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

Expectation of volitional arm movement has prolonged effects on the grip force exerted on a pinched object

Humans closely coordinate the grip force exerted on a hand-held object with changes in the load arising from the object's dynamics. Recent work suggests the grip force is responsive to the predictability of the load forces as well. The well-known grip-force-load-force coupling is intermittent when the load arising from volitional movements fluctuates predictably, whereas grip force increases when loads are unpredictable. Here, we studied the influence of expected but uncertain volitional movements on the digit forces during a static grasp. Young, healthy participants used a pinch grasp to hold an instrumented object and track visual targets by moving the object. We quantified the mean grip force, the temporal decline in grip force (slacking), and the coupling between the pressing digit forces that yield the grip force during static prehension with no expectation of movement, and during the static phase of a choice reaction time task, when the participant expected to move the object after a variable duration. Simply expecting to move the object led to sustained (for at least 5 s) higher magnitude and lower slacking in the grip force, and weaker coupling between the pressing digit forces. These effects were modulated by the direction of the expected movement and the object's mass. The changes helped to maintain the safety margin for the current grasp and likely facilitated the transition from static to dynamic object manipulation. Influence of expected actions on the current grasp may have implications for manual dexterity and its well-known loss with age.

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.

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 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.

Feedforward and Feedback Control Share an Internal Model of the Arm's Dynamics

Recent work has shown that, when countering external forces, the nervous system adjusts not only predictive (i.e., feedforward) control of reaching but also reflex (i.e., feedback) responses to mechanical perturbations. Here we show that altering the physical properties of the arm (i.e., intersegmental dynamics) causes the nervous system to adjust feedforward control and that this learning transfers to feedback responses even though the latter were never directly trained. Forty-five human participants (30 females) performed a single-joint elbow reaching task and countered mechanical perturbations that created pure elbow motion. In our first experiment, we altered intersegmental dynamics by asking participants to generate pure elbow movements when the shoulder joint was either free to rotate or locked by the robotic manipulandum. With the shoulder unlocked, we found robust activation of shoulder flexor muscles for pure elbow flexion trials, as required to counter the interaction torques that arise at the shoulder because of forearm rotation. After locking the shoulder joint, which cancels these interaction torques, we found a substantial reduction in shoulder muscle activity over many trials. In our second experiment, we tested whether such learning transfers to feedback control. Mechanical perturbations applied to the arm with the shoulder unlocked revealed that feedback responses also account for intersegmental dynamics. After locking the shoulder joint, we found a substantial reduction in shoulder feedback responses, as appropriate for the altered intersegmental dynamics. Our work suggests that feedforward and feedback control share an internal model of the arm's dynamics.SIGNIFICANCE STATEMENT Here we show that altering the physical properties of the arm causes people to learn new motor commands and that this learning transfers to their reflex responses to unexpected mechanical perturbations, even though the reflex responses were never directly trained. Our results suggest that feedforward motor commands and reflex responses share an internal model of the arm's dynamics.

Real-time slacking as a default mode of grip force control: implications for force minimization and personal grip force variation

During trial-to-trial movement adaptation, the motor system systematically reduces extraneous muscle forces when kinematic errors experienced on previous movements are small, a phenomenon termed "slacking." There is also growing evidence that the motor system slacks continuously (i.e., in real-time) during arm movement or grip force control, but the initiation of this slacking is not well-characterized, obfuscating its physiological cause. Here, we addressed this issue by asking participants ( n = 32) to track discrete force targets presented visually using isometric grip force, then applying a brief, subtle error-clamp to that visual feedback on random trials. Participants reduced their force in an exponential fashion, on these error-clamp trials, except when the target force was <10% maximum voluntary contraction (MVC). This force drift began <250 ms after the onset of the error-clamp, consistent with slacking being an ongoing process unmasked immediately after the motor system finished reacting to the last veridical feedback. Above 10% MVC, the slacking rate increased linearly with grip force magnitude. Grip force variation was approximately 50-100% higher with veridical feedback, largely due to heightened signal power at ~1 Hz, the band of visuomotor feedback control. Finally, the slacking rate measured for each participant during error-clamp trials correlated with their force variation during control trials. That is, participants who slacked more had greater force variation. These results suggest that real-time slacking continuously reduces grip force until visual error prompts correction. Whereas such slacking is suited for force minimization, it may also account for ~30% of the variability in personal grip force variation. NEW & NOTEWORTHY We provide evidence that a form of slacking continuously conditions real-time grip force production. This slacking is well-suited to promote efficiency but is expected to increase force variation by triggering additional feedback corrections. Moreover, we show that the rate at which a person slacks is substantially correlated with the variation of their grip force. In combination, at the neurophysiological level, our results suggest slacking is caused by one or more relatively smooth neural adaptations.

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.

Force illusions and drifts observed during muscle vibration

We explored predictions of a scheme that views position and force perception as a result of measuring proprioceptive signals within a reference frame set by ongoing efferent process. In particular, this hypothesis predicts force illusions caused by muscle vibration and mediated via changes in both afferent and efferent components of kinesthesia. Healthy subjects performed accurate steady force production tasks by pressing with the four fingers of one hand (the task hand) on individual force sensors with and without visual feedback. At various times during the trials, subjects matched the perceived force using the other hand. High-frequency vibration was applied to one or both of the forearms (over the hand and finger extensors). Without visual feedback, subjects showed a drop in the task hand force, which was significantly smaller under the vibration of that forearm. Force production by the matching hand was consistently higher than that of the task hand. Vibrating one of the forearms affected the matching hand in a manner consistent with the perception of higher magnitude of force produced by the vibrated hand. The findings were consistent between the dominant and nondominant hands. The effects of vibration on both force drift and force mismatching suggest that vibration led to shifts in both signals from proprioceptors and the efferent component of perception, the referent coordinate and/or coactivation command. The observations fit the hypothesis on combined perception of kinematic-kinetic variables with little specificity of different groups of peripheral receptors that all contribute to perception of forces and coordinates. NEW & NOTEWORTHY We show that vibration of hand/finger extensors produces consistent errors in finger force perception. Without visual feedback, finger force drifted to lower values without a drift in the matching force produced by the other hand; hand extensor vibration led to smaller finger force drift. The findings fit the scheme with combined perception of kinematic-kinetic variables and suggest that vibration leads to consistent shifts of the referent coordinate and, possibly, of coactivation command to the effector.

Systematic, Unintended Drifts in the Cyclic Force Produced with the Fingertips

Cyclic isometric finger-force patterns established using visual feedback show systematic drifts when the feedback is removed. Force changes at multiple time scales and in opposite directions have been reported. For further characterization of these drifts, healthy subjects produced isometric, cyclic finger force with and without visual feedback at various initial amplitudes and frequencies. We hypothesized that on feedback removal, the amplitude will be attracted toward a preferred value that is frequency dependent. We found that the amplitude always increased after feedback removal. The magnitude of the amplitude increase changed with initial frequency, but it was invariant over the explored range of initial amplitudes. Thus, the existence of a preferred amplitude of force oscillations was not supported. We interpret these results within the referent configuration and the referent configuration back-coupling hypotheses. These data will inform a mathematical model of finger-force drifts. However, currently, they raise more questions than they answer, and a coherent account of finger-force drifts remains a challenge.

Unintentional drifts during quiet stance and voluntary body sway

We explored unintentional drifts in voluntary whole-body sway tasks following the removal of visual feedback. The main hypothesis was that the unintentional drifts were produced by drifts of referent coordinates for salient performance variables. Young healthy subjects stood quietly on a force platform and also performed voluntary body sway at 0.5 Hz both in the anterio-posterior and medio-lateral directions. Visual feedback on the center of pressure (COP) coordinate was provided and then turned off. During quiet stance trials, the subjects matched the initial COP coordinate with a target shifted by 3 cm anterior, posterior, left, or right from the coordinate during natural standing and activated the right tibialis anterior to 30% of its maximal voluntary contraction. During cyclical voluntary sway task, the nominal sway amplitude was always 4 cm while the midpoint was at one of the four mentioned locations. Removing visual feedback caused COP drifts during quiet stance trials that were consistent across trials performed by a subject but could be in opposite directions across subjects; there was a consistent drop in the activation level of tibialis anterior. During voluntary body sway, removing visual feedback caused a consistent increase in the voluntary sway amplitude and a drift of the midpoint that was consistent within but not across subjects. Motor equivalent and non-motor equivalent inter-cycle motion components were quantified within the space of muscle groups (muscle modes) under visual feedback and at the end of the period without visual feedback. Throughout the trial, there were large motor equivalent motion components, and they increased over the period without visual feedback. The results corroborate the idea that referent coordinate drifts at different levels of the control hierarchy can lead to unintentional drifts in performance. It suggests that directions of COP drifts are defined by two main factors, drift of the body referent coordinate toward the actual coordinate (that can lead to fall) and an opposite drift to ensure body motion to a safer location. Analysis of motor equivalence suggests that postural stability is not compromised during unintentional drifts in performance in contrast to earlier studies of multi-finger tasks. This may be due to the vital importance of postural stability for everyday actions.

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.

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.

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.

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.