It is argued that the equilibrium point model can lead to new insights regarding transition and stability processes in movement coordination. The role of movement control parameters on equifinality and phase-resetting is discussed; not only control but also external control parameters can affect the global dynamical regime.

The following questions are discussed: (1) Who determines the nature of “control variables”? (2) Is the “positional monopoly” healthy? (3) Does a descending command alter reflex threshold alone without eoncomitantly altering stiffness? (4) How does the CNS deal with history-dependent effects? (5) Should we abandon the idea that the CNS controls classical Newtonian variables such as muscle length?

Generation of swing phase limb trajectory over obstacles during locomotion should be a reasonable test for the λ model proposed by Feldman and Levin. The observed features such as lack of simple amplitude scaling of endpoint (toe) trajectories for different obstacle heights, complex shaped toe velocity profiles, and exploitation of passive intersegmental dynamics to control limb elevation cannot be adequately explained by the λ model.

It is proposed here that the spinal network of proprioceptive feedback from length and force receptors constitutes the mechanism underlying the coordination of activation thresholds for muscles acting about the same and neighboring joints. For the most part, these circuits come between motoneurons and supraspinal signals, invalidating the idea that the activation thresholds constitute control variables for the motor system.

The lambda model predicts that the command received by each motor nucleus during locomotion is specific for the joint at which its muscle acts and is independent of external conditions. However, investigation of the commands received by motor nuclei during fictive locomotion and of the sensitivity of these commands to feedback from the limb during locomotion indicates that neither condition is satisfied.

The experiments Feldman and Levin suggest do not definitively test their proposed solution to the problem of selecting muscle activations. Their test of the movement directions that elicit EMG activity can be interpreted without regard to the form of the central commands, and their fast elbow flexion test is based on a forward computation that obscures the insensitivity of the predicted trajectory to the details of the putative commands.

Models of central control variables (CVs) that are expressed in positional reference frames and rely on proprioception as the dominant specifier of muscle activation patterns have not yet been shown to be adequate for the description of fast, voluntary movement, even of single joints. An alternative model with illustrative data is proposed.

An alternative multi-joint extension to the lambda model is proposed. According to this extension, the activity of a muscle depends not only on the difference between lambda and length of that muscle, but also on the difference between lambda and length of other muscles. This 2-D extension can describe more neurophysiological experiments than the extension proposed in the target article.

The problem for the CNS in any particular movement task is to coordinate the various frames of reference appropriate to the task. Control variables are determined by this coordination. The coordination problem varies greatly from task to task, and so no single set of control variables is likely to account for a broad range of movement tasks.

The model identifies a spatial coordinate frame within which the sensorimotor apparatus produces movement. Its spatial nature simplifies its coupling with spatial reference frames used concurrently by vision and proprioception. While the positional reference frame addresses the performance of spatial tasks, it seems to have little to say about movements involving energy expenditure as the principle component of the task.

A key feature of the lambda model is the hypothesis of a local spring-like muscle-reflex system defined by a central control variable that has units of position. This is intriguing, especially for a study of postural stability in large-scale systems, but it has limited direct application to skilled everyday movements. If movement is considered as a goal-directed, neuro-optimization problem, however, theavailabilityof lambda-like peripheral models (vs. conventional musculoskeletal models) deserves exploration.

Three issues related to Feldman and Levin's treatment of biological variability are discussed. We question the usefulness of the indirect component of δλ. We suggest that trade-offs between speed and accuracy in aimed movements support identification of δλ, rather than λ, as a control variable. We take issue with the authors' proposal for resolving redundancy in multi-joint movements, given recent data.

Whereas the λ model provides a useful technique to describe complex movements, the focus on control variables in this model limits its potential for interpreting the activity and function of many cells in motor areas of the CNS.

Generalizing the notion that muscles are positional frames of reference, a high-dimensional muscle space is defined for multi-muscle systems with an embedded low-dimensional motor manifold of functional articulators. A central representation of such a manifold is proposed as computational body schema. The example of the jaw-tongue system is presented, discussing the relation of functional articulators with kinematic invariances and control problems.

Parameters of the lambda model seem tightly linked to certain characteristics of human performance influenced by weightlessness. This commentary suggests that there is a valuable opportunity to probe the lambda model using the changed environment experienced during space flight. The likely benefits are a better model and a better understanding ofthe consequences of weightlessness for human performance.

The λ model suggests that detailed kinematics arise from changes in control variables and need not be explicitly planned. However, we have shown that when moving a grasped object, grip force is precisely modulated in phase with acceleration-dependent inertial load. This suggests that the motor system can predict detailed kinematics. This prediction may be based on a forward model of the dynamics of the loaded limb.

Recent results have shown that the relative activation of muscles is different for isometric contractions and for movements. These results exclude an explanation of muscle activation patterns by a combination ofreciprocal and coactivation commands. These results also indicate that joint stiffness is not uniquely determined and that it may be different for isometric contractions and movements.

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. (shrink)

Evidence for a dichotomy between the planning of an action and its on-line control in humans is reviewed. This evidence suggests that planning and control each serve a specialized purpose utilizing distinct visual representations. Evidence from behavioral studies suggests that planning is influenced by a large array of visual and cognitive information, whereas control is influenced solely by the spatial characteristics of the target, including such things as its size, shape, orientation, and so forth. Evidence from brain imaging and neuropsychology (...) suggests that planning and control are subserved by separate visual centers in the posterior parietal lobes, each constituting part of a larger network for planning and control. Planning appears to rely on phylogenetically newer regions in the inferior parietal lobe, along with the frontal lobes and basal ganglia, whereas control appears to rely on older regions in the superior parietal lobe, along with the cerebellum. Key Words: action; apraxia; control; illusions; optic ataxia; PET; planning; reaching;. (shrink)

The posterior parietal cortex (PPC) is the most likely site where egocentric spatial relationships are represented in the brain. PPC cells receive visual, auditory, somaesthetic, and vestibular sensory inputs; oculomotor, head, limb, and body motor signals; and strong motivational projections from the limbic system. Their discharge increases not only when an animal moves towards a sensory target, but also when it directs its attention to it. PPC lesions have the opposite effect: sensory inattention and neglect. The PPC does not seem (...) to contain a “map” of the location of objects in space but a distributed neural network for transforming one set of sensory vectors into other sensory reference frames or into various motor coordinate systems. Which set of transformation rules is used probably depends on attention, which selectively enhances the synapses needed for making a particular sensory comparison or aiming a particular movement. (shrink)

Engineers use neural networks to control systems too complex for conventional engineering solutions. To examine the behavior of individual hidden units would defeat the purpose of this approach because it would be largely uninterpretable. Yet neurophysiologists spend their careers doing just that! Hidden units contain bits and scraps of signals that yield only arcane hints about network function and no information about how its individual units process signals. Most literature on single-unit recordings attests to this grim fact. On the other (...) hand, knowing a system's function and describing it with elegant mathematics tell one very little about what to expect of interneuronal behavior. Examples of simple networks based on neurophysiology are taken from the oculomotor literature to suggest how single-unit interpretability might decrease with increasing task complexity. It is argued that trying to explain how any real neural network works on a cell-by-cell, reductionist basis is futile and we may have to be content with trying to understand the brain at higher levels of organization. (shrink)

The lambda model of Feldman & Levin for intentional hand movement is compared with a hemispheric motor model (IIMM). Both models imply similar conclusions independently. This increases the validity of both models.

Vision is so closely identified with visual phenomenology that we sometimes forget that the visual system does more than deliver our experience of the world. Vision also plays a critical role in the control of our movements, from picking up our coffee cups to playing tennis. But the visual control of movement has, until recently, been relatively neglected. Indeed, traditional accounts of vision, while acknowledging the role of vision in motor control, have simply regarded such control as part of a (...) larger function – that of constructing an internal model of the external world. Even though such accounts might postulate separate ‘modules’ for the processing of different visual features, such as motion, colour, texture, and form, in most of these accounts there is an implicit assumption that, in the end, vision delivers a single representation of the external world – a kind of simulacrum of the real thing that serves as the perceptual foundation for all visually driven thought and action. (shrink)

This target article draws together two groups of experimental studies on the control of human movement through peripheral feedback and centrally generated signals of motor commands. First, during natural movement, feedback from muscle, joint, and cutaneous afferents changes; in human subjects these changes have reflex and kinesthetic consequences. Recent psychophysical and microneurographic evidence suggests that joint and even cutaneous afferents may have a proprioceptive role. Second, the role of centrally generated motor commands in the control of normal movements and movements (...) following acute and chronic deafferentation is reviewed. There is increasing evidence that subjects can perceive their motor commands under various conditions, but that this is inadequate for normal movement; deficits in motor performance arise when the reliance on proprioceptive feedback is abolished either experimentally or because of pathology. During natural movement, the CNS appears to have access to functionally useful input from a range of peripheral receptors as well as from internally generated command signals. The unanswered questions that remain suggest a number of avenues for further research. (shrink)

We argue that the concept of a control variable (CV) as described by Feldman and Levin needs to be revised because it does not account for the influence of sensory feedback from the periphery. We provide evidence from the realm of rhythmic movements that sensory feedback can permanently alter the frequency and phase of a centrally generated rhythm.

The lambda model provides a physiologically grounded terminology for describing muscle function and emphasizes the important influence of environmental and reflex-mediated effects on final states. However, lambda itself is only a convenient point on the length-tension curve; its importance should not be overemphasized. Ascribing movement to changes in a lambda-based frame of reference is generally valid, but it leaves unanswered a number of questions concerning mechanisms.

Two aspects of the target article, (1) the extension of the equilibrium point theory to multi-joint movements, and (2) the consequence that the EMG pattern is not directly controlled by the central nervous system (CNS), are discussed in light of the experiments on upper trunk bending in humans. The principle component kinematic analysis and the analysis of the EMG data, obtained under microgravity and additional loading conditions, support the application of Feldman and Levin's for multi-joint pointing movement to equilibrium control (...) during upper trunk movement. (shrink)

The equilibrium-point hypothesis (the λ-model) is superior to all other models of single-joint control and provides deep insights into the mechanisms of control of multi-joint movements. Attempts at associating control variables with neurophysiological variables look confusing rather than promising. Probabilistic mechanisms may play an important role in movement generation in redundant systems.

We emphasize the relevance to cognitive psychology of Feldman and Levin's theoretical position. Traditional views of motor control have failed to clearly separate “production control” at the level of motor command, based on task-independent CV (control variables), from intentional “product control” based on task-dependent parameters. Because F&L's approach concentrates on the first process (trajectory formation), it can distinguish the product control stage.

Feldman and Levin present a model for movement control in which the system is said to seek equilibrium points, active movement being produced by shifting frames of reference in space. It is argued that whatever merit this model might have is limited to an understanding of “the how” and not “the why” we move. In this way the authors seem to be forced into a dualistic position leaving the upper level of the proposed control hierarchy “floating.”.

The lambda model of servocontrol seems superior to the alpha model in terms of dealing with the mechanical complexities of nonlinear and multiarticular muscles. Both, however, can be trivialized by noting that the “control variable” may simply be the sum of descending influences at propriospinal interneurons in the case of the lambda model or in the muscles themselves in the case of the alpha model. The notion that the brain explicitly computes output in terms of any such control variables may (...) be an engineering metaphor, useful for conceptual understanding but not for generating predictive hypotheses about higher motor circuitry. (shrink)

Important similarities exist between the dynamical concepts implicit in Feldman & Levin's extended λ model and those basic to a dynamical systems approach. We argue that careful application of the key concepts of control and order parameters, equilibria, and stability, can relate known facts of neuromuscular processes to the observables of functional, task-specific behavior.

We affirm the dynamical systems approach taken by Feldman and Levin, but argue that a more mathematically rigorous and standard exposition of the model according to dynamical systems theory would greatly increase readability and testability. Such an explication would also have heuristic value, suggesting new variations of the model. We present one such variant, a new solution to the redundancy problem.

Understanding of the λ model has greatly increased in recent years as evidenced by most of the commentaries. Some commentators underscored the potential of the model to integrate aspects of different sensorimotor systems in the production of movement. Other commentators focused on not-yet-fully-developed parts of the model. A few persisted in misunderstanding some of its basic concepts, and on these grounds they reject it. In responding to commentaries we continue to elaborate on some fundamental points of the model, especially control (...) variables, the idea of movement production by shifting the positional frame of reference and the hypothesis of biomechanical correspondence in motor control. We also continue to develop our ideas on the intrinsic generation of the frame of reference associated with external space and utilized for the control of arm movement and locomotion. The dynamic principles underlying the model are discussed in light of the dynamical systems approach. (shrink)

The search for simplifying principles in motor control motivates the target article. One method that the CNS uses to simplify the task of controlling a limb's mechanical properties is absent from the article. Evidence from multi-joint, force-field measurements and from kinematics that points to the existence of multi-joint primitives as control variables is discussed.

The conservative strategy proposed by the authors suggests a solution of the degrees-of-freedom problem of the controller. However, several simple motor control tasks cannot be explained by this strategy. A nonconservative strategy, in which more parameters of the control signal vary, can account for these simple motor tasks. However, the simplicity that distinguishes the proposed model from many others is lost.

Kinematic properties of reaching movements reflect constraints imposed on the joint angles. Contemporary models present solutions to the redundancy problem by a pseudoinverse procedure (Whitney 1969) or without any inversion (Berkenblit et al. 1986). Feldman & Levin suggest a procedure based on a regular inversion. These procedures are considered as an outcome of a more general approach.

The trade-off between force and length of muscle as adjusted by neural signals is a critical fact in the dynamics of motor control. Whether we call it “length-tension effect,” “feedback-like,” “invariant condition,” or “spring-like” is unimportant. We must not let semantics or details of representation obscure the basic physics of effects introduced by this trade-off in muscle.

Extrapersonal frames of reference for aimed movements are representationally convenient. They may, however, carry associated costs when the movement is executed in terms of the complex coordination of multiple joints they require. Studies that have measured both fingertip and joint paths suggest the motor systems may seek a compromise between simplicity of extrapersonal spatial representation and computational simplicity of multi-joint execution.

Examination of infant spontaneous and goal-directed arm movements supports Feldman and Levin's hypothesis of a functional hierarchy. Early infant movements are dominated by biomechanical and dynamic factors without external frames of reference. Development involves not only learning to generate these frames of reference, but also protecting the higher-level goal of the movement from internal and external perturbations.

Neurophysiological evidence consonant with F&L's lambda model is reviewed and results of additional experiments are presented. The evidence shows that there are neurons in the motor cortex that respond to selective band widths of passive sinusoidal movements; the additional data show how, with movement, directionally sensitive population vectors can be shown to emerge from the data.