Stabilization of the total force in multi-finger pressing tasks studied with the 'inverse piano' technique

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.

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.

The control and perception of antagonist muscle action

The review covers a range of topics related to the role of the antagonist muscles in agonist-antagonist pairs within the theory of the neural control of movements with spatial referent coordinates, the principle of abundance, and the uncontrolled manifold hypothesis. It starts with the mechanical role of the antagonist in stopping movements and providing necessary levels of effector mechanical characteristics for fast movements. Further, it discusses the role of antagonist muscle activation bursts during voluntary movements, force production, and postural tasks. Recent studies show that agonist and antagonist motor units are united into common groups related to two basic commands, reciprocal and coactivation. A number of phenomena are considered including intra-muscle synergies stabilizing net force production, unintentional force drifts during isometric force production, effects of voluntary muscle coactivation on force production and perception, and perceptual errors caused by various factors including lack of visual feedback and muscle vibration. Taken together, the findings suggest inherent instability of neural commands (time functions of the stretch reflex threshold) to antagonist muscles requiring visual information for accurate performance. They also suggest that neural commands to antagonist muscles are not readily incorporated into kinesthetic perception leading to illusions and errors in matching tasks.

Synergic control in asymptomatic welders during multi-finger force exertion and load releasing while standing

Motor synergies, i.e., neural mechanisms that organize multiple motor elements to ensure stability of actions, are affected by several neurological condition. Asymptomatic welders showed impaired synergy controlling the stability of multi-finger action compared to non-welders and this impairment was associated with microstructural damage in the globus pallidus. We further explored the effect of welding-related metal exposure on multi-finger synergy and extended our investigation to posture-stabilizing synergy during a standing task. Occupational, MRI, and performance-stabilizing synergies during multi-finger accurate force production and load releasing while standing were obtained from 29 welders and 19 age- and sex-matched controls. R2* and R1 relaxation rate values were used to estimate brain iron and manganese content, respectively, and diffusion tensor imaging was used to reflect brain microstructural integrity. Associations of brain MRI (caudate, putamen, globus pallidus, and red nucleus), and motor synergy were explored by group status. The results revealed that welders had higher R2* values in the caudate (p = 0.03), putamen (p = 0.01), and red nucleus (p = 0.08, trend) than controls. No group effect was revealed on multi-finger synergy index during steady-state phase of action (ΔVZss). Compared to controls, welders exhibited lower ΔVZss (-0.106 ± 0.084 vs. 0.160 ± 0.092, p = 0.04) and variance that did not affect the performance variable (VUCM, 0.022 ± 0.003 vs. 0.038 ± 0.007, p = 0.03) in the load releasing, postural task. The postural synergy index, ΔVZss, was associated negatively with higher R2* in the red nucleus in welders (r = -0.44, p = 0.03), but not in controls. These results suggest that the synergy index in the load releasing during a standing task may reflect welding-related neurotoxicity in workers with chronic metals exposure. This finding may have important clinical and occupational health implications.

Synergies Stabilizing Vertical Posture in Spaces of Control Variables

In this study, we address the question: Can the central nervous system stabilize vertical posture in the abundant space of neural commands? We assume that the control of vertical posture is associated with setting spatial referent coordinates (RC) for the involved muscle groups, which translates into two basic commands, reciprocal and co-activation. We explored whether the two commands co-varied across trials to stabilize the initial postural state. Young, healthy participants stood quietly against an external horizontal load and were exposed to smooth unloading episodes. Linear regression between horizontal force and center of mass coordinate during the unloading phase was computed to define the intercept (RC) and slope (apparent stiffness, k). Hyperbolic regression between the intercept and slope across unloading episodes and randomization analysis both demonstrated high indexes of co-variation stabilizing horizontal force in the initial state. Higher co-variation indexes were associated with lower average k values across the participants suggesting destabilizing effects of muscle coactivation. Analysis of deviations in the {RC; k} space keeping the posture unchanged (motor equivalent) between two states separated by a voluntary quick body sway showed significantly larger motor equivalent deviations compared to non-motor equivalent ones. This is the first study demonstrating posture-stabilizing synergies in the space of neural control variables using various computational methods. It promises direct applications to studies of postural disorders and rehabilitation.

Inverse Saxophone—A Device to Study the Role of Individual Finger Perturbations on Grasp Stability

The efficient coordination of fingertip forces to maintain static equilibrium while grasping an object continues to intrigue scientists. While many studies have explored this coordination, most of these studies assumed that interactions of hands primarily occur with rigid inanimate objects. Instead, our daily interactions with living and nonliving entities involve many dynamic, compliant, or fragile bodies. This paper investigates the fingertip force coordination on a manipulandum that changes its shape while grasping it. We designed a five-finger perturbation system with linear actuators at positions corresponding to each finger that would protrude outward from the center of the handle or retract toward the center of the handle as programmed. The behavior of the perturbed fingers and the other fingers while grasping this device was studied. Based on previous experiments on expanding and contracting handles, we hypothesized that each finger would exhibit a comparable response to similar horizontal perturbations. However, the response of the little finger was significantly different from the other fingers. We speculate that the central nervous system demonstrates preferential recruitment of some fingers over others while performing a task.

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.

The Nature of Finger Enslaving: New Results and Their Implications

We present a review on the phenomenon of unintentional finger action seen when other fingers of the hand act intentionally. This phenomenon (enslaving) has been viewed as a consequence of both peripheral (e.g., connective tissue links and multifinger muscles) and neural (e.g., projections of corticospinal pathways) factors. Recent studies have shown relatively large and fast drifts in enslaving toward higher magnitudes, which are not perceived by subjects. These and other results emphasize the defining role of neural factors in enslaving. We analyze enslaving within the framework of the theory of motor control with spatial referent coordinates. This analysis suggests that unintentional finger force changes result from drifts of referent coordinates, possibly reflecting the spread of cortical excitation.

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.

Production and Perception of Intentional and Unintentional Actions

Physical approach to biological movement is based on the idea of control with referent spatial coordinates for effectors, from the whole body to single muscles. Within this framework, neural control signals induce changes in parameters of corresponding biology-specific laws of nature, and motor performance emerges as a result of interaction with the external force field. This approach is naturally compatible with the principle of abundance and the uncontrolled manifold hypothesis, which offer the framework for analysis of movement stability. The presence of two basic commands, reciprocal and co-activation, makes even single-effector tasks abundant and allows stabilizing their performance at the control level. Kinesthetic perception can be viewed as the process of estimating afferent signals within a reference system provided by the efferent process. Percepts are reflections of stable iso-perceptual manifolds in the combined afferent-efferent multi-dimensional space. This approach offers new, logical and based on laws of nature, interpretations for such phenomena as muscle co-activation, unintentional drifts in performance, and vibration-induced kinesthetic illusions. It also allows predicting new phenomena such as counter-intuitive effects of muscle co-activation of force production and perception, vibration-induced force illusions, performance drifts at two different speeds, and high variability in matching the contribution of individual elements in multi-element tasks. This approach can be developed for various subfields of movement studies including studies of athletics, movement disorders, and movement rehabilitation.

Efference copy in kinesthetic perception: a copy of what is it?

A number of notions in the fields of motor control and kinesthetic perception have been used without clear definitions. In this review, we consider definitions for efference copy, percept, and sense of effort based on recent studies within the physical approach, which assumes that the neural control of movement is based on principles of parametric control and involves defining time-varying profiles of spatial referent coordinates for the effectors. The apparent redundancy in both motor and perceptual processes is reconsidered based on the principle of abundance. Abundance of efferent and afferent signals is viewed as the means of stabilizing both salient action characteristics and salient percepts formalized as stable manifolds in high-dimensional spaces of relevant elemental variables. This theoretical scheme has led recently to a number of novel predictions and findings. These include, in particular, lower accuracy in perception of variables produced by elements involved in a multielement task compared with the same elements in single-element tasks, dissociation between motor and perceptual effects of muscle coactivation, force illusions induced by muscle vibration, and errors in perception of unintentional drifts in performance. Taken together, these results suggest that participation of efferent signals in perception frequently involves distorted copies of actual neural commands, particularly those to antagonist muscles. Sense of effort is associated with such distorted efferent signals. Distortions in efference copy happen spontaneously and can also be caused by changes in sensory signals, e.g., those produced by muscle vibration.

Distortions of the Efferent Copy during Force Perception: A Study of Force Drifts and Effects of Muscle Vibration

We used a finger force matching task to explore the role of efferent signals in force perception. Healthy, young participants performed accurate force production tasks at different force levels with the index and middle fingers of one hand (task-hand). They received visual feedback during an early part of each trial only. After the feedback was turned off, the force drifted toward lower magnitudes. After 5 s of the drift, the participants matched the force with the same finger pair of the other hand (match-hand). The match-hand consistently overshot the task-hand force by a magnitude invariant over the initial force levels. During force matching, both hands were lifted and lowered smoothly to estimate their referent coordinate (RC) and apparent stiffness values. These trials were performed without muscle vibration and under vibration applied to the finger/hand flexors or extensors of the task-hand or match-hand. Effects of vibration were seen in the match-hand only; they were the same during vibration of flexors and extensors. We interpret the vibration-induced effects as consequences of using distorted copies of the central commands to the task-hand during force matching. In particular, using distorted copies of the RC for the antagonist muscle group could account for the differences between the task-hand and match-hand. We conclude that efferent signals may be distorted before their participation in the perceptual process. Such distortions emerge spontaneously and may be amplified by the response of sensory endings to muscle vibration combined over both agonist and antagonist muscle groups.

Finger interdependence and unintentional force drifts: Lessons from manipulations of visual feedback

We explored the phenomenon of unintentional finger force drift by using visual feedback on the force produced either by explicitly instructed (master) finger pairs or by non-instructed (enslaved) finger pairs. In particular, we drew contrasting predictions from two hypotheses: that force drifts represented consequences of drifts in effector referent coordinates at the level of individual fingers vs. at the level of finger modes (hypothetical variables accounting for the finger force interdependence). Subjects performed accurate force production with two fingers of a hand, index-ring or middle-little. They received visual feedback on the force produced either by the master fingers or by the other two, enslaved, fingers. The feedback scale was adjusted to ensure that the subjects did not know the difference between these two, randomly presented, conditions. Under feedback on the master finger force, enslaved force showed a consistent drift upward. Under feedback on the enslaved finger force, master force showed a consistent drift downward. The subjects were unaware of the force drifts, which could reach over 35% of the initial force magnitude. The data support the hypothesis on drifts in the referent coordinate at the level of individual digits, not finger modes, as the origin of unintentional force drifts. The consistent increase in the relative amount of force produced by the enslaved fingers suggests that the commonly used methods to quantify enslaving should include relatively brief force production tasks.

Laws of nature that define biological action and perception

We describe a physical approach to biological functions, with the emphasis on the motor and sensory functions. The approach assumes the existence of biology-specific laws of nature uniting salient physical variables and parameters. In contrast to movements in inanimate nature, actions are produced by changes in parameters of the corresponding laws of nature. For movements, parameters are associated with spatial referent coordinates (RCs) for the effectors. Stability of motor actions is ensured by the abundant mapping of RCs across hierarchical control levels. The sensory function is viewed as based on an interaction of efferent and afferent signals leading to an iso-perceptual manifold where percepts of salient sensory variables are stable. This approach offers novel interpretations for a variety of known neurophysiological and behavioral phenomena and makes a number of novel testable predictions. In particular, we discuss novel interpretations for the well-known phenomena of agonist-antagonist co-activation and vibration-induced illusions of both position and force. We also interpret results of several new experiments with unintentional force changes and with analysis of accuracy of perception of variables produced by elements of multi-element systems. Recently, this approach has been expanded to interpret motor disorders including spasticity and consequences of subcortical disorders (such as Parkinson's disease). We suggest that the approach can be developed for cognitive functions.

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.

Sloppy, But Acceptable, Control of Biological Movement: Algorithm-Based Stabilization of Subspaces in Abundant Spaces

In this paper, we develop an algorithm-based approach to the problem of stability of salient performance variables during motor actions. This problem is reformulated as stabilizing subspaces within high-dimensional spaces of elemental variables. Our main idea is that the central nervous system does not solve such problems precisely, but uses simple rules that achieve success with sufficiently high probability. Such rules can be applied even if the central nervous system has no knowledge of the mapping between small changes in elemental variables and changes in performance. We start with a rule ”Act on the most nimble” (the AMN-rule), when changes in the local feedback-based loops occur for the most unstable variable first. This rule is implemented in a task-specific coordinate system that facilitates local control. Further, we develop and supplement the AMN-rule to improve the success rate. Predictions of implementation of such algorithms are compared with the results of experiments performed on the human hand with both visual and mechanical perturbations. We conclude that physical, including neural, processes associated with everyday motor actions can be adequately represented with a set of simple algorithms leading to sloppy, but satisfactory, solutions. Finally, we discuss implications of this scheme for motor learning and motor disorders.

Quantitative analysis of multi-element synergy stabilizing performance: comparison of three methods with respect to their use in clinical studies

A number of analyses associated with the uncontrolled manifold (UCM) hypothesis have been used recently to investigate stability of actions across populations. We explored whether some of those methods have an advantage for clinical studies because they require fewer trials to achieve consistent findings. We compared the number of trials needed for the analysis of inter-trial variance, analysis of motor equivalence, and analysis in the space of referent coordinates. Young healthy adults performed four-finger accurate force production tasks under visual feedback with the right (dominant) and left hand over three days. Three methods [analytical (M1), experimental (M2), and cumulative mean (M3) methods] were used to define the minimal number of trials required to reach certain statistical criteria. Two of these methods, M1 and M2, showed qualitatively similar results. Fewer trials (M1: 5-13, M2: 4-10) were needed for analysis of motor equivalence compared to inter-trial variance analysis (M1: 14-24, M2: 10-14). The third method (M3) showed no major differences among the outcome variables. The index of synergy in the inter-trial variance analysis required a very small number of trials (M1, M2: 2-4). Variables related to referent coordinates required only a few trials (under 3), whereas the synergy index in this analysis required the largest number of trials (M1: 24-34, M2: 12-16). This is the first study to quantify the number of trials needed for UCM-based methods of assessing motor coordination broadly used in clinical studies. Clinical studies can take advantage of specific recommendations based on the current data regarding the number of trials needed for each analysis thus allowing minimizing the test session duration without compromising data reliability.

Individual preferences in motor coordination seen across the two hands: relations to movement stability and optimality

The framework of the uncontrolled manifold (UCM) hypothesis was used to explore variables related to stability of task performance in the two hands of young healthy individuals. Fourteen young adults performed four-finger accurate constant force production tasks interrupted by a voluntary quick force pulse production and by an externally imposed displacement of all fingers. Three groups of variables were used to quantify stability of steady force production: (1) indices of the inter-trial variance were computed within the UCM and orthogonal to the UCM; (2) indices of motor equivalence were computed between steady-state intervals separated by the force pulse and by the finger-lifting episode; and (3) referent coordinate and apparent stiffness were computed using the data during the ascending phase of the finger-lifting episode. In another task, the subjects performed accurate constant force production with visual feedback removal after the 8th second, and the drop in the total force after the removal was computed. There were differences between the right and left hand in some outcome variables such as variance within the UCM, and the timing of anticipatory synergy adjustments prior to the force pulse, consistent with the dynamic dominance hypothesis. There were significant correlations between the two hands for indices that were unrelated to accuracy of performance: variance within the UCM, index of motor equivalence, referent coordinate, apparent stiffness, and the drop of total force after visual feedback removal. We interpret these findings within the concept of stability-optimality trade-off. In particular, we conclude that individual subjects select particular, person-specific solutions within the spectrum allowed by the explicit task constraints, and this choice is consistent between the two hands. We conclude with a hypothesis that selecting specific solutions within the stability-optimality trade-off may represent an individual's personal preference consistent between the two hands.

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 steady hand force production explored across spaces and methods of analysis

We used the framework of the uncontrolled manifold (UCM) hypothesis and explored the reliability of several outcome variables across different spaces of analysis during a very simple four-finger accurate force production task. Fourteen healthy, young adults performed the accurate force production task with each hand on 3 days. Small spatial finger perturbations were generated by the "inverse piano" device three times per trial (lifting the fingers 1 cm/0.5 s and lowering them). The data were analyzed using the following main methods: (1) computation of indices of the structure of inter-trial variance and motor equivalence in the space of finger forces and finger modes, and (2) analysis of referent coordinates and apparent stiffness values for the hand. Maximal voluntary force and the index of enslaving (unintentional finger force production) showed good to excellent reliability. Strong synergies stabilizing total force were reflected in both structure of variance and motor equivalence indices. Variance within the UCM and the index of motor equivalent motion dropped over the trial duration and showed good to excellent reliability. Variance orthogonal to the UCM and the index of non-motor equivalent motion dropped over the 3 days and showed poor to moderate reliability. Referent coordinate and apparent stiffness indices co-varied strongly and both showed good reliability. In contrast, the computed index of force stabilization showed poor reliability. The findings are interpreted within the scheme of neural control with referent coordinates involving the hierarchy of two basic commands, the r-command and c-command. The data suggest natural drifts in the finger force space, particularly within the UCM. We interpret these drifts as reflections of a trade-off between stability and optimization of action. The implications of these findings for the UCM framework and future clinical applications are explored in the discussion. Indices of the structure of variance and motor equivalence show good reliability and can be recommended for applied studies.

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.

Timing and extent of finger force enslaving during a dynamic force task cannot be explained by EMG activity patterns

Finger enslaving is defined as the inability of the fingers to move or to produce force independently. Such finger enslaving has predominantly been investigated for isometric force tasks. The aim of this study was to assess whether the extent of force enslaving is dependent on relative finger movements. Ten right-handed subjects (22–30 years) flexed the index finger while counteracting constant resistance forces (4, 6 and 8 N) orthogonal to the fingertip. The other, non-instructed fingers were held in extension. EMG activities of the mm. flexor digitorum superficialis (FDS) and extensor digitorum (ED) in the regions corresponding to the index, middle and ring fingers were measured. Forces exerted by the non-instructed fingers increased substantially (by 0.2 to 1.4 N) with flexion of the index finger, increasing the enslaving effect with respect to the static, pre-movement phase. Such changes in force were found 260–370 ms after the initiation of index flexion. The estimated MCP joint angle of the index finger at which forces exerted by the non-instructed fingers started to increase varied between 4° and 6°. In contrast to the finger forces, no significant changes in EMG activity of the FDS regions corresponding to the non-instructed fingers upon index finger flexion were found. This mismatch between forces and EMG of the non-instructed fingers, as well as the delay in force development are in agreement with connective tissue linkages being slack when the positions of the fingers are similar, but pulled taut when one finger moves relative to the others. Although neural factors cannot be excluded, our results suggest that mechanical connections between muscle-tendon structures were (at least partly) responsible for the observed increase in force enslaving during index finger flexion.

Unsteady steady-states: central causes of unintentional force drift

We applied the theory of synergies to analyze the processes that lead to unintentional decline in isometric fingertip force when visual feedback of the produced force is removed. We tracked the changes in hypothetical control variables involved in single fingertip force production based on the equilibrium-point hypothesis, namely the fingertip referent coordinate (R _FT) and its apparent stiffness (C _FT). The system's state is defined by a point in the {R _FT; C _FT} space. We tested the hypothesis that, after visual feedback removal, this point (1) moves along directions leading to drop in the output fingertip force, and (2) has even greater motion along directions that leaves the force unchanged. Subjects produced a prescribed fingertip force using visual feedback and attempted to maintain this force for 15 s after the feedback was removed. We used the "inverse piano" apparatus to apply small and smooth positional perturbations to fingers at various times after visual feedback removal. The time courses of R _FT and C _FT showed that force drop was mostly due to a drift in R _FT toward the actual fingertip position. Three analysis techniques, namely hyperbolic regression, surrogate data analysis, and computation of motor-equivalent and non-motor-equivalent motions, suggested strong covariation in R _FT and C _FT stabilizing the force magnitude. Finally, the changes in the two hypothetical control variables {R _FT; C _FT} relative to their average trends also displayed covariation. On the whole, the findings suggest that unintentional force drop is associated with (a) a slow drift of the referent coordinate that pulls the system toward a low-energy state and (b) a faster synergic motion of R _FT and C _FT that tends to stabilize the output fingertip force about the slowly drifting equilibrium point.

On the nature of unintentional action: a study of force/moment drifts during multifinger tasks

We explored the origins of unintentional changes in performance during accurate force production in isometric conditions seen after turning visual feedback off. The idea of control with referent spatial coordinates suggests that these phenomena could result from drifts of the referent coordinate for the effector. Subjects performed accurate force/moment production tasks by pressing with the fingers of a hand on force sensors. Turning the visual feedback off resulted in slow drifts of both total force and total moment to lower magnitudes of these variables; these drifts were more pronounced in the right hand of the right-handed subjects. Drifts in individual finger forces could be in different direction; in particular, fingers that produced moments of force against the required total moment showed an increase in their forces. The force/moment drift was associated with a drop in the index of synergy stabilizing performance under visual feedback. The drifts in directions that changed performance (non-motor equivalent) and in directions that did not (motor equivalent) were of about the same magnitude. The results suggest that control with referent coordinates is associated with drifts of those referent coordinates toward the corresponding actual coordinates of the hand, a reflection of the natural tendency of physical systems to move toward a minimum of potential energy. The interaction between drifts of the hand referent coordinate and referent orientation leads to counterdirectional drifts in individual finger forces. The results also demonstrate that the sensory information used to create multifinger synergies is necessary for their presence over the task duration.

Synergies in the space of control variables within the equilibrium-point hypothesis

We use an approach rooted in the recent theory of synergies to analyze possible co-variation between two hypothetical control variables involved in finger force production based on the equilibrium-point (EP) hypothesis. These control variables are the referent coordinate (R) and apparent stiffness (C) of the finger. We tested a hypothesis that inter-trial co-variation in the {R; C} space during repeated, accurate force production trials stabilizes the fingertip force. This was expected to correspond to a relatively low amount of inter-trial variability affecting force and a high amount of variability keeping the force unchanged. We used the "inverse piano" apparatus to apply small and smooth positional perturbations to fingers during force production tasks. Across trials, R and C showed strong co-variation with the data points lying close to a hyperbolic curve. Hyperbolic regressions accounted for over 99% of the variance in the {R; C} space. Another analysis was conducted by randomizing the original {R; C} data sets and creating surrogate data sets that were then used to compute predicted force values. The surrogate sets always showed much higher force variance compared to the actual data, thus reinforcing the conclusion that finger force control was organized in the {R; C} space, as predicted by the EP hypothesis, and involved co-variation in that space stabilizing total force.

Task-specific stability of abundant systems: Structure of variance and motor equivalence

Our main goal was to test a hypothesis that transient changes in performance of a steady-state task would result in motor equivalence. We also estimated effects of visual feedback on the amount of reorganization of motor elements. Healthy subjects performed two variations of a four-finger pressing task requiring accurate production of total pressing force (F TOT) and total moment of force (M TOT). In the Jumping-Target task, a sequence of target jumps required transient changes in either F TOT or M TOT. In the Step-Perturbation task, the index finger was lifted by 1cm for 0.5s leading to a change in both F TOT and M TOT. Visual feedback could have been frozen for one of these two variables in both tasks. Deviations in the space of finger modes (hypothetical commands to individual fingers) were quantified in directions of unchanged F TOT and M TOT (motor equivalent - ME) and in directions that changed F TOT and M TOT (non-motor equivalence - nME). Both the ME and nME components increased when the performance changed. After transient target jumps leading to the same combination of F TOT and M TOT, the changes in finger modes had a large residual ME component with only a very small nME component. Without visual feedback, an increase in the nME component was observed without consistent changes in the ME component. Results from the Step-Perturbation task were qualitatively similar. These findings suggest that both external perturbations and purposeful changes in performance trigger a reorganization of elements of an abundant system, leading to large ME change. These results are consistent with the principle of motor abundance corroborating the idea that a family of solutions is facilitated to stabilize values of important performance variables.

Task-specific stability of multifinger steady-state action

The authors explored task-specific stability during accurate multifinger force production tasks with different numbers of instructed fingers. Subjects performed steady-state isometric force production tasks and were instructed not to interfere voluntarily with transient lifting-and-lowering perturbations applied to the index finger. The main results were (a) intertrial variance in the space of finger modes at steady states was larger within the subspace that had no effect on the total force (the uncontrolled manifold [UCM]); (b) perturbations caused large deviations of finger modes within the UCM (motor equivalence); and (c) deviations caused by the perturbation showed larger variance within the UCM. No significant effects of the number of task fingers were noted in any of the 3 indicators. The results are discussed within the frameworks of the UCM and referent configuration hypotheses. The authors conclude, in particular, that all the tasks were effectively 4-finger tasks with different involvement of task and nontask fingers.

Motor equivalence during multi-finger accurate force production

We explored stability of multi-finger cyclical accurate force production action by analysis of responses to small perturbations applied to one of the fingers and inter-cycle analysis of variance. Healthy subjects performed two versions of the cyclical task, with and without an explicit target. The "inverse piano" apparatus was used to lift/lower a finger by 1 cm over 0.5 s; the subjects were always instructed to perform the task as accurate as they could at all times. Deviations in the spaces of finger forces and modes (hypothetical commands to individual fingers) were quantified in directions that did not change total force (motor equivalent) and in directions that changed the total force (non-motor equivalent). Motor equivalent deviations started immediately with the perturbation and increased progressively with time. After a sequence of lifting-lowering perturbations leading to the initial conditions, motor equivalent deviations were dominating. These phenomena were less pronounced for analysis performed with respect to the total moment of force with respect to an axis parallel to the forearm/hand. Analysis of inter-cycle variance showed consistently higher variance in a subspace that did not change the total force as compared to the variance that affected total force. We interpret the results as reflections of task-specific stability of the redundant multi-finger system. Large motor equivalent deviations suggest that reactions of the neuromotor system to a perturbation involve large changes in neural commands that do not affect salient performance variables, even during actions with the purpose to correct those salient variables. Consistency of the analyses of motor equivalence and variance analysis provides additional support for the idea of task-specific stability ensured at a neural level.

Stability of multifinger action in different state spaces

We investigated stability of action by a multifinger system with three methods: analysis of intertrial variance, application of transient perturbations, and analysis of the system's motion in different state spaces. The "inverse piano" device was used to apply transient (lifting-and-lowering) perturbations to individual fingers during single- and two-finger accurate force production tasks. In each trial, the perturbation was applied either to a finger explicitly involved in the task or one that was not. We hypothesized that, in one-finger tasks, task-specific stability would be observed in the redundant space of finger forces but not in the nonredundant space of finger modes (commands to explicitly involved fingers). In two-finger tasks, we expected that perturbations applied to a nontask finger would not contribute to task-specific stability in mode space. In contrast to our expectations, analyses in both force and mode spaces showed lower stability in directions that did not change total force output compared with directions that did cause changes in total force. In addition, the transient perturbations led to a significant increase in the enslaving index. We consider these results within a theoretical scheme of control with referent body configurations organized hierarchically, using multiple few-to-many mappings organized in a synergic way. The observed volatility of enslaving, greater equifinality of total force compared with elemental variables, and large magnitude of motor equivalent motion in both force and mode spaces provide support for the concept of task-specific stability of performance and the existence of multiple neural loops, which ensure this stability.

Motor synergies during manual tracking differ between familiar and unfamiliar trajectories

Synergistic control of the effector space allows high precision in task-relevant degrees of freedom, while noise is limited to task-irrelevant degrees of freedom. The present study investigates whether this typical structure of the variance-covariance matrix of the joint angles during manual tracking differs between familiar and unfamiliar trajectories. Subjects tracked a target moving in 2D on a graphics tablet with a hand-held pen, while their arm movements were not restricted. Subjects familiarized themselves with one target trajectory during an initial training block with 40 periodic trials. In the following test block, this familiar trajectory and several unfamiliar trajectories were presented in a mixed-block design to study prediction effects at the level of endpoint and joint trajectories. The differences in the synergistic control of arm movements were analyzed using the "uncontrolled manifold method." The results showed smaller variances and weaker motor synergies during tracking of familiar trajectories than during tracking of unfamiliar trajectories. The decrease in the synergy index was due to a stronger decrease in the variance irrelevant than of the variance relevant for pen position. In the context of motor control theory, these results suggest that tracking movements on familiar and unfamiliar target trajectories do not only differ in the available knowledge about target location but also apply different strategies to control the effector space.

Equifinality and its violations in a redundant system: multifinger accurate force production

We explored a hypothesis that transient perturbations applied to a redundant system result in equifinality in the space of task-related performance variables but not in the space of elemental variables. The subjects pressed with four fingers and produced an accurate constant total force level. The "inverse piano" device was used to lift and lower one of the fingers smoothly. The subjects were instructed "not to intervene voluntarily" with possible force changes. Analysis was performed in spaces of finger forces and finger modes (hypothetical neural commands to fingers) as elemental variables. Lifting a finger led to an increase in its force and a decrease in the forces of the other three fingers; the total force increased. Lowering the finger back led to a drop in the force of the perturbed finger. At the final state, the sum of the variances of finger forces/modes computed across repetitive trials was significantly higher than the variance of the total force/mode. Most variance of the individual finger force/mode changes between the preperturbation and postperturbation states was compatible with constant total force. We conclude that a transient perturbation applied to a redundant system leads to relatively small variance in the task-related performance variable (equifinality), whereas in the space of elemental variables much more variance occurs that does not lead to total force changes. We interpret the results within a general theoretical scheme that incorporates the ideas of hierarchically organized control, control with referent configurations, synergic control, and the uncontrolled manifold hypothesis.

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.