How Variability and Effort Determine Coordination at Large Forces

Motor control is a challenging task for the central nervous system, since it involves redundant degrees of freedom, nonlinear dynamics of actuators and limbs, as well as noise. When an action is carried out, which factors does your nervous system consider to determine the appropriate set of muscle forces between redundant degrees-of-freedom? Important factors determining motor output likely encompass effort and the resulting motor noise. However, the tasks used in many previous motor control studies could not identify these two factors uniquely, as signal-dependent noise monotonically increases as a function of the effort. To address this, a recent paper introduced a force control paradigm involving one finger in each hand that can disambiguate these two factors. It showed that the central nervous system considers both force noise and amplitude, with a larger weight on the absolute force and lower weights on both noise and normalized force. While these results are valid for the relatively low force range considered in that paper, the magnitude of the force shared between the fingers for large forces is not known. This paper investigates this question experimentally, and develops an appropriate Markov chain Monte Carlo method in order to estimate the weightings given to these factors. Our results demonstrate that the force sharing strongly depends on the force level required, so that for higher force levels the normalized force is considered as much as the absolute force, whereas the role of noise minimization becomes negligible.     

Tactile feedback plays a critical role in maximum finger force production

This study investigates the role of cutaneous feedback on maximum voluntary force (MVF), finger force deficit (FD) and finger independence (FI). FD was calculated as the difference between the sum of maximal individual finger forces during single-finger pressing tasks and the maximal force produced by those fingers during an all-finger pressing task. FI was calculated as the average non-task finger forces normalized by the task-finger forces and subtracted from 100 percent. Twenty young healthy right-handed males participated in the study. Cutaneous feedback was removed by administering ring block digital anesthesia on the 2nd, 3rd, 4th and 5th digits of the right hands. Subjects were asked to press force sensors with maximal effort using individual digits as well as all four digits together, with and without cutaneous feedback. Results from the study showed a 25% decrease in MVF for the individual fingers as well as all the four fingers pressing together after the removal of cutaneous feedback. Additionally, more than 100% increase in FD after the removal of cutaneous feedback was observed in the middle and ring fingers. No changes in FI values were observed between the two conditions. Results of this study suggest that the central nervous system utilizes cutaneous feedback and the feedback mechanism plays a critical role in maximal voluntary force production by the hand digits.     

Understanding finger coordination through analysis of the structure of force variability

 Most common motor acts involve highly redundant effector systems. Understanding how such systems are controlled by the nervous system is a long-standing scientific challenge. Most proposals for solving this problem are based on the assumption that a particular solution, which optimizes additional constraints, is selected by the nervous system out of the many possible solutions. This study attempts to address this question in the context of coordinating individual finger forces to produce a controlled total force oscillation between 5% and 35% of each subject's maximum force of voluntary contraction, under two different combinations of four fingers. The structure of variability of individual finger forces was evaluated with respect to hypotheses that, at each instance in time, subjects attempt to: (1) stabilize the value of total force and (2) stabilize the total moment created by the fingers about the long axis passing through the forearm and midline of the hand. The results provide evidence that a range of goal-equivalent finger force combinations is generated to stabilize the values of total force and the total moment. The control of total force was specified explicitly by the task. However, it was stabilized only near the time of peak force. In contrast, the total moment was stabilized throughout most of the force cycle. The results lead to the suggestion that successful task performance is achieved, not by selecting a single optimal solution, but by discovering an appropriate control law that selectively stabilizes certain combinations of degrees of freedom relevant to the task while releasing from control other combinations. Received: 2 February 2001 / Accepted in revised form: 21 June 2001     

Saccadic eye movements minimize the consequences of motor noise

The durations and trajectories of our saccadic eye movements are remarkably stereotyped. We have no voluntary control over these properties but they are determined by the movement amplitude and, to a smaller extent, also by the movement direction and initial eye orientation. Here we show that the stereotyped durations and trajectories are optimal for minimizing the variability in saccade endpoints that is caused by motor noise. The optimal duration can be understood from the nature of the motor noise, which is a combination of signal-dependent noise favoring long durations, and constant noise, which prefers short durations. The different durations of horizontal vs. vertical and of centripetal vs. centrifugal saccades, and the somewhat surprising properties of saccades in oblique directions are also accurately predicted by the principle of minimizing movement variability. The simple and sensible principle of minimizing the consequences of motor noise thus explains the full stereotypy of saccadic eye movements. This suggests that saccades are so stereotyped because that is the best strategy to minimize movement errors for an open-loop motor system.     

Neuromotor noise, error tolerance and velocity-dependent costs in skilled performance

In motor tasks with redundancy neuromotor noise can lead to variations in execution while achieving relative invariance in the result. The present study examined whether humans find solutions that are tolerant to intrinsic noise. Using a throwing task in a virtual set-up where an infinite set of angle and velocity combinations at ball release yield throwing accuracy, our computational approach permitted quantitative predictions about solution strategies that are tolerant to noise. Based on a mathematical model of the task expected results were computed and provided predictions about error-tolerant strategies (Hypothesis 1). As strategies can take on a large range of velocities, a second hypothesis was that subjects select strategies that minimize velocity at release to avoid costs associated with signal- or velocity-dependent noise or higher energy demands (Hypothesis 2). Two experiments with different target constellations tested these two hypotheses. Results of Experiment 1 showed that subjects chose solutions with high error-tolerance, although these solutions also had relatively low velocity. These two benefits seemed to outweigh that for many subjects these solutions were close to a high-penalty area, i.e. they were risky. Experiment 2 dissociated the two hypotheses. Results showed that individuals were consistent with Hypothesis 1 although their solutions were distributed over a range of velocities. Additional analyses revealed that a velocity-dependent increase in variability was absent, probably due to the presence of a solution manifold that channeled variability in a task-specific manner. Hence, the general acceptance of signal-dependent noise may need some qualification. These findings have significance for the fundamental understanding of how the central nervous system deals with its inherent neuromotor noise.     

Role of uncertainty in sensorimotor control

Neural signals are corrupted by noise and this places limits on information processing. We review the processes involved in goal-directed movements and how neural noise and uncertainty determine aspects of our behaviour. First, noise in sensory signals limits perception. We show that, when localizing our hand, the central nervous system (CNS) integrates visual and proprioceptive information, each with different noise properties, in a way that minimizes the uncertainty in the overall estimate. Second, noise in motor commands leads to inaccurate movements. We review an optimal-control framework, known as 'task optimization in the presence of signal-dependent noise', which assumes that movements are planned so as to minimize the deleterious consequences of noise and thereby minimize inaccuracy. Third, during movement, sensory and motor signals have to be integrated to allow estimation of the body's state. Models are presented that show how these signals are optimally combined. Finally, we review how the CNS deals with noise at the neural and network levels. In all of these processes, the CNS carries out the tasks in such a way that the detrimental effects of noise are minimized. This shows that it is important to consider effects at the neural level in order to understand performance at the behavioural level.     

Perceived Cost and Intrinsic Motor Variability Modulate the Speed-Accuracy Trade-Off

Fitts’ Law describes the speed-accuracy trade-off of human movements, and it is an elegant strategy that compensates for random and uncontrollable noise in the motor system. The control strategy during targeted movements may also take into account the rewards or costs of any outcomes that may occur. The aim of this study was to test the hypothesis that movement time in Fitts’ Law emerges not only from the accuracy constraints of the task, but also depends on the perceived cost of error for missing the targets. Subjects were asked to touch targets on an iPad^® screen with different costs for missed targets. We manipulated the probability of error by comparing children with dystonia (who are characterized by increased intrinsic motor variability) to typically developing children. The results show a strong effect of the cost of error on the Fitts’ Law relationship characterized by an increase in movement time as cost increased. In addition, we observed a greater sensitivity to increased cost for children with dystonia, and this behavior appears to minimize the average cost. The findings support a proposed mathematical model that explains how movement time in a Fitts-like task is related to perceived risk.     

Learning with slight forgetting optimizes sensorimotor transformation in redundant motor systems

Recent theoretical studies have proposed that the redundant motor system in humans achieves well-organized stereotypical movements by minimizing motor effort cost and motor error. However, it is unclear how this optimization process is implemented in the brain, presumably because conventional schemes have assumed a priori that the brain somehow constructs the optimal motor command, and largely ignored the underlying trial-by-trial learning process. In contrast, recent studies focusing on the trial-by-trial modification of motor commands based on error information suggested that forgetting (i.e., memory decay), which is usually considered as an inconvenient factor in motor learning, plays an important role in minimizing the motor effort cost. Here, we examine whether trial-by-trial error-feedback learning with slight forgetting could minimize the motor effort and error in a highly redundant neural network for sensorimotor transformation and whether it could predict the stereotypical activation patterns observed in primary motor cortex (M1) neurons. First, using a simple linear neural network model, we theoretically demonstrated that: 1) this algorithm consistently leads the neural network to converge at a unique optimal state; 2) the biomechanical properties of the musculoskeletal system necessarily determine the distribution of the preferred directions (PD; the direction in which the neuron is maximally active) of M1 neurons; and 3) the bias of the PDs is steadily formed during the minimization of the motor effort. Furthermore, using a non-linear network model with realistic musculoskeletal data, we demonstrated numerically that this algorithm could consistently reproduce the PD distribution observed in various motor tasks, including two-dimensional isometric torque production, two-dimensional reaching, and even three-dimensional reaching tasks. These results may suggest that slight forgetting in the sensorimotor transformation network is responsible for solving the redundancy problem in motor control.     

Optimality,stochasticity, and variability in motor behavior

Recent theories of motor control have proposed that the nervous system acts as a stochastically optimal controller, i.e. it plans and executes motor behaviors taking into account the nature and statistics of noise. Detrimental effects of noise are converted into a principled way of controlling movements. Attractive aspects of such theories are their ability to explain not only characteristic features of single motor acts, but also statistical properties of repeated actions. Here, we present a critical analysis of stochastic optimality in motor control which reveals several difficulties with this hypothesis. We show that stochastic control may not be necessary to explain the stochastic nature of motor behavior, and we propose an alternative framework, based on the action of a deterministic controller coupled with an optimal state estimator, which relieves drawbacks of stochastic optimality and appropriately explains movement variability. Action Editor: Frances K. Skinner     

The Force Synergy of Human Digits in Static and Dynamic Cylindrical Grasps

This study explores the force synergy of human digits in both static and dynamic cylindrical grasping conditions. The patterns of digit force distribution, error compensation, and the relationships among digit forces are examined to quantify the synergetic patterns and coordination of multi-finger movements. This study recruited 24 healthy participants to perform cylindrical grasps using a glass simulator under normal grasping and one-finger restricted conditions. Parameters such as the grasping force, patterns of digit force distribution, and the force coefficient of variation are determined. Correlation coefficients and principal component analysis (PCA) are used to estimate the synergy strength under the dynamic grasping condition. Specific distribution patterns of digit forces are identified for various conditions. The compensation of adjacent fingers for the force in the normal direction of an absent finger agrees with the principle of error compensation. For digit forces in anti-gravity directions, the distribution patterns vary significantly by participant. The forces exerted by the thumb are closely related to those exerted by other fingers under all conditions. The index-middle and middle-ring finger pairs demonstrate a significant relationship. The PCA results show that the normal forces of digits are highly coordinated. This study reveals that normal force synergy exists under both static and dynamic cylindrical grasping conditions.     

Force variability is mostly not motor noise: Theoretical implications for motor control

Variability in muscle force is a hallmark of healthy and pathological human behavior. Predominant theories of sensorimotor control assume ‘motor noise’ leads to force variability and its ‘signal dependence’ (variability in muscle force whose amplitude increases with intensity of neural drive). Here, we demonstrate that the two proposed mechanisms for motor noise (i.e. the stochastic nature of motor unit discharge and unfused tetanic contraction) cannot account for the majority of force variability nor for its signal dependence. We do so by considering three previously underappreciated but physiologically important features of a population of motor units: 1) fusion of motor unit twitches, 2) coupling among motoneuron discharge rate, cross-bridge dynamics, and muscle mechanics, and 3) a series-elastic element to account for the aponeurosis and tendon. These results argue strongly against the idea that force variability and the resulting kinematic variability are generated primarily by ‘motor noise.’ Rather, they underscore the importance of variability arising from properties of control strategies embodied through distributed sensorimotor systems. As such, our study provides a critical path toward developing theories and models of sensorimotor control that provide a physiologically valid and clinically useful understanding of healthy and pathologic force variability.     

Do Humans Optimally Exploit Redundancy to Control Step Variability in Walking?

It is widely accepted that humans and animals minimize energetic cost while walking. While such principles predict average behavior, they do not explain the variability observed in walking. For robust performance, walking movements must adapt at each step, not just on average. Here, we propose an analytical framework that reconciles issues of optimality, redundancy, and stochasticity. For human treadmill walking, we defined a goal function to formulate a precise mathematical definition of one possible control strategy: maintain constant speed at each stride. We recorded stride times and stride lengths from healthy subjects walking at five speeds. The specified goal function yielded a decomposition of stride-to-stride variations into new gait variables explicitly related to achieving the hypothesized strategy. Subjects exhibited greatly decreased variability for goal-relevant gait fluctuations directly related to achieving this strategy, but far greater variability for goal-irrelevant fluctuations. More importantly, humans immediately corrected goal-relevant deviations at each successive stride, while allowing goal-irrelevant deviations to persist across multiple strides. To demonstrate that this was not the only strategy people could have used to successfully accomplish the task, we created three surrogate data sets. Each tested a specific alternative hypothesis that subjects used a different strategy that made no reference to the hypothesized goal function. Humans did not adopt any of these viable alternative strategies. Finally, we developed a sequence of stochastic control models of stride-to-stride variability for walking, based on the Minimum Intervention Principle. We demonstrate that healthy humans are not precisely “optimal,” but instead consistently slightly over-correct small deviations in walking speed at each stride. Our results reveal a new governing principle for regulating stride-to-stride fluctuations in human walking that acts independently of, but in parallel with, minimizing energetic cost. Thus, humans exploit task redundancies to achieve robust control while minimizing effort and allowing potentially beneficial motor variability.     

Stabilisation of walking by intrinsic muscle properties revealed in a three-dimensional muscle-driven simulation

A fundamental question in movement science is how humans perform stable movements in the presence of disturbances such as contact with objects. It remains unclear how the nervous system, with delayed responses to disturbances, maintains the stability of complex movements. We hypothesised that intrinsic muscle properties (i.e. the force–length–velocity properties of muscle fibres and tendon elasticity) may help stabilise human walking by responding instantaneously to a disturbance and providing forces that help maintain the movement trajectory. To investigate this issue, we generated a 3D muscle-driven simulation of walking and analysed the changes in the simulation's motion when a disturbance was applied to models with and without intrinsic muscle properties. Removing the intrinsic properties reduced the stability; this was true when the disturbing force was applied at a variety of times and in different directions. Thus, intrinsic muscle properties play a unique role in stabilising walking, complementing the delayed response of the central nervous system.     

Optimal trajectory formation of constrained human arm reaching movements

Opening a door, turning a steering wheel, and rotating a coffee mill are typical examples of human movements that are constrained by the physical environment. The constraints decrease the mobility of the human arm and lead to redundancy in the distribution of actuator forces (either joint torques or muscle forces). Due to this actuator redundancy, there is an infinite number of ways to form a specific arm trajectory. However, humans form trajectories in a unique way. How do humans resolve the redundancy of the constrained motions and specify the hand trajectory? To investigate this problem, we examine human arm movements in a crank-rotation task. To explain the trajectory formation in constrained point-to-point motions, we propose a combined criterion minimizing the hand contact force change and the actuating force change over the course of movement. Our experiments show a close matching between predicted and experimental data.     

Hand function: peripheral and central constraints on performance.

The hand is one of the most fascinating and sophisticated biological motor systems. The complex biomechanical and neural architecture of the hand poses challenging questions for understanding the control strategies that underlie the coordination of finger movements and forces required for a wide variety of behavioral tasks, ranging from multidigit grasping to the individuated movements of single digits. Hence, a number of experimental approaches, from studies of finger movement kinematics to the recording of electromyographic and cortical activities, have been used to extend our knowledge of neural control of the hand. Experimental evidence indicates that the simultaneous motion and force of the fingers are characterized by coordination patterns that reduce the number of independent degrees of freedom to be controlled. Peripheral and central constraints in the neuromuscular apparatus have been identified that may in part underlie these coordination patterns, simplifying the control of multi-digit grasping while placing certain limitations on individuation of finger movements. We review this evidence, with a particular emphasis on how these constraints extend through the neuromuscular system from the behavioral aspects of finger movements and forces to the control of the hand from the motor cortex.     

Variability in the interpolated twitch torque for maximal and submaximal voluntary contractions.

The superimposed twitch technique is frequently used to study the degree of motor unit activation during voluntary effort. This technique is one of the preferred methods to determine the activation deficit (AD) in normal, athletic, and patient populations. One of the limitations of the superimposed twitch technique is its variability under given contractile conditions. The objective of this research was to determine the source(s) of variability in the superimposed twitch force (STF) for repeat measurements. We hypothesized that the variability in the AD measurements may be caused by the timing of the twitch force relative to the onset of muscle activation, by force transients during the twitch application, by small variations in the actual force from the nominal target force, and by variations in the resting twitch force. Twenty-eight healthy subjects participated in this study. Sixteen of these subjects participated in a protocol involving contractions at 50% of their maximal voluntary contraction (MVC) effort, whereas the remaining 12 participated in a protocol involving contractions at 100% of their MVC. Doublet-twitch stimuli were superimposed onto the 50 and 100% effort knee extensor muscle contractions, and the resting twitch forces, voluntary knee extensor forces, and STFs were then measured. The mean resting twitch forces obtained before and after 8 s of 50% of MVC were the same. Similarly, the mean STFs determined at 1, 3, 5, and 7 s into the 50% MVC were the same. The variations in twitch force were significantly smaller after accounting for the actual force at twitch application than those calculated from the prescribed forces during the 50% MVC protocol (P < 0.05). Furthermore, the AD and the actual force showed statistically significant negative correlations for the 50% MVC tests. The interpolated twitch torque determined for the maximal effort contractions ranged from 1 to 70%. In contrast to the protocol at 50% of MVC, negative correlations were only observed in 5 of the 12 subjects during the 100% effort contractions. These results suggest that small variations in the actual force from the target force can account for the majority of the variations in the STFs for submaximal but not maximal effort contractions. For the maximal effort contractions, large variations in the STF exist due to undetermined causes.     

A 3-D dynamic model of human finger for studying free movements.

The purpose of this work is to develop a 3D inverse dynamic model of the human finger for estimating the muscular forces involved during free finger movements. A review of the existing 3D models of the fingers is presented, and an alternative one is proposed. The validity of the model has been proved by means of two simulations: free flexion-extension motion of all joints, and free metacarpophalangeal (MCP) adduction motion. The simulation shows the need for a dynamic model including inertial effects when studying fast movements and the relevance of modelling passive forces generated by the structures studying free movements, such as the force exerted by the muscles when they are stretched and the passive action of the ligaments over the MCP joint in order to reproduce the muscular force pattern during the simulation of the free MCP abduction-adduction movements.     

Intermediate representations in the formation of arm trajectories

Psychophysical evidence shows that the planning of an arm trajectory is specified by the central nervous system in extrinsic coordinates. The complex issue of translating the planning of arm movements into muscle forces is discussed in relation to the recent discovery of structures in the brainstem and in the spinal cord. These structures represent discrete maps of motor behavior. Remarkably, the force outputs, produced by activating different zones of the map, sumvectorially. This vectorial combination of motor outputs is a mechanism for producing a vast repertoire of motor behaviors in a simple fashion.     

Influence of haptic guidance in learning a novel visuomotor task

In (re)learning of movements, haptic guidance can be used to direct the needed adaptations in motor control. Haptic guidance influences the main driving factors of motor adaptation, execution error, and control effort in different ways. Human-control effort is dissipated in the interactions that occur during haptic guidance. Minimizing the control effort would reduce the interaction forces and result in adaptation. However, guidance also decreases the magnitude of the execution errors, which could inhibit motor adaptation. The aim of this study was to assess how different types of haptic guidance affect kinematic adaptation in a novel visuomotor task. Five groups of subjects adapted to a reaching task in which the visual representation of the hand was rotated 30°. Each group was guided by a different force field. The force fields differed in magnitude and direction in order to discern the adaptation based on execution errors and control effort. The results demonstrated that the execution error did indeed play a key role in adaptation. The more the guiding forces restricted the occurrence of execution errors, the smaller the amount and rate of adaptation. However, the force field that enlarged the execution errors did not result in an increased rate of adaptation. The presence of a small amount of adaptation in the groups who did not experience execution errors during training suggested that adaptation could be driven on a much slower rate and on the basis of minimization of control effort as was evidenced by a gradual decrease of the interaction forces during training. Remarkably, also in the group in which the subjects were passive and completely guided, a small but significant adaptation occurred. The conclusion is that both minimization of execution errors and control effort drives kinematic adaptation in a novel visuomotor task, but the latter at a much slower rate.     

Age-related changes in finger coordination in static prehension tasks.

We studied age-related changes in the performance of maximal and accurate submaximal force and moment production tasks. Elderly and young subjects pressed on six dimensional force sensors affixed to a handle with a T-shaped attachment. The weight of the whole system was counterbalanced with another load. During tasks that required the production of maximal force or maximal moment by all of the digits, young subjects were stronger than elderly. A greater age-related deficit was seen in the maximal moment production tests. During maximal force production tests, elderly subjects showed larger relative involvement of the index and middle fingers; they moved the point of thumb force application upward (toward the index and middle fingers), whereas the young subjects rolled the thumb downward. During accurate force/moment production trials, elderly persons were less accurate in the production of both total moment and total force. They produced higher antagonistic moments, i.e., moment by fingers that acted against the required direction of the total moment. Both young and elderly subjects showed negative covariation of finger forces across repetitions of a ramp force production task. In accurate moment production tasks, both groups showed negative covariation of two components of the total moment: those produced by the normal forces and those produced by the tangential forces. However, elderly persons showed lower values of the indexes of both finger force covariation and moment covariation. We conclude that age is associated with an impaired ability to produce both high moments and accurate time profiles of moments. This impairment goes beyond the well-documented deficits in finger and hand force production by elderly persons. It involves worse coordination of individual digit forces and of components of the total moment. Some atypical characteristics of finger forces may be viewed as adaptive to the increased variability in the force production with age.