Stability of multifinger action in different state spaces

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.

Role of Post-Trial Visual Feedback on Unintentional Force Drift During Isometric Finger Force Production Tasks

A reduction in fingertip forces during a visually occluded isometric task is called unintentional drift. In this study, unintentional drift was studied for two conditions, with and without "epilogue." We define epilogue as the posttrial visual feedback in which the outcome of the just-concluded trial is shown before the start of the next trial. For this study, 14 healthy participants were recruited and were instructed to produce fingertip forces to match a target line at 15% maximum voluntary contraction. The results showed a significant reduction in unintentional drift in the epilogue condition. This reduction is probably due to the difference in the shift in λ, the threshold of the tonic stretch reflex, the hypothetical control variable that the central controller can set.

Unintentional Force Drifts as Consequences of Indirect Force Control with Spatial Referent Coordinates

We explored the phenomenon of unintentional force drifts in the absence of visual feedback. Based on the idea of direct force control with internal models and on the idea of indirect force control with referent coordinates to the involved muscle groups, contrasting predictions were drawn for changes in the drift magnitude when acting against external spring loads. Fifteen young subjects performed typical accurate force production tasks by pressing with the Index finger at 20% of maximal voluntary contraction (MVC) in isometric conditions and while acting against one of the three external springs with different stiffness. The visual feedback on the force was turned off after 5 s. At the end of each 20-s trial, the subjects relaxed and then tried to reproduce the final force level. The force drifts were significantly smaller in the spring conditions, particularly when acting against more compliant springs. The subjects were unaware of the force drifts and, during force matching, produced forces close to the initial force magnitude, which were not different across the conditions. There was a trend toward larger drifts during performance by the dominant hand. We view these observations as strong arguments in favor of the theory of control with spatial referent coordinates. In particular, force drifts were likely consequences of drifts of referent coordinates to both agonist and antagonist muscles. The lack of drift effects on both perception-to-report and perception-to-act fit the scheme of kinesthetic perception based on the interaction of efferent (referent coordinate) and afferent processes.

Frequency-Dependent Effects on Coordination and Prefrontal Hemodynamics During Finger Force Production Tasks

Behavioral stability partially depends on the variability of net outcomes by means of the co-varied adjustment of individual elements such as multi-finger forces. The properties of cyclic actions affect stability and variability of the performance as well as the activation of the prefrontal cortex that is an origin of subcortical structure for the coordinative actions. Little research has been done on the issue of the relationship between stability and neuronal response. The purpose of the study was to investigate the changes in the neural response, particularly at the prefrontal cortex, to the frequencies of isometric cyclic finger force production. The main experimental task was to produce finger forces while matching the produced force to sine-wave templates as accurately as possible. Also, the hemodynamics responses of the prefrontal cortex, including oxy-hemoglobin concentration (ΔHbO) and the functional connectivity, were measured using functional near-infrared spectroscopy. The frequency conditions comprised 0.1, 1, and 2 Hz. The uncontrolled manifold (UCM) approach was applied to compute synergy indices in time-series. The relative phase (RP), the coefficient of variation (CV) of the peak and trough force values were computed as the indices of performance accuracy. The statistical parametric mapping (SPM) was implemented to compare the synergy indices of three frequency conditions in time-series. A less accurate performance in the high-frequency condition was caused not by the RP, but mainly by the inconsistent peak force values (CV; p < 0.01, η p 2 = 0.90). The SPM analysis revealed that the synergy indices were larger in the low-frequency than in high-frequency conditions. Further, the ΔHbO remained unchanged under all frequency conditions, while the functional connectivity decreased with an increase in the frequency of cyclic force production. The current results suggested that the concurrent activation of the prefrontal region mainly depends on the frequency of cyclic force production, which was associated with the strength of stability indices and performance errors. The current study is the first work to uncover the effect of frequency on the multi-finger synergies as to the hemodynamic response in the prefrontal cortex, which possibly provides a clue of the neural mechanism of synergy formation and its changes.

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.

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.

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.

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.

Perturbation-induced fast drifts in finger enslaving

We explored changes in finger forces and in an index of unintentional finger force production (enslaving) under a variety of visual feedback conditions and positional finger perturbations. In particular, we tested a hypothesis that enslaving would show a consistent increase with time at characteristic times of about 1-2 s. Young healthy subjects performed accurate force production tasks under visual feedback on the total force of the instructed fingers (index and ring) or enslaved fingers (middle and little). Finger feedback was covertly alternated between master and enslaved fingers in a random fashion. The feedback could be presented over the first 5 s of the trial only or over the whole trial duration (21 s). After 5 s, the fingers were lifted by 1 cm, and after 15 s, the fingers were lowered to the initial position. The force of the instructed fingers drifted toward lower magnitudes in all conditions except the one with continuous feedback on that force. The force of enslaved fingers showed variable behavior across conditions. In all conditions, the index of enslaving showed a consistent increase with the time constant varying between 1 and 3 s. We interpret the results as pointing at the spread of excitation to enslaved fingers (possibly, in the cortical M1 areas). The relatively fast changes in enslaving under positional finger perturbations suggest that quick changes of the input into M1 from pre-M1 areas can accelerate the hypothesized spread of cortical excitation.

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.

On the origin of finger enslaving: control with referent coordinates and effects of visual feedback

When a person tries to press with a finger, other fingers of the hand produce force unintentionally. We explored this phenomenon of enslaving during unintentional force drifts in the course of continuous force production by pairs of fingers of a hand. Healthy subjects performed accurate force production tasks by finger pairs Index-Middle, Middle-Ring, and Ring-Little with continuous visual feedback on the combined force of the instructed (master) fingers or of the noninstructed (enslaved) fingers. The feedback scale was adjusted to ensure that the subjects did not know the difference between these two, randomly presented, conditions. Across all finger pairs, enslaved force showed a drift upward under feedback on the master finger force, and master force showed a drift downward under feedback on the enslaved finger force. The subjects were unaware of the force drifts, which could reach over 50% of the initial force magnitude over 15 s. Across all conditions, the index of enslaving increased by ∼50% over the trial duration. The initial moment of force magnitude in pronation-supination was not a consistent predictor of the force drift magnitude. These results falsify the hypothesis that the counter-directional force drifts reflected drifts in the moment of force. They suggest that during continuous force production, enslaving increases with time, possibly due to the spread of excitation over cortical finger representations or other mechanisms, such as increased synchronization of firing of α-motoneurons innervating different compartments of extrinsic flexors. These changes in enslaving, interpreted at the level of control with referent coordinates for the fingers, can contribute to a variety of phenomena, including unintentional force drifts.NEW & NOTEWORTHY We report a consistent slow increase in finger enslaving (force production by noninstructed fingers) when visual feedback was presented on the force produced by either two instructed fingers or two noninstructed fingers of the hand. In contrast, force drifts could be in opposite directions depending on the visual feedback. We interpret enslaving and its drifts at the level of control with referent coordinates for the involved muscles, possibly reflecting spread of cortical excitation.

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.

Finger pressing task data collected with and without post-trial performance feedback

The dataset presented in the article consists of finger forces of participants during a finger pressing task. The finger pressing task involves the production of fingertip forces using Index, Middle, Ring, and Little (I, M, R&L) fingers of the right hand. The participant performed two types of task, namely MVC task and visual occlusion task. The participants completed the Maximum Voluntary Contraction (MVC) task first, where they were instructed to produce maximum possible force from each finger individually and all fingers together. The visually occluded finger pressing task followed the MVC task. In this task, the participant's visual feedback was removed after 8s. There were two conditions in this task, one with post-trial performance feedback (referred to as "epilogue" condition in this manuscript) and another that does not have this post-trial performance feedback (referred to as "no epilogue" condition in this manuscript). The epilogue condition is a particular case of post-trial visual feedback where, at the end of each trial, the performance in that trial is shown to the participant. This was followed by the next trial. Normalization of force levels for visual occlusion tasks was performed for the forces with the participants produced in the MVC task. Fourteen healthy participants were recruited for performing the experiments. For the experiments, they were instructed to produce fingertip forces using four fingers of the right hand with the target line at 15% MVC (15% of the force that they produced in the MVC task). The two visual occlusion conditions had 30 trials each. In both conditions, a single trial lasted 16 s. For the initial 8 s, there is visual feedback, which follows an eight-second visual occlusion period where there is no visual feedback. The dataset consists of three files; the first file has the data of Maximum Voluntary Contraction (MVC) data, the second file has the data for the "without epilogue" condition, and the third file has the data of "epilogue" case.

Long-term practice of isolated finger movements reduces enslaved response of tonically contracting little finger abductor to tonic index finger abduction

The purpose of this study was to elucidate whether the long-term practice of isolated finger movements reduces the enslaved response of the little finger abductor to the index finger abduction. The right-handed participants tonically or phasically abducted the index finger, while they maintained at rest or tonic abduction of the little finger. The enslaved response of the tonically contracting little finger abductor to the tonic abduction of the index finger was greater than the response of the same muscle at rest in the nonpianists. This indicates that the tonic contraction of the little finger abductor enhances the enslaving drive from the tonically contracting index finger abductor to the little finger abductor. The enslaved response of the tonically contracting little finger abductor to the tonic abduction of the index finger in the pianists was significantly smaller than that in the nonpianists, but such a significant group difference was absent when the little finger abductor was at rest. This indicates that the inhibitory process on the enslaving drive from the tonically contracting index finger abductor to the tonically active little finger abductor is unmasked through the long-term practice.

Force-stabilizing synergies can be retained by coordinating sensory-blocked and sensory-intact digits

The present study examined the effects of selective digital deafferentation on the multi-finger synergies as a function of total force requirement and the number of digits involved in isometric pressing. 12 healthy adults participated in maximal and sub-maximal isometric pressing tasks with or without digital anesthesia to selective digits from the right hand. Our results indicate that selective anesthesia paradigm induces changes in both anesthetized (local) and non-anesthetized (non-local) digits’ performance, including: (1) decreased maximal force abilities in both local and non-local digits; (2) reduced force share during multi-finger tasks from non-local but not local digits; (3) decreased force error-making; and (4) marginally increased motor synergies. These results reinforce the contribution of somatosensory feedback in the process of maximal voluntary contraction force, motor performance, and indicate that somatosensation may play a role in optimizing secondary goals during isometric force production rather than ensuring task performance.

Beyond rambling and trembling: effects of visual feedback on slow postural drift

We explored one of the unusual predictions of the concept of back-coupling within the theoretical scheme of the control of posture and movement with setting referent coordinates for the effectors. This concept implies slow drifts of referent coordinates toward actual coordinates leading to unintentional drift in performance. During standing, such slow drifts may lead to a protective step or even a fall and, therefore, corrections are expected leading to body sway at frequencies under 0.1 Hz. Young healthy subjects stood on the force platform quietly for 60 s under two single-task conditions, with eyes open and closed, and two double-task conditions, matching an irrelevant muscle activation signal to a target (MATCH) and performing a subtraction task. The latter was performed with eyes open and closed. The rambling-trembling decomposition was applied to the displacements of the center of pressure in the anterior-posterior direction. Spectral analysis was used to quantify power within typical ranges for Tr and Rm, as well as for a slow Rm component (under 0.1 Hz) addressed as Drift. Closing eyes led to a significant increase in Rm and Tr, but no effects on Drift. Drift increased significantly in the MATCH task with no changes in Rm and a drop in Tr. No effects of the subtraction task were seen on Drift. Overall, our findings suggest that unintentional slow drift of referent body orientation towards the actual body orientation leads to Drift, a specific example of back-coupling reflected in postural sway. This observation can be also seen as an example of physiological minimization of activity of motoneurons. Natural visual feedback is used to avoid the COP drift and/or correct it quickly and effectively; this ability is compromised when vision is used for an unrelated task.

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.

Performance drifts in two-finger cyclical force production tasks performed by one and two actors

We explored changes in the cyclical two-finger force performance task caused by turning visual feedback off performed either by the index and middle fingers of the dominant hand or by two index fingers of two persons. Based on an earlier study, we expected drifts in finger force amplitude and midpoint without a drift in relative phase. The subjects performed two rhythmical tasks at 1 Hz while paced by an auditory metronome. One of the tasks required cyclical changes in total force magnitude without changes in the sharing of the force between the two fingers. The other task required cyclical changes in the force sharing without changing total force magnitude. Subjects were provided with visual feedback, which showed total force magnitude and force sharing via cursor motion along the vertical and horizontal axes, respectively. Further, visual feedback was turned off, first on the variable that was not required to change and then on both variables. Turning visual feedback off led to a mean force drift toward lower magnitudes while force amplitude increased. There was a consistent drift in the relative phase in the one-hand task with the index finger leading the middle finger. No consistent relative phase drift was seen in the two-person tasks. The shape of the force cycle changed without visual feedback reflected in the lower similarity to a perfect cosine shape and in the higher time spent at lower force magnitudes. The data confirm findings of earlier studies regarding force amplitude and midpoint changes, but falsify predictions of an earlier proposed model with respect to the relative phase changes. We discuss factors that could contribute to the observed relative phase drift in the one-hand tasks including the leader-follower pattern generalized for two-effector tasks performed by one person.

Unintentional force changes in cyclical tasks performed by an abundant system: Empirical observations and a dynamical model

The study explored unintentional force changes elicited by removing visual feedback during cyclical, two-finger isometric force production tasks. Subjects performed two types of tasks at 1Hz, paced by an auditory metronome. One - Force task - required cyclical changes in total force while maintaining the sharing, defined as relative contribution of a finger to total force. The other task - Share task - required cyclical changes in sharing while keeping total force unchanged. Each trial started under full visual feedback on both force and sharing; subsequently, feedback on the variable that was instructed to stay constant was frozen, and finally feedback on the other variable was also removed. In both tasks, turning off visual feedback on total force elicited a drop in the mid-point of the force cycle and an increase in the peak-to-peak force amplitude. Turning off visual feedback on sharing led to a drift of mean share toward 50:50 across both tasks. Without visual feedback there was consistent deviation of the two force time series from the in-phase pattern (typical of the Force task) and from the out-of-phase pattern (typical of the Share task). This finding is in contrast to most earlier studies that demonstrated only two stable patterns, in-phase and out-of-phase. We interpret the results as consequences of drifts of parameters in a dynamical system leading in particular to drifts in the referent finger coordinates toward their actual coordinates. The relative phase desynchronization is caused by the right-left differences in the hypothesized drift processes, consistent with the dynamic dominance hypothesis.

Effects of visual feedback and memory on unintentional drifts in performance during finger-pressing tasks

This study tested two hypotheses on the nature of unintentional force drifts elicited by removing visual feedback during accurate force production tasks. The role of working memory (memory hypothesis) was explored in tasks with continuous force production, intermittent force production, and rest intervals over the same time interval. The assumption of unintentional drifts in referent coordinate for the fingertips was tested using manipulations of visual feedback: young healthy subjects performed accurate steady-state force production tasks by pressing with the two index fingers on individual force sensors with visual feedback on the total force, sharing ratio, both, or none. Predictions based on the memory hypothesis have been falsified. In particular, we observed consistent force drifts to lower force values during continuous force production trials only. No force drift or drifts to higher forces were observed during intermittent force production trials and following rest intervals. The hypotheses based on the idea of drifts in referent finger coordinates have been confirmed. In particular, we observed superposition of two drift processes: a drift of total force to lower magnitudes and a drift of the sharing ratio to 50:50. When visual feedback on total force only was provided, the two-finger forces showed drifts in opposite directions. We interpret the findings as evidence for the control of motor actions with changes in referent coordinates for participating effectors. Unintentional drifts in performance are viewed as natural relaxation processes in the involved systems; their typical time reflects stability in the direction of the drift. The magnitude of the drift was higher in the right (dominant) hand, which is consistent with the dynamic dominance hypothesis.

Optimality and stability of intentional and unintentional actions: I. Origins of drifts in performance

We address the nature of unintentional changes in performance in two papers. This first paper tested a hypothesis that unintentional changes in performance variables during continuous tasks without visual feedback are due to two processes. First, there is a drift of the referent coordinate for the salient performance variable toward the actual coordinate of the effector. Second, there is a drift toward minimum of a cost function. We tested this hypothesis in four-finger isometric pressing tasks that required the accurate production of a combination of total moment and total force with natural and modified finger involvement. Subjects performed accurate force-moment production tasks under visual feedback, and then visual feedback was removed for some or all of the salient variables. Analytical inverse optimization was used to compute a cost function. Without visual feedback, both force and moment drifted slowly toward lower absolute magnitudes. Over 15 s, the force drop could reach 20% of its initial magnitude while moment drop could reach 30% of its initial magnitude. Individual finger forces could show drifts toward both higher and lower forces. The cost function estimated using the analytical inverse optimization reduced its value as a consequence of the drift. We interpret the results within the framework of hierarchical control with referent spatial coordinates for salient variables at each level of the hierarchy combined with synergic control of salient variables. The force drift is discussed as a natural relaxation process toward states with lower potential energy in the physical (physiological) system involved in the task.

Towards physics of neural processes and behavior

Behavior of biological systems is based on basic physical laws, common across inanimate and living systems, and currently unknown physical laws that are specific for living systems. Living systems are able to unite basic laws of physics into chains and clusters leading to new stable and pervasive relations among variables (new physical laws) involving new parameters and to modify these parameters in a purposeful way. Examples of such laws are presented starting from the tonic stretch reflex. Further, the idea of control with referent coordinates is formulated and merged with the idea of hierarchical control and the principle of abundance. The notion of controlled stability of behaviors is linked to the idea of structured variability, which is a common feature across living systems and actions. The explanatory and predictive power of this approach is illustrated with respect to the control of both intentional and unintentional movements, the phenomena of equifinality and its violations, preparation to quick actions, development of motor skills, changes with aging and neurological disorders, and perception.

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.

Effects of unilateral stroke on multi-finger synergies and their feed-forward adjustments

We explored the changes in multi-finger synergies in patients after a single cortical stroke with mild motor impairments. We hypothesized that both synergy indices and anticipatory synergy adjustments prior to the initiation of a self-paced quick action would be diminished in the patients compared to age-matched controls. The patients with history of cortical stroke, and age-matched controls (n=12 in each group) performed one-finger and multi-finger accurate force production tasks involving both steady-state and quick force pulse production. Finger interdependence (enslaving) and multi-finger synergies stabilizing total force were quantified. The stroke patients showed lower maximal finger forces, in particular in the contralesional hand, which also showed increased enslaving indices. Multi-finger synergies during steady-state force production were, however, unchanged after stroke. In contrast, a drop in the synergy index prior to the force pulse generation was significantly delayed in the stroke patients. Our results show that mild cortical stroke leads to no significant changes in multifinger synergies, but there is impairment in feed-forward adjustments of the synergies prior to a quick action, a drop in the maximal force production, and an increase in enslaving. We conclude that studies of synergies reveal two aspects of synergic control differentially affected by cortical stroke.

Fifty Years of Physics of Living Systems

The equilibrium-point hypothesis and its more recent version, the referent configuration hypothesis, represent the physical approach to the neural control of action. This hypothesis can be naturally combined with the idea of hierarchical control of movements and of synergic organization of the abundant systems involved in all actions. Any action starts with defining trajectories of a few referent coordinates for a handful of salient task-specific variables. Further, referent coordinates at hierarchically lower levels emerge down to thresholds of the tonic stretch reflex for the participating muscles. Stability of performance with respect to salient variables is reflected in the structure of inter-trial variance and phenomena of motor equivalence. Three lines of recent research within this framework are reviewed. First, synergic adjustments of the referent coordinate and apparent stiffness have been demonstrated during finger force production supporting the main idea of control with referent coordinates. Second, the notion of unintentional voluntary movements has been introduced reflecting unintentional drifts in referent coordinates. Two types of unintentional movements have been observed with different characteristic times. Third, this framework has been applied to studies of impaired movements in neurological patients. Overall, the physical approach searching for laws of nature underlying biological movement has been highly stimulating and productive.

Unintentional movements induced by sequential transient perturbations in a multi-joint positional task

We explored the phenomenon of unintentional movements of a multi-joint effector produced by multiple transient changes in the external force. The subjects performed a position-holding task against a constant bias force produced by a robot and were instructed not to intervene voluntarily with arm movements produced by changes in the robot force. The robot produced a smooth force increase leading to hand movement from the trunk, followed by a dwell time. Then, the force dropped to its initial value leading to hand movement toward the initial position but with an undershot. Such perturbation episodes were repeated four times in a row. The accumulated perturbation and undershoot distances kept increasing without saturation within the sequence of four perturbation episode. The limb apparent stiffness before dwell time increased over sequential perturbations while apparent stiffness after dwell time decreased. We interpret the results as consequences of a drift of the hand referent coordinate (RC) caused by a hypothesized RC-back-coupling mechanism and a coupled drift of the apparent stiffness. The results show that RC-back-coupling continues to lead to unintentional movements over repeated perturbations and is accompanied by a relatively slow re-setting process.

The nature of constant and cyclic force production: unintentional force-drift characteristics

We explored unintentional changes in forces during performance of constant and cyclic force-production tasks (F-tasks) after visual feedback removal. Based on earlier studies, we expected all force parameters to drop exponentially with time. We also explored possible role of working memory in the force drop phenomena. Healthy subjects performed constant or cyclic isometric F-tasks with the index finger under visual feedback. The cyclic task was paced by a metronome. Removing visual feedback resulted in a consistent force drop in constant F-tasks and a qualitatively similar drift in the mean force in the cyclic F-task. Both were slow with characteristic times of about 10-20 s. In contrast, force amplitude in the cyclic F-task increased quickly (within 1-2 s). When the subjects were asked to stop producing force for 5 s after the visual feedback disappeared and then resume force production, no downward force drift was seen in constant F-tasks, while in cyclic F-tasks, the drift of the mean force was present and an exaggerated increase in force amplitude was also observed. We conclude that while working memory limitations may influence cyclic F-tasks, their role in determining the force drift in constant F-tasks is limited. The results of both experiments are interpreted within the referent configuration hypothesis supplemented with an idea of unintentional drift of referent coordinates (RC-back-coupling) induced by differences between the referent and actual body configurations.

Unintentional changes in the apparent stiffness of the multi-joint limb

We explored the phenomenon of unintentional changes in the apparent stiffness of the human arm produced by transient changes in the external force. The subjects performed a positional task against a constant baseline force and were instructed not to react to changes in the force. A HapticMaster robot produced a smooth force increase (a perturbation) leading to a hand movement, followed by a dwell time. No visible hand drift was observed during the dwell time. After the robot force dropped to its initial baseline value, the hand moved toward the initial position but stopped short of it. Small perturbations were applied at different time intervals along different directions during the dwell time. Arm apparent stiffness distribution in a horizontal plane was approximated with an ellipse. The apparent stiffness magnitude along the main axis of the ellipse showed a non-monotonic increase with dwell time, while the apparent stiffness along the minor axis did not change significantly. We interpreted the early part of the changes in the apparent stiffness as due to peripheral muscle properties. The later part is interpreted as caused by a combination of two processes: a drift in the referent hand coordinate due to the hypothesized back-coupling between the referent and actual hand coordinates and an implicit instruction to keep the hand steady when no changes in robot-generated force took place. The data provide support for the idea of back-coupling between the referent and actual body configurations, which may be an important contributor to stability of motor actions.

Force-stabilizing synergies in motor tasks involving two actors

We investigated the ability of two persons to produce force-stabilizing synergies in accurate multi-finger force production tasks under visual feedback on the total force only. The subjects produced a time profile of total force (the sum of two hand forces in one-person tasks and the sum of two subject forces in two-person tasks) consisting of a ramp-up, steady-state, and ramp-down segments; the steady-state segment was interrupted in the middle by a quick force pulse. Analyses of the structure of inter-trial finger force variance, motor equivalence, anticipatory synergy adjustments (ASAs), and the unintentional drift of the sharing pattern were performed. The two-person performance was characterized by a dramatically higher amount of inter-trial variance that did not affect total force, higher finger force deviations that did not affect total force (motor equivalent deviations), shorter ASAs, and larger drift of the sharing pattern. The rate of sharing pattern drift correlated with the initial disparity between the forces produced by the two persons (or two hands). The drift accelerated following the quick force pulse. Our observations show that sensory information on the task-specific performance variable is sufficient for the organization of performance-stabilizing synergies. They suggest, however, that two actors are less likely to follow a single optimization criterion as compared to a single performer. The presence of ASAs in the two-person condition might reflect fidgeting by one or both of the subjects. We discuss the characteristics of the drift in the sharing pattern as reflections of different characteristic times of motion within the subspaces that affect and do not affect salient 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.