Hierarchies of synergies: an example of two-hand, multi-finger tasks

Hierarchical Organization and Adjustment of Force Coordination in Response to Self-Triggered and External-Triggered Cues in Simulated Archery Performance

The purpose of this study was to investigate the hierarchical organization of digit force production and its effect on stability and performance during the simulated archery task. The simulated archery shooting task required the production of a prescribed level of force in virtual space with the left hand and an equivalent force with all 4 fingers of right hand. A single trial had 2 phases, including static force production as aiming in archery and quick force release to shoot the virtual arrow. The timing of the force release was determined by the participant's choice or response to the external cue. The coordination indices, that is, the synergy index, of force stabilization were quantified in 2 hierarchies by decomposing the variance components. The accuracy and precision of the hit position of the virtual arrow were calculated as performance-related indices. The results confirmed that the precision, that is, reproducibility, of the performance was greater when the force release time was determined by the self-selected time, suggesting the beneficial effect of the anticipatory mechanism. There was a distinct synergistic organization of digit forces for the stabilization of net forces in both bimanual and multifinger levels, which was especially correlated with the precision of performance.

Three Levels of Neural Control Contributing to Performance-stabilizing Synergies in Multi-finger Tasks

We tested a hypothesis on force-stabilizing synergies during four-finger accurate force production at three levels: (1) The level of the reciprocal and coactivation commands, estimated as the referent coordinate and apparent stiffness of all four fingers combined; (2) The level of individual finger forces; and (3) The level of firing of individual motor units (MU). Young, healthy participants performed accurate four-finger force production at a comfortable, non-fatiguing level under visual feedback on the total force magnitude. Mechanical reflections of the reciprocal and coactivation commands were estimated using small, smooth finger perturbations applied by the "inverse piano" device. Firing frequencies of motor units in the flexor digitorum superficialis (FDS) and extensor digitorum communis (EDC) were estimated using surface recording. Principal component analysis was used to identify robust MU groups (MU-modes) with parallel changes in the firing frequency. The framework of the uncontrolled manifold hypothesis was used to compute synergy indices in the spaces of referent coordinate and apparent stiffness, finger forces, and MU-mode magnitudes. Force-stabilizing synergies were seen at all three levels. They were present in the MU-mode spaces defined for MUs in FDS, in EDC, and pooled over both muscles. No effects of hand dominance were seen. The synergy indices defined at different levels of analysis showed no correlations across the participants. The findings are interpreted within the theory of control with spatial referent coordinates for the effectors. We conclude that force stabilization gets contributions from three levels of neural control, likely associated with cortical, subcortical, and spinal circuitry.

Force matching: motor effects that are not reported by the actor

We explored unintentional drifts of finger forces during force production and matching task. Based on earlier studies, we predicted that force matching with the other hand would reduce or stop the force drift in instructed fingers while uninstructed (enslaved) fingers remain unaffected. Twelve young, healthy, right-handed participants performed two types of tasks with both hands (task hand and match hand). The task hand produced constant force at 20% of MVC level with the Index and Ring fingers pressing in parallel on strain gauge force sensors. The Middle finger force wasn't instructed, and its enslaved force was recorded. Visual feedback on the total force by the instructed fingers was either present throughout the trial or only during the first 5 s (no-feedback condition). The other hand matched the perceived force level of the task hand starting at either 4, 8, or 15 s from the trial initiation. No feedback was ever provided for the match hand force. After the visual feedback was removed, the task hand showed a consistent drift to lower magnitudes of total force. Contrary to our prediction, over all conditions, force matching caused a brief acceleration of force drift in the task hand, which then reached a plateau. There was no effect of matching on drifts in enslaved finger force. We interpret the force drifts within the theory of control with spatial referent coordinates as consequences of drifts in the command (referent coordinate) to the antagonist muscles. This command is not adequately incorporated into force perception.

Two classes of action-stabilizing synergies reflecting spinal and supraspinal circuitry

We explored force-stabilizing synergies during accurate four-finger constant force production tasks in spaces of finger modes (commands to fingers computed to account for the finger interdependence) and of motor unit (MU) firing frequencies. The main specific hypothesis was that the multifinger synergies would disappear during unintentional force drifts without visual feedback on the force magnitude, whereas MU-based synergies would be robust to such drifts. Healthy participants performed four-finger accurate cyclical force production trials followed by trials of constant force production. Individual MUs were identified in the flexor digitorum superficialis (FDS) and extensor digitorum communis (EDC). Principal component analysis was applied to motor unit frequencies to identify robust MU groups (MU-modes) with parallel scaling of the firing frequencies in FDS, in EDC, and the combined MUs of FDS + EDC. The framework of the uncontrolled manifold hypothesis was used to quantify force-stabilizing synergies when visual feedback on the force magnitude was available and 15 s after turning the visual feedback off. Removing visual feedback led to a force drift toward lower magnitudes, accompanied by the disappearance of multifinger synergies. In contrast, MU-mode synergies were minimally affected by removing visual feedback off and continued to be robust for the FDS and for the EDC, while being absent for the (FDS + EDC) analysis. We interpret the findings within the theory of hierarchical control of action with spatial referent coordinates. The qualitatively different behavior of the multifinger and MU-mode-based synergies likely reflects the difference in the involved neural circuitry, supraspinal for the former and spinal for the latter.NEW & NOTEWORTHY Two types of synergies, in the space of commands to individual fingers and in the space of motor unit groups, show qualitatively different behaviors during accurate multifinger force-production tasks. After removing visual feedback, finger force synergies disappear, whereas motor unit-based synergies persist. These results point at different neural circuitry involved in these two basic classes of synergies: supraspinal for multieffector synergies, and spinal for motor unit-based synergies.

Motor unit-based synergies in a non-compartmentalized muscle

The concept of synergies has been used to address the grouping of motor elements contributing to a task with the covariation of these elements reflecting task stability. This concept has recently been extended to groups of motor units with parallel scaling of the firing frequencies with possible contributions of intermittent recruitment (MU-modes) in compartmentalized flexor and extensor muscles of the forearm stabilizing force magnitude in finger pressing tasks. Here, we directly test for the presence and behavior of MU-modes in the tibialis anterior, a non-compartmentalized muscle. Ten participants performed an isometric cyclical dorsiflexion force production task at 1 Hz between 20 and 40% of maximal voluntary contraction and electromyographic (EMG) data were collected from two high-density wireless sensors placed on the skin over the right tibialis anterior. EMG data were decomposed into individual motor unit frequencies and resolved into sets of MU-modes. Inter-cycle analysis of MU-mode magnitudes within the framework of the uncontrolled manifold (UCM) hypothesis was used to quantify force-stabilizing synergies. Two or three MU-modes were identified in all participants and trials accounting, on average, for 69% of variance and were robust to cross-validation measurements. Strong dorsiflexion force-stabilizing synergies in the space of MU-modes were present in all participants and for both electrode locations as reflected in variance within the UCM (median 954, IQR 511-1924) exceeding variance orthogonal to the UCM (median 5.82, IQR 2.9-17.4) by two orders of magnitude. In contrast, MU-mode-stabilizing synergies in the space of motor unit frequencies were not present. This study offers strong evidence for the existence of synergic control mechanisms at the level of motor units independent of muscle compartmentalization, likely organized within spinal cord circuitry.

Effects of hand muscle function and dominance on intra-muscle synergies

The goal of the study was to explore the effects of hand dominance and muscle function (prime mover vs. supporting muscle) on recently discovered intra-muscle synergies as potential windows into their neural origin. Healthy right-handed subjects performed accurate cyclical force production tasks while pressing with the middle phalanges and distal phalanges of the fingers of the dominant and non-dominant hand. Surface electromyography was used to identify individual motor unit action potentials in two muscles, flexor digitorum superficialis (FDS) and extensor digitorum communis (EDC). Stable motor unit groups (MU-modes) were defined in each muscle and in both muscles together. The composition of the MU-modes allowed linking them to the reciprocal and co-activation command. Force-stabilizing synergies were quantified in each hand and during force production at both sites using the framework of the uncontrolled manifold hypothesis. Force-stabilizing synergies were seen in the spaces of MU-modes from FDS and EDC separately, but not of MU-modes defined for both muscles together. Synergy indices were similar for both hands and both sites of force application. In contrast, force-stabilizing synergies in the space of finger forces were present in the non-dominant hand and absent in the dominant hand. The data suggest existence of distributed mechanisms of synergic control. Finger force synergies are likely to reflect functioning of subcortical loops involving the basal ganglia and cerebellum, while MU-mode synergies are likely to reflect spinal circuitry. Studies of both force-based and motor-unit-based synergies may be clinically valuable for distinguishing effects of spinal and supraspinal disorders.

Intramuscle Synergies: Their Place in the Neural Control Hierarchy

We accept a definition of synergy introduced by Nikolai Bernstein and develop it for various actions, from those involving the whole body to those involving a single muscle. Furthermore, we use two major theoretical developments in the field of motor control—the idea of hierarchical control with spatial referent coordinates and the uncontrolled manifold hypothesis—to discuss recent studies of synergies within spaces of individual motor units (MUs) recorded within a single muscle. During the accurate finger force production tasks, MUs within hand extrinsic muscles form robust groups, with parallel scaling of the firing frequencies. The loading factors at individual MUs within each of the two main groups link them to the reciprocal and coactivation commands. Furthermore, groups are recruited in a task-specific way with gains that covary to stabilize muscle force. Such force-stabilizing synergies are seen in MUs recorded in the agonist and antagonist muscles but not in the spaces of MUs combined over the two muscles. These observations reflect inherent trade-offs between synergies at different levels of a control hierarchy. MU-based synergies do not show effects of hand dominance, whereas such effects are seen in multifinger synergies. Involuntary, reflex-based, force changes are stabilized by intramuscle synergies but not by multifinger synergies. These observations suggest that multifinger (multimuscle synergies) are based primarily on supraspinal circuitry, whereas intramuscle synergies reflect spinal circuitry. Studies of intra- and multimuscle synergies promise a powerful tool for exploring changes in spinal and supraspinal circuitry across patient populations.

Reciprocal and coactivation commands at the level of individual motor units in an extrinsic finger flexor-extensor muscle pair

We explored the synergic organization of motor units in extrinsic finger muscles, flexor digitorum superficialis (FDS), and extensor digitorum communis (EDC). Healthy subjects produced accurate cyclical force by pressing with the middle phalanges of one of the three fingers (Index, Middle, and Ring) and all three together. Two wireless sensor arrays were used to record and identify motor unit action potentials in FDS and EDC. Stable motor unit groups were identified within each muscle and across both muscles. Analysis of motor units combined over the two muscles showed one of the first two motor unit groups with consistently opposite signs of the loading factors for the FDS and EDC motor units, and the other group with consistently same signs of the loading factors for the two muscles. We interpret the two motor unit groups as reflections of the reciprocal and co-activation commands within the theory of control with spatial referent coordinates. Force changes within the cycle were primarily associated with the modulation of the co-activation motor unit group. Analysis of inter-cycle variance within the spaces of motor unit groups defined for FDS and EDC separately showed force-stabilizing synergies across both single-finger and three-finger tasks. In contrast, analysis within the motor unit groups defined across both muscles failed to show force-stabilizing synergies. We interpret these results as a reflection of the trade-off across levels within a hierarchical control system.

Interpersonal motor synergy: coworking strategy depends on task constraints

We investigated the role of task constraints on interpersonal interactions. Twenty-one pairs of coworkers performed a finger force production task on force sensors placed at two ends of a seesaw-like apparatus and matched a combined target force of 20 N for 23 s over 10 trials. There were two experimental conditions: 1) FIXED: the seesaw apparatus was mechanically held in place so that the only task constraint was to match the 20 N resultant force, and 2) MOVING: the lever in the apparatus was allowed to rotate freely around its fulcrum, acting like a seesaw, so an additional task constraint to (implicitly) balance the resultant moment was added. We hypothesized that the additional task constraint of moment stabilization imposed on the MOVING condition would deteriorate task performance compared with the FIXED condition; however, this was rejected, as the performance of the force matching task was similar between two conditions. We also hypothesized that the central nervous systems (CNSs) would employ distinct coworking strategies or interpersonal motor synergy (IPMS) between conditions to satisfy different task constraints, which was supported by our results. Negative covariance between coworker's forces in the FIXED condition suggested a force stabilization strategy, whereas positive covariance in the MOVING condition suggested a moment stabilization strategy, implying that independent CNSs adopt distinct IPMSs depending on task constraints. We speculate that in the absence of a central neural controller, shared visual and mechanical connections between coworkers may suffice to trigger modulations in the cerebellum of each CNS to satisfy competing task constraints.NEW & NOTEWORTHY To the best of our knowledge, this is the first study to investigate the coworking behavior or IPMS when an additional task constraint is imposed. Our proposed analytical framework quantifies IPMS and allows for investigating variability in offline (i.e., across multiple repetitions) and online (i.e., across time) control, which is novel in coworking research. Understanding variability while performing a task is essential, as repeating a task is not always possible, as in therapeutic contexts.

Are synergies continuously present in cyclical movements? An example with the basketball dribble task

In human movement, synergies occur when two or more variables co-vary to stabilize a performance goal. The concept of motor redundancy is associated with the existence of several strategies to complete the same task, which enables a movement system to adapt to an ever-changing environment. This feature provides the system with the ability of being flexible enough to produce adaptive movements, but also stable enough to produce acceptable outputs which is a key issue in motor performance. In a kinetic chain of movement, two proximal joints might reciprocally compensate to stabilize an end-effector (i.e., the most distal segment in the limb that interacts with the environment). End-effector variables are 'controlled', and directly linked to performance, whereas the task relevant elements are allowed by the system to have high variability, providing adaptability. In basketball dribbling, we hypothesized that shoulder and elbow variability contributes to stabilize the dribble height as an end-effector performance variable. A specific computational procedure based on the UCM (i.e., Uncontrolled Manifold) notion was used to capture synergies in two groups according to the experience level: amateurs and professionals. Results identified synergy presence during the basketball dribbling, which only occurred when the wrist reached its peak height. The control of the wrist peak height is achieved due to a reciprocal compensation between shoulder and elbow which stabilizes the dribbling height.

One more time about motor (and non-motor) synergies

We revisit the concept of synergy based on the recently translated classical book by Nikolai Bernstein (On the construction of movements, Medgiz, Moscow 1947; Latash, Bernstein's Construction of Movements, Routledge, Abingdon 2020b) and progress in understanding the physics and neurophysiology of biological action. Two aspects of synergies are described: organizing elements into stable groups (modes) and ensuring dynamical stability of salient performance variables. The ability of the central nervous system to attenuate synergies in preparation for a quick action-anticipatory synergy adjustments-is emphasized. Recent studies have demonstrated synergies at the level of hypothetical control variables associated with spatial referent coordinates for effectors. Overall, the concept of synergies fits naturally the hierarchical scheme of control with referent coordinates with an important role played by back-coupling loops within the central nervous system and from peripheral sensory endings. Further, we review studies showing non-trivial changes in synergies with development, aging, fatigue, practice, and a variety of neurological disorders. Two aspects of impaired synergic control-impaired stability and impaired agility-are introduced. The recent generalization of the concept of synergies for non-motor domains, including perception, is discussed. We end the review with a list of unresolved and troubling issues.

Synergies at the level of motor units in single-finger and multi-finger tasks

We explored the organization of motor units recorded in the flexor digitorum superficialis into stable groups (MU-modes) and force-stabilizing synergies in spaces of MU-modes. Young, healthy participants performed one-finger and three-finger accurate cyclical force production tasks. Two wireless sensor arrays (Trigno Galileo, Delsys, Inc.) were placed over the proximal and distal portions of the muscle for surface recording and identification of motor unit action potentials. Principal component analysis with Varimax rotation and factor extraction was used to identify MU-modes. The framework of the uncontrolled manifold hypothesis was used to analyze inter-cycle variance in the space of MU-modes and compute the index of force-stabilizing synergy. Multiple linear regression between the first MU-mode in the three-finger task and the first MU-modes in the three single-finger tasks showed no differences between the data recorded by the two electrodes suggesting that MU-modes were unlikely to be synonymous with muscle compartments. Multi-MU-mode synergies stabilizing task force were documented across all tasks. In contrast, there were no force-stabilizing synergies in the three-finger task analyzed in the space of individual finger forces. Our results confirm the synergic organization of motor units in single-finger tasks and, for the first time, expand this result to multi-finger tasks. We offer an interpretation of the findings within the theoretical scheme of control with spatial referent coordinates expanded to the analysis of individual motor units. The results confirm trade-offs between synergies at different hierarchical levels and expand this notion to intra-muscle synergies.

Role of Tactile Noise in the Control of Digit Normal Force

Whenever we grasp and lift an object, our tactile system provides important information on the contact location and the force exerted on our skin. The human brain integrates signals from multiple sites for a coherent representation of object shape, inertia, weight, and other material properties. It is still an open question whether the control of grasp force occurs at the level of individual fingers or whether it is also influenced by the control and the signals from the other fingers of the same hand. In this work, we approached this question by asking participants to lift, transport, and replace a sensorized object, using three- and four-digit grasp. Tactile input was altered by covering participant's fingertips with a rubber thimble, which reduced the reliability of the tactile sensory input. In different experimental conditions, we covered between one and three fingers opposing the thumb. Normal forces at each finger and the thumb were recorded while grasping and holding the object, with and without the thimble. Consistently with previous studies, reducing tactile sensitivity increased the overall grasping force. The gasping force increased in the covered finger, whereas it did not change from baseline in the remaining bare fingers (except the thumb for equilibrium constraints). Digit placement and object tilt were not systematically affected by rubber thimble conditions. Our results suggest that, in each finger opposing thumb, digit normal force is controlled locally in response to the applied tactile perturbation.

Number of Trials Necessary to Apply Analysis Within the Framework of the Uncontrolled Manifold Hypothesis at Different Levels of Hierarchical Synergy Control

The uncontrolled manifold hypothesis is a method used to quantify motor synergies, defined as a specific central nervous system organization that maintains the task-specific stability of motor actions. The UCM allows for inter-trial variance analysis between consecutive trials. However, despite the large body of literature within this framework, there is no report on the number of movement repetitions required for reliable results. Based on the hypothetical hierarchical control of motor synergies, this study aims to determine the minimum number of trials necessary to achieve a good to excellent level of reliability. Thirteen young, healthy participants performed fifteen bilateral isometric contractions of elbow flexion when visual feedback was provided. The force and electromyography data were recorded to investigate synergies at different levels of hierarchical control. The intraclass correlation coefficient was used to determine the reliability of the variance indices. Based on the obtained results, at least twelve trials are required to analyze the inter-trial variance in both force and muscle synergies within the UCM framework.

What do people match when they try to match force? Analysis at the level of hypothetical control variables

We used the theory of control with spatial referent coordinates (RC) to explore how young, healthy persons modify finger pressing force and match forces between the two hands. Three specific hypotheses were tested related to patterns of RC and apparent stiffness (defined as the slope of force-coordinate relation) used in the presence of visual feedback on the force and in its absence. The subjects used the right hand to produce accurate force under visual feedback; further the force could be increased or decreased, intentionally or unintentionally (induced by controlled lifting or lowering of the fingertips). The left hand was used to match force without visual feedback before and after the force change; the match hand consistently underestimated the actual force change in the task hand. The "inverse piano" device was used to compute RC and apparent stiffness. We found very high coefficients of determination for the inter-trial hyperbolic regressions between RC and apparent stiffness in the presence of visual feedback; the coefficients of determination dropped significantly without visual feedback. There were consistent preferred sharing patterns in the space of RC and apparent stiffness between the task and match hands across subjects. In contrast, there was much less consistency between the task and match hands in the magnitudes of RC and apparent stiffness observed in individual trials. Compared to the task hand, the match hand showed consistently lower magnitudes of apparent stiffness and, correspondingly, larger absolute magnitudes of RC. Involuntary force changes produced by lifting and lowering the force sensors led to significantly lower force changes compared to what could be expected based on the computed values of apparent stiffness and sensor movement amplitude. The results confirm the importance of visual feedback for stabilization of force in the space of hypothetical control variables. They suggest the existence of personal traits reflected in preferred ranges of RC and apparent stiffness across the two hands. They also show that subjects react to external perturbations, even when instructed "not to interfere": Such perturbations cause unintentional and unperceived drifts in both RC and apparent stiffness.

Performance-Stabilizing Synergies in a Complex Motor Skill: Analysis Based on the Uncontrolled Manifold Hypothesis

The authors studied indices of stability (ΔV) of two time-varying variables, hand coordinate and velocity, during accurate throw of a small ball into the basket. Ten participants performed the throwing task with eyes-open (vision) and -closed (no vision) conditions. In the latter condition, participants closed their eyes prior to initiating the throw. The intertrial variance in the joint configuration space (and joint velocity space) was analyzed based on the uncontrolled manifold hypothesis. The results confirmed the presence of both coordinate- and velocity-stabilizing synergies (ΔV > 0). Intertrial variance was larger in the no-vision condition compared with the vision condition. Over the movement duration, ΔV did not change for the coordinate-related analysis but dropped consistently for the velocity-related analysis. The authors interpret the findings within the idea of hierarchical control and trade-off between synergy indices at different levels of the hierarchy.

Stability of hand force production. II. Ascending and descending synergies

We combined the theory of neural control of movement with referent coordinates and the uncontrolled manifold hypothesis to investigate multifinger coordination. We tested hypotheses related to stabilization of performance by covarying control variables, translated into apparent stiffness and referent coordinate, at different levels of an assumed hierarchy of control. Subjects produced an accurate combination of total force and total moment of force with the four fingers under visual feedback on both variables and after feedback was partly or completely removed. The "inverse piano" device was used to estimate control variables. We observed strong synergies in the space of hypothetical control variables that stabilized total force and moment of force, as well as weaker synergies stabilizing individual finger forces; whereas the former were attenuated by alteration of visual feedback, the latter were much less affected. In addition, we investigated the organization of "ascending synergies" stabilizing task-level control variables by covaried adjustments of finger-level control variables. We observed intertrial covariation of individual fingers' referent coordinates that stabilized hand-level referent coordinate, but we observed no such covariation for apparent stiffness. The observations suggest the existence of both descending and ascending synergies in a hierarchical control system. They confirm a trade-off between synergies at different levels of control and corroborate the hypothesis on specialization of different fingers for the control of force and moment. The results provide strong evidence for the importance of central back-coupling loops in ensuring stability of action. NEW & NOTEWORTHY We expand analysis of action in the space of hypothetical control variables to hierarchically organized multieffector systems. We also introduce the novel concept of ascending synergies, which reflect covariation of control variables to individual effectors (fingers) that stabilize task-specific control variables at a hierarchically higher, task-specific level (hand).

Stability of hand force production. I. Hand level control variables and multifinger synergies

We combined the theory of neural control of movement with referent coordinates and the uncontrolled manifold hypothesis to explore synergies stabilizing the hand action in accurate four-finger pressing tasks. In particular, we tested a hypothesis on two classes of synergies, those among the four fingers and those within a pair of control variables, stabilizing hand action under visual feedback and disappearing without visual feedback. Subjects performed four-finger total force and moment production tasks under visual feedback; the feedback was later partially or completely removed. The "inverse piano" device was used to lift and lower the fingers smoothly at the beginning and at the end of each trial. These data were used to compute pairs of hypothetical control variables. Intertrial analysis of variance within the finger force space was used to quantify multifinger synergies stabilizing both force and moment. A data permutation method was used to quantify synergies among control variables. Under visual feedback, synergies in the spaces of finger forces and hypothetical control variables were found to stabilize total force. Without visual feedback, the subjects showed a force drift to lower magnitudes and a moment drift toward pronation. This was accompanied by disappearance of the four-finger synergies and strong attenuation of the control variable synergies. The indexes of the two types of synergies correlated with each other. The findings are interpreted within the scheme with multiple levels of abundant variables.NEW & NOTEWORTHY We extended the idea of hierarchical control with referent spatial coordinates for the effectors and explored two types of synergies stabilizing multifinger force production tasks. We observed synergies among finger forces and synergies between hypothetical control variables that stabilized performance under visual feedback but failed to stabilize it after visual feedback had been removed. Indexes of two types of synergies correlated with each other. The data suggest the existence of multiple mechanisms stabilizing motor actions.

Postural Hand Synergies during Environmental Constraint Exploitation

Humans are able to intuitively exploit the shape of an object and environmental constraints to achieve stable grasps and perform dexterous manipulations. In doing that, a vast range of kinematic strategies can be observed. However, in this work we formulate the hypothesis that such ability can be described in terms of a synergistic behavior in the generation of hand postures, i.e., using a reduced set of commonly used kinematic patterns. This is in analogy with previous studies showing the presence of such behavior in different tasks, such as grasping. We investigated this hypothesis in experiments performed by six subjects, who were asked to grasp objects from a flat surface. We quantitatively characterized hand posture behavior from a kinematic perspective, i.e., the hand joint angles, in both pre-shaping and during the interaction with the environment. To determine the role of tactile feedback, we repeated the same experiments but with subjects wearing a rigid shell on the fingertips to reduce cutaneous afferent inputs. Results show the persistence of at least two postural synergies in all the considered experimental conditions and phases. Tactile impairment does not alter significantly the first two synergies, and contact with the environment generates a change only for higher order Principal Components. A good match also arises between the first synergy found in our analysis and the first synergy of grasping as quantified by previous work. The present study is motivated by the interest of learning from the human example, extracting lessons that can be applied in robot design and control. Thus, we conclude with a discussion on implications for robotics of our findings.

Analytical Inverse Optimization in Two-Hand Prehensile Tasks

The authors explored application of analytical inverse optimization (ANIO) method to the normal finger forces in unimanual and bimanual prehensile tasks with discrete and continuously changing constraints. The subjects held an instrumented handle vertically with one or two hands. The external torque and grip force changed across trials or within a trial continuously. Principal component analysis showed similar percentages of variance accounted for by the first two principal components across tasks and conditions. Compared to unimanual tasks, bimanual tasks showed significantly more frequent inability to find a cost function leading to a stable solution. In cases of stable solutions, similar second-order polynomials were computed as cost functions across tasks and condition. The bimanual tasks, however, showed significantly worse goodness-of-fit index values. The authors show that ANIO can be used in tasks with slowly changing constraints making it an attractive tool to study optimality of performance in special populations. They also show that ANIO can fail in multifinger tasks, likely due to irreproducible behavior across trials, more likely to happen in bimanual tasks compared to unimanual tasks.

Interpersonal synergies: static prehension tasks performed by two actors

We investigated multidigit synergies stabilizing components of the resultant force vector during joint performance of a static prehension task by two persons as compared to similar tasks performed by a single person using both hands. Subjects transferred the instrumented handle from the right hand to the left hand (one-person condition) or passed that handle to another person (two-person condition) while keeping the handle's position and orientation stationary. Only three digits were involved per hand, the thumb, the index finger, and the middle finger; the forces and moments produced by the digits were measured by six-component sensors. We estimated the performance-stabilizing synergies within the uncontrolled manifold framework by quantifying the intertrial variance structure of digit forces and moments. The analysis was performed at three levels: between hands, between virtual finger and virtual thumb (imagined digits producing the same mechanical variables as the corresponding actual digits combined) produced by the two hands (in both interpersonal and intrapersonal conditions), and between the thumb and virtual finger for one hand only. Additionally, we performed correlation and phase synchronization analyses of resultant tangential forces and internal normal forces. Overall, the one-person conditions were characterized by higher amount of intertrial variance that did not affect resultant normal force components, higher internal components of normal forces, and stronger synchronization of the normal forces generated by the hands. Our observations suggest that in two-person tasks, when participants try to achieve a common mechanical outcome, the performance-stabilizing synergies depend on non-visual information exchange, possibly via the haptic and proprioceptive systems. Therefore, synergies quantified in tasks using visual feedback only may not be generalizable to more natural tasks.

Can discrete joint action be synergistic? Studying the stabilization of interpersonal hand coordination

The human perceptual-motor system is tightly coupled to the physical and informational dynamics of a task environment. These dynamics operate to constrain the high-dimensional order of the human movement system into low-dimensional, task-specific synergies-functional groupings of structural elements that are temporarily constrained to act as a single coordinated unit. The aim of the current study was to determine whether synergistic processes operate when coacting individuals coordinate to perform a discrete joint-action task. Pairs of participants sat next to each other and each used 1 arm to complete a pointer-to-target task. Using the uncontrolled manifold (UCM) analysis for the first time in a discrete joint action, the structure of joint-angle variance was examined to determine whether there was synergistic organization of the degrees of freedom employed at the interpersonal or intrapersonal levels. The results revealed that the motor actions performed by coactors were synergistically organized at both the interpersonal and intrapersonal levels. More importantly, however, the interpersonal synergy was found to be significantly stronger than the intrapersonal synergies. Accordingly, the results provide clear evidence that coacting individuals can become temporarily organized to form single synergistic 2-person systems during performance of a discrete joint action.

Motor control hierarchy in joint action that involves bimanual force production

The concept of hierarchical motor control has been viewed as a means of progressively decreasing the number of variables manipulated by each higher control level. We tested the hypothesis that turning an individual bimanual force-production task into a joint (two-participant) force-production task would lead to positive correlation between forces produced by the two hands of the individual participant (symmetric strategy) to enable negative correlation between forces produced by two participants (complementary strategy). The present study consisted of individual and joint tasks that involved both unimanual and bimanual conditions. In the joint task, 10 pairs of participants produced periodic isometric forces, such that the sum of forces that they produced matched a target force cycling between 5% and 10% of maximum voluntary contraction at 1 Hz. In the individual task, individuals attempted to match the same target force. In the joint bimanual condition, the two hands of each participant adopted a symmetric strategy of force, whereas the two participants adopted a complementary strategy of force, highlighting that the bimanual action behaved as a low level of a hierarchy, whereas the joint action behaved as an upper level. The complementary force production was greater interpersonally than intrapersonally. However, whereas the coherence was highest at 1 Hz in all conditions, the frequency synchrony was stronger intrapersonally than interpersonally. Moreover, whereas the bimanual action exhibited a smaller error and variability of force than the unimanual action, the joint action exhibited a less-variable interval and force than the individual action.

Prehension synergies during fatigue of a single digit: adaptations in control with referent configurations

The effects of muscle fatigue on the stability of precision grasps are not well known. The purpose of the current study was to investigate the effects of exercise-induced fatigue of a digit on prehension synergies in a static precision grasp. One group of participants performed the fatiguing exercise using the thumb (group-thumb) and the second group performed the exercise using the index finger (group-index). Grasp force and load-resisting force-stabilizing synergies were weaker during fatigue for group-thumb and showed no significant change for group-index. These results indicate that fatiguing the thumb compromises the stability of the precision grasp more than when the index finger is fatigued. Our results support the idea of hierarchical organization of prehension control. We proffer an explanation of our results based on two control constructs: a) Principle of superposition. This principle states that prehension can be viewed as a superposition of two independent processes controlling the slip and the tilt of the object respectively; and b) The referent configuration hypothesis. According to this hypothesis, the neural control of actions is associated with defining a set of referent values for task-related coordinates (given an external force field) defined as the referent configuration.

Inter-limb force coupling is resistant to distorted visual feedback in chronic hemiparetic stroke

OBJECTIVE

Interlimb coupling between impaired and non-impaired limbs after stroke has been a common observation. The aim of this study was to examine interlimb interactions in force production in responses to altered visual gain in hemiparetic stroke survivors.

DESIGN

prospective clinical study

METHODS

A convenient sample of 7 hemiparetic stroke subjects (3 women and 4 men; mean age 56.0 years (standard errors 12.8) of age; history of stroke: mean duration 61.6 months (standard errors 53.3)) participated in the study. Subjects performed bilateral elbow flexion to varying total force targets from 3% to 60% maximal contraction forces with normal visual gain (1:1) and to a 10% maximal voluntary contraction target with altered visual gains (1/8, 1/4, 1/2, 2, 4, and 8) for the force of the less-impaired, ipsilesional side.

RESULTS

Across all conditions, the forces produced by both impaired and non-impaired limb changed proportionally to their maximal voluntary contraction force, such that relative contributions of each limb's force to the total force remained unchanged. In conditions with altered visual gain, high and low, the total force showed errors in the direction of under-shooting.

CONCLUSION

Our findings indicate that there is a strong interlimb force coupling in hemiparetic stroke, resistant to distorted visual feedback. It may reflect a default sharing pattern dominant after stroke.

Effects of aging on force coordination in bimanual task performance

We investigated within- and between-hands grip-load force coordination in both healthy young and older adult participants during bimanual tasks involving realistic actions. Age-related changes in manual behaviors such as grip force production and safety margins were expected in older adults. Within-hand grip-load coordination was expected to decrease with aging during the performance of dynamic actions, but not static actions. The effects of task and hand dominance on task performance were also evaluated. Grip force production increased with age; however, changes in fingertip frictional properties with aging increased the risk of object slip. Indices of within-hand grip-load coordination did not alter with age, but such indices were affected by task goals. The action of connecting two independent objects, particularly with rotational action, was associated with declines in all indices of within- and between-hands force coordination, independent of age. Evidence of task-specific differences in within-hand grip-load coordination in the current data set suggests that individual hand specification emerges and persists with age in everyday bimanual prehension tasks, independent of the action role assigned to the dominant and non-dominant hands.

Effects of muscle vibration on multi-finger interaction and coordination

The purpose of this study was to investigate the effects of changes in the proprioceptive signals induced by muscle vibration on multi-finger interaction and coordination. We hypothesized that unintended force production by non-instructed fingers (enslaving) would increase with muscle vibration while synergy indices during steady-state force production would drop. The framework of the uncontrolled manifold hypothesis was used to quantify indices of multi-finger synergies stabilizing total force during steady-state force production and anticipatory changes in these indices (anticipatory synergy adjustments, ASAs) in preparation to a quick force pulse production with and without hand-muscle vibration at 80 Hz. The dominant hands of twelve healthy right-handed subjects were tested under three conditions: no vibration, vibration of the palmar surface of the hand, and vibration of the forearm applied over the flexor muscles. There were no significant effects of vibration on maximal voluntary force. The magnitude of enslaving was larger during vibration of the hand compared to the other two conditions. During steady-state force production, strong synergies stabilizing total force were seen in all three conditions; however, indices of force-stabilizing synergies were lower during vibration of the hand. Prior to the force pulse initiation, the synergy index started to drop earlier and over a larger magnitude without vibration compared to either vibration condition. Effects of vibration on enslaving and synergy index may be due to diffuse reflex effects of the induced afferent activity on alpha-motoneuronal pools innervating the extrinsic flexor compartments. We conclude that multi-finger synergies are not based on signals from muscle receptors. The smaller synergy indices and ASAs may reflect supraspinal effects of the vibration-induced afferent activity, in particular its interactions with trans-thalamic loops.

Bilateral synergies in foot force production tasks

We analysed the effects of task symmetry during bilateral accurate force production tasks performed by the two feet. In particular, we tested a hypothesis that bilateral deficit would lead to higher indices of synergies defined as co-varied adjustments in the two forces across trials that reduced total force variability. The subjects produced steady-state force followed by a quick force pulse into the target. The two feet could be acting both into plantar flexion and into dorsiflexion (symmetrical tasks), or in opposite directions (asymmetrical task). We used the framework of the uncontrolled manifold hypothesis to quantify two variance components, one of which did not change total force (V UCM), while the other did (V ORT). Synergy indices during the asymmetrical task were higher than in either symmetrical task. The difference was due to higher V UCM (compared to the symmetrical plantar flexion task) or lower V ORT (compared to the symmetrical dorsiflexion task). The synergy index showed a drop (anticipatory synergy adjustment, ASA) starting 100-150 ms prior to the force pulse initiation. The ASA tended to be shorter and of a smaller magnitude for the asymmetrical task. This is the first demonstration of bilateral synergies during accurate force production by the legs. We conclude that bilateral deficit has no or weak effects on two-leg synergies. The results fit the earlier introduced scheme with two groups of neural variables defining average performance of a redundant system and patterns of co-variation among its elemental variables, respectively.

Effects of fatigue on synergies in a hierarchical system

We investigated the effect of fatigue produced by timed maximal voluntary contraction (MVC) of the index finger of one of the hands on performance in MVC and accurate cyclic force production tasks in right-handed subjects. Based on earlier studies, we hypothesized that fatigue would produce an increase in the indices of force-stabilizing synergies in both hands as well as between the hands in two-hand tasks. Synergies were defined as co-varied adjustments of commands to fingers (modes) across cycles that stabilized total force. Fatigue caused a significant reduction in the MVC of the exercised as well as the non-exercised hand. Indices of finger enslaving (lack of individuation) increased with fatigue in both hands, although the increase was significant in the exercised hand only. In contrast to the significant effects of fatigue on MVC forces performed by the non-exercised hand, there were no comparable transfer effects on the root mean square errors during accurate force production. During one-hand tasks, both hands showed high indices of force-stabilizing synergies. These indices were larger in the left hand. Fatigue led to a general increase in synergy indices. Exercise by the left hand had stronger effects on synergy indices seen in both hands. Exercise by the right hand showed ipsilateral effects only. Smaller effects of fatigue were observed on accuracy of performance of the force-down segments of the force cycles compared to the force-up segments. For the bimanual tasks, synergies were analyzed at two hierarchical levels, two-hand (four-finger) and within-a-hand (two-finger). An increase in the synergy index with fatigue was observed at the lower (two-finger) level of the hierarchy only. We interpret the lack of effects of fatigue at the upper (two-hand) level as a consequence of a trade-off between synergies at different levels of the hierarchy. The differences between the hands are discussed within the dynamic dominance hypothesis.

Age effects on rotational hand action

We investigated age-related differences in finger coordination during rotational hand actions. Two hypotheses based on earlier studies were tested: higher safety margins and lower synergy indices were expected in the elderly. Young and elderly subjects held a handle instrumented with five six-component force sensors and performed discrete accurate pronation and supination movements. The weight of the system was counterbalanced with another load. Indices of synergies stabilizing salient performance variables, such as total normal force, total tangential force, moments produced by these forces, and total moment of force were computed at two levels of a hypothetical control hierarchy, at the virtual finger-thumb level and at the individual finger level. At each level, synergy indices reflected the normalized difference between the sum of the variances of elemental variables and variance of their combined output, both computed at comparable phases over repetitive trials. The elderly group performed the task slower and showed lower safety margins for the thumb during the rotation phase. Overall, the synergy indices were not lower in the elderly group. In several cases, these indices were significantly higher in the elderly than in the younger participants. Hence, both main hypotheses have been falsified. We interpret the unexpectedly low safety margins in the elderly as resulting from several factors such as increased force variability, impaired feed-forward control, and the fact that there was no danger of dropping the object. Our results suggest that in some natural tasks, such as the one used in this study, healthy elderly persons show no impairment, as compared to younger persons, in their ability to organize digits into synergies stabilizing salient performance variables.

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.

Prehension synergies during smooth changes of the external torque

We studied characteristics of digit action and their co-variation patterns across trials (prehension synergies) during static holding of an object while the external torque could change slowly and smoothly. The subjects held in the air an instrumented handle with an attachment that allowed a smooth change in the external torque over about 12 s; the load was always kept constant. Series of trials were performed under three conditions: The torque could be zero throughout the trial, or it could change slowly requiring a smooth change of the effort from a non-zero pronation value to zero (PR-0) or from a non-zero supination value to zero (SU-0). The handle was kept vertical at all times. Indices of variance and co-variation of elemental variables (forces and moments of force produced by individual digits) stabilizing such performance variables as total normal force, total tangential force, and total moment of force were computed at two levels of an assumed control hierarchy. At the upper level, the task is shared between the thumb and virtual finger (an imagined digit with the mechanical action equal to that of the four fingers), while at the lower level, the action of the virtual finger is shared among the actual four fingers. We analyzed the total moment of force as the sum of the moments of force produced by the thumb and virtual finger and also as the sum of the moments of force produced by the normal forces and tangential forces. The results showed that the adjustments in the total moment of force were produced primarily with changes in the moment produced by the virtual finger and by changes in the moment produced by the normal forces. The normal force of the thumb at the final state (which was the same across conditions) was larger in the two conditions with changes in the external torque. The safety margin was significantly higher in the PR-0 condition, and it dropped with the decrease in the external torque. A co-contraction index was computed to reflect the moment of force production by the fingers acting against the total moment produced by the virtual finger. It was higher for the SU-0 condition. Most variance indices dropped with a decrease in the external torque. The co-variation indices, however, remained unchanged over the trial duration. They showed signs of a trade-off between the two levels of the assumed hierarchy: larger indices at the higher level corresponded to smaller indices at the lower level. This study and the previous one (Sun et al. in Exp Brain Res 209:571-585, 2011) document several previously unknown features of prehensile tasks. The results show that characteristics of digit action and interaction in such tasks depend not only on the magnitudes of external constraints but also on a variety of other factors including time changes in the constraints and their history.

Manipulation of a fragile object by elderly individuals

We investigated strategies of healthy elderly participants (74-84 years old) during prehension and transport of an object with varying degrees of fragility. Fragility was specified as the maximal normal force that the object could withstand without collapsing. Specifically, kinetic and kinematic variables as well as and force covariation indices were quantified and compared to those shown by young healthy persons (19-28 years old). We tested three hypotheses related to age-related changes in two safety margins (slip safety margin and crush safety margin) and indices of force covariation. Compared to young controls, elderly individuals exhibited a decrease in object acceleration and an increase in movement time, an increase in grip force production, a decrease in the correlation between grip and load forces, an overall decrease in indices of multi-digit synergies, and lower safety margin indices computed with respect to both dropping and crushing the object. Elderly participants preferred to be at a relatively lower risk of crushing the object even if this led to a higher risk of dropping it. Both groups showed an increase in the index of synergy stabilizing total normal force produced by the four fingers with increased fragility of the object. Age-related changes are viewed as a direct result of physiological changes due to aging, not adaptation to object fragility. Such changes in overall characteristics of prehension likely reflect diminished synergic control by the central nervous system of finger forces with aging. The findings corroborate an earlier hypothesis on an age-related shift from synergic to element-based control.

Age-related changes in optimality and motor variability: an example of multifinger redundant tasks

We used two methods, analytical inverse optimization (ANIO) and uncontrolled manifold (UCM) analysis of synergies, to explore age-related changes in finger coordination during accurate force and moment of force production tasks. The two methods address two aspects of the control of redundant systems: Finding an optimal solution (an optimal sharing pattern) and using variable solutions across trials (covarying finger forces) that are equally able to solve the task. Young and elderly subjects produced accurate combinations of total force and moment by pressing with the four fingers of the dominant hand on individual force sensors. In session-1, single trials covered a broad range of force-moment combinations. Principal component (PC) analysis showed that the first two PCs explained about 90% and 75% of finger force variance for the young and elderly groups, respectively. The magnitudes of the loading coefficients in the PCs suggested that the young subjects used mechanical advantage to produce moment while elderly subjects did not (confirmed by analysis of moments produced by individual digits). A co-contraction index was computed reflecting the magnitude of moment produced by fingers acting against the required direction of the total moment. This index was significantly higher in the young group. The ANIO approach yielded a quadratic cost function with linear terms. In the elderly group, the contribution of the forces produced by the middle and ring fingers to the cost function value was much smaller than in the young group. The angle between the plane of experimental observations and the plane of optimal solutions (D-angle), was very small (about 1.5°) in the young group and significantly larger (about 5°) in the elderly group. In session-2, four force-moment combinations were used with multiple trials at each. Covariation among finger forces (multifinger synergies) stabilizing total force, total moment, and both was seen in both groups with larger synergy indices in the young group. Multiple regression analysis has shown that, at higher force magnitudes, the synergy indices defined with the UCM method were significantly related to the percent of variance accounted by the first two PCs and to the D-angle computed using the ANIO method. We interpret the results as pointing at a transition with age from synergic control to element-based control (back-to-elements hypothesis). Optimization and analysis of synergies are complementary approaches that focus on two aspects of multidigit coordination, sharing and covariation, respectively.

Prehension of half-full and half-empty glasses: time and history effects on multi-digit coordination

We explored how digit forces and indices of digit coordination depend on the history of getting to a particular set of task parameters during static prehension tasks. The participants held in the right hand an instrumented handle with a light-weight container attached on top of the handle. At the beginning of each trial, the container could be empty, filled to the half with water (0.4 l), or filled to the top (0.8 l). The water was pumped in/out of the container at a constant, slow rate over 10 s. At the end of each trial, the participants always held a half-filled container that has just been filled (Empty-Half), emptied (Full-Half) or stayed half-filled throughout the trial (Half-Only). Indices of covariation (synergy indices) of elemental variables (forces and moments of force produced by individual digits) stabilizing such performance variables as total normal force, total tangential force, and total moment of force were computed at two levels of an assumed control hierarchy. At the upper level, the task is shared between the thumb and virtual finger (an imagined digit with the mechanical action equal to that of the four fingers), while at the lower level the action of the virtual finger is shared among the actual four fingers. Filling or emptying the container led to a drop in the safety margin (proportion of grip force over the slipping threshold) below the values observed in the Half-Only condition. Synergy indices at both levels of the hierarchy showed changes over the Full-Half and Empty-Half condition. These changes could be monotonic (typical of moment of force and normal force) or non-monotonic (typical of tangential force). For both normal and tangential forces, higher synergy indices at the higher level of the hierarchy corresponded to lower indices at the lower level. Significant differences in synergy indices across conditions were seen at the final steady state showing that digit coordination during steady holding an object is history dependent. The observations support an earlier hypothesis on a trade-off between synergies at the two levels of a hierarchy. They also suggest that, when a change in task parameters is expected, the neural strategy may involve producing less stable (easier to change) actions. The results suggest that synergy indices may be highly sensitive to changes in a task variable and that effects of such changes persist after the changes are over.

Visual information interacts with neuromuscular factors in the coordination of bimanual isometric force

The role of perceptual-motor processes in the coordination and control of movement is a long standing issue. Nevertheless, there is no coherence on theoretical perspectives with their being frameworks that emphasize perceptual, motor and perceptual-motor processes in coordination and control. The purpose of this study was to examine the interactive effects of visual information and factors of neuromuscular organization (force level, force direction, and homologous muscle pairs) on coordination patterns in bimanual isometric force production. In Experiment 1, the participants were required to abduct two index fingers isometrically and produce simultaneous forces such that their sum matched the constant force target specified at two force levels (10 and 40% of maximum voluntary contraction (MVC)). Visual information of the force outputs was either present or absent between conditions. The results showed that the coordination patterns interact with visual feedback in that the two finger forces exhibit negative correlation with vision and positive correlation without vision, with stronger correlation in each case found at higher force levels. In Experiment 2, the force direction and muscles involved in the task were different between the hands. In comparison with Experiment 1, the negative correlation was stronger with vision at 40% MVC (but equal at 10% MVC), and positive correlation was weaker without vision at 10% MVC (but equal at 40% MVC). The findings provide further evidence that the coordination patterns in bimanual isometric force production are specified by the interaction of task-relevant visual information and force level and, to a lesser degree by force direction and the muscles involved in the task. The capacity to exploit information mediates coordination and control, and the effective utilization of information is dependent on the specific action.

Multi-finger pressing synergies change with the level of extra degrees of freedom

The purpose of this study was to test the principle of motor abundance, which has been hypothesized as the principle by which the central nervous system controls the excessive degrees of freedom of the human movements, in contrast to the traditional negative view of motor redundancy. This study investigated the changes in force stabilizing and moment stabilizing synergies for multi-finger pressing tasks involving different number of fingers. Twelve healthy subjects produced a constant pressing force while watching visual feedback of the total pressing force for the fingers involved in each task. Based on the principle of motor abundance, it was hypothesized that the multi-finger synergies for the total force stabilizing synergy and the total moment stabilizing synergy would be greater as the number of task finger increases. Force stabilizing and moment stabilizing synergies were quantified using the framework of the uncontrolled manifold analysis. It was found that strong force stabilizing synergies existed for all the finger combinations. The index of force stabilizing synergies was greater when the task involved more number of fingers. The index of moment stabilizing synergies was negative for the two-finger combination, representing moment destabilizing synergies. However, the index of moment stabilizing synergies was positive for three-finger and four-finger combinations, representing strong moment stabilizing synergies for these finger combinations. We interpret the findings as an evidence for the principle of abundance for stabilization of both, total force as well as total moment.

Multi-finger interaction during involuntary and voluntary single finger force changes

Two types of finger interaction are characterized by positive co-variation (enslaving) or negative co-variation (error compensation) of finger forces. Enslaving reflects mechanical and neural connections among fingers, while error compensation results from synergic control of fingers to stabilize their net output. Involuntary and voluntary force changes by a finger were used to explore these patterns. We hypothesized that synergic mechanisms will dominate during involuntary force changes, while enslaving will dominate during voluntary finger force changes. Subjects pressed with all four fingers to match a target force that was 10% of their maximum voluntary contraction (MVC). One of the fingers was unexpectedly raised 5.0 mm at a speed of 30.0 mm/s. During finger raising the subject was instructed "not to intervene voluntarily". After the finger was passively lifted and a new steady-state achieved, subjects pressed down with the lifted finger, producing a pulse of force voluntarily. The data were analyzed in terms of finger forces and finger modes (hypothetical commands to fingers reflecting their intended involvement). The target finger showed an increase in force during both phases. In the involuntary phase, the target finger force changes ranged between 10.71 ± 1.89% MVC (I-finger) and 16.60 ± 2.26% MVC (L-finger). Generally, non-target fingers displayed a force decrease with a maximum amplitude of -1.49 ± 0.43% MVC (L-finger). Thus, during the involuntary phase, error compensation was observed--non-lifted fingers showed a decrease in force (as well as in mode magnitude). During the voluntary phase, enslaving was observed--non-target fingers showed an increase in force and only minor changes in mode magnitude. The average change in force of non-target fingers ranged from 21.83 ± 4.47% MVC for R-finger (M-finger task) to 0.71 ± 1.10% MVC for L-finger (I-finger task). The average change in mode of non-target fingers was between -7.34 ± 19.27% MVC for R-finger (L-finger task) and 7.10 ± 1.38% MVC for M-finger (I-finger task). We discuss a range of factors affecting force changes, from purely mechanical effects of finger passive lifting to neural synergic adjustments of commands to individual fingers. The data fit a recently suggested scheme that merges the equilibrium-point hypothesis (control with referent configurations) with the idea of hierarchical synergic control of multi-element systems.

Optimality vs. variability: an example of multi-finger redundant tasks

Two approaches to motor redundancy, optimization and the principle of abundance, seem incompatible. The former predicts a single, optimal solution for each task, while the latter assumes that families of equivalent solutions are used. We explored the two approaches using a four-finger pressing task with the requirement to produce certain combination of total normal force and a linear combination of normal forces that approximated the total moment of force in static conditions. In the first set of trials, many force-moment combinations were used. Principal component (PC) analysis showed that over 90% of finger force variance was accounted for by the first two PCs. The analytical inverse optimization (ANIO) approach was applied to these data resulting in quadratic cost functions with linear terms. Optimal solutions formed a hyperplane ("optimal plane") in the four-dimensional finger force space. In the second set of trials, only four force-moment combinations were used with multiple repetitions. Finger force variance within each force-moment combination in the second set was analyzed within the uncontrolled manifold (UCM) hypothesis. Most finger force variance was confined to a hyperplane (the UCM) compatible with the required force-moment values. We conclude that there is no absolute optimal behavior, and the ANIO yields the best fit to a family of optimal solutions that differ across trials. The difference in the force-producing capabilities of the fingers and in their moment arms may lead to deviations of the "optimal plane" from the subspace orthogonal to the UCM. We suggest that the ANIO and UCM approaches may be complementary in the analysis of motor variability in redundant systems.

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.

Motor synergies and the equilibrium-point hypothesis

The article offers a way to unite three recent developments in the field of motor control and coordination: (1) The notion of synergies is introduced based on the principle of motor abundance; (2) The uncontrolled manifold hypothesis is described as offering a computational framework to identify and quantify synergies; and (3) The equilibrium-point hypothesis is described for a single muscle, single joint, and multijoint systems. Merging these concepts into a single coherent scheme requires focusing on control variables rather than performance variables. The principle of minimal final action is formulated as the guiding principle within the referent configuration hypothesis. Motor actions are associated with setting two types of variables by a controller, those that ultimately define average performance patterns and those that define associated synergies. Predictions of the suggested scheme are reviewed, such as the phenomenon of anticipatory synergy adjustments, quick actions without changes in synergies, atypical synergies, and changes in synergies with practice. A few models are briefly reviewed.

Motor control theories and their applications

We describe several influential hypotheses in the field of motor control including the equilibrium-point (referent configuration) hypothesis, the uncontrolled manifold hypothesis, and the idea of synergies based on the principle of motor abundance. The equilibrium-point hypothesis is based on the idea of control with thresholds for activation of neuronal pools; it provides a framework for analysis of both voluntary and involuntary movements. In particular, control of a single muscle can be adequately described with changes in the threshold of motor unit recruitment during slow muscle stretch (threshold of the tonic stretch reflex). Unlike the ideas of internal models, the equilibrium-point hypothesis does not assume neural computations of mechanical variables. The uncontrolled manifold hypothesis is based on the dynamic system approach to movements; it offers a toolbox to analyze synergic changes within redundant sets of elements related to stabilization of potentially important performance variables. The referent configuration hypothesis and the principle of abundance can be naturally combined into a single coherent scheme of control of multi-element systems. A body of experimental data on healthy persons and patients with movement disorders are reviewed in support of the mentioned hypotheses. In particular, movement disorders associated with spasticity are considered as consequences of an impaired ability to shift threshold of the tonic stretch reflex within the whole normal range. Technical details and applications of the mentioned hypo-theses to studies of motor learning are described. We view the mentioned hypotheses as the most promising ones in the field of motor control, based on a solid physical and neurophysiological foundation.

Manipulation of a fragile object

We investigated strategies of adjustments in kinetic and kinematic patterns, and in multi-digit synergies during quick vertical transport of an instrumented handle that collapsed when the grasping force exceeded a certain magnitude (quantified with a fragility index). The collapse threshold of the object was set using a novel electromagnetic device. Moving a fragile object is viewed as a task with two constraints on the grip force defined by the slipping and crushing thresholds. When moving more fragile objects, subjects decreased object peak acceleration, increased movement time, showed a drop in the safety margin (SM) (extra force over the slipping threshold), and showed a tendency toward violating the minimum-jerk criterion. Linear regression analysis of grip force against load force has shown tight coupling between the two with a decline in the coefficient of determination with increased fragility index. The SM was lower in bimanual tasks, compared to unimanual tasks, for both fragile and non-fragile objects. Two novel indices have been introduced and studied, the SM due to fragility and the drop-crush index. Both indices showed a decrease with increased object fragility. Changes in the drop-crush index showed that the subjects would rather crush the fragile objects as opposed to dropping them, possibly reflecting the particular experimental procedure. We did not find differences between the performance indices of the dominant and non-dominant hand thus failing to support the recently formulated dominance hypothesis. The synergies stabilizing grip force were quantified at two levels of an assumed two-level control hierarchy using co-variation indices between elemental variables across trials. There were strong synergies at the upper level of the hierarchy (the task is shared between the opposing groups of digits) that weakened with an increase in object fragility. At the lower level (action of an effector is shared among the four fingers), higher fragility led to higher synergy indices. Analysis of force variance showed that an increase in object fragility was accompanied by exploring a smaller range of equivalent combinations of elemental variables. The additional constraint imposed by high fragility facilitated synergies at the lower level of the hierarchy, while there was evidence for a trade-off between synergies at the two levels.

Prehension synergies and control with referent hand configurations

We used the framework of the equilibrium-point hypothesis (in its updated form based on the notion of referent configuration) to investigate the multi-digit synergies at two levels of a hypothetical hierarchy involved in prehensile actions. Synergies were analyzed at the thumb-virtual finger (VF) level (VF is an imaginary digit with the mechanical action equivalent to that of the four actual fingers) and at the individual finger level. The subjects performed very quick vertical movements of a handle into a target. A load could be attached off-center to provide a pronation or supination torque. In a few trials, the handle was unexpectedly fixed to the table and the digits slipped off the sensors. In such trials, the hand stopped at a higher vertical position and rotated into pronation or supination depending on the expected torque. The aperture showed non-monotonic changes with a large, fast decrease and further increase, ending up with a smaller distance between the thumb and the fingers as compared to unperturbed trials. Multi-digit synergies were quantified using indices of co-variation between digit forces and moments of force across unperturbed trials. Prior to the lifting action, high synergy indices were observed at the individual finger level while modest indices were observed at the thumb-VF level. During the lifting action, the synergies at the individual finger level disappeared while the synergy indices became higher at the thumb-VF level. The results support the basic premise that, within a given task, setting a referent configuration may be described with a few referent values of variables that influence the equilibrium state, to which the system is attracted. Moreover, the referent configuration hypothesis can help interpret the data related to the trade-off between synergies at different hierarchical levels.

Mechanical analysis and hierarchies of multidigit synergies during accurate object rotation

We studied the mechanical variables (the grip force and the total moment of force) and multidigit synergies at two levels (the virtual finger-thumb level, VF-TH, and the individual finger level, IMRL) of a hypothetical control hierarchy during accurate rotation of a hand-held instrumented handle. Synergies were defined as covaried changes in elemental variables (forces and moments of force) that stabilize the output at a particular level. Indices of multidigit synergies showed higher values at the hierarchically higher level (VF-TH) for both normal and tangential forces. The moment of force was stabilized at both hierarchical levels during the steady-state phases but not during the movement. The results support the principles of superposition and of mechanical advantage. They also support an earlier hypothesis on an inherent tradeoff between synergies at the two hierarchical levels, although the controller showed more subtle and versatile synergic control than the one hypothesized earlier.

Dimensionality reduction in control and coordination of the human hand

The concept of kinematic synergies is proposed to address the dimensionality reduction problem in control and coordination of the human hand. This paper develops a method for extracting kinematic synergies from joint-angular-velocity profiles of hand movements. Decomposition of a limited set of synergies from numerous movements is a complex optimization problem. This paper splits the decomposition process into two stages. The first stage is to extract synergies from rapid movement tasks using singular value decomposition (SVD). A bank of template functions is then created from shifted versions of the extracted synergies. The second stage is to find weights and onset times of the synergies based on l(1) -minimization, whose solutions provide sparse representations of hand movements using synergies.

The organization of intralimb and interlimb synergies in response to different joint dynamics

We sought to understand differences in joint coordination between the dominant and nondominant arms when performing repetitive tasks. The uncontrolled manifold approach was used to decompose the variability of joint motions into components that reflect the use of motor redundancy or movement error. First, we hypothesized that coordination of the dominant arm would demonstrate greater use of motor redundancy to compensate for interaction forces than would coordination of the nondominant arm. Secondly, we hypothesized that when interjoint dynamics were more complex, control of the interlimb relationship would remain stable despite differences in control of individual hand paths. Healthy adults performed bimanual tracing of two orientations of ellipses that resulted in different magnitudes of elbow interaction forces. For the dominant arm, joint variance leading to hand path error was the same for both ellipsis orientations, whereas joint variance reflecting the use of motor redundancy increased when interaction moment was highest. For the nondominant arm, more joint error variance was found when interaction moment was highest, whereas motor redundancy did not differ across orientations. There was no apparent difference in interjoint dynamics between the two arms. Thus, greater skill exhibited by the dominant arm may be related to its ability to utilize motor redundancy to compensate for the effect of interaction forces. However, despite the greater error associated with control of the nondominant hand, control of the interlimb relationship remained stable when the interaction moment increased. This suggests separate levels of control for inter- versus intra-limb coordination in this bimanual task.