Spinal sensorimotor systems and their supraspinal control

Tissue engineering the monosynaptic circuit of the stretch reflex arc with co-culture of embryonic motoneurons and proprioceptive sensory neurons

The sensory circuit of the stretch reflex arc is composed of intrafusal muscle fibers and their innervating proprioceptive neurons that convert mechanical information regarding muscle length and tension into action potentials that synapse onto the homonymous motoneurons in the ventral spinal cord which innervate the extrafusal fibers of the same muscle. To date, the in vitro synaptic connection between proprioceptive sensory neurons and spinal motoneurons has not been demonstrated. A functional in vitro system demonstrating this connection would enable the understanding of feedback by the integration of sensory input into the spinal reflex arc. Here we report a co-culture of rat embryonic motoneurons and proprioceptive sensory neurons from dorsal root ganglia (DRG) in a defined serum-free medium on a synthetic silane substrate (DETA). Furthermore, we have demonstrated functional synapse formation in the co-culture by immunocytochemistry and electrophysiological analysis. This work will be valuable for enabling in vitro model systems for the study of spinal motor control and related pathologies such as spinal cord injury, muscular dystrophy and spasticity by improving our understanding of the integration of the mechanosensitive feedback mechanism.

In Vivo Measurement of Conduction Velocities in Afferent and Efferent Nerve Fibre Groups in Mice

Electrophysiological investigations in mice, particularly with altered myelination, require reference data of the nerve conduction velocity (CV). CVs of different fibre groups were determined in the hindlimb of anaesthetized adult mice. Differentiation between afferent and efferent fibres was performed by recording at dorsal roots and stimulating at ventral roots, respectively. Correspondingly, recording or stimulation was performed at peripheral hindlimb nerves. Stimulation was performed with graded strength to differentiate between fibre groups. CVs of the same fibre groups were different in different nerves of the hindlimb. CVs for motor fibres were for the tibial nerve (Tib) 38.5±4.0 m/s (Aγ: 16.7±3.0 m/s), the sural nerve (Sur) 39.3±3.1 m/s (12.0±0.8 m/s) and the common peroneal nerve (Per) 46.7±4.7 m/s (22.2±4.4 m/s). CVs for group I afferents were 47.4±3.1 m/s (Tib), 43.8±3.8 m/s (Sur), 55.2±6.1 m/s (Per) and 42.9±4.3 m/s for the posterior biceps (PB). CVs of higher threshold afferents, presumably muscle and cutaneous, cover a broad range and do not really exhibit nerve specific differences. Ranges are for group II 22-38 m/s, for group III 9-19 m/s, and for group IV 0.8-0.9 m/s. Incontrovertible evidence was found for the presence of motor fibres in the sural nerve. The results are useful as references for further electrophysiological investigations particularly in genetically modified mice with myelination changes.

Myofibrillar disorganization characterizes myopathy of camptocormia in Parkinson's disease

Camptocormia is a highly disabling syndrome that occurs in various diseases but is particularly associated with Parkinson's disease (PD). Although first described nearly 200 years ago, the morphological changes associated with camptocormia are still under debate and the pathophysiology is unknown. We analyzed paraspinal muscle biopsies of 14 PD patients with camptocormia and compared the findings to sex-matched postmortem controls of comparable age to exclude biopsy site-specific changes. Camptocormia in PD showed a consistent lesion pattern composed of myopathic changes with type-1 fiber hypertrophy, loss of type-2 fibers, loss of oxidative enzyme activity, and acid phosphatase reactivity of lesions. Ultrastructurally, myofibrillar disorganization and Z-band streaming up to electron-dense patches/plaques were seen in the lesions. No aberrant protein aggregation, signs of myositis or mitochondriopathy were found, but the mitochondrial content of paraspinal muscles in patients and controls was markedly higher than known from limb biopsies. Additionally, we were able to demonstrate a link between the severity of the clinical syndrome and the degree of the myopathic changes. Because of the consistent lesion pattern, we propose criteria for the diagnosis of camptocormia in PD from muscle biopsies. The morphological changes show obvious parallels to the muscle pathology of experimental tenotomy reported in the 1970s, which depend on an intact innervation and do not occur after interruption of the myotactic reflexes. A dysregulation of the proprioception could be part of the pathogenesis of camptocormia in Parkinson's disease, particularly in view of the clinical symptoms of rigidity and loss of muscle strength.

Experimental knee joint pain during strength training and muscle strength gain in healthy subjects: a randomized controlled trial

OBJECTIVE

Knee joint pain and reduced quadriceps strength are cardinal symptoms in many knee pathologies. In people with painful knee pathologies, quadriceps exercise reduces pain, improves physical function, and increases muscle strength. A general assumption is that pain compromises muscle function and thus may prevent effective rehabilitation. This study evaluated the effects of experimental knee joint pain during quadriceps strength training on muscle strength gain in healthy individuals.

METHODS

Twenty-seven healthy untrained volunteers participated in a randomized controlled trial of quadriceps strengthening (3 times per week for 8 weeks). Participants were randomized to perform resistance training either during pain induced by injections of painful hypertonic saline (pain group, n = 13) or during a nonpainful control condition with injection of isotonic saline (control group, n = 14) into the infrapatellar fat pad. The primary outcome measure was change in maximal isokinetic muscle strength in knee extension/flexion (60, 120, and 180 degrees/second).

RESULTS

The group who exercised with pain had a significantly larger improvement in isokinetic muscle strength at all angular velocities of knee extension compared to the control group. In knee flexion there were improvements in isokinetic muscle strength in both groups with no between-group differences.

CONCLUSION

Experimental knee joint pain improved the training-induced gain in muscle strength following 8 weeks of quadriceps training. It remains to be studied whether knee joint pain has a positive effect on strength gain in patients with knee pathology.

TENDON REFLEX AND STRATEGIES FOR QUANTIFICATION, WITH NOVEL METHODS INCORPORATING WIRELESS ACCELEROMETER REFLEX QUANTIFICATION DEVICES, A PERSPECTIVE REVIEW

The deep tendon reflex is a fundamental aspect of a neurological examination. The two major parameters of the tendon reflex are response and latency, which are presently evaluated qualitatively during a neurological examination. The reflex loop is capable of providing insight into the status and therapy response of both upper and lower motor neuron syndromes. Attempts have been made to ascertain reflex response and latency; however, these systems are relatively complex, resource intensive, with issues of consistent and reliable accuracy. The solution presented is a wireless quantified reflex device using tandem three-dimensional (3D) wireless accelerometers to obtain response based on acceleration waveform amplitude and latency derived from temporal acceleration waveform disparity. Three specific aims have been established for the proposed wireless quantified reflex device:

(1) Demonstrate the wireless quantified reflex device is reliably capable of ascertaining quantified reflex response and latency using a quantified input.

(2) Evaluate the precision of the device using an artificial reflex system.

(3) Conduct a longitudinal study respective of subjects with healthy patellar tendon reflexes, using the wireless quantified reflex evaluation device to obtain quantified reflex response and latency.

Aim 1 has led to a steady evolution of the wireless quantified reflex device from a singular 2D wireless accelerometer capable of measuring reflex response to a tandem 3D wireless accelerometer capable of reliably measuring reflex response and latency. The hypothesis for aim 1 is that a reflex quantification device can be established for reliably measuring reflex response and latency for the patellar tendon reflex, comprised of an integrated system of wireless 3D MEMS accelerometers. Aim 2 further emphasized the reliability of the wireless quantified reflex device by evaluating an artificial reflex system. The hypothesis for aim 2 is that the wireless quantified reflex device can obtain reliable reflex parameters (response and latency) from an artificial reflex device. Aim 3 synthesizes the findings relevant to aim 1 and 2, while applying the wireless accelerometer reflex quantification device to a longitudinal study of healthy patellar tendon reflexes. The hypothesis for aim 3 is that during a longitudinal evaluation of the deep tendon reflex the parameters for reflex response and latency can be measured with a considerable degree of accuracy, reliability, and reproducibility. Enclosed is a detailed description of a wireless quantified reflex device with research findings and potential utility of the system, inclusive of a comprehensive description of tendon reflexes, prior reflex quantification systems, and correlated applications.

VIRTUAL PROPRIOCEPTION

Virtual proprioception represents a novel means of developing cortical reorganization of alternative strategies for hemiparetic gait. Fundamentals of the device are motor control plasticity, aftereffect, and visual-based biofeedback. Two wireless three-dimensional (3D) microelectromechanical systems (MEMS) accelerometers are placed on the femur (upper leg) of both the affected and unaffected limbs above the lateral epicondyle next to the knee joint. The acceleration data from the two wireless 3D MEMS accelerometers are fed back to the user in real time by visual output from a portable laptop PC. Given the virtual proprioception feedback, the user can then adjust the original gait while walking to an improved alternative gait strategy. First, hemiparetic gait is comprehensively discussed. The inherent roles of proprioception with locomotion and issues with traumatic brain injury are considered. Then, the technology advance of accelerometers and gait analysis is detailed. Virtual proprioception is tested and evaluated, while demonstrating the capacity to improve disparities in hemiparetic gait during real time.

Hoffmann reflex in a rat bipedal walking model

The rat bipedal walking model (RBWM) refers to rats that acquired anatomical and functional characteristics for bipedal walking after the completion of a long-term motor training program. We recorded the Hoffmann reflex (H-reflex) of the forelimb and hindlimb in RBWM and control (not trained, normal) rats to evaluate the effects of bipedal walking on central nervous system (CNS) activity. The H-reflex recorded from the hindlimbs of the RBWM was significantly inhibited compared with that in the control. Furthermore, the inhibition of the H-reflex recorded from both forelimbs and hindlimbs by paired pulse stimulation tended to be enhanced in RBWM. These results indicate that bipedal walking or bipedal walking training cause functional changes in spinal reflex pathways in the CNS.

Role of L-DOPA in Spinal Nociceptive Reflex Activity: Higher Sensitivity of Aδ Versus C Fibre-Evoked Nociceptive Reflexes to L-DOPA

The role of L-DOPA in spinal nociceptive reflex activity has been re-evaluated. In high spinal cats, with supraspinal loops being excluded, the onset of reflex facilitation induced by noxious radiant heat is delayed after injection of L-DOPA by 4 to 10 s, i.e. the early component of nociceptive reflex facilitation is blocked, while the late component persisted. Further investigations have shown that the early component of reflex facilitation induced by noxious radiant heat is mediated by Aδ-fibres and the late component by C-fibres. Therefore, it can be assumed that L-DOPA, like opioids, preferentially blocks the transmission in nociceptive reflex pathways from Aδ-fibres.

Does the nervous system depend on kinesthetic information to control natural limb movements?

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.

Implications of neural networks for how we think about brain function

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.

Chapter 7--interindividual variability and its implications for locomotor adaptation following peripheral nerve and/or spinal cord injury

Following injury to the nervous system, there is a range of possible functional outcomes that can only be partly explained by the extent of injury. Moreover, treatments effective in certain individuals might not work in others. Why such variability from one individual to another, in terms of functional outcomes and responsiveness to a given treatment following a similar injury? The answer to that question is not simple, and to begin to answer we must first consider that individuals of the same species can be quite variable in terms of neuronal circuit parameters involved in performing a given task. Interindividual variability can be subtle but the term "variability" in this chapter will be used to denote marked differences between individuals at the systems level (e.g., spinal reflexes, bursts of muscle activity, kinematics) during the same motor behavior, with an emphasis on locomotion. Injury to any level of the nervous system, in turn, can further compound this variability by altering spared neuronal connections. The aim of the present chapter is to (1) review studies that have investigated interindividual variability, (2) review studies that have described variable adaptive mechanisms following spinal and/or peripheral nerve lesions during locomotion, and (3) discuss the implications of intersubject variability for locomotor adaptation.

Functional subdivision of feline spinal interneurons in reflex pathways from group Ib and II muscle afferents; an update

A first step towards understanding the operation of a neural network is identification of the populations of neurons that contribute to it. Our aim here is to reassess the basis for subdivision of adult mammalian spinal interneurons that mediate reflex actions from tendon organs (group Ib afferents) and muscle spindle secondary endings (group II afferents) into separate populations. Re-examining the existing experimental data, we find no compelling reasons to consider intermediate zone interneurons with input from group Ib afferents to be distinct from those co-excited by group II afferents. Similar patterns of distributed input have been found in subpopulations that project ipsilaterally, contralaterally or bilaterally, and in both excitatory and inhibitory interneurons; differences in input from group I and II afferents to individual interneurons showed intra- rather than inter-population variation. Patterns of reflex actions evoked from group Ib and II afferents and task-dependent changes in these actions, e.g. during locomotion, may likewise be compatible with mediation by premotor interneurons integrating information from both group I and II afferents. Pathological changes after injuries of the central nervous system in humans and the lineage of different subclasses of embryonic interneurons may therefore be analyzed without need to consider subdivision of adult intermediate zone interneurons into subpopulations with group Ib or group II input. We propose renaming these neurons 'group I/II interneurons'.

Differences in unconditioned and conditioned responses of the human withdrawal reflex during stance: muscle responses and biomechanical data

The aim of this study was to characterize differences between unconditioned and classically conditioned lower limb withdrawal reflexes in young subjects during standing. Electromyographic activity in the main muscle groups and biomechanical signals from a strain-gauge-equipped platform on which subjects stood were recorded from 17 healthy subjects during unconditioned stimulus (US)-alone trials and during auditory conditioning stimuli (CS) and US trials. In US-alone trials the leg muscle activation sequence was characteristic: ipsilateral, distal muscles were activated prior to proximal muscles; contralaterally the sequence was reversed. In CSUS trials latencies were shorter. Subjects unloaded the stimulated leg and shifted body weight to the supporting leg. In US-alone and in CSUS trials leg forces on each side were inversely related and asymmetric, due to preparation for unloading, whilst conditioned responses (CR), representing the unloading preparation, were symmetric. The trajectory of the center of vertical pressure during US-alone trials moved initially forward (a preparatory balance reaction) and to the stimulation side, followed by a large lateral shift to the side of the supporting limb. During CSUS trials the forwards shift was absent but the CR (early lateral shift) represented a preponed preparatory unloading. Electrophysiological and biomechanical responses of the classically conditioned lower limb withdrawal reflex in standing subjects changed significantly in CSUS trials compared to US-alone trials with higher sensitivity in the biomechanics. These findings will serve as a basis for a subsequent study on a group of patients with cerebellar diseases in whom the success of establishing procedural processes is known to be impaired.

What does body configuration in microgravity tell us about the contribution of intra- and extrapersonal frames of reference for motor control?

The authors report that the reorganization of body configuration during weightlessness is based on an intrapersonal frame of reference such as the configuration of the support surface and the position of the body's center of gravity. These results stress the importance of “knowledge” of the state of internal geometric structures, which cannot be directly signalled by specific receptors responsible for direct dialogue with the physical external world.

Reciprocal and coactivation commands are not sufficient to describe muscle activation patterns

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.

Frames of reference interact and are task-dependent

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 λ model for motor control: More than meets the eye

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.

Grip force adjustments during rapid hand movements suggest that detailed movement kinematics are predicted

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.

Let us accept a “controlled trade-off” model of motor control

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.

Equilibrium-point control? Yes! Deterministic mechanisms of control? No!

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.

The unobservability of central commands: Why testing hypotheses is so difficult

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.

Biological variability and control of movements via δλ

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.

A few reasons why psychologlsts can adhere to Feldman and Levin's model

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.

Levers to generate movement

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?

Kinematic invariances and body schema

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.

Tendon elasticity and positional control

The spring-like behaviour of a joint following a sudden change of torque is partly a result of the elastic properties of tendons. A large fall in a muscle with a long tendon may be accompanied by tendon recoil causing joint movements as large as 20°.

Command invariants and the frame of reference for human movement

We describe a solution to the redundancy problem related to that proposed in Feldman & Levin's target article. We suggest that the system may use a fixed mapping between commands organized at the level of degrees of freedom and commands to individual muscles. This proposal eliminates the need to maintain an explicit representation of musculoskeletalgeometry in planning movements.

Frameworks on shifting sands

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.”

Conservative or nonconservative control schemes

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.

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.

Origins of origins of motor control

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.

Spatial frames for motor control would be commensurate with spatial frames for vision and proprioception, but what about control of energy flows?

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.

Interneurons as backseat drivers and the elusive control variable

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.

Two joints are more than twice one joint

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.

Control parameters, equilibria, and coordination dynamics

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.

Shifting frames of reference but the same old point of view

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.

Inverse kinematic problem: Solutions by pseudoinversion, inversion and no-inversion

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.

Natural unconstrained movements obey rules different from constrained elementary movements

The concept of a conservative control strategy minimizing the number of degrees of freedom used is criticised with reference to 3-D simple reaching and grasping experiments. The vector error in a redundant system would not be the prime controlled variable, but rather the posture for reaching, as exemplified by nearly straight displacements in joint space as opposed to curved ones in task space.