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

Optical Myography-Based Sensing Methodology of Application of Random Loads to Muscles during Hand-Gripping Training

Hand-gripping training is important for improving the fundamental functions of human physical activity. Bernstein's idea of "repetition without repetition" suggests that motor control function should be trained under changing states. The randomness level of load should be visualized for self-administered screening when repeating various training tasks under changing states. This study aims to develop a sensing methodology of random loads applied to both the agonist and antagonist skeletal muscles when performing physical tasks. We assumed that the time-variability and periodicity of the applied load appear in the time-series feature of muscle deformation data. In the experiment, 14 participants conducted the gripping tasks with a gripper, ball, balloon, Palm clenching, and paper. Crumpling pieces of paper (paper exercise) involves randomness because the resistance force of the paper changes depending on the shape and layers of the paper. Optical myography during gripping tasks was measured, and time-series features were analyzed. As a result, our system could detect the random movement of muscles during training.

The Controversial Relationship between Body Mass Index and Handgrip Strength in the Elderly: An Overview

Body mass index (BMI) is one of the most commonly used anthropometric measurements. BMI is measured by dividing an individual's weight by their height. In the elderly, the aging process causes physiological changes to organ systems as well as body composition. The most noticeable changes occur in the musculoskeletal system-that is, of decreased muscle strength. Handgrip strength is one of the most commonly considered criteria to measure muscle strength. Various factors, including age, gender and anthropometric measurements such as BMI, are known to affect a person's muscle strength. In addition, weight and height affect the handgrip strength of an elderly person. However, whether BMI directly affects handgrip strength in the elderly is still debated. Several studies have stated that BMI has a relationship with handgrip strength in the elderly, while other studies have found no relationship between BMI and handgrip strength. BMI and handgrip strength is still controversial and requires further research.

Unintentional force drifts in the lower extremities

We explored the phenomenon of unintentional force drift seen in the absence of visual feedback during knee extension contractions in isometric conditions. Based on the importance of knee extensors for the anti-gravity function, we hypothesized that such force drifts would be slower and smaller compared to those reported for the upper extremities. We also explored possible effects of foot dominance and gender on the force drifts. Young healthy persons produced isometric knee extension contractions to different levels, ranging from 15 to 25% of maximal voluntary contraction force, with the help of visual feedback, and then, the visual feedback was turned off. Force change over the time interval without visual feedback was quantified. In the absence of visual feedback, force drifted to smaller magnitudes. The drift magnitude expressed in percent of the initial force magnitude was smaller for smaller initial force levels, ranging between 8 and 15% of the initial force for the initial force magnitude of 15% and 25% of maximal voluntary contraction force. The time exponent of the force drift was independent of the initial force magnitude and was, on average, 6.45 s. There were no significant effects of foot dominance or gender, although the male subjects tended to show stronger scaling of the drift magnitude with the initial force level compared to the female subjects. The results show that unintentional force drift is a common phenomenon across limbs and muscle groups. This conclusion fits the theory of control with spatial referent coordinates and the general tendency of all natural systems to drift to states with lower potential energy.

Unintentional drifts in performance during one-hand and two-hand finger force production

We explored the phenomena of force drifts and unintentional finger force production (enslaving), and their dependence on visual feedback. Predictions have been drawn based on the theory of control with spatial referent coordinates for condition with feedback on instructed (master) finger force, enslaved finger force, and total force for one-hand and two-hand tasks. Subjects produced force under the different feedback conditions without their knowledge. No feedback condition was also used for the one-hand tasks. Overall, feedback of master finger force led to an increase in the enslaved force, feedback on the slave finger force led to a drop in the master force, feedback on the total force led to balanced drifts in the master force down and enslaved force up, and under the no-feedback condition, master and total force drifted down with large variability in the enslaved force drifts. The patterns were the same in both hands in the two-hand tasks when feedback was provided on the forces of one hand only (without subject's knowledge). The index of enslaving always drifted toward higher values. We interpret the findings as reflecting three main factors: drifts in the referent coordinates toward actual finger coordinates, spread of cortical excitation over representations of the fingers, and robust sharing of referent coordinates between the two hands in bimanual tasks. The large consistent drifts in enslaving toward higher values have to be considered in studies of multi-finger synergies.

Normative reference values and predicting factors of handgrip strength for dominant and non-dominant hands among healthy Malay adults in Malaysia

INTRODUCTION

Handgrip strength (HGS) measures the maximum voluntary force of the hand, which has been used to assess individual health status indirectly. Although several factors related to HGS have been identified, studies among adults in Malaysia are lacking. This study aimed to provide the normative reference HGS values and determine its predictor factors among healthy adults of Malay ethnic in Malaysia.

METHODOLOGY

This study was a part of the Prospective Urban Rural Epidemiology (PURE) study carried out among adults aged between 35 to 70 years old residing in urban and rural Malaysian communities. A standardised questionnaire was used to assess the socio-demographic information and physical activity level of respondents who provided written informed consent to participate in this study. HGS was measured using Jamar's dynamometer. A total of 3,446 healthy adults of Malay ethnic were included in this study. Descriptive data were used to derive the normative reference values for HGS using means and standard deviations stratified by age and gender. The predictors of HGS were determined using a general linear model (GLM).

RESULTS

Mean HGS ranged from 38.48 (± 9.40) kg for the dominant hand of men aged 35-40 years to 16.53 (± 5.69) kg for the non-dominant hand of women aged 61-70 years. The ANOVA indicated that there was a significant descending trend of HGS as age increased for both genders (p < 0.05). The ANOVA also revealed that participants working in blue- or white-collar jobs had higher HGS than their counterparts who are homemakers (p < 0.05). The GLM shows that, age, occupation type, socio-economic status (SES), physical activity level and BMI significantly predicted dominant HGS among male and meanwhile, only age, SES and BMI significantly predicted dominant HGS among female.

CONCLUSION

HGS normative values provided herein can serve as a guide for interpreting HGS measurements obtained from healthy Asian adults especially Malay ethnic. The clinicians and researcher can use the established HGS reference values as comparison in their patients or participants. Furthermore, during a rehabilitation process, the clinicians and researchers could use the normal score ranges to document the progress of HGS and provide feedback to the patients. Further study with prospective study design is needed to determine the causal effect association of the predictors and HGS.

Optimality, Stability, and Agility of Human Movement: New Optimality Criterion and Trade-Offs

This review of movement stability, optimality, and agility is based on the theory of motor control with changes in spatial referent coordinates for the effectors, the principle of abundance, and the uncontrolled manifold hypothesis. A new optimality principle is suggested based on the concept of optimal sharing corresponding to a vector in the space of elemental variables locally orthogonal to the uncontrolled manifold. Motion along this direction is associated with minimal components along the relatively unstable directions within the uncontrolled manifold leading to a minimal motor equivalent motion. For well-practiced actions, this task-specific criterion is followed in spaces of referent coordinates. Consequences of the suggested framework include trade-offs among stability, optimality, and agility, unintentional changes in performance, hand dominance, finger specialization, individual traits in performance, and movement disorders in neurological patients.

Effect of pinch types on pinch force sense in healthy adults

Pinch force sense plays an important role in the performance of daily finger movements, including tip, key, palmar pinch. The present study investigated the roles of pinch type in the sensation of pinch force among healthy participants in the ipsilateral force reproduction trial. This study instructed forty healthy adult subjects (20 women and 20 men) in producing reference forces at different levels [10, 30, 50% maximal voluntary isometric contraction (MVIC)] by adopting 3 pinch types (tip, key, and palmar pinches) and in reproducing the above force levels with the identical hand. Our study revealed that subjects are significantly more sensitive detecting alterations of pinching forces with tip pinch but not key or palmar pinch under high forces (30 and 50% MVIC) but not at lower force levels (10% MVIC).

Hierarchical and synergistic organization of control variables during the multi-digit grasp of a free and an externally fixed object

In the referent control theory, grip force emerges by designating the referent aperture (R_a) as a threshold position inside the object. This study quantified R_a and investigated whether the synergistic control of digit referent coordinate (RC) and apparent stiffness (k) depend on the external mechanical constraints on the hand-held object. Subjects held a motorized handle capable of adjusting the grip width and performed static multi-digit prehension tasks in which the handle was free and externally fixed in different conditions. The RC and k of individual digits were reconstructed from the changes in digit normal forces and the positions as the grip width was modulated. RCs of the thumb and virtual finger were used to calculate the width and midpoint of R_a, and synergy indices quantifying the task-specific covariation in the space of the digit normal forces and {RC, k} variables were computed. We found that the k and width of the R_a were larger when holding a free handle than the fixed handle. The higher stiffness in the free condition could be a strategy to ensure grip stability. The midpoint of R_a was skewed toward the virtual finger, reflecting different magnitudes of k for the two digits. Further, the normal forces and control variables {RC, k} displayed synergistic covariation for stabilization of the total grasping force. Finally, the synergies were weaker when the handle was externally fixed, demonstrating the dependence of synergies on external constraints. These results add to the current literature by demonstrating that grasp control involves modulation of digit apparent stiffness in addition to the referent coordinate and by identifying the synergistic organization of the control variables during static grasp.

Effects of Forearm Compression Sleeves on Muscle Hemodynamics and Muscular Strength and Endurance Parameters in Sports Climbing: A Randomized, Controlled Crossover Trial

Purpose: Wearing compression garments is a commonly used intervention in sports to improve performance and facilitate recovery. Some evidence supports the use of forearm compression to improve muscle tissue oxygenation and enhance sports climbing performance. However, evidence is lacking for an effect of compression garments on hand grip strength and specific sports climbing performance. The purpose of this study was to evaluate the immediate effects of forearm compression sleeves on muscular strength and endurance of finger flexor muscles in sports climbers.

Materials and Methods: This randomized crossover study included 24 sports climbers who performed one familiarization trial and three subsequent test trials while wearing compression forearm sleeves (COMP), non-compressive placebo forearm sleeves (PLAC), or no forearm sleeves (CON). Test trials consisted of three performance measurements (intermittent hand grip strength and endurance measurements, finger hang, and lap climbing) at intervals of at least 48 h in a randomized order. Muscle oxygenation during hand grip and finger hang measurements was assessed by near-infrared spectroscopy. The maximum blood lactate level, rate of perceived exertion, and forearm muscle pain were also determined directly after the lap climbing trials.

Results: COMP resulted in higher changes in oxy[heme] and tissue oxygen saturation (StO₂) during the deoxygenation (oxy[heme]: COMP –10.7 ± 5.4, PLAC –6.7 ± 4.3, CON –6.9 ± 5.0 [μmol]; p = 0.014, η_p² = 0.263; StO₂: COMP –4.0 ± 2.2, PLAC –3.0 ± 1.4, CON –2.8 ± 1.8 [%]; p = 0.049, η_p² = 0.194) and reoxygenation (oxy [heme]: COMP 10.2 ± 5.3, PLAC 6.0 ± 4.1, CON 6.3 ± 4.9 [μmol]; p = 0.011, η_p² = 0.274; StO₂: COMP 3.5 ± 1.9, PLAC 2.4 ± 1.2, CON 2.3 ± 1.9 [%]; p = 0.028, η_p² = 0.225) phases of hand grip measurements, whereas total [heme] concentrations were not affected. No differences were detected between the conditions for the parameters of peak force and fatigue index in the hand grip, time to failure and hemodynamics in the finger hang, or performance-related parameters in the lap climbing measurements (p ≤ 0.05).

Conclusions: Forearm compression sleeves did not enhance hand grip strength and endurance, sports climbing performance parameters, physiological responses, or perceptual measures. However, they did result in slightly more pronounced changes of oxy [heme] and StO₂ in the deoxygenation and reoxygenation phases during the hand grip strength and endurance measurements.

Sequential contact-based adaptive grasping for robotic hands

This paper proposes a novel type of grasping strategy that draws inspiration from the role of touch and the importance of wrist motions in human grasping. The proposed algorithm, which we call Sequential Contact-based Adaptive Grasping, can be used to reactively modify a given grasp plan according to contacts arising between the hand and the object. This technique, based on a systematic constraint categorization and an iterative task inversion procedure, is shown to lead to synchronized motions of the fingers and the wrist, as it can be observed in humans, and to increase grasp success rate by substantially mitigating the relevant problems of object slippage during hand closure and of uncertainties caused by the environment and by the perception system. After describing the grasping problem in its quasi-static aspects, the algorithm is derived and discussed with some simple simulations. The proposed method is general as it can be applied to different kinds of robotic hands. It refines a priori defined grasp plans and significantly reduces their accuracy requirements by relying only on a forward kinematic model and elementary contact information. The efficacy of our approach is confirmed by experimental results of tests performed on a collaborative robot manipulator equipped with a state-of-the-art underactuated soft hand.

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

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

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.

Effect of Bench Press Load Knowledge on One Repetition Maximum Strength

ABSTRACT

Snarr, RL, Adams, K, and Cook, J. Effect of bench press load knowledge on one repetition maximum strength. J Strength Cond Res 35(8): 2121-2126, 2021-Knowledge of a given load and visual feedback are crucial while performing a given task. Although previous literature has examined the consequences of lifting a submaximal weight, the removal of load knowledge has yet to be examined under maximal effort. Therefore, the purpose of this investigation was to examine the differences in 1 repetition maximum (1RM) bench press values between a known and unknown external load. Twenty resistance-trained subjects (10 male subjects and 10 female subjects) completed 2 trials of a 1RM bench press protocol separated by 48-72 hours. The two 1RM trials consisted of (a) a traditional 1RM lift in which subjects could see the external load and (b) a 1RM lift in which the external load was blocked from view of the subject. Trials were randomized for all subjects. Results indicated that no differences were observed when the load was known vs. unknown within all subjects (p = 0.094; Cohen's d = 0.03; intraclass correlation coefficient = 0.99). In addition, 40% decreased and 15% increased their 1RM, despite the unknown condition. A statistical difference was found between the initial 1RM estimation vs. measured 1RM during the known load trial (p = 0.034, Cohen's d = 0.07). Practitioners should note that load knowledge before a maximal lift does not appear to present any significant detrimental effects on performance. Therefore, training during a "blinded" condition may present a unique modality and additional balance component that would not be presented during a traditional maximal lift. Further examination of attentional focus and muscle activation differences are warranted.

Reproducibility and agreement between three positions for handgrip assessment

The protocol established for taking hand grip dynamometry measurements determines that the patient must be in a sitting position. This protocol cannot be applied due to the patient’s conditions in some cases, such as abdominal surgery, musculoskeletal spine or hip injuries. The purpose was to determine the reproducibility and level of agreement between the Handgrip dynamometry in supine position with the elbow flexed or extended, and the one measured in the sitting position, the design was a descriptive cross-sectional study. The population were young apparently healthy between 18 and 30 years of age (N = 201). Handgrip measurement was performed on both upper limbs in a sitting position with a flexed elbow, a supine position with a flexed elbow, and supine position with the elbow extended. Reproducibility was nearly perfect in all positions (ICC 0.95–0.97). Regarding the level of agreement for the comparison between sitting and supine positions with a flexed elbow, an average difference of − 0.406. For supine position with an extended elbow and supine position with a flexed elbow, the average difference was − 1.479. Considering the results, clinicians or researchers can choose any of the positions evaluated herein and obtain reliable results as long as the standardization process is followed.

The type of visual biofeedback influences maximal handgrip strength and activation strategies

PURPOSE

This study investigated the effects of force and electromyographic (EMG) feedbacks on forearm muscle activations and handgrip maximal isometric voluntary contraction (MIVC).

METHODS

Sixteen males performed a set of MIVC in four different feedback conditions: (1) NO-FB: no feedback is given to the participant; (2) FORCE-FB: participants received a visual feedback of the produced force; (3) AGO-FB: participants received a visual feedback of the EMG activity of two agonist grip muscles; (4) ANTAGO-FB: participants received a visual feedback of the EMG activity of two hand extensors muscles. Each feedback was displayed by monitoring the signal of either force or electrical activity of the corresponding muscles.

RESULTS

Compared to NO-FB, FORCE-FB was associated with a higher MIVC force (+ 11%, P < 0.05), a higher EMG activity of agonist and antagonist muscles (+ 8.7% and + 9.2%, respectively, P < 0.05) and a better MIVC/EMG ratio with the agonist muscles (P < 0.05). AGO-FB was associated with a higher EMG activity of agonist muscles (P < 0.05) and ANTAGO-FB was associated with a higher EMG activity of antagonist muscles (P < 0.05). MIVC force was higher in the agonist feedback condition than in the antagonist feedback condition (+ 5.9%, P < 0.05).

CONCLUSION

Our results showed that the MIVC force can be influenced by different visuals feedback, such as force or EMG feedbacks. Moreover, these results suggested that the type of feedback employed could modify the EMG-to-force relationships. Finally, EMG biofeedback could represent an interesting tool to optimize motor strategies. But in the purpose of performing the highest strength independently of the strategy, the force feedback should be recommended.

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

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

Laws of nature that define biological action and perception

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

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.

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.

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.

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

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

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.

Moving a hand-held object: Reconstruction of referent coordinate and apparent stiffness trajectories

This study used the framework of the referent configuration hypothesis and slow changes in the external conditions during vertical oscillation of a hand-held object to infer the characteristics of hypothetical control variables. The study had two main objectives: (1) to show that hypothetical control variables, namely, referent coordinates and apparent stiffness of vertical hand position and grip force can be measured in an experiment; and (2) to establish relation(s) between these control variables that yield the classic grip-force-load-force coupling. Healthy subjects gripped a handle and performed vertical oscillations between visual targets at one of five metronome-prescribed frequencies. A HapticMaster robot was used to induce slow changes in the vertical force applied to the handle, while the size of the handle was changed slowly leading to changes in the grip aperture. The subjects were instructed not to react to possible changes in the external forces. A linear, second-order model was used to reconstruct the referent coordinate and apparent stiffness values for each phase of the vertical oscillation cycle using across-cycle regressions. The reconstructed time profiles of the referent coordinates and apparent stiffness showed consistent trends across subjects and movement frequencies. To validate the method, these values were used to predict the vertical force and the grip force applied to the handle for movement cycles that were not utilized in the reconstruction process. Analysis of the coupling between the four variables, two referent coordinates and two apparent stiffness values, revealed a single strong constraint reflecting the coupling between the grip force and vertical force. We view these data as providing experimental support for the idea of controlling natural, multi-muscle actions with shifts in a low-dimensional set of referent coordinates.

Intentional and unintentional multi-joint movements: their nature and structure of variance

We tested predictions of a hierarchical scheme on the control of natural movements with referent body configurations. Subjects occupied an initial hand position against a bias force generated by a HapticMaster robot. A smooth force perturbation was applied to the hand consisting of an increase in the bias force, keeping it at a new level for 5s, and decreasing it back to the bias value. When the force returned to the bias value, the arm stopped at a position different from the initial one interpreted as an involuntary movement. We then asked subjects to make voluntary movements to targets corresponding to the measured end-position of the unintentional movements. No target for hand orientation was used. The joint configuration variance was compared between intentional and unintentional movements within the framework of the uncontrolled manifold hypothesis. Our central hypothesis was that both unintentional and intentional movements would be characterized by structure of joint configuration variance reflecting task-specific stability of salient performance variables, such as hand position and orientation. The analysis confirmed that most variance at the final steady states was compatible with unchanged values of both hand position and orientation following both intentional and unintentional movements. We interpret unintentional movements as consequences of back-coupling between the actual and referent configurations at the task level. The results suggested that both intentional and unintentional movements resulted from shifts of the body referent configuration produced intentionally or as a result of the hypothesized back-coupling. Inter-trial variance signature reflects similar task-specific stability properties of the system following both types of movements, intentional and unintentional.

Characteristics of unintentional movements by a multijoint effector

The authors explored the phenomenon of unintentional changes in the equilibrium state of a multijoint effector produced by transient changes in the external force. The subjects performed a position-holding task against a constant force produced by a robot and were instructed not to intervene voluntarily with movements produced by changes in the robot force. The robot produced a smooth force increase leading to a hand movement, followed by a dwell time. Then, the force dropped to its initial value leading to hand movement toward the initial position, but the hand stopped short of the initial position. The undershoot magnitude increased linearly with the peak hand displacement and exponentially with dwell time (time constant of about 1 s). For long dwell times, the hand stopped at about half the total distance to the initial position. The authors interpret the results as consequences of a drift of the referent hand coordinate. Our results provide support for back-coupling between the referent and actual body configurations during multijoint actions and produce the first quantitative analysis of this phenomenon. This mechanism can also explain the phenomena of slacking and force drop after turning visual feedback off during accurate force production task.

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.

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.

Unintentional movements produced by back-coupling between the actual and referent body configurations: violations of equifinality in multi-joint positional tasks

We tested several predictions of a recent theory that combines the ideas of control with referent configurations, hierarchical control, and the uncontrolled manifold (UCM) hypothesis. In particular, we tested a hypothesis that unintentional changes in hand coordinate can happen following a long-lasting transient perturbation. The subjects grasped a handle with the right hand, occupied an initial position against a bias force produced by the HapticMaster robot, and then tried not to react to changes in the robot-produced force. Changes in the force were smooth and transient; they always ended with the same force as the bias force. The force-change amplitude and the time the force was kept at the new level (dwell time) varied across conditions. After the transient force change was over, the handle rested in a position that differed significantly from the initial position. The amplitude of this unintentional movement increased with the amplitude of transient force change and with the dwell time. In the new position, the across-trials joint configuration variance was mostly confined to a subspace compatible with the average handle coordinate and orientation (the UCMs for these variables). We view these results as the first experimental support for the hypothesis on back-coupling between the referent and actual body configurations during multi-joint actions. The results suggest that even under the instruction "not to react to transient force changes," the subjects may be unable to prevent unintentional drift of the referent configuration. The structure of joint configuration variance after such movements was similar to that in earlier reports on joint configuration variance after intentional movements. We conclude that the intentional and unintentional movements are products of a single neural system that can lead to intentional and unintentional shifts of the referent body configuration.

Task-specific stability in muscle activation space during unintentional movements

We used robot-generated perturbations applied during position-holding tasks to explore stability of induced unintentional movements in a multidimensional space of muscle activations. Healthy subjects held the handle of a robot against a constant bias force and were instructed not to interfere with hand movements produced by changes in the external force. Transient force changes were applied leading to handle displacement away from the initial position and then back toward the initial position. Intertrial variance in the space of muscle modes (eigenvectors in the muscle activations space) was quantified within two subspaces, corresponding to unchanged handle coordinate and to changes in the handle coordinate. Most variance was confined to the former subspace in each of the three phases of movement, the initial steady state, the intermediate position, and the final steady state. The same result was found when the changes in muscle activation were analyzed between the initial and final steady states. Changes in the dwell time between the perturbation force application and removal led to different final hand locations undershooting the initial position. The magnitude of the undershot scaled with the dwell time, while the structure of variance in the muscle activation space did not depend on the dwell time. We conclude that stability of the hand coordinate is ensured during both intentional and unintentional actions via similar mechanisms. Relative equifinality in the external space after transient perturbations may be associated with varying states in the redundant space of muscle activations. The results fit a hierarchical scheme for the control of voluntary movements with referent configurations and redundant mapping between the levels of the hierarchy.