Optimality and stability of intentional and unintentional actions: II. Motor equivalence and structure of variance.

We address the nature of unintentional changes in performance in two papers. This second paper tested hypotheses related to stability of task-specific performance variables estimated using the framework of the uncontrolled manifold (UCM) hypothesis. Our first hypothesis was that selective stability of performance variables would be observed even when the magnitudes of those variables drifted unintentionally because of the lack of visual feedback. Our second hypothesis was that stability of a variable would depend on the number of explicit task constraints. Subjects performed four-finger isometric pressing tasks that required the accurate production of a combination of total moment and total force with natural or modified finger involvement under full visual feedback, which was removed later for some or all of the salient variables. We used inter-trial analysis of variance and drifts in the space of finger forces within the UCM and within the orthogonal to the UCM space. The two variance components were used to estimate a synergy index stabilizing the force/moment combination, while the two drift components were used to estimate motor equivalent and non-motor equivalent force changes, respectively. Without visual feedback, both force and moment drifted toward lower absolute magnitudes. The non-motor equivalent component of motion in the finger force space was larger than the motor equivalent component for variables that stopped receiving visual feedback. In contrast, variables that continued to receive visual feedback showed larger motor equivalent component, compared to non-motor equivalent component, over the same time interval. These data falsified the first hypothesis; indeed, selective stabilization of a variable over the duration of a trial allows expecting comparably large motor equivalent components both with and without visual feedback. Adding a new constraint (presented as a target magnitude of middle finger force) resulted in a drop in the synergy index in support of the second hypothesis. We interpret the force drift as a natural relaxation process toward states with lower potential energy in the physical (physiological) system involved in the task. The results show that presenting sensory feedback on a performance variable makes synergies stabilizing that variable dependent on that particular sensory feedback.

The synergic control of multi-finger force production: stability of explicit and implicit task components.

Manipulating objects with the hands requires the accurate production of resultant forces including shear forces; effective control of these shear forces also requires the production of internal forces normal to the surface of the object(s) being manipulated. In the present study, we investigated multi-finger synergies stabilizing shear and normal components of force, as well as drifts in both components of force, during isometric pressing tasks requiring a specific magnitude of shear force production. We hypothesized that shear and normal forces would evolve similarly in time and also show similar stability properties as assessed by the decomposition of inter-trial variance within the uncontrolled manifold hypothesis. Healthy subjects were required to accurately produce total shear and total normal forces with four fingers of the hand during a steady-state force task (with and without visual feedback) and a self-paced force pulse task. The two force components showed similar time profiles during both shear force pulse production and unintentional drift induced by turning the visual feedback off. Only the explicitly instructed components of force, however, were stabilized with multi-finger synergies. No force-stabilizing synergies and no anticipatory synergy adjustments were seen for the normal force in shear force production trials. These unexpected qualitative differences in the control of the two force components-which are produced by some of the same muscles and show high degree of temporal coupling-are interpreted within the theory of control with referent coordinates for salient variables. These observations suggest the existence of two classes of neural variables: one that translates into shifts of referent coordinates and defines changes in magnitude of salient variables, and the other controlling gains in back-coupling loops that define stability of the salient variables. Only the former are shared between the explicit and implicit task components.

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.

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.

Analytical Inverse Optimization in Two-Hand Prehensile Tasks.

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

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.

Interpersonal synergies: static prehension tasks performed by two actors.

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

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.

Processes underlying unintentional finger-force changes in the absence of visual feedback.

Previous reports show that the forces produced by the fingers of one hand drop exponentially over time in the absence of visual feedback on the forces. We study the force production by the index fingers of both hands with no visual feedback. Subjects produced a specified total force with a specific contribution from each finger by pressing on force sensors. We observed that in the absence of visual feedback: (1) The finger forces dropped with time by an amount proportional to the magnitude of the initial force. For low initial force values (<7 % of MVC of individual finger force), the finger forces showed an increase; (2) the total force (sum of finger forces) evolution showed similar features; (3) finger forces changed in a way that facilitated more equitable force production by the two fingers; (4) all the force-time changes resemble exponential functions with similar time constants (~15 s). We propose that two processes interact to produce these patterns. (1) RC back-coupling: The central nervous system defines referent coordinates (RCs) for the digit tips, and the difference between the referent and actual coordinates leads to force production. If actual coordinates are not allowed to move to referent ones, referent coordinates show a slow drift toward the actual ones, leading to a force drop. (2) Sensory adaptation: This process, possibly related to sensory receptor characteristics, leads to an increase in finger force. RC back-coupling provides a common account of this and other reported phenomena of hand force or position changes across transient, external perturbations.

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.

Learning to combine high variability with high precision: lack of transfer to a different task.

The authors studied effects of practicing a 4-finger accurate force production task on multifinger coordination quantified within the uncontrolled manifold hypothesis. During practice, task instability was modified by changing visual feedback gain based on accuracy of performance. The authors also explored the retention of these effects, and their transfer to a prehensile task. Subjects practiced the force production task for 2 days. After the practice, total force variability decreased and performance became more accurate. In contrast, variance of finger forces showed a tendency to increase during the first practice session while in the space of finger modes (hypothetical commands to fingers) the increase was under the significance level. These effects were retained for 2 weeks. No transfer of these effects to the prehensile task was seen, suggesting high specificity of coordination changes. The retention of practice effects without transfer to a different task suggests that further studies on a more practical method of improving coordination are needed.

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.

Postural sway and perceived comfort in pointing tasks.

In this study, we explored relations between indices of postural sway and perceived comfort during pointing postures performed by standing participants. The participants stood on a force plate, grasped a pointer with the dominant (right) hand, and pointed to targets located at four positions and at two distances from the body. We quantified postural sway over 60-s intervals at each pointing posture, and found no effects of target location or distance on postural sway indices. In contrast, comfort ratings correlated significantly with indices of one of the sway components, trembling. Our observations support the hypothesis that rambling and trembling sway components involve different neurophysiological mechanisms. They also suggest that subjective perception of comfort may be more important than the actual posture for postural sway.

Internal forces during static prehension: effects of age and grasp configuration.

The authors studied effects of healthy aging on 3 components of the internal force vector during static prehensile tasks. Young and older subjects held an instrumented handle using a 5-digit prismatic grasp under different digit configurations and external torques. Across digit configurations, older subjects showed larger internal normal (grip) and tangential (load-resisting) digit force components and larger internal moment of force. In contrast to earlier reports, safety margin values were not higher in the older subjects. The results show that the increased grip force in older persons is a specific example of a more general age-related problem reflected in the generation of large internal force vectors in prehensile tasks. It is possible that the higher internal forces increase the apparent stiffness of the hand+handle system and, hence, contribute to its stability. This strategy, however, may be maladaptive, energetically wasteful, and inefficient in ensuring safety of hand-held objects.

Factors affecting grip force: anatomy, mechanics, and referent configurations.

The extrinsic digit muscles naturally couple wrist action and grip force in prehensile tasks. We explored the effects of wrist position on the steady-state grip force and grip-force change during imposed changes in the grip aperture [apparent stiffness (AS)]. Subjects held an instrumented handle steady using a prismatic five-digit grip. The grip aperture was changed slowly, while the subjects were instructed not to react voluntarily to these changes. An increase in the aperture resulted in an increase in grip force, and its contraction resulted in a proportional drop in grip force. The AS values (between 4 and 6 N/cm) were consistent across a wide range of wrist positions. These values were larger when the subjects performed the task with eyes open as compared to eyes-closed trials. They were also larger for trials that started from a larger initial aperture. After a sequence of aperture increase and decrease to the initial width, grip force dropped by about 25% without the subjects being aware of this. We interpret the findings within the referent configuration hypothesis of grip-force production. The results support the idea of back-coupling between the referent and actual digit coordinates. According to this idea, the central nervous system defines referent coordinates for the digit tips, and the difference between the referent and actual coordinates leads to force production. If actual coordinates are not allowed to move to referent ones, referent coordinates show a relatively slow drift toward the actual ones.

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

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

Enslaving in a serial chain: interactions between grip force and hand force in isometric tasks.

This study was motivated by the double action of extrinsic hand muscles that produce grip force and also contribute to wrist torque. We explored interactions between grip force and wrist torque in isometric force production tasks. In particular, we tested a hypothesis that an intentional change in one of the two kinetic variables would produce an unintentional change in the other (enslaving). When young healthy subjects produced accurate changes in the grip force, only minor effects on the force produced by the hand (by wrist flexion/extension action) were observed. In contrast, a change in the hand force produced consistent changes in grip force in the same direction. The magnitude of such unintentional grip force change was stronger for intentional hand force decrease as compared to hand force increase. These effects increased with the magnitude of the initial grip force. When the subjects were asked to produce accurate total force computed as the sum of the hand and grip forces, strong negative covariation between the two forces was seen across trials interpreted as a synergy stabilizing the total force. An index of this synergy was higher in the space of "modes," hypothetical signals to the two effectors that could be changed by the controller one at a time. We interpret the complex enslaving effects (positive force covariation) as conditioned by typical everyday tasks. The presence of synergic effects (negative, task-specific force covariation) can be naturally interpreted within the referent configuration hypothesis.