistent with the proportionality of changes in stiffness to the inertial loads. The phase departed from antiphase in proportion to the asymmetry of inertial loads. The size of departures decreased with increasing ankle torque. An account was developed in terms of muscular, circulatory, and nervous functions.     

On the Role of Visual Afferent Information for the Control of Aiming Movements Toward Targets of Different Sizes

The authors investigated (a) whether the specificity of practice hypothesis is mediated by the importance of visual afferent information for the control of manual aiming movements and (b) how movement planning and online correction processes to the movement initial impulse are affected by the withdrawal of visual information in transfer. In acquisition, participants (N = 40) aimed at targets of different sizes in a full-vision or in a target-only condition before being transferred to a target-only condition without knowledge of results. The results supported the hypothesis that learning is specific to the source or sources of afferent information that are more likely to ensure optimal performance. The results also suggested that individuals will not always use visual afferent information more extensively when aiming at a small rather than at a large target. Instead, in a temporally constrained task, the relative efficiency of visually based corrections appears to mediate how exclusively an individual will rely on online visual afferent information for movement control. Finally, the detailed kinematic analysis performed in the present study clearly indicated that online modifications to the movement primary impulse are possible, arguing for a continuous or pseudo-continuous control of relatively slow aiming movements on the basis of visual afferent input.     

On the role of visual afferent information for the control of aiming movements toward targets of different sizes

The authors investigated (a). whether the specificity of practice hypothesis is mediated by the importance of visual afferent information for the control of manual aiming movements and (b). how movement planning and online correction processes to the movement initial impulse are affected by the withdrawal of visual information in transfer. In acquisition, participants (N = 40) aimed at targets of different sizes in a full-vision or in a target-only condition before being transferred to a target-only condition without knowledge of results. The results supported the hypothesis that learning is specific to the source or sources of afferent information that are more likely to ensure optimal performance. The results also suggested that individuals will not always use visual afferent information more extensively when aiming at a small rather than at a large target. Instead, in a temporally constrained task, the relative efficiency of visually based corrections appears to mediate how exclusively an individual will rely on online visual afferent information for movement control. Finally, the detailed kinematic analysis performed in the present study clearly indicated that online modifications to the movement primary impulse are possible, arguing for a continuous or pseudo-continuous control of relatively slow aiming movements on the basis of visual afferent input.     

A Riemannian geometry theory of human movement: The geodesic synergy hypothesis

Mass-inertia loads on muscles change with posture and with changing mechanical interactions between the body and the environment. The nervous system must anticipate changing mass-inertia loads, especially during fast multi-joint coordinated movements. Riemannian geometry provides a mathematical framework for movement planning that takes these inertial interactions into account. To demonstrate this we introduce the controlled (vs. biomechanical) degrees of freedom of the body as the coordinate system for a configuration space with movements represented as trajectories. This space is not Euclidean. It is endowed at each point with a metric equal to the mass-inertia matrix of the body in that configuration. This warps the space to become Riemannian with curvature at each point determined by the differentials of the mass-inertia at that point. This curvature takes nonlinear mass-inertia interactions into account with lengths, velocities, accelerations and directions of movement trajectories all differing from those in Euclidean space. For newcomers to Riemannian geometry we develop the intuitive groundwork for a Riemannian field theory of human movement encompassing the entire body moving in gravity and in mechanical interaction with the environment. In particular we present a geodesic synergy hypothesis concerning planning of multi-joint coordinated movements to achieve goals with minimal muscular effort.     

The representation of predictive force control and internal forward models: evidence from lesion studies and brain imaging

Force control on the basis of prediction avoids time delays from sensory feedback during motor performance. Thus, self-produced loads arising from gravitational and inertial forces during object manipulation can be compensated for by simultaneous anticipatory changes in grip force. It has been suggested that internal forward models predict the consequences of our movements, so that grip force can be programmed in anticipation of movement-induced loads. The cerebellum has been proposed as the anatomical correlate of such internal models. Here, we present behavioural data from patients with cerebellar damage and data from brain imaging in healthy subjects further elucidating the role of the cerebellum in predictive force control. Patients with cerebellar damage exhibited clear deficits in the coupling between grip force and load. A positron-emission-tomography (PET) paradigm that separated the process of the grip force/load coupling from the isolated production of similar grip forces and loads was developed. Interaction and conjunction analyses revealed a strong activation peak in the ipsilateral posterior cerebellum particularly devoted to the predictive coupling between grip force and load. Both approaches clearly demonstrate that the cerebellum plays a major role in force prediction that cannot be compensated for by other sensorimotor structures in case of cerebellar disease. However, evidence suggests that also extra-cerebellar structures may significantly contribute to predictive force control: (1) grip force/load coupling may also be impaired after cerebral and peripheral sensorimotor lesions, (2) a coupling-related activation outside the cerebellum was observed in our PET study, and (3) the scaling of the grip force level and the dynamic grip force coupling are dissociable aspects of grip force control.     

A Linked Muscular Activation Model for Movement Generation and Control

A new model for movement control is presented which incorporates characteristics of impulse-variability and mass-spring models. Movements in the model were controlled with phasic torque impulses in agonist and antagonist muscles and a tonic agonist torque.

Characteristics of the phasic agonist and antagonist torque profiles were based on observed properties of movement-related EMGs and muscle isometric torques. Variability of the phasic impulses depended on impulse magnitude as in impulse-variability models. The model therefore predicted a speed-accuracy tradeoff for limb movement. The time of onset and magnitude of the antagonist torque depended on the magnitude of the preceding agonist torque as indicated in studies of movement-related EMGs. This led to the new concept of linkage between the agonist and antagonist muscle forces which was shown to be important for reducing variability of fast movements. Progressive development of linkage during practice could explain the previous findings of decreased movement variability with practice coupled with increased variability of movement-related EMGs.

It was concluded that an inherently variable motor system deals with the variability associated with generation of large muscle forces by linking the forces produced by opposing muscles. In this way, variability in net joint torques and in movements can be decreased without the need for the nervous system to closely regulate the individual torques.     

The zoom lens of attention: Simulating shuffled versus normal text reading using the SWIFT model

Assumptions on the allocation of attention during reading are crucial for theoretical models of eye guidance. The zoom lens model of attention postulates that attentional deployment can vary from a sharp focus to a broad window. The model is closely related to the foveal load hypothesis, i.e., the assumption that the perceptual span is modulated by the difficulty of the fixated word. However, these important theoretical concepts for cognitive research have not been tested quantitatively in eye movement models. Here we show that the zoom lens model, implemented in the SWIFT model of saccade generation, captures many important patterns of eye movements. We compared the model's performance to experimental data from normal and shuffled text reading. Our results demonstrate that the zoom lens of attention might be an important concept for eye movement control in reading.     

Understanding movement control in infants through the analysis of limb intersegmental dynamics

One important component in the understanding of the control of limb movements is the way in which the central nervous system accounts for joint forces and torques that may be generated not only by muscle actions but by gravity and by passive reactions related to the movements of limb segments. In this study, we asked how the neuromotor system of young infants controls a range of active and passive forces to produce a stereotypic, nonintentional movement. We specifically analyzed limb intersegmental dynamics in spontaneous, cyclic leg movements (kicking) of varying intensity in supine 3-month-old human infants. Using inverse dynamics, we calculated the contributions of active (muscular) and passive (motion-dependent and gravitational) torque components at the hip, knee, and ankle joints from three-dimensional limb kinematics. To calculate joint torques, accurate estimates were needed of the limb's anthropometric parameters, which we determined using a model of the human body. Our analysis of limb intersegmental dynamics explicitly quantified the complex interplay of active and passive forces producing the simple, involuntary kicking movements commonly seen in 3-month-old infants. our results revealed that in nonvigorous kicks, hip joint reversal was the result of an extensor torque due to gravity, opposed by the combined flexor effect of the muscle torque and the total motion-dependent torque. The total motion-dependent torque increased as a hip flexor torque in more vigorous kicks; an extensor muscle torque was necessary to counteract the flexor influences of the total motion-dependent torque and, in the case of large ranges of motion, a flexor gravity torque as well. Thus, with changing passive torque influences due to motions of the linked segments, the muscle torques were adjusted to produce a net torque to reverse the kicking motion. As a consequence, despite considerable heterogeneity in the intensity, range of motion, coordination, and movement context of each kick, smooth trajectories resulted from the muscle torque, counteracting and complementing not only gravity but also the motion-dependent torques generated by movement of the linked segments.     

Transfer of movement sequences: bigger is better

Experiment 1 was conducted to determine if proportional transfer from "small to large" scale movements is as effective as transferring from "large to small." We hypothesize that the learning of larger scale movement will require the participant to learn to manage the generation, storage, and dissipation of forces better than when practicing smaller scale movements. Thus, we predict an advantage for transfer of larger scale movements to smaller scale movements relative to transfer from smaller to larger scale movements. Experiment 2 was conducted to determine if adding a load to a smaller scale movement would enhance later transfer to a larger scale movement sequence. It was hypothesized that the added load would require the participants to consider the dynamics of the movement to a greater extent than without the load. The results replicated earlier findings of effective transfer from large to small movements, but consistent with our hypothesis, transfer was less effective from small to large (Experiment 1). However, when a load was added during acquisition transfer from small to large was enhanced even though the load was removed during the transfer test. These results are consistent with the notion that the transfer asymmetry noted in Experiment 1 was due to factors related to movement dynamics that were enhanced during practice of the larger scale movement sequence, but not during the practice of the smaller scale movement sequence. The findings that the movement structure is unaffected by transfer direction but the movement dynamics are influenced by transfer direction is consistent with hierarchal models of sequence production.     

Individuality of movements in music – Finger and body movements during playing of the flute

The achievement of mastery in playing a composition by means of a musical instrument typically requires numerous repetitions and corrections according to the keys and notations of the music piece. Nevertheless, differences in the interpretation of the same music piece by highly skilled musicians seem to be recognizable. The present study investigated differences within and between skilled flute players in their finger and body movements playing the same piece several times on the same and on different days. Six semiprofessional and four professional musicians played an excerpt of Mozart’s Flute Concerto No. 2 several times on three different days. Finger and body movements were recorded by 3D motion capture and analyzed by linear and nonlinear classification approaches. The findings showed that the discrete and continuous movement timing data correctly identified individuals up to 100% by means of their finger movements and up to 94% by means of their body movements. These robust examples of identifying individual movement patterns contradict the prevailing models of small, economic finger movements that are favored in the didactic literature for woodwind players and question traditional recommendations for teaching the learning of motor skills.