Anatol G. Feldman

Once More on the Equilibrium-Point Hypothesis (λ Model) for Motor Control

The equilibrium control hypothesis (λ model) is considered with special reference to the following concepts: (a) the length-force invariant characteristic (IC) of the muscle together with central and reflex systems subserving its activity; (b) the tonic stretch reflex threshold (λ) as an independent measure of central commands descending to alpha and gamma motoneurons; (c) the equilibrium point, defined in terms of λ, IC and static load characteristics, which is associated with the notion that posture and movement are controlled by a single mechanism; and (d) the muscle activation area (a reformulation of the “size principle”)— the area of kinematic and command variables in which a rank-ordered recruitment of motor units takes place. The model is used for the interpretation of various motor phenomena, particularly electromyographic patterns. The stretch reflex in the λ model has no mechanism to follow-up a certain muscle length prescribed by central commands. Rather, its task is to bring the system to an ...

The origin and use of positional frames of reference in motor control

A hypothesis about sensorimotor integration (the λ model) is described and applied to movement control and kinesthesia. The central idea is that the nervous system organizes positional frames of reference for the sensorimotor apparatus and produces active movements by shifting the frames in terms of spatial coordinates. Kinematic and electromyographic patterns are not programmed, but emerge from the dynamic interaction among the system s components, including external forces within the designated frame of reference. Motoneuronal threshold properties and proprioceptive inputs to motoneurons may be cardinal components of the physiological mechanism that produces positional frames of reference. The hypothesis that intentional movements are produced by shifting the frame of reference is extended to multi-muscle and multi-degrees-of-freedom systems with a solution of the redundancy problem that allows the control of a joint alone or in combination with other joints to produce any desired limb configuration and movement trajectory. The model also implies that for each motor behavior, the nervous system uses a strategy that minimizes the number of changeable control variables and keeps the parameters of these changes invariant. Examples are provided of simulated kinematic and electromyographic signals from single- and multi-joint arm movements produced by suggested patterns of control variables. Empirical support is provided and additional tests of the model are suggested. The model is contrasted with others based on the ideas of programming of motoneuronal activity, muscle forces, stiffness, or movement kinematics.

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 arms EP and its actual position and on the limbs 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.

A critical evaluation of the force control hypothesis in motor control

The ability to formulate explicit mathematical models of motor systems has played a central role in recent progress in motor control research. As a result of these modeling efforts and in particular the incorporation of concepts drawn from control systems theory, ideas about motor control have changed substantially. There is growing emphasis on motor learning and particularly on predictive or anticipatory aspects of control that are related to the neural representation of dynamics. Two ideas have become increasingly prominent in mathematical modeling of motor function—forward internal models and inverse dynamics. The notion of forward internal models which has drawn from work in adaptive control arises from the recognition that the nervous system takes account of dynamics in motion planning. Inverse dynamics, a complementary way of adjusting control signals to deal with dynamics, has proved a simple means to establish the joint torques necessary to produce desired movements. In this paper, we review the force control formulation in which inverse dynamics and forward internal models play a central role. We present evidence in its favor and describe its limitations. We note that inverse dynamics and forward models are potential solutions to general problems in motor control—how the nervous system establishes a mapping between desired movements and associated control signals, and how control signals are adjusted in the context of motor learning, dynamics and loads. However, we find little empirical evidence that specifically supports the inverse dynamics or forward internal model proposals per se. We further conclude that the central idea of the force control hypothesis—that control levels operate through the central specification of forces—is flawed. This is specifically evident in the context of attempts to incorporate physiologically realistic muscle and reflex mechanisms into the force control model. In particular, the formulation offers no means to shift between postures without triggering resistance due to postural stabilizing mechanisms.

The role of stretch reflex threshold regulation in normal and impaired motor control

Some hypotheses suggest that stretch reflex threshold regulation may be an essential element of motor control. Disturbances in this mechanism may lead to motor dysfunction. We investigated this possibility by comparing stretch reflex threshold regulation in 11 spastic hemiparetic and 6 normal subjects. Subjects sat with their arms fully supported in a forearm and hand mold attached to a manipulandum mounted on and controlled by a torque motor. They remained completely passive while their elbow was extended from 30 degrees flexion through an arc of 100 degrees. Displacement and velocity of the forearm were measured as well as EMG signals from 2 elbow flexors and 2 elbow extensors, when the elbow flexors were stretched at each of 7 velocities. Velocities ranged from 8 to 160 degrees/s for hemiparetic subjects and from 32 to 300 degrees/s for normal subjects. Phase diagrams (velocity versus angle) were plotted and the threshold angles (lambda) for muscle activation at each velocity of stretch were used to determine the static stretch reflex threshold (lambda) and the slope (mu) of the relationship between the lambda s and velocity. Our main findings were that static and dynamic stretch reflex thresholds were decreased in spastic hemiparetic compared to normal subjects and that the thresholds depended on velocity. The static threshold value correlated with the severity of clinically measured spasticity. In addition, the range of regulation of lambda was decreased in the patients compared to normal. This may explain some of the problems of force and position regulation as well as hypertonus (and weakness) common to these patients.

Testing hypotheses and the advancement of science: recent attempts to falsify the equilibrium point hypothesis

Criticisms of the equilibrium point (EP) hypothesis have recently appeared that are based on misunderstandings of some of its central notions. Starting from such interpretations of the hypothesis, incorrect predictions are made and tested. When the incorrect predictions prove false, the hypothesis is claimed to be falsified. In particular, the hypothesis has been rejected based on the wrong assumptions that it conflicts with empirically defined joint stiffness values or that it is incompatible with violations of equifinality under certain velocity-dependent perturbations. Typically, such attempts use notions describing the control of movements of artificial systems in place of physiologically relevant ones. While appreciating constructive criticisms of the EP hypothesis, we feel that incorrect interpretations have to be clarified by reiterating what the EP hypothesis does and does not predict. We conclude that the recent claims of falsifying the EP hypothesis and the calls for its replacement by EMG-force control hypothesis are unsubstantiated. The EP hypothesis goes far beyond the EMG-force control view. In particular, the former offers a resolution for the famous posture-movement paradox while the latter fails to resolve it.

Recruitment and sequencing of different degrees of freedom during pointing movements involving the trunk in healthy and hemiparetic subjects.

Abstract Previous studies have shown that in neurologically normal subjects the addition of trunk motion during a reaching task does not affect the trajectory of the arm endpoint. Typically, the trunk begins to move before the onset and continues to move after the offset of the arm endpoint displacement. This observation shows that the potential contribution of the trunk to the motion of the arm endpoint toward a target is neutralized by appropriate compensatory movements of the shoulder and elbow. We tested the hypothesis that cortical and subcortical brain lesions may disrupt the timing of trunk and arm endpoint motion in hemiparetic subjects. Eight hemiparetic and six age-matched healthy subjects were seated on a stool with the right (dominant) arm in front of them on a table. The tip of the index finger (the arm endpoint) was initially at a distance of 20 cm from the midline of the chest. Wrist, elbow, and upper body positions as well as the coordinates of the arm endpoint were recorded with a three-dimensional motion analysis system (Optotrak) by infrared light-emitting diodes placed on the tip of the finger, the styloid process of the ulna, the lateral epicondyle of the humerus, the acromion processes bilaterally, and the sternal notch. In response to a preparatory signal, subjects lifted their arm 1–2 cm above the table and in response to a ”go” signal moved their endpoint as fast as possible from a near to a far target located at a distance of 35 cm and at a 45° angle to the right or left of the sagittal midline of the trunk. After a pause (200– 500 ms) they moved the endpoint back to the near target. Pointing movements were made without trunk motion (control trials) or with a sagittal motion of the trunk produced by means of a hip flexion or extension (test trials). In one set of test trials, subjects were required to move the trunk forward while moving the arm to the target (”in-phase movements”). In the other set, subjects were required to move the trunk backward when the arm moved to the far target (”out-of-phase movements”). Compared with healthy subjects, movements in hemiparetic subjects were segmented, slower, and characterized by a greater variability and by deflection of the trajectory from a straight line. In addition, there was a moderate increase in the errors in movement direction and extent. These deficits were similar in magnitude whether or not the trunk was involved. Although hemiparetic subjects were able to compensate the influence of the trunk motion on the movement of the arm endpoint, they accomplished this by making more segmented movements than healthy subjects. In addition, they were unable to stabilize the sequence of trunk and arm endpoint movements in a set of trials. It is concluded that recruitment and sequencing of different degrees of freedom may be impaired in this population of patients. This inability may partly be responsible for other deficits observed in hemiparetic subjects, including an increase in movement segmentation and duration. The lack of stereotypic movement sequencing may imply that these subjects had deficits in learning associated with short-term memory.

Reaching in reality and virtual reality: a comparison of movement kinematics in healthy subjects and in adults with hemiparesis

BackgroundVirtual reality (VR) is an innovative tool for sensorimotor rehabilitation increasingly being employed in clinical and community settings. Despite the growing interest in VR, few studies have determined the validity of movements made in VR environments with respect to real physical environments. The goal of this study was to compare movements done in physical and virtual environments in adults with motor deficits to those in healthy individuals.MethodsThe participants were 8 healthy adults and 7 adults with mild left hemiparesis due to stroke. Kinematics of functional arm movements involving reaching, grasping and releasing made in physical and virtual environments were analyzed in two phases: 1) reaching and grasping the ball and 2) ball transport and release. The virtual environment included interaction with an object on a 2D computer screen and haptic force feedback from a virtual ball. Temporal and spatial parameters of reaching and grasping were determined for each phase.ResultsIndividuals in both groups were able to reach, grasp, transport, place and release the virtual and real ball using similar movement strategies. In healthy subjects, reaching and grasping movements in both environments were similar but these subjects used less wrist extension and more elbow extension to place the ball on the virtual vertical surface. Participants with hemiparesis made slower movements in both environments compared to healthy subjects and during transport and placing of the ball, trajectories were more curved and interjoint coordination was altered. Despite these differences, patients with hemiparesis also tended to use less wrist extension during the whole movement and more elbow extension at the end of the placing phase.ConclusionDifferences in movements made by healthy subjects in the two environments may be explained by the use of a 2D instead of a 3D virtual environment and the absence of haptic feedback from the VR target. Despite these differences, our findings suggest that both healthy subjects and individuals with motor deficits used similar movement strategies when grasping and placing a ball in the two reality conditions. This suggests that training of arm movements in VR environments may be a valid approach to the rehabilitation of patients with motor disorders.

Reciprocal and coactivation commands for fast wrist movements

SummaryAccording to the equilibriumpoint 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° 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. In addition, although kinematics and EMG are strongly dependent on peripheral conditions, the same does not appear to be the case for basic central commands (R and C).

Movement reorganization to compensate for fatigue during sawing

Peripheral (muscle) aspects of fatigue are well documented. However, little is known about the central aspects of fatigue that could influence, in particular, multijoint coordination. To investigate the central aspects of fatigue, we compared the multijoint kinematics of nonfatigued and fatigued individuals while sawing. Muscle fatigue was associated with decreases in sawing force and movement amplitude at the elbow whereas the basic characteristics of the saw trajectory, including the movement direction, extent and duration, remained invariant. This invariance was maintained by increasing the movement amplitude at the wrist, shoulder and trunk. The system thus takes advantage of the redundancy of the motor apparatus to maintain the endpoint trajectory despite fatigue.