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Results for “equilibrium-point hypothesis”

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At least 19 recordsLinked to original sources

PubMed1992

Independent control of joint stiffness in the framework of the equilibrium-point hypothesis.

In the framework of the equilibrium-point hypothesis, virtual trajectories and joint stiffness patterns have been reconstructed during two motor tasks practiced against a constant bias torque. One task required a voluntary increase in joint stiffness while preserving the original joint position. The other task involved fast elbow flexions over 36 degrees. Joint stiffness gradually subsided after the termination of fast movements. In both tasks, the external torque could slowly and unexpectedly change. The subjects were required not to change their motor commands if the torque changed, i.e. "to do the same no matter what the motor did". In both tasks, changes in joint stiffness were accompanied by unchanged virtual trajectories that were also independent of the absolute value of the bias torque. By contrast, the intercept of the joint compliant characteristic with the angle axis, r(t)-function, has demonstrated a clear dependence upon both the level of coactivation and external load. We assume that a template virtual trajectory is generated at a certain level of the motor hierarchy and is later scaled taking into account some commonly changing dynamic factors of the movement execution, for example, external load. The scaling leads to the generation of commands to the segmental structures that can be expressed, according to the equilibrium-point hypothesis, as changes in the thresholds of the tonic stretch reflex for corresponding muscles.

Adult↗

PubMed1998

Recent tests of the equilibrium-point hypothesis (lambda model).

The lambda model of the equilibrium-point hypothesis (Feldman & Levin, 1995) is an approach to motor control which, like physics, is based on a logical system coordinating empirical data. The model has gone through an interesting period. On one hand, several nontrivial predictions of the model have been successfully verified in recent studies. In addition, the explanatory and predictive capacity of the model has been enhanced by its extension to multimuscle and multijoint systems. On the other hand, claims have recently appeared suggesting that the model should be abandoned. The present paper focuses on these claims and concludes that they are unfounded. Much of the experimental data that have been used to reject the model are actually consistent with it.

Electromyography↗

PubMed1994

Abnormal motor patterns in the framework of the equilibrium-point hypothesis: a cause for dystonic movements?

Until now, the equilibrium-point hypothesis (lambda model) of motor control has assumed nonintersecting force-length characteristics of the tonic stretch reflex for individual muscles. Limited data from animal experiments suggest, however, that such intersections may occur. We have assumed the possibility of intersection of the characteristics of the tonic stretch reflex and performed a computer simulation of movement trajectories and electromyographic patterns. The simulation has demonstrated, in particular, that a transient change in the slope of the characteristic of an agonist muscle may lead to temporary movement reversals, hesitations, oscillations, and multiple electromyographic bursts that are typical of movements of patients with dystonia. The movement patterns of three patients with idiopathic dystonia during attempts at fast single-joint movements (in the elbow, wrist, and ankle) were recorded and compared with the results of the computer simulation. This approach considers that motor disorders in dystonia result from faulty control patterns that may not correlate with any morphological or neurophysiological changes. It provides a basis for the high variability of dystonic movements. The uniqueness of abnormal motor patterns in dystonia, that precludes statistical analysis across patients, may result from subtle differences in the patterns of intersecting characteristics of the tonic stretch reflex. The applicability of our analysis to disordered multijoint movement patterns is discussed.

Adult↗

PubMed1985

Isometric torque-angle relationship and movement-related activity of human elbow flexors: implications for the equilibrium-point hypothesis.

Since the moment arms for the elbow-flexor muscles are longest at intermediate positions of the elbow and shorter at the extremes of the range of motion, it was expected that the elbow torque would also show a peak at an intermediate angle provided the activity of the flexor muscles remained constant. We measured the isometric elbow torque at different elbow angles while the subject attempted to keep constant the electromyographic activity (EMG) of the brachioradialis muscle. The torque-angle relationship thus obtained exhibited a peak, as expected, but the shape of the relationship varied widely among subjects. This was due in part to differences in the variation of the biceps brachii EMG with elbow angle among the different subjects. The implications of these observations for the equilibrium-point hypothesis of movement were investigated as follows. The subject performed elbow movements in the presence of an external torque (which tended to extend the elbow joint) provided by a weight-and-pulley arrangement. We found in the case of flexion movements that invariably there was a transient increase in flexor EMG, as would seem necessary for initiating the movement. However, the steady-state EMG after the movement could be greater or less than the pre-movement EMG. Specifically, the least flexor EMG was required for equilibrium in the intermediate range of elbow angles, compared to the extremes of the range of motion. The EMG-angle relationship, however, varied with the muscle and the subject. The observation that the directions of change in the transient and the steady-state EMG are independent of each other militates against the generality of the equilibrium-point hypothesis. However, a form of the hypothesis which includes the effects of the stretch reflex is not contradicted by this observation.

Arm↗

PubMed1998

Rejecting the equilibrium-point hypothesis.

The lambda version of the equilibrium-point (EP) hypothesis as developed by Feldman and colleagues has been widely used and cited with insufficient critical understanding. This article offers a small antidote to that lack. First, the hypothesis implicitly, unrealistically assumes identical transformations of lambda into muscle tension for antagonist muscles. Without that assumption, its definitions of command variables R, C, and lambda are incompatible and an EP is not defined exclusively by R nor is it unaffected by C. Second, the model assumes unrealistic and unphysiological parameters for the damping properties of the muscles and reflexes. Finally, the theory lacks rules for two of its three command variables. A theory of movement should offer insight into why we make movements the way we do and why we activate muscles in particular patterns. The EP hypothesis offers no unique ideas that are helpful in addressing either of these questions.

Humans↗

PubMed1996

Equilibrium-point control hypothesis examined by measured arm stiffness during multijoint movement.

For the last 20 years, it has been hypothesized that well-coordinated, multijoint movements are executed without complex computation by the brain, with the use of springlike muscle properties and peripheral neural feedback loops. However, it has been technically and conceptually difficult to examine this "equilibrium-point control" hypothesis directly in physiological or behavioral experiments. A high-performance manipulandum was developed and used here to measure human arm stiffness, the magnitude of which during multijoint movement is important for this hypothesis. Here, the equilibrium-point trajectory was estimated from the measured stiffness, the actual trajectory, and the generated torque. Its velocity profile differed from that of the actual trajectory. These results argue against the hypothesis that the brain sends as a motor command only an equilibrium-point trajectory similar to the actual trajectory.

Adult↗

PubMed1994

Reconstruction of equilibrium trajectories and joint stiffness patterns during single-joint voluntary movements under different instructions.

A method for reconstructing joint compliant characteristics during voluntary movements was applied to the analysis of oscillatory and unidirectional elbow flexion movements. In different series, the subjects were given one of the following instructions: (1) do not intervene voluntarily; (2) keep the trajectory; (3) in cases of perturbations, return back to the starting position as quickly as possible (only during unidirectional movements). Under the instruction 'keep trajectory', the apparent joint stiffness increased by 50% to 250%. During oscillatory movements, this was accompanied by a decrease in the maximal difference between the actual and equilibrium joint trajectories and, in several cases, led to a change in the phase relation between the two trajectories. The coefficients of correlation between joint torque and angle were very high (commonly, over 0.9) under the 'do not intervene' instruction. They dropped to about 0.6 under the 'keep trajectory' and to about 0.3 under the 'return back' instructions. Under these two instructions, the low values of the coefficients of correlation did not allow reconstruction of segments of equilibrium trajectories and joint stiffness values in all the subjects. The results provide further support for the lambda-version of the equilibrium-point hypothesis and for using the instruction 'do not intervene voluntarily' to obtain reproducible time patterns of the central motor command.

Behavioral Sciences↗

PubMed1994

The effects of practice on movement distance and final position reproduction: implications for the equilibrium-point control of movements.

Predictions of two views on single-joint motor control, namely programming of muscle force patterns and equilibrium-point control, were compared with the results of experiments with reproduction of movement distance and final location during fast unidirectional elbow flexions. Two groups of subjects were tested. The first group practiced movements over a fixed distance (36 degrees), starting from seven different initial positions (distance group, DG). The second group practiced movements from the same seven initial positions to a fixed final location (location group, LG). Later, all the subjects were tested at the practiced task with their eyes closed, and then, unexpectedly for the subjects, they were tested at the other, unpracticed task. In both groups, the task to reproduce final position had lower indices of final position variability than the task to reproduce movement distance. Analysis of the linear regression lines between initial position and final position (or movement distance) also demonstrated a better (more accurate) performance during final position reproduction than during distance reproduction. The data are in a good correspondence with the predictions of the equilibrium-point hypothesis, but not with the predictions of the force-pattern control approach.

Adult↗

PubMed1994

Control of fast elbow movement: a study of electromyographic patterns during movements against unexpectedly decreased inertial load.

Predictions of three models of single-joint motor control were compared with experimental observations of the changes in electromyographic (EMG) patterns during fast voluntary movements against an unexpectedly reduced inertial load. The subjects performed elbow flexions over 40 degrees "as fast as possible" in two series. During the first series, an approximately 40% decrease in inertia, simulated by a torque-motor, might occur unpredictably on half of the trials (unloaded trials). During the second series, all the trials were unloaded. The major findings are: (1) no differences in the antagonist burst latency in unexpectedly unloaded and unperturbed trials; (2) a decrease in the antagonist latency during expected unloadings; (3) a small, statistically non significant decrease in the first agonist burst EMG integral; and (4) a larger, statistically significant increase in the antagonist burst EMG integral in unexpectedly unloaded trials as compared to unperturbed trials. The data are in good correspondence with a version of the equilibrium-point hypothesis that assumes central programming of the beginning of the antagonist burst and incorporates the possibility of reflex-induced changes in EMG amplitudes.

Acceleration↗

PubMed1992

Reciprocal and coactivation commands for fast wrist movements.

According to the equilibrium-point hypothesis, movements are produced by means of displacement of the invariant torque/angle characteristic (IC) of the joint and change in its slope. Displacement is produced via the central reciprocal (R) command while the coactivation (C) command specifies the slope of the IC. Neurophysiologically, the R command is associated with reciprocal changes in the membrane potentials of agonist and antagonist motoneurons while the C command is associated with their simultaneous depolarisation. These commands were investigated in single joint wrist movements by perturbation methods. Subjects normally made free flexion movements to a target at 30 degrees but on random trials they were either opposed by a spring-like load or assisted by a load. The former was generated using negative linear position feedback; the latter using positive position feedback to a torque motor. Subjects were instructed not to correct errors arising from perturbations. Both peak velocity and EMG patterns were strongly affected by load conditions. Subjects undershot or overshot the target when opposing or assisting loads were presented, respectively. However, after removing the load (700 ms later), the target position was regained indicating that the IC was stable despite the perturbation. In two other experiments, subjects initially trained to reach the target with opposing or assisting loads, while on random trials, the load was not presented. Depending on training conditions, the subject shifted the IC by different amounts. The slope of the IC varied independently of the magnitude of its positional shift. We conclude that R and C commands can be specified independently.(ABSTRACT TRUNCATED AT 250 WORDS)

Adult↗

PubMed1992

Effects of practice on final position reproduction.

Three subjects practiced fast, accurate 36 degrees elbow flexion movements to a 2.5 degrees target for 14 sessions of 100 trials (total, 1400 trials). Subjects then returned for a 15th experimental session in which they were asked to perform 15 movements under identical conditions to the practice condition. They were then tested under three experimental conditions without visual feedback: (1) identical to the practice conditions, (2) with small shifts in starting position (+/- 3 degrees of the practiced starting position), that were insufficient for subjective discrimination and, therefore, subjects were instructed to repeat the practiced movements; and (3) with a large shift in starting position (range, +/- 15 degrees of the practiced starting position), under the instruction to move to the same target. Experimental conditions 2 and 3 demonstrated that shifts in starting position were partially correlated with shifts in final position. These results are interpreted from the point of view of the equilibrium-point hypothesis of motor control.

Adult↗

PubMed1996

On the role of recurrent inhibitory feedback in motor control.

This article reviews presumed roles of recurrent inhibition in motor control, that have been proposed over the past five decades. The discussion is structured in an order of increasing complexity. It starts out with the simplest and earliest circuit, that is recurrent self-inhibition of skeleto-motoneurons, and related functions. It soon becomes clear that in order to understand recurrent inhibition, we must look beyond the simple self-inhibitory CNS circuit. First, recurrent inhibition must be seen in the context of other neural circuits. Second, some quantitative features appear to be correlated with features of the neuromusculo-skeletal periphery. Third, the aspect of lateral inhibition between different members of a motoneuron pool as well as between different motoneuron pools points to the essential multiple input-multiple output structure of recurrent inhibition that again can be understood only by correlating it with features of the neuromusculo-skeletal periphery. Another extension results from the discovery that recurrent inhibition affects not only skeleto-motoneurons, but also gamma-motoneurons, Ia inhibitory interneurons mediating reciprocal inhibition between antagonist motoneurons, other Renshaw cells and cells of origin of the ventral spinocerebellar tract (VSCT). Then the view broadens again, investigating the potential role that recurrent inhibition plays in two far-ranging theories of motor control, the inverse-dynamics approach and the equilibrium-point hypothesis. Finally, the present author tries to formulate, in broad strokes, a personal functional interpretation of recurrent inhibition. All the functional considerations, right or wrong, should yield ideas for new experiments, and this then is the last objective of this review.

Animals↗

PubMed1991

Reconstruction of shifting elbow joint compliant characteristics during fast and slow movements.

The purpose of this study was to experimentally investigate the applicability of the equilibrium-point hypothesis to the dynamics of single-joint movements. Subjects were trained to perform relatively slow (movement time 600-1000 ms) or fast (movement time 200-300 ms) single-joint elbow flexion movements against a constant extending torque bias. They were instructed to reproduce the same time pattern of central motor command for a series of movements when the external torque could slowly and unpredictably increase, decrease, or remain constant. For fast movements, the total muscle torque was calculated as a sum of external and inertial components. Analysis of the data allowed reconstruction of the elbow joint compliant characteristics at different times during execution of the learned motor command. "Virtual" trajectories of the movements, representing time-varying changes in a central control parameter, were reconstructed and compared with the "actual" trajectories. For slow movements, the actual trajectories lagged behind the virtual ones. There were no consistent changes in the joint stiffness during slow movements. Similar analysis of experiments without voluntary movements demonstrated a lack of changes in the central parameters, supporting the assumption that the subjects were able to keep the same central motor command in spite of externally imposed unexpected torque perturbations. For the fast movements, the virtual trajectories were N-shaped, and the joint stiffness demonstrated a considerable increase near the middle of the movement. These findings contradict an hypothesis of monotonic joint compliant characteristic translation at a nearly constant rate during such movements.

Adult↗

PubMed1992

Virtual trajectories, joint stiffness, and changes in the limb natural frequency during single-joint oscillatory movements.

In the framework of the equilibrium-point hypothesis, virtual trajectories and patterns of joint stiffness were reconstructed during voluntary single-joint oscillatory movements in the elbow joint at a variety of frequencies and against two inertial loads. At low frequencies, virtual trajectories were in-phase with the actual joint trajectories. Joint stiffness changed at a doubled frequency. An increase in movement frequency and/or inertial load led to an increase in the difference between the peaks of the actual and virtual trajectories and in both peak and averaged values of joint stiffness. At a certain, critical frequency, virtual trajectory was nearly flat. Further increase in movement frequency led to a 180 degree phase shift between the actual and virtual trajectories. The assessed values of the natural frequency of the system "limb + manipulandum" were close to the critical frequencies for both low and high inertial loads. Peak levels and integrals of the electromyograms of two flexor and two extensor muscles changed monotonically with movement frequency without any special behavior at the critical frequencies. Nearly flat virtual trajectories at the natural frequency make physical sense as hypothetical control signals, unlike the electromyographic recordings, since a system at its natural frequency requires minimal central interference. Modulation of joint stiffness is assumed to be an important adaptive mechanism attenuating difference between the system's natural frequency and desired movement frequency. Virtual trajectory is considered a behavioral observable. Phase transitions between the virtual and actual trajectories are illustrations of behavioral discontinuities introduced by slow changes in a higher level control parameter, movement frequency. Relative phase shift between these two trajectories may be considered an order parameter.

Adult↗

PubMed1997

Control processes underlying elbow flexion movements may be independent of kinematic and electromyographic patterns: experimental study and modelling.

Using a non-linear dynamic model based on the lambda version of the equilibrium-point hypothesis, we investigated the shape and duration of the control patterns underlying discrete elbow movements. The model incorporates neural control variables, time-, position- and velocity-dependent intrinsic muscle and reflex properties. Two control variables (R and C) specify a positional frame of reference for activation of flexor and extensor motoneurons. The variable R (reciprocal command) specifies the referent joint angle (R) at which the transition of net flexor to extensor active torque or vice versa can be observed during changes in the actual joint angle elicited by an external force. The variable C (coactivation command) surrounds the transition angle by an angular range in which flexor and extensor muscles may be simultaneously active (if C > 0) or silent (if C < or = 0). An additional, time-dimensional control variable (mu command) influences the dependency of the threshold of the stretch reflex on movement velocity. This control variable is responsible for the reflex damping. Changes in the R command result in shifts in the equilibrium state of the system, a dynamical process leading to electromyographic modifications and movement production. Commands C and mu provide movement stability and effective energy dissipation preventing oscillations at the end of movement. A comparison of empirical and model data was carried out. A monotonic ramp-shaped pattern of the R command can account for the empirical kinematic and electromyographic patterns of the fastest elbow flexion movements made with or without additional inertia, as well as of self-paced movements. The rate of the shifts used in simulation was different for the three types of movements but independent of movement distance (20-80 degrees). This implies that, for a given type of movement, the distance is encoded by the duration of shift in the equilibrium state. The model also reproduces the kinematic and electromyographic patterns of the fastest uncorrected movements opposed in random trials by a high load (80-90% of the maximal) generated by position feedback to a torque motor. The following perturbation effects were simulated: a substantial decrease in the arm displacement (from 60-70 degrees to 5-15 degrees) and movement duration (to about 100 ms) so that these movements ended near the peak velocity of those which were not perturbed; a prolongation of the first agonist electromyographic burst as long as the load was applied; the suppression of the antagonist burst during the dynamic and static phases of movements: the reappearance of the antagonist burst in response to unloading accompanied by a short-latency suppression of agonist activity. These kinematic and electromyographic features of both perturbed and non-perturbed movements were reproduced by using the same control patterns which elicited a monotonic shift in the equilibrium state of the system ending before the peak velocity of non-perturbed movements. Our results suggest that the neural control processes underlying the fastest unopposed changes in the arm position are completed long before the end of the movement and phasic electromyographic activity. Neither the timing nor the amplitude of electromyographic bursts are planned but rather they represent the long-lasting dynamic response of central, reflex and mechanical components of the system to a monotonic, short-duration shift in the system's equilibrium state.

Adult↗

PubMed1998

Are complex control signals required for human arm movement?

It has been proposed that the control signals underlying voluntary human arm movement have a "complex" nonmonotonic time-varying form, and a number of empirical findings have been offered in support of this idea. In this paper, we address three such findings using a model of two-joint arm motion based on the lambda version of the equilibrium-point hypothesis. The model includes six one- and two-joint muscles, reflexes, modeled control signals, muscle properties, and limb dynamics. First, we address the claim that "complex" equilibrium trajectories are required to account for nonmonotonic joint impedance patterns observed during multijoint movement. Using constant-rate shifts in the neurally specified equilibrium of the limb and constant cocontraction commands, we obtain patterns of predicted joint stiffness during simulated multijoint movements that match the nonmonotonic patterns reported empirically. We then use the algorithm proposed by Gomi and Kawato to compute a hypothetical equilibrium trajectory from simulated stiffness, viscosity, and limb kinematics. Like that reported by Gomi and Kawato, the resulting trajectory was nonmonotonic, first leading then lagging the position of the limb. Second, we address the claim that high levels of stiffness are required to generate rapid single-joint movements when simple equilibrium shifts are used. We compare empirical measurements of stiffness during rapid single-joint movements with the predicted stiffness of movements generated using constant-rate equilibrium shifts and constant cocontraction commands. Single-joint movements are simulated at a number of speeds, and the procedure used by Bennett to estimate stiffness is followed. We show that when the magnitude of the cocontraction command is scaled in proportion to movement speed, simulated joint stiffness varies with movement speed in a manner comparable with that reported by Bennett. Third, we address the related claim that nonmonotonic equilibrium shifts are required to generate rapid single-joint movements. Using constant-rate equilibrium shifts and constant cocontraction commands, rapid single-joint movements are simulated in the presence of external torques. We use the procedure reported by Latash and Gottlieb to compute hypothetical equilibrium trajectories from simulated torque and angle measurements during movement. As in Latash and Gottlieb, a nonmonotonic function is obtained even though the control signals used in the simulations are constant-rate changes in the equilibrium position of the limb. Differences between the "simple" equilibrium trajectory proposed in the present paper and those that are derived from the procedures used by Gomi and Kawato and Latash and Gottlieb arise from their use of simplified models of force generation.

Arm↗

PubMedDate not supplied

[Hypothesis on the equilibrium point and variability of amplitude, speed and time of single-joint movement].

Problems of single-joint movement variability are analysed in the framework of the equilibrium-point hypothesis (the lambda-model). Control of the movements is described with three parameters related to movement amplitude speed, and time. Three strategies emerge from this description. Only one of them is likely to lead to a Fitts' type speed-accuracy trade-off. Experiments were performed to test one of the predictions of the model. Subjects performed identical sets of single-joint fast movements with open or closed eyes and some-what different instructions. Movements performed with closed eyes were characterized with higher peak speeds and unchanged variability in seeming violation of the Fitt's law and in a good correspondence to the model.

Humans↗

PubMed1995

Paradoxical effects of practice of fast single-joint movements.

We studied the effects of extensive practice of fast, unidirectional, single-joint elbow flexions against a small extending torque bias upon the kinematic and electromyographic (EMG) characteristics of the movements as well as upon the reconstructed hypothetical control patterns (equilibrium trajectories). The subjects were tested at different distances, both with and without the bias torque prior to and after the practice sessions. The basic finding was paradoxical: The subjects did not improve their performance at the practiced task (against the bias) and at other distances in the same condition; however, they showed an increase in movement speed and a decrease in movement time at all distances in unpracticed conditions (without the bias). Changes in the EMG patterns were similar in both conditions. We hypothesize that the principle of learning the dynamics of interaction with the experimental setup in combination with a very steep learning curve form the basis for the observed paradoxical effects of practice. The equilibrium-point hypothesis of movement control provides the least controversial description of these effects as compared to the force-control and EMG-control approaches.

Adult↗