Threshold position control and the principle of minimal interaction in motor actions

Referent Control of Side-to-Side Body-Weight Transfer During Standing and Stepping in Adults

Research suggests that locomotion may be primarily caused by shifting stable body balance from one location in the environment to another with subsequent rhythmical muscle activation by the central pattern generator (CPG), constituting a multi-level control system. All levels interact with environmental forces affected by proprioceptive and vestibular reflexes as well as vision. A similar multi-level control schema is likely used to shift body balance laterally when the body weight is rhythmically transferred from side-to-side. In order to do so, the system shifts a specific body posture in space. This body posture is referred to as the threshold or referent body posture, R, at which all muscles involved can be at rest but are activated depending on the deflection of the actual body posture, Q, from R. This concept has previously been investigated for forward and backward locomotion. The purpose of the present study was to verify if it was also applicable to locomotor tasks in other directions such as sidestepping. We predicted that during sidestepping, the actual and referent posture can transiently match each other bringing the activity of multiple muscles to a minimum. The existence of such minima was demonstrated in healthy adults performing three locomotor tasks involving shifts of the body weight from side-to-side thus further supporting the validity of the multi-level control scheme of locomotion.

Identifying Referent Control Variables Underlying Goal-Directed Arm Movements

The referent control theory (RCT) for action and perception is an advanced formulation of the equilibrium-point hypothesis. The RCT suggests that rather than directly specifying the desired motor outcome, the nervous system controls action and perception indirectly by setting the values of parameters of physical and physiological laws. This is done independently of values of kinematic and kinetic variables including electromyographic patterns describing the motor outcome. One such parameter-the threshold muscle length, λ, at which motoneurons of a given muscle begin to be recruited, has been identified experimentally. In RCT, a similar parameter, the referent arm position, R, has been defined for multiple arm muscles as the threshold arm position at which arm muscles can be quiescent but activated depending on the deflection of the actual arm position, Q, from R. Changes in R result in reciprocal changes in the activity of opposing muscle groups. We advanced the explanatory power of RCT by combining the usual biomechanical descriptions of motor actions with the identification of the timing of R underlying arm movements made with reversals in three directions and to three different extents. We found that in all movements, periods of minimization of the activity of multiple muscles could be identified at ∼61%-86% of the reaching extent in each direction. These electromyographic minimization periods reflect the spatial coordinates at which the R and Q overlap during the production of movements with reversals. The findings support the concept of the production of arm movement by shifting R.

Tapping on a target: dealing with uncertainty about its position and motion

Reaching movements are guided by estimates of the target object's location. Since the precision of instantaneous estimates is limited, one might accumulate visual information over time. However, if the object is not stationary, accumulating information can bias the estimate. How do people deal with this trade-off between improving precision and reducing the bias? To find out, we asked participants to tap on targets. The targets were stationary or moving, with jitter added to their positions. By analysing the response to the jitter, we show that people continuously use the latest available information about the target's position. When the target is moving, they combine this instantaneous target position with an extrapolation based on the target's average velocity during the last several hundred milliseconds. This strategy leads to a bias if the target's velocity changes systematically. Having people tap on accelerating targets showed that the bias that results from ignoring systematic changes in velocity is removed by compensating for endpoint errors if such errors are consistent across trials. We conclude that combining simple continuous updating of visual information with the low-pass filter characteristics of muscles, and adjusting movements to compensate for errors made in previous trials, leads to the precise and accurate human goal-directed movements.

Human Control Model Estimation in Physical Human-Machine Interaction: A Survey

The study of human-machine interaction as a unique control system was one of the first research interests in the engineering field, with almost a century having passed since the first works appeared in this area. At the same time, it is a crucial aspect of the most recent technological developments made in application fields such as collaborative robotics and artificial intelligence. Learning the processes and dynamics underlying human control strategies when interacting with controlled elements or objects of a different nature has been the subject of research in neuroscience, aerospace, robotics, and artificial intelligence. The cross-domain nature of this field of study can cause difficulties in finding a guiding line that links motor control theory, modelling approaches in physiological control systems, and identifying human-machine general control models in manipulative tasks. The discussed models have varying levels of complexity, from the first quasi-linear model in the frequency domain to the successive optimal control model. These models include detailed descriptions of physiologic subsystems and biomechanics. The motivation behind this work is to provide a complete view of the linear models that could be easily handled both in the time domain and in the frequency domain by using a well-established methodology in the classical linear systems and control theory.

Multi-expert learning of adaptive legged locomotion

Achieving versatile robot locomotion requires motor skills that can adapt to previously unseen situations. We propose a multi-expert learning architecture (MELA) that learns to generate adaptive skills from a group of representative expert skills. During training, MELA is first initialized by a distinct set of pretrained experts, each in a separate deep neural network (DNN). Then, by learning the combination of these DNNs using a gating neural network (GNN), MELA can acquire more specialized experts and transitional skills across various locomotion modes. During runtime, MELA constantly blends multiple DNNs and dynamically synthesizes a new DNN to produce adaptive behaviors in response to changing situations. This approach leverages the advantages of trained expert skills and the fast online synthesis of adaptive policies to generate responsive motor skills during the changing tasks. Using one unified MELA framework, we demonstrated successful multiskill locomotion on a real quadruped robot that performed coherent trotting, steering, and fall recovery autonomously and showed the merit of multi-expert learning generating behaviors that can adapt to unseen scenarios.

Quantitative Modeling of Spasticity for Clinical Assessment, Treatment and Rehabilitation

Spasticity, a common symptom in patients with upper motor neuron lesions, reduces the ability of a person to freely move their limbs by generating unwanted reflexes. Spasticity can interfere with rehabilitation programs and cause pain, muscle atrophy and musculoskeletal deformities. Despite its prevalence, it is not commonly understood. Widely used clinical scores are neither accurate nor reliable for spasticity assessment and follow up of treatments. Advancement of wearable sensors, signal processing and robotic platforms have enabled new developments and modeling approaches to better quantify spasticity. In this paper, we review quantitative modeling techniques that have been used for evaluating spasticity. These models generate objective measures to assess spasticity and use different approaches, such as purely mechanical modeling, musculoskeletal and neurological modeling, and threshold control-based modeling. We compare their advantages and limitations and discuss the recommendations for future studies. Finally, we discuss the focus on treatment and rehabilitation and the need for further investigation in those directions.

A systematic evaluation of the evidence for perceptual control theory in tracking studies

Perceptual control theory (PCT) proposes that perceptual inputs are controlled to intentional 'reference' states by hierarchical negative feedback control, evidence for which comes from manual tracking experiments in humans. We reviewed these experiments to determine whether tracking is a process of perceptual control, and to assess the state-of-the-evidence for PCT. A systematic literature search was conducted of peer-review journal and book chapters in which tracking data were simulated with a PCT model (13 studies, 53 participants). We report a narrative review of these studies and a qualitative assessment of their methodological quality. We found evidence that individuals track to individual-specific endogenously-specified reference states and act against disturbances, and evidence that hierarchical PCT can simulate complex tracking. PCT's learning algorithm, reorganization, was not modelled. Limitations exist in the range of tracking conditions under which the PCT model has been tested. Future PCT research should apply the PCT methodology to identify control variables in real-world tasks and develop hierarchical PCT architectures for goal-oriented robotics to test the plausibility of PCT model-based action control.

Development of vertical and forward jumping skills in typically developing children in the context of referent control of motor actions

The empirically based referent control theory of motor actions provides a new framework for understanding locomotor maturation. Mature movement patterns of referent control are characterized by periods of minimization of activity across multiple muscles (global electromyographic [EMG] minima) resulting from transient matching between actual and referent body configurations. We identified whether locomotor maturation in young children was associated with (a) development of referent control and (b) children's frequency of participation in everyday activities evaluated by parents. Kinematics and EMG activity were recorded from typically developing children (n = 15, 3-5 years) and young adults (n = 10, 18-25 years) while walking, vertical or forward jumping. Presence and location of global EMG minima in movement cycles, slopes of ankle vertical/sagittal displacements, and shoulder displacement ratios were evaluated. Children had fewer global EMG minima compared to adults during specific phases of vertical and forward jumps. Ankle displacement profiles for walking and jumping forward were related to each other in adults, whereas those for walking and vertical jumping were related in children. Higher frequency of participation was significantly correlated with more mature jumping patterns in children. A decrease in the number of global EMG minima and changes in ankle movement patterns could be indicators of locomotor immaturity in typically developing children.

Brain Activation Changes During Balance- and Attention-Demanding Tasks in Middle- and Older-Aged Adults With Multiple Sclerosis

Functional near-infrared spectroscopy was used to evaluate prefrontal cortex activation differences between older adults with multiple sclerosis (MS) and healthy older adults (HOA) during the performance of a balance- and attention-demanding motor task. Ten older adults with MS and 12 HOA underwent functional near-infrared spectroscopy recording while talking, virtual beam walking, or virtual beam walking while talking on a self-paced treadmill. The MS group demonstrated smaller increases in prefrontal cortex oxygenation levels than HOA during virtual beam walking while talking than talking tasks. These findings indicate a decreased ability to allocate additional attentional resources in challenging walking conditions among MS compared with HOA. This study is the first to investigate brain activation dynamics during the performance of balance- and attention-demanding motor tasks in persons with MS.

Deciphering the functional role of spatial and temporal muscle synergies in whole-body movements

Voluntary movement is hypothesized to rely on a limited number of muscle synergies, the recruitment of which translates task goals into effective muscle activity. In this study, we investigated how to analytically characterize the functional role of different types of muscle synergies in task performance. To this end, we recorded a comprehensive dataset of muscle activity during a variety of whole-body pointing movements. We decomposed the electromyographic (EMG) signals using a space-by-time modularity model which encompasses the main types of synergies. We then used a task decoding and information theoretic analysis to probe the role of each synergy by mapping it to specific task features. We found that the temporal and spatial aspects of the movements were encoded by different temporal and spatial muscle synergies, respectively, consistent with the intuition that there should a correspondence between major attributes of movement and major features of synergies. This approach led to the development of a novel computational method for comparing muscle synergies from different participants according to their functional role. This functional similarity analysis yielded a small set of temporal and spatial synergies that describes the main features of whole-body reaching movements.

Referent control of the orientation of posture and movement in the gravitational field

This study addresses the question of how posture and movement are oriented with respect to the direction of gravity. It is suggested that neural control levels coordinate spatial thresholds at which multiple muscles begin to be activated to specify a referent body orientation (RO) at which muscle activity is minimized. Under the influence of gravity, the body is deflected from the RO to an actual orientation (AO) until the emerging muscle activity and forces begin to balance gravitational forces and maintain body stability. We assumed that (1) during quiet standing on differently tilted surfaces, the same RO and thus AO can be maintained by adjusting activation thresholds of ankle muscles according to the surface tilt angle; (2) intentional forward body leaning results from monotonic ramp-and-hold shifts in the RO; (3) rhythmic oscillation of the RO about the ankle joints during standing results in body swaying. At certain sway phases, the AO and RO may transiently overlap, resulting in minima in the activity of multiple muscles across the body. EMG kinematic patterns of the 3 tasks were recorded and explained based on the RO concept that implies that these patterns emerge due to referent control without being pre-programmed. We also confirmed the predicted occurrence of minima in the activity of multiple muscles at specific body configurations during swaying. Results re-affirm previous rejections of model-based computational theories of motor control. The role of different descending systems in the referent control of posture and movement in the gravitational field is considered.

Principles of Motor Recovery After Neurological Injury Based on a Motor Control Theory

Problems of neurological rehabilitation are considered based on two levels of the International Classification of Functioning (ICF)-Body Structures and Function level and Activity level-and modulating factors related to the individual and the environment. Specifically, at the Body Structures and Function level, problems addressed include spasticity, muscle weakness, disordered muscle activation patterns and disruptions in coordinated movement. At the Activity level, deficits in multi-joint and multi-segment upper limb reaching movements are reviewed. We address how physiologically well established principles in the control of actions, Threshold Control and Referent Control as outlined in the Equilibrium-Point theory can help advance the understanding of underlying deficits that may limit recovery at each level.

Robotic exoskeletons: a perspective for the rehabilitation of arm coordination in stroke patients

Upper-limb impairment after stroke is caused by weakness, loss of individual joint control, spasticity, and abnormal synergies. Upper-limb movement frequently involves abnormal, stereotyped, and fixed synergies, likely related to the increased use of sub-cortical networks following the stroke. The flexible coordination of the shoulder and elbow joints is also disrupted. New methods for motor learning, based on the stimulation of activity-dependent neural plasticity have been developed. These include robots that can adaptively assist active movements and generate many movement repetitions. However, most of these robots only control the movement of the hand in space. The aim of the present text is to analyze the potential of robotic exoskeletons to specifically rehabilitate joint motion and particularly inter-joint coordination. First, a review of studies on upper-limb coordination in stroke patients is presented and the potential for recovery of coordination is examined. Second, issues relating to the mechanical design of exoskeletons and the transmission of constraints between the robotic and human limbs are discussed. The third section considers the development of different methods to control exoskeletons: existing rehabilitation devices and approaches to the control and rehabilitation of joint coordinations are then reviewed, along with preliminary clinical results available. Finally, perspectives and future strategies for the design of control mechanisms for rehabilitation exoskeletons are discussed.

Arm-trunk coordination for beyond-the-reach movements in adults with stroke

BACKGROUND

By involving additional degrees of freedom, the nervous system may preserve hand trajectories when making pointing movements with or without trunk displacement. Previous studies indicate that the potential contribution of trunk movement to hand displacement for movements made within arm reach is neutralized by appropriate compensatory shoulder and elbow rotations. For beyond-the-reach movements, compensatory coordination is attenuated after the hand peak velocity, allowing trunk movement to contribute to hand displacement.

OBJECTIVE

To investigate if the timing and spatial coordination of arm and trunk movements during beyond-the-reach movements is preserved in stroke.

METHODS

Eleven healthy control subjects and 11 individuals with mild-to-moderate chronic unilateral hemiparesis participated. Arm and trunk kinematics during 60 target reaches to an ipsilaterally placed target were recorded. In 30% of randomly chosen trials, trunk movement was unexpectedly prevented (blocked-trunk trials) by an electromagnetic device, resulting in divergence of the hand trajectory from that in free-trunk trials. Hand trajectories and elbow-shoulder interjoint coordination were compared between trials.

RESULTS

In stroke participants, hand trajectory divergence occurred at a shorter movement extent and interjoint coordination patterns diverged at a relatively greater distance compared to controls. Thus, arm movements in stroke participants only partially compensated trunk displacement resulting in the trunk movement contributing to arm movement earlier and to a larger extent during reaching.

CONCLUSION

Individuals with mild-to-moderate stroke have deficits in timing and spatial coordination of arm and trunk movements during different parts of a reaching movement. This deficit may be targeted in therapy to improve upper limb function.

Effect of 14 days of bed rest in older adults on parameters of the body sway and on the local ankle function

This study explored the effects of a 14-day horizontal bed rest (BR) without countermeasures on postural sway, maximal voluntary torque and precision of voluntary torque matching. Sixteen subjects were tested before, immediately after and two weeks after BR. The increase in frequency and amplitude after BR was comparable for both sway subcomponents (rambling and trembling) in medial-lateral direction. But in anterior-posterior direction, rambling increased more in frequency (-7% vs. +31%, p < 0.05) while trembling increased more in amplitude (+35% vs. +84%, p < 0.05). The drop in maximal voluntary torque after BR was present for plantar flexion (p < 0.05) but not for dorsal flexion. After the BR, the subjects were less precise in the dorsal flexion torque matching task (p < 0.05). All the observed parameters, except the dorsal flexion torque matching error, returned back to the pre-BR values after the two weeks of re-conditioning. Results of this study indicate that body sway subcomponents responded differently to BR. Based on these findings, it was not possible to draw clear assumptions on the effects of neural and structural changes on body sway.

Anticipatory synergy adjustments: preparing a quick action in an unknown direction

We studied a mechanism of feed-forward control of a multi-finger action, namely anticipatory synergy adjustments (ASAs), prior to a quick force correction in response to a change in the gain of the visual feedback. Synergies were defined as co-varied across trials adjustments of commands to fingers that stabilized (decreased variance of) the total force. We hypothesized that ASAs would be highly sensitive to prior information about the timing of the action but not to information on its direction, i.e., on whether the gain would go up or down. The subjects produced accurate constant total force by pressing with four fingers on individual force sensors. The feedback signal could change from veridical (the sum of finger forces) to modified, with the middle finger force multiplied by 0.2 or by 1.8. The timing of the gain change and its direction could be known or unknown to the subject in advance. When the timing of the gain change was known, ASA was seen as a drop in the synergy index starting about 250-300 ms prior to the first visible correction of the total force. When the gain change timing was unknown, ASAs started much later, less than 100 ms prior to the total force correction. The magnitude of synergy index changes was significantly larger under the "time known" conditions. Information on the direction of the visual gain change had no effect on the ASA timing, while the ASA magnitude was somewhat larger when this information was not available to the subject. After the total force correction, the synergy index was significantly larger for the force signal computed using the modified gain values as compared to the synergy index value for the actual total force. We conclude that ASAs represent an important feed-forward motor control mechanism that allows preparing for a quick action even when the direction of the action is not known in advance. The results emphasize the subtle control of multi-finger synergies that are specific to the exact contributions of individual fingers to performance variables. The data fit well the central back-coupling hypothesis of synergies and the idea of control with referent body configurations.

On the Ecological Approach to Information and Control for Roboticists

The ongoing and increasingly important trend in robotics to conceive designs that decentralize control is paralleled by currently active research paradigms in the study of perception and action. James Gibson's ecological approach is one of these paradigms. Gibson's approach emerged in part as a reaction to representationalist and computationalist approaches, which devote the bulk of their resources to the study of internal processes. The ecological approach instead focuses on constraints and ambient energy patterns in the animal-environment coalition. The present article reviews how the emphasis on the environment by ecological psychologists has given rise to the concepts of direct perception, higher order information, active information pick up, information-based control laws, prospective control, and direct learning. Examples are included to illustrate these concepts and to show how they can be applied to the construction of robots. Action is described as emergent and self-organized. It is argued that knowledge about perception, action, and learning as it occurs in living organisms may facilitate the construction of robots, more obviously so if the aim is to construct (to some extent) biologically plausible robots.

Static prehension of a horizontally oriented object in three dimensions

We studied static prehension of a horizontally oriented object. Specific hypotheses were explored addressing such issues as the sharing patterns of the total moment of force across the digits, presence of mechanically unnecessary digit forces, and trade-off between multi-digit synergies at the two levels of the assumed control hierarchy. Within the assumed hierarchy, at the upper level, the task is shared between the thumb and virtual finger (an imagined finger producing a wrench equal to the sum of the wrenches of individual fingers). At the lower level, action of the virtual finger is shared among the four actual fingers. The subjects held statically a horizontally oriented handle instrumented with six-component force/torque sensors with different loads and torques acting about the long axis of the handle. The thumb acted from above while the four fingers supported the weight of the object. When the external torque was zero, the thumb produced mechanically unnecessary force of about 2.8 N, which did not depend on the external load magnitude. When the external torque was not zero, tangential forces produced over 80% of the total moment of force. The normal forces by the middle and ring fingers produced consistent moments against the external torque, while the normal forces of the index and little fingers did not. Force and moment variables at both hierarchical levels were stabilized by covaried across trials adjustments of forces/moments produced by individual digits with the exception of the normal force analyzed at the lower level of the hierarchy. There was a trade-off between synergy indices computed at the two levels of the hierarchy for the three components of the total force vector, but not for the moment of force components. Overall, the results have shown that task mechanics are only one factor that defines forces produced by individual digits. Other factors, such as loading sensory receptors may lead to mechanically unnecessary forces. There seems to be no single rule (for example, ensuring similar safety margin values) that would describe sharing of the normal and tangential forces and be valid across tasks. Fingers that are traditionally viewed as less accurate (e.g., the ring finger) may perform more consistently in certain tasks. The observations of the trade-off between the synergy indices computed at two levels for the force variables but not for the moment of force variables suggest that the degree of redundancy (the number of excessive elemental variables) at the higher level is an important factor.

Unpredictable elbow joint perturbation during reaching results in multijoint motor equivalence

Motor equivalence expresses the idea that movement components reorganize in the face of perturbations to preserve the value of important performance variables, such as the hand's position in reaching. A formal method is introduced to evaluate this concept quantitatively: changes in joint configuration due to unpredictable elbow perturbation lead to a smaller change in performance variables than expected given the magnitude of joint configuration change. This study investigated whether motor equivalence was present during the entire movement trajectory and how magnitude of motor equivalence was affected by constraints imposed by two different target types. Subjects pointed to spherical and cylindrical targets both with and without an elbow joint perturbation produced by a low- or high-stiffness elastic band. Subjects' view of their arm was blocked in the initial position, and the perturbation condition was randomized to avoid prediction of the perturbation or its magnitude. A modification of the uncontrolled manifold method variance analysis was used to investigate how changes in joint configuration on perturbed vs. nonperturbed trials (joint deviation vector) affected the hand's position or orientation. Evidence for motor equivalence induced by the perturbation was present from the reach onset and increased with the strength of the perturbation after 40% of the reach, becoming more prominent as the reach progressed. Hand orientation was stabilized more strongly by motor equivalent changes in joint configuration than was three-dimensional position regardless of the target condition. Results are consistent with a recent model of neural control that allows for flexible patterns of joint coordination while resisting joint configuration deviations in directions that affect salient performance variables. The observations also fit a general scheme of synergic control with referent configurations defined across different levels of the motor hierarchy.

Two stages and three components of the postural preparation to action

Previous studies of postural preparation to action/perturbation have primarily focused on anticipatory postural adjustments (APAs), the changes in muscle activation levels resulting in the production of net forces and moments of force. We hypothesized that postural preparation to action consists of two stages: (1) Early postural adjustments (EPAs), seen a few hundred ms prior to an expected external perturbation and (2) APAs seen about 100 ms prior to the perturbation. We also hypothesized that each stage consists of three components, anticipatory synergy adjustments seen as changes in covariation of the magnitudes of commands to muscle groups (M-modes), changes in averaged across trials levels of muscle activation, and mechanical effects such as shifts of the center of pressure. Nine healthy participants were subjected to external perturbations created by a swinging pendulum while standing in a semi-squatting posture. Electrical activity of twelve trunk and leg muscles and displacements of the center of pressure were recorded and analyzed. Principal component analysis was used to identify four M-modes within the space of muscle activations using indices of integrated muscle activation. This analysis was performed twice, over two phases, 400-700 ms prior to the perturbation and over 200 ms just prior to the perturbation. Similar robust results were obtained using the data from both phases. An index of a multi-M-mode synergy stabilizing the center of pressure displacement was computed using the framework of the uncontrolled manifold hypothesis. The results showed high synergy indices during quiet stance. Each of the two stages started with a drop in the synergy index followed by a change in the averaged across trials activation levels in postural muscles. There was a very long electromechanical delay during the early postural adjustments and a much shorter delay during the APAs. Overall, the results support our main hypothesis on the two stages and three components of the postural preparation to action/perturbation. This is the first study to document anticipatory synergy adjustments in whole-body tasks. We interpret the results within the referent configuration hypothesis (an extension of the equilibrium-point hypothesis): The early postural adjustment is based primarily on changes in the coactivation command, while the APAs involve changes in the reciprocal command. The results fit an earlier hypothesis that whole-body movements are controlled by a neuromotor hierarchy where each level involves a few-to-many mappings organized to stabilize its overall output.

Stages in learning motor synergies: a view based on the equilibrium-point hypothesis

This review describes a novel view on stages in motor learning based on recent developments of the notion of synergies, the uncontrolled manifold hypothesis, and the equilibrium-point hypothesis (referent configuration) that allow to merge these notions into a single scheme of motor control. The principle of abundance and the principle of minimal final action form the foundation for analyses of natural motor actions performed by redundant sets of elements. Two main stages of motor learning are introduced corresponding to (1) discovery and strengthening of motor synergies stabilizing salient performance variable(s) and (2) their weakening when other aspects of motor performance are optimized. The first stage may be viewed as consisting of two steps, the elaboration of an adequate referent configuration trajectory and the elaboration of multi-joint (multi-muscle) synergies stabilizing the referent configuration trajectory. Both steps are expected to lead to more variance in the space of elemental variables that is compatible with a desired time profile of the salient performance variable ("good variability"). Adjusting control to other aspects of performance during the second stage (for example, esthetics, energy expenditure, time, fatigue, etc.) may lead to a drop in the "good variability". Experimental support for the suggested scheme is reviewed.

Control of wrist position and muscle relaxation by shifting spatial frames of reference for motoneuronal recruitment: possible involvement of corticospinal pathways

It has previously been established that muscles become active in response to deviations from a threshold (referent) position of the body or its segments, and that intentional motor actions result from central shifts in the referent position. We tested the hypothesis that corticospinal pathways are involved in threshold position control during intentional changes in the wrist position in humans. Subjects moved the wrist from an initial extended to a final flexed position (and vice versa). Passive wrist muscle forces were compensated with a torque motor such that wrist muscle activity was equalized at the two positions. It appeared that motoneuronal excitability tested by brief muscle stretches was also similar at these positions. Responses to mechanical perturbations before and after movement showed that the wrist threshold position was reset when voluntary changes in the joint angle were made. Although the excitability of motoneurons was similar at the two positions, the same transcranial magnetic stimulus (TMS) elicited a wrist extensor jerk in the extension position and a flexor jerk in the flexion position. Extensor motor-evoked potentials (MEPs) elicited by TMS at the wrist extension position were substantially bigger compared to those at the flexion position and vice versa for flexor MEPs. MEPs were substantially reduced when subjects fully relaxed wrist muscles and the wrist was held passively in each position. Results suggest that the corticospinal pathway, possibly with other descending pathways, participates in threshold position control, a process that pre-determines the spatial frame of reference in which the neuromuscular periphery is constrained to work. This control strategy would underlie not only intentional changes in the joint position, but also muscle relaxation. The notion that the motor cortex may control motor actions by shifting spatial frames of reference opens a new avenue in the analysis and understanding of brain function.

Arm path fragmentation and spatiotemporal features of hand reaching in healthy subjects and stroke patients

Arm motion in healthy humans is characterized by smooth and relatively short paths. The current study focused on 3D reaching in stroke patients. Sixteen right-hemiparetic stroke patients and 8 healthy adults performed 42 reaching movements towards 3 visual targets located at an extended arm distance. Performance was assessed in terms of spatial and temporal features of the movement; i.e., hand path, arm posture and smoothness. Differences between groups and within subjects were hypothesized for spatial and temporal aspects of reaching under the assumption that both are independent. As expected, upper limb motion of patients was characterized by longer and jerkier hand paths and slower speeds. Assessment of the number of sub-movements within each movement did not clearly discriminate between groups. Principal component analyses revealed specific clusters of either spatial or temporal measures, which accounted for a large proportion of the variance in patients but not in healthy controls. These findings support the notion of a separation between spatial and temporal features of movement. Stroke patients may fail to integrate the two aspects when executing reaching movements towards visual targets.

Palmar arch modulation in patients with hemiparesis after a stroke

Hand shape modulation has traditionally been studied within the framework of reach-to-grasp tasks by examining the control of arm transport, grip aperture scaling, and finger joint excursions. However, global parameters characterizing arm and hand movement can be enhanced by additional knowledge of biomechanical changes in the hand. We previously examined palmar arch modulation during grasping in healthy subjects by identifying thenar and hypothenar displacement. This method was used to characterize hand shape modulation in 10 stroke survivors with mild hand paresis, as assessed by the Chedoke-McMaster clinical scale, during two types of grasps (spherical, cylindrical). Palmar arch modulation was examined during the three phases of prehensile movement: transport shaping (P1), preshaping (P2), and contact shaping (P3). Compared to the control group, the stroke survivors showed significant differences (spherical: F (2,18) = 12.025, P < 0.001; cylindrical: F (2,18) = 9.054, P < 0.001) in palmar arch modulation particularly during P3 wherein fine adjustments are made to the grip in preparation for object manipulation. While control subjects completed most of hand shape modulation early in the task, stroke survivors took longer to complete each phase. Furthermore, stroke survivors started with a flatter hand which required relatively more arch modulation during the latter part of the task, thereby reflecting a temporal and spatial concurrency between the phases. Stroke survivors with well-recovered hand grasping ability tended to incorporate compensations/adaptations in hand posture during specific grasping phases. Palmar arch analysis provides us with a more complete understanding about how hand biomechanics, specifically palmar concavity articulation, is changed post-stroke. This will allow us to better identify the motor compensations used for grasping and to re-focus rehabilitation interventions to reduce compensations and improve functional motor recovery.

Joint coordination during bimanual transport of real and imaginary objects

We studied multi-joint coordination during tasks of transporting real and imaginary objects with two arms. One of the arms was unexpectedly arrested in one-third of trials performed. In the absence of perturbation, multi-joint synergies stabilizing the distance between the arms early and late in the movement were seen in both conditions and even were stronger in the imaginary object condition. However, quick adjustments in the non-perturbed arm were seen only in the real object condition, whereas the non-perturbed arm did not react to the perturbation in the imaginary object condition. We conclude that tactile information is important for the central nervous system to quickly respond to perturbations in bimanual tasks. The results underscore potential differences between stability in the absence of external perturbations that may be ensured by setting a reference aperture between the hands and stability that requires adjustments in this reference aperture following a major perturbation.

The equilibrium-point hypothesis--past, present and future

This chapter is a brief account of fundamentals of the equilibrium-point hypothesis or more adequately called the threshold control theory (TCT). It also compares the TCT with other approaches to motor control. The basic notions of the TCT are reviewed with a major focus on solutions to the problems of multi-muscle and multi-degrees of freedom redundancy. The TCT incorporates cognitive aspects by explaining how neurons recognize that internal (neural) and external (environmental) events match each other. These aspects as well as how motor learning occurs are subjects of further development of the TCT hypothesis.

Hierarchical control of static prehension: I. Biomechanics

We explored the action of digits during static prehension tasks involving one hand or two hands of one or two persons. Three hypotheses were tested: to prevent slippage of the object, grip force and safety margin (SM) would be largest in bimanual conditions, particularly involving two persons; the distribution of tangential forces would not differ among tested conditions, thus preserving the vertical orientation of the object in a stereotypical way; and the mechanical advantage of fingers would be used to maintain rotational equilibrium. The multi-digit synergies are discussed in the companion paper (Gorniak et al. 2009, in review). The subjects held vertical one of the two handles, a narrow one and a wide one. They used the four fingers of the right hand opposed by either the right hand thumb, the left hand thumb, the left hand index finger, the thumb of an experimenter, the index finger of an experimenter, or an inanimate object. Forces and moments of force produced by each digit were recorded. The first two hypotheses were falsified. Both grip force and SM were the largest in the one-hand task, and they were the lowest for the tasks involving two persons. The distribution of tangential forces among fingers was significantly different in the one-hand task. The mechanical advantage hypothesis was supported across all the tested conditions. The results suggest that the neural controller uses a different strategy in the one-hand task as compared to other tasks, while bimanual prehension involving two persons differs from one-person two-hand tasks. The findings do not support a hypothesis that normal (grip) forces are adjusted to ensure a particular value of the SM. Maintaining rotational equilibrium was achieved differently in different tasks. In particular, the one-hand task was characterized by large intercompensated adjustments in different contributors to the total moment of force, which could be described as chain effects; such adjustments were all but absent in the other conditions. The findings may be interpreted within the framework of the reference configuration hypothesis, in which digit forces emerge due to the discrepancies between the actual and the centrally defined (reference) hand aperture.

Hierarchical control of static prehension: II. Multi-digit synergies

The purpose of this study was to explore the ability of the central nervous system (CNS) to organize synergies at two levels of a hypothetical control hierarchy involved in two-hand multi-finger prehension tasks with one or more persons participating in the task together. At the higher level of the hierarchy, the total force and moment of force produced on an object are distributed between the thumb and the virtual finger (an imagined finger with mechanical output equal to the involved fingers of the hand), while at the lower level the virtual finger action is distributed among the four fingers. We tested a hypothesis that the CNS is able to organize synergies at only one level of the hierarchy. The subjects held vertically one of the two handles, a narrow one and a wide one. They used the four fingers of the right hand opposed by the right hand thumb, the left hand thumb, the left hand index finger, the thumb of an experimenter, the index finger of an experimenter, or an inanimate object. Forces and moments of force produced by each digit were recorded. Indices of synergies stabilizing the mechanical output variables at each of the two levels were computed. Contrary to the expectations, force and moment of force stabilizing synergies were found at one or both levels of the hierarchy across all tasks. Unimanual tasks exhibited higher synergy indices compared to all tasks, while intrapersonal synergy indices were higher than those of interpersonal synergies. The results suggest that both feed-forward and feedback mechanisms may be used to create force and moment of force stabilizing synergies. We invoke the notion of chain effects and generalize it for relations among variance components related to stabilization of different mechanical variables. The reference configuration hypothesis offers a fruitful framework for analysis of prehension synergies.

The inactivation principle: mathematical solutions minimizing the absolute work and biological implications for the planning of arm movements

An important question in the literature focusing on motor control is to determine which laws drive biological limb movements. This question has prompted numerous investigations analyzing arm movements in both humans and monkeys. Many theories assume that among all possible movements the one actually performed satisfies an optimality criterion. In the framework of optimal control theory, a first approach is to choose a cost function and test whether the proposed model fits with experimental data. A second approach (generally considered as the more difficult) is to infer the cost function from behavioral data. The cost proposed here includes a term called the absolute work of forces, reflecting the mechanical energy expenditure. Contrary to most investigations studying optimality principles of arm movements, this model has the particularity of using a cost function that is not smooth. First, a mathematical theory related to both direct and inverse optimal control approaches is presented. The first theoretical result is the Inactivation Principle, according to which minimizing a term similar to the absolute work implies simultaneous inactivation of agonistic and antagonistic muscles acting on a single joint, near the time of peak velocity. The second theoretical result is that, conversely, the presence of non-smoothness in the cost function is a necessary condition for the existence of such inactivation. Second, during an experimental study, participants were asked to perform fast vertical arm movements with one, two, and three degrees of freedom. Observed trajectories, velocity profiles, and final postures were accurately simulated by the model. In accordance, electromyographic signals showed brief simultaneous inactivation of opposing muscles during movements. Thus, assuming that human movements are optimal with respect to a certain integral cost, the minimization of an absolute-work-like cost is supported by experimental observations. Such types of optimality criteria may be applied to a large range of biological movements.

When performing reaching and grasping movements, the brain has to choose one trajectory among an infinite set of possibilities. Nevertheless, because human and animal movements provide highly stereotyped features, motor strategies used by the brain were assumed to be optimal according to certain optimality criteria. In this study, we propose a theoretical model for motor planning of arm movements that minimizes a compromise between the absolute work exerted by the muscles and the integral of the squared acceleration. We demonstrate that under these assumptions agonistic and antagonistic muscles are inactivated during overlapping periods of time for quick enough movements. Moreover, it is shown that only this type of criterion can predict these inactivation periods. Finally, experimental evidence is in agreement with the predictions of the model. Indeed, we report the existence of simultaneous inactivation of opposing muscles during fast vertical arm movements. Therefore, this study suggests that biological movements partly optimize the energy expenditure, integrating both inertial and gravitational forces during the motor planning process.

Palmar arch dynamics during reach-to-grasp tasks

The relationship between arm transport and grip aperture scaling has traditionally been used to study the control of reaching and grasping. Since the palmar concavity forms a postural base of the hand, intuitively it should play an essential role in hand shape modulation during grasping. This role however has not yet been investigated. This study investigated whether hand shape modulation was initiated at the palmar level or at the level of the finger joints during two types of power grasps (spherical, cylindrical). Hand shape modulation was studied in eight healthy adults and was characterized by the change in palmar arch movement during three phases of the reach-to-grasp tasks, traditionally defined as arm transport, hand preshaping and object contact. Palmar arch kinematics changed significantly during arm transport for both types of grasp (spherical 47.4%, cylindrical 63.7%). Approximately 16% more modulation was observed when grasping the cylindrical as compared to the spherical object. This was counterbalanced by relatively less modulation during the preshaping and object contact phases compared to the spherical grasp. These results showed that the three grasping phases occurred concurrently in a common time window. Furthermore, an increase in the duration of either one of the components impacted the execution of the others. A secondary finding was that hand shape modulation began at the same time or within 125 ms of the initiation of arm transport for both grasp types. In most cases (60%), movement in the palmar arch occurred prior to movement at the metacarpophalangeal joint (MCP) of the index and middle fingers. The same was observed when palmar arch modulation was compared with the time of movement initiation in the proximal interphalangeal (PIP) joints of the index and middle fingers (60-75%). Thus palmar and finger joint movement were initiated almost simultaneously and hand shape modulation began early in the reach-to-grasp task. The findings show that hand shape and arm transport were modulated together and suggest that prehensile movement, including both palmar arch and finger configuration, is planned as early as the intent to grasp.

Is voluntary control of natural postural sway possible?

The authors explored whether standing human participants could voluntarily decrease the amplitude of their natural postural sway when presented with explicit visual feedback and a target. Participants (N = 9) stood quietly, without any feedback and with feedback on the center of pressure coordinate or the head orientation. They were unable to decrease sway amplitude when presented with visual feedback and a target. Decreasing target size led to contrasting effects on the 2 fractions of sway: rambling and trembling. The smaller target was associated with a decrease in rambling and an increase in trembling. Those observations suggest that sway represents a superposition of at least 2 independent processes. They also suggest that providing visual feedback on a variable tied to body sway may not be an effective way to decrease postural sway in young healthy people.

Do synergies decrease force variability? A study of single-finger and multi-finger force production

We tested a hypothesis that force production by multi-finger groups leads to lower indices of force variability as compared to similar single-finger tasks. Three experiments were performed with quick force production, steady-state force production under visual feedback, and steady-state force production without visual feedback. In all experiments, a range of force levels was used computed as percentages of the maximal voluntary contraction force for each involved finger combination. Force standard deviation increased linearly with force magnitude across all three experiments and all finger combinations. There were modest differences between multi-finger and single-finger tasks in the indices of force variability, significant only in the tasks with steady-state force production under visual feedback. When fingers acted in groups, each finger showed significantly higher force variability as compared to its single-finger task and as compared to the multi-finger group as a whole. Fingers that were not instructed to produce force also showed close to linear relations between force standard deviation and force magnitude. For these fingers, indices of force variability were much higher as compared to those computed for the forces produced by instructed fingers. We interpret the findings within a feed-forward scheme of multi-finger control with two inputs only one of which is related to the explicit task. The total force variability reflects variability in only the task-related component, while variability of the finger forces is also due to variability of the component that is not related to the task. The findings tentatively suggest that total force variability originates at an upper level of the control hierarchy in accordance to the Weber-Fechner law rather than reflects a "neural noise" at the segmental level.

Multi-muscle synergies in an unusual postural task: quick shear force production

We considered a hypothetical two-level hierarchy participating in the control of vertical posture. The framework of the uncontrolled manifold (UCM) hypothesis was used to explore the muscle groupings (M-modes) and multi-M-mode synergies involved in the stabilization of a time profile of the shear force in the anterior-posterior direction. Standing subjects were asked to produce pulses of shear force into a target using visual feedback while trying to minimize the shift of the center of pressure (COP). Principal component analysis applied to integrated muscle activation indices identified three M-modes. The composition of the M-modes was similar across subjects and the two directions of the shear force pulse. It differed from the composition of M-modes described in earlier studies of more natural actions associated with large COP shifts. Further, the trial-to-trial M-mode variance was partitioned into two components: one component that does not affect a particular performance variable (V(UCM)), and its orthogonal component (V(ORT)). We argued that there is a multi-M-mode synergy stabilizing this particular performance variable if V(UCM) is higher than V(ORT). Overall, we found a multi-M-mode synergy stabilizing both shear force and COP coordinate. For the shear force, this synergy was strong for the backward force pulses and nonsignificant for the forward pulses. An opposite result was found for the COP coordinate: the synergy was stronger for the forward force pulses. The study shows that M-mode composition can change in a task-specific way and that two different performance variables can be stabilized using the same set of elemental variables (M-modes). The different dependences of the ΔV indices for the shear force and COP coordinate on the force pulse direction supports applicability of the principle of superposition (separate controllers for different performance variables) to the control of different mechanical variables in postural tasks. The M-mode composition allows a natural mechanical interpretation.

Threshold position control signifies a common spatial frame of reference for motor action and kinesthesia

Abundance of muscle spindles is most likely related to gradual recruitment and functional specialization of motor units, as well as to their fundamental role in reflex intermuscular interaction and cooperation with other sensory systems. Spindle afferents per se usually convey ambiguous kinesthetic information to the brain. Experimental data indicate that the nervous system cannot use efferent copies, i.e., pre-programmed imitations of motor commands to muscles to overcome this ambiguity and form adequate position sense. Instead, position sense becomes adequate when proprioceptive signals are interpreted in reference to the threshold limb position set by the brain. By resetting the threshold position, the nervous system not only appropriately adjusts kinesthetic sense but also causes motor action. This brief analysis illustrates not only that action and perception are coupled [J.J. Gibson, The Senses Considered as Perceptual Systems. George Allen and Unwin Ltd., London, 1968; W.H. Warren, The dynamics of perception and action. Psychol. Rev. 113 (2006) 358-89] but also that they are accomplished in the same spatial frame of reference selected and manipulated by the brain.

Relationship between stretch reflex thresholds and voluntary arm muscle activation in patients with spasticity

Previous studies have shown that deficits in agonist-antagonist muscle activation in the single-joint elbow system in patients with spastic hemiparesis are directly related to limitations in the range of regulation of the thresholds of muscle activation. We extended these findings to the double-joint, shoulder-elbow system in these patients. Ten non-disabled individuals and 11 stroke survivors with spasticity in upper limb muscles participated. Stroke survivors had sustained a single unilateral stroke 6-36 months previously, had full pain-free passive range of motion of the affected shoulder and elbow and had some voluntary control of the arm. EMG activity from four elbow and two shoulder muscles was recorded during quasi-static (<5 degrees /s) stretching of elbow flexors/extensors and during slow voluntary elbow flexion/extension movement through full range. Stretches and active movements were initiated from full elbow flexion or extension with the shoulder in three different initial positions (60 degrees , 90 degrees , 145 degrees horizontal abduction). SRTs were defined as the elbow angle at which EMG signals began to exceed 2SD of background noise. SRT angles obtained by passive muscle stretch were compared with the angles at which the respective muscles became activated during voluntary elbow movements. SRTs in elbow flexors were correlated with clinical spasticity scores. SRTs of elbow flexors and extensors were within the biomechanical range of the joint and varied with changes in the shoulder angle in all subjects with hemiparesis but could not be reached in this range in all healthy subjects when muscles were initially relaxed. In patients, limitations in the regulation of SRTs resulted in a subdivision of all-possible shoulder-elbow arm configurations into two areas, one in which spasticity was present ("spatial spasticity zone") and another in which it was absent. Spatial spasticity zones were different for different muscles in different patients but, taken together, for all elbow muscles, the zones occupied a large part of elbow-shoulder joint space in each patient. The shape of the boundary between the spasticity and no-spasticity zones depended on the state of reflex inter-joint interaction. SRTs in single- and double-joint flexor muscles correlated with the positions at which muscles were activated during voluntary movements, for all shoulder angles, and this effect was greater in elbow flexor muscles (brachioradialis, biceps brachii). Flexor SRTs correlated with clinical spasticity in elbow flexors only when elbow muscles were at mid-length (90 degrees ). These findings support the notion that motor impairments after CNS damage are related to deficits in the specification and regulation of SRTs, resulting in the occurrence of spasticity zones in the space of elbow-shoulder configurations. It is suggested that the presence of spatial spasticity zones might be a major cause of motor impairments in general and deficits in inter-joint coordination in particular in patients with spasticity.