Computational motor control: feedback and accuracy

Exploring motor skill acquisition in bimanual coordination: insights from navigating a novel maze task

In this study, we introduce a novel maze task designed to investigate naturalistic motor learning in bimanual coordination. We developed and validated an extended set of movement primitives tailored to capture the full spectrum of scenarios encountered in a maze game. Over a 3-day training period, we evaluated participants' performance using these primitives and a custom-developed software, enabling precise quantification of performance. Our methodology integrated the primitives with in-depth kinematic analyses and thorough thumb pressure assessments, charting the trajectory of participants' progression from novice to proficient stages. Results demonstrated consistent improvement in maze performance and significant adaptive changes in joint behaviors and strategic recalibrations in thumb pressure distribution. These findings highlight the central nervous system's adaptability in orchestrating sophisticated motor strategies and the crucial role of tactile feedback in precision tasks. The maze platform and setup emerge as a valuable foundation for future experiments, providing a tool for the exploration of motor learning and coordination dynamics. This research underscores the complexity of bimanual motor learning in naturalistic environments, enhancing our understanding of skill acquisition and task efficiency while emphasizing the necessity for further exploration and deeper investigation into these adaptive mechanisms.

Temporal properties of the speed-accuracy trade-off for arm-pointing movements in various directions around the body

Human body movements are based on the intrinsic trade-off between speed and accuracy. Fitts's law (1954) shows that the time required for movement is represented by a simple logarithmic equation and is applicable to a variety of movements. However, few studies have determined the role of the direction in modulating the performance of upper limb movements and the effects of the interactions between direction and distance and between direction and target size. This study examined the variations in temporal properties of the speed-accuracy trade-off in arm-pointing movements that directly manipulate objects according to the direction, distance, and target size. Participants performed pointing movements to the targets with 3 different sizes presented at 15 locations (5 directions and 3 distances) on a horizontal plane. Movement time (MT) for each trial in each condition was obtained. Subsequently, Mackenzie's model (1992), MT = a + b log2(D/W +1), where D and W represent the distance and width of the target, respectively, was fitted. The slope factor b, a fitted parameter in the equation, was calculated and evaluated according to the changes in the direction, distance, and target size. The results showed that MTs exhibited anisotropy in the hemifield, being the smallest in the right-forward direction. Additionally, the slope factor b, as a function of distance, was smaller in the rightward direction than in the forward and left-forward directions. These results suggest that the degree of difficulty of upper limb movements expands heterogeneously in various directions around the body.

Profiles of movement speed and positional variability based on extended LQG for various noises

Stochastic optimal control has been studied to explain the characteristics of human upper-arm reaching movements. The optimal movement based on an extended linear quadratic Gaussian (LQG) demonstrated that control-dependent noise is the essential factor of the speed-accuracy trade-off in the point-to-point reaching movement. Furthermore, the extended LQG reproduced the profiles of movement speed and positional variability. However, the expected value and variance were computed based on the Monte Carlo method in these studies, which is not considered efficient. In this study, I obtained update equations to efficiently compute the expected value and variance based on the extended LQG. Using the update equations, I computed the profiles of simulated movement speed and positional variability for various amplitudes of noises in a point-to-point reaching movement. The profiles of movement speed were basically bell-shaped for the noises. The speed peak was changed by the control-dependent noise and state-dependent observation noise. The positional variability changed for various noises, and the period during which the variability changed differed with the noise type. Efficient computation in stochastic optimal control based on the extended LQG would contribute to the elucidation of motor control under various noises.

Anatomical bases of fast parietal grasp control in humans: A diffusion-MRI tractography study

The dorso-posterior parietal cortex (DPPC) is a major node of the grasp/manipulation control network. It is assumed to act as an optimal forward estimator that continuously integrates efferent outflows and afferent inflows to modulate the ongoing motor command. In agreement with this view, a recent per-operative study, in humans, identified functional sites within DPPC that: (i) instantly disrupt hand movements when electrically stimulated; (ii) receive short-latency somatosensory afferences from intrinsic hand muscles. Based on these results, it was speculated that DPPC is part of a rapid grasp control loop that receives direct inputs from the hand-territory of the primary somatosensory cortex (S1) and sends direct projections to the hand-territory of the primary motor cortex (M1). However, evidence supporting this hypothesis is weak and partial. To date, projections from DPPC to M1 grasp zone have been identified in monkeys and have been postulated to exist in humans based on clinical and transcranial magnetic studies. This work uses diffusion-MRI tractography in two samples of right- (n = 50) and left-handed (n = 25) subjects randomly selected from the Human Connectome Project. It aims to determine whether direct connections exist between DPPC and the hand control sectors of the primary sensorimotor regions. The parietal region of interest, related to hand control (hereafter designated DPPC_hand), was defined permissively as the 95% confidence area of the parietal sites that were found to disrupt hand movements in the previously evoked per-operative study. In both hemispheres, irrespective of handedness, we found dense ipsilateral connections between a restricted part of DPPC_hand and focal sectors within the pre and postcentral gyrus. These sectors, corresponding to the hand territories of M1 and S1, targeted the same parietal zone (spatial overlap > 92%). As a sensitivity control, we searched for potential connections between the angular gyrus (AG) and the pre and postcentral regions. No robust pathways were found. Streamline densities identified using AG as the starting seed represented less than 5 % of the streamline densities identified from DPPC_hand. Together, these results support the existence of a direct sensory-parietal-motor loop suited for fast manual control and more generally, for any task requiring rapid integration of distal sensorimotor signals.

Attention Guides the Motor-Timing Strategies in Finger-Tapping Tasks When Moving Fast and Slow

Human beings adapt the spontaneous pace of their actions to interact with the environment. Yet, the nature of the mechanism enabling such adaptive behavior remains poorly understood. The aim of the present contribution was to examine the role of attention in motor timing using (a) time series analysis, and (b) a dual task paradigm. In a series of two studies, a finger-tapping task was used in sensorimotor synchronization with various tempi (from 300 to 1,100 ms) and motor complexity (one target vs. six targets). Time series analyzes indicated that two different timing strategies were used depending on the speed constraints. At slow tempi, tapping sequences were characterized by strong negative autocorrelations, suggesting the implication of cognitive predictive timing. When moving at fast and close-to-spontaneous tempi, tapping sequences were characterized by less negative autocorrelations, suggesting that timing properties emerged from body movement dynamics. The analysis of the dual-task reaction times confirmed that both the temporal and spatial constraints impacted the attentional resources allocated to the finger-tapping tasks. Overall, our work suggests that moving fast and slow involve distinct timing strategies that are characterized by contrasting attentional demands.

Important Movement Concepts: Clinical Versus Neuroscience Perspectives

Human movement is complex, presenting clinical and research challenges regarding how it is described and investigated. This paper discusses the commonalities and differences on how human movement is conceptualized from neuroscientific and clinical perspectives with respect to postural control; the limitations of linear measures; movement efficiency with respect to metabolic energy cost and selectivity; and, how muscle synergy analysis may contribute to our understanding of movement variability. We highlight the role of sensory information on motor performance with respect to the base of support and alignment, illustrating a potential disconnect between the clinical and neuroscientific perspectives. The purpose of this paper is to discuss the commonalities and differences in how movement concepts are defined and operationalized by Bobath clinicians and the neuroscientific community to facilitate a common understanding and open the dialogue on the research practice gap.

Experimental and theoretical study of velocity fluctuations during slow movements in humans

Moving smoothly is generally considered as a higher-order goal of motor control and moving jerkily as a witness of clumsiness or pathology, yet many common and well-controlled movements (e.g., tracking movements) have irregular velocity profiles with widespread fluctuations. The origin and nature of these fluctuations have been associated with the operation of an intermittent process but in fact remain poorly understood. Here we studied velocity fluctuations during slow movements, using combined experimental and theoretical tools. We recorded arm movement trajectories in a group of healthy participants performing back-and-forth movements at different speeds, and we analyzed velocity profiles in terms of series of segments (portions of velocity between 2 minima). We found that most of the segments were smooth (i.e., corresponding to a biphasic acceleration) and had constant duration irrespective of movement speed and linearly increasing amplitude with movement speed. We accounted for these observations with an optimal feedback control model driven by a staircase goal position signal in the presence of sensory noise. Our study suggests that one and the same control process can explain the production of fast and slow movements, i.e., fast movements emerge from the immediate tracking of a global goal position and slow movements from the successive tracking of intermittently updated intermediate goal positions. NEW & NOTEWORTHY We show in experiments and modeling that slow movements could result from the brain tracking a sequence of via points regularly distributed in time and space. Accordingly, slow movements would differ from fast movement by the nature of the guidance and not by the nature of control. This result could help in understanding the origin and nature of slow and segmented movements frequently observed in brain disorders.

Does motor expertise facilitate amplitude differentiation of lower limb-movements in an asymmetrical bipedal coordination task?

The motor system's natural tendency is to move the limbs over equal amplitudes, for example in walking. However, in many situations in which people must perform complex movements, a certain degree of amplitude differentiation of the limbs is required. Visual and haptic feedback have recently been shown to facilitate such independence of limb movements. However, it is unknown whether motor expertise moderates the extent to which individuals are able to differentiate the amplitudes of their limb-movements while being supported with visual and haptic feedback. To answer this question 14 pre-professional dancers were compared to 14 non-dancers on simultaneously generating a small displacement with one foot, and a larger one with the other foot, in four different feedback conditions. In two conditions, haptic guidance was offered, either in a passive or active mode. In the other two conditions, veridical and enhanced visual feedback were provided. Surprisingly, no group differences were found regarding the degree to which the visual or haptic feedback assisted the generation of the different target amplitudes of the feet (mean amplitude difference between the feet). The correlation between the displacements of the feet and the standard deviation of the continuous relative phase between the feet, reflecting the degree of independence of the feet movements, also failed to show between-group differences. Sample entropy measures, indicating the predictability of the foot movements, did show a group difference. In the haptically-assisted conditions, the dancers demonstrated more predictable coordination patterns than the non-dancers as reflected by lower sample entropy values whereas the reverse was true in the visual-feedback conditions. The results demonstrate that motor expertise does not moderate the extent to which haptic tracking facilitates the differentiation of the amplitudes of the lower limb movements in an asymmetrical bipedal coordination task.

Unifying Speed-Accuracy Trade-Off and Cost-Benefit Trade-Off in Human Reaching Movements

Two basic trade-offs interact while our brain decides how to move our body. First, with the cost-benefit trade-off, the brain trades between the importance of moving faster toward a target that is more rewarding and the increased muscular cost resulting from a faster movement. Second, with the speed-accuracy trade-off, the brain trades between how accurate the movement needs to be and the time it takes to achieve such accuracy. So far, these two trade-offs have been well studied in isolation, despite their obvious interdependence. To overcome this limitation, we propose a new model that is able to simultaneously account for both trade-offs. The model assumes that the central nervous system maximizes the expected utility resulting from the potential reward and the cost over the repetition of many movements, taking into account the probability to miss the target. The resulting model is able to account for both the speed-accuracy and the cost-benefit trade-offs. To validate the proposed hypothesis, we confront the properties of the computational model to data from an experimental study where subjects have to reach for targets by performing arm movements in a horizontal plane. The results qualitatively show that the proposed model successfully accounts for both cost-benefit and speed-accuracy trade-offs.

When Non-Dominant Is Better than Dominant: Kinesiotape Modulates Asymmetries in Timed Performance during a Synchronization-Continuation Task

There is a growing consensus regarding the specialization of the non-dominant limb (NDL)/hemisphere system to employ proprioceptive feedback when executing motor actions. In a wide variety of rhythmic tasks the dominant limb (DL) has advantages in speed and timing consistency over the NDL. Recently, we demonstrated that the application of Kinesio^® Tex (KT) tape, an elastic therapeutic device used for treating athletic injuries, improves significantly the timing consistency of isochronous wrist’s flexion-extensions (IWFEs) of the DL. We argued that the augmented precision of IWFEs is determined by a more efficient motor control during movements due to the extra-proprioceptive effect provided by KT. In this study, we tested the effect of KT on timing precision of IWFEs performed with the DL and the NDL, and we evaluated the efficacy of KT to counteract possible timing precision difference between limbs. Young healthy subjects performed with and without KT (NKT) a synchronization-continuation task in which they first entrained IWFEs to paced auditory stimuli (synchronization phase), and subsequently continued to produce motor responses with the same temporal interval in the absence of the auditory stimulus (continuation phase). Two inter-onset intervals (IOIs) of 550-ms and 800-ms, one within and the other beyond the boundaries of the spontaneous motor tempo, were tested. Kinematics was recorded and temporal parameters were extracted and analyzed. Our results show that limb advantages in performing proficiently rhythmic movements are not side-locked but depend also on speed of movement. The application of KT significantly reduces the timing variability of IWFEs performed at 550-ms IOI. KT not only cancels the disadvantages of the NDL but also makes it even more precise than the DL without KT. The superior sensitivity of the NDL to use the extra-sensory information provided by KT is attributed to a greater competence of the NDL/hemisphere system to rely on sensory input. The findings in this study add a new piece of information to the context of motor timing literature. The performance asymmetries here demonstrated as preferred temporal environments could reflect limb differences in the choice of sensorimotor control strategies for the production of human movement.

Daily modulation of the speed-accuracy trade-off

Goal-oriented arm movements are characterized by a balance between speed and accuracy. The relation between speed and accuracy has been formalized by Fitts' law and predicts a linear increase in movement duration with task constraints. Up to now this relation has been investigated on a short-time scale only, that is during a single experimental session, although chronobiological studies report that the motor system is shaped by circadian rhythms. Here, we examine whether the speed-accuracy trade-off could vary during the day. Healthy adults carried out arm-pointing movements as accurately and fast as possible toward targets of different sizes at various hours of the day, and variations in Fitts' law parameters were scrutinized. To investigate whether the potential modulation of the speed-accuracy trade-off has peripheral and/or central origins, a motor imagery paradigm was used as well. Results indicated a daily (circadian-like) variation for the durations of both executed and mentally simulated movements, in strictly controlled accuracy conditions. While Fitts' law was held for the whole sessions of the day, the slope of the relation between movement duration and task difficulty expressed a clear modulation, with the lowest values in the afternoon. This variation of the speed-accuracy trade-off in executed and mental movements suggests that, beyond execution parameters, motor planning mechanisms are modulated during the day. Daily update of forward models is discussed as a potential mechanism.

Signal-independent noise in intracortical brain-computer interfaces causes movement time properties inconsistent with Fitts' law

OBJECTIVE

Do movements made with an intracortical BCI (iBCI) have the same movement time properties as able-bodied movements? Able-bodied movement times typically obey Fitts' law: [Formula: see text] (where MT is movement time, D is target distance, R is target radius, and [Formula: see text] are parameters). Fitts' law expresses two properties of natural movement that would be ideal for iBCIs to restore: (1) that movement times are insensitive to the absolute scale of the task (since movement time depends only on the ratio [Formula: see text]) and (2) that movements have a large dynamic range of accuracy (since movement time is logarithmically proportional to [Formula: see text]).

APPROACH

Two participants in the BrainGate2 pilot clinical trial made cortically controlled cursor movements with a linear velocity decoder and acquired targets by dwelling on them. We investigated whether the movement times were well described by Fitts' law.

MAIN RESULTS

We found that movement times were better described by the equation [Formula: see text], which captures how movement time increases sharply as the target radius becomes smaller, independently of distance. In contrast to able-bodied movements, the iBCI movements we studied had a low dynamic range of accuracy (absence of logarithmic proportionality) and were sensitive to the absolute scale of the task (small targets had long movement times regardless of the [Formula: see text] ratio). We argue that this relationship emerges due to noise in the decoder output whose magnitude is largely independent of the user's motor command (signal-independent noise). Signal-independent noise creates a baseline level of variability that cannot be decreased by trying to move slowly or hold still, making targets below a certain size very hard to acquire with a standard decoder.

SIGNIFICANCE

The results give new insight into how iBCI movements currently differ from able-bodied movements and suggest that restoring a Fitts' law-like relationship to iBCI movements may require non-linear decoding strategies.

Effect of Position- and Velocity-Dependent Forces on Reaching Movements at Different Speeds

The speed of voluntary movements is determined by the conflicting needs of maximizing accuracy and minimizing mechanical effort. Dynamic perturbations, e.g., force fields, may be used to manipulate movements in order to investigate these mechanisms. Here, we focus on how the presence of position- and velocity-dependent force fields affects the relation between speed and accuracy during hand reaching movements. Participants were instructed to perform reaching movements under visual control in two directions, corresponding to either low or high arm inertia. The subjects were required to maintain four different movement durations (very slow, slow, fast, very fast). The experimental protocol included three phases: (i) familiarization—the robot generated no force; (ii) force field—the robot generated a force; and (iii) after-effect—again, no force. Participants were randomly assigned to four groups, depending on the type of force that was applied during the “force field” phase. The robot was programmed to generate position-dependent forces—with positive (K+) or negative stiffness (K−)—or velocity-dependent forces, with either positive (B+) or negative viscosity (B−). We focused on path curvature, smoothness, and endpoint error; in the latter we distinguished between bias and variability components. Movements in the high-inertia direction are smoother and less curved; smoothness also increases with movement speed. Endpoint bias and variability are greater in, respectively, the high and low inertia directions. A robust dependence on movement speed was only observed in the longitudinal components of both bias and variability. The strongest and more consistent effects of perturbation were observed with negative viscosity (B−), which resulted in increased variability during force field adaptation and in a reduction of the endpoint bias, which was retained in the subsequent after-effect phase. These findings confirm that training with negative viscosity produces lasting effects in movement accuracy at all speeds.

Impact of Prolonged Temporal Discrimination Threshold on Finger Movements of Parkinson's Disease

INTRODUCTION

Sensory information is essential for the precise control of movement. Patients with Parkinson's disease (PD) have higher-order sensory dysfunctions including prolonged temporal discrimination threshold (TDT). However, the impact of prolonged TDT on parkinsonian motor deficits is uncertain.

METHODS

This study includes 33 PD patients and 24 healthy controls. TDT values were measured in the index finger. Using coin rotation task (CRT), dexterous finger movement was assessed. Using an inertial sensor, the speed, amplitude, and frequency of finger tapping were measured. The impact of prolonged index finger TDT on two different finger movements was analyzed using the general estimating equation.

RESULTS

Compared to healthy controls, TDT was prolonged in the PD patients. There was no impact of TDT on mean values or decrement for amplitude and speed, as well as mean values, decrement and variability of tapping frequency. However, prolonged TDT had a significant impact on the variability in amplitude (B = 436.905 × 10-4, Wald χ2 = 9.140, p = 0.014) and speed (B = 425.655 × 10-4, Wald χ2 = 9.876, p = 0.014) of finger tapping. There was a marginal correlation between TDT and CRT. In addition, CRT correlated with variability in amplitude and speed of finger tapping.

CONCLUSION

In PD, cutaneous temporal discriminative sensory dysfunction appears to be related to increased variabilities in the speed and amplitude of fast repetitive finger movements and disturbed finger dexterity.

Does the Length of Elbow Flexors and Visual Feedback Have Effect on Accuracy of Isometric Muscle Contraction in Men after Stroke?

The aim of the study was to determine the effect of different muscle length and visual feedback information (VFI) on accuracy of isometric contraction of elbow flexors in men after an ischemic stroke (IS).

MATERIALS AND METHODS

Maximum voluntary muscle contraction force (MVMCF) and accurate determinate muscle force (20% of MVMCF) developed during an isometric contraction of elbow flexors in 90° and 60° of elbow flexion were measured by an isokinetic dynamometer in healthy subjects (MH, n = 20) and subjects after an IS during their postrehabilitation period (MS, n = 20).

RESULTS

In order to evaluate the accuracy of the isometric contraction of the elbow flexors absolute errors were calculated. The absolute errors provided information about the difference between determinate and achieved muscle force.

CONCLUSIONS

There is a tendency that greater absolute errors generating determinate force are made by MH and MS subjects in case of a greater elbow flexors length despite presence of VFI. Absolute errors also increase in both groups in case of a greater elbow flexors length without VFI. MS subjects make greater absolute errors generating determinate force without VFI in comparison with MH in shorter elbow flexors length.

Sensorimotor control of tracking movements at various speeds for stroke patients as well as age-matched and young healthy subjects

There are aging- and stroke-induced changes on sensorimotor control in daily activities, but their mechanisms have not been well investigated. This study explored speed-, aging-, and stroke-induced changes on sensorimotor control. Eleven stroke patients (affected sides and unaffected sides) and 20 control subjects (10 young and 10 age-matched individuals) were enrolled to perform elbow tracking tasks using sinusoidal trajectories, which included 6 target speeds (15.7, 31.4, 47.1, 62.8, 78.5, and 94.2 deg/s). The actual elbow angle was recorded and displayed on a screen as visual feedback, and three indicators, the root mean square error (RMSE), normalized integrated jerk (NIJ) and integral of the power spectrum density of normalized speed (IPNS), were used to investigate the strategy of sensorimotor control. Both NIJ and IPNS had significant differences among the four groups (P<0.01), and the values were ranked in the following order: young controls < age-matched controls Collapse

Key Words Collapse

MESH Headings

• Adult
• Case-Control Studies
• Elbow/physiopathology
• Female
• Humans
• Male
• Middle Aged
• Movement/physiology
• Psychomotor Performance/physiology
• Stroke/physiopathology
• Young Adult

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Grants Collapse

Affiliation(s)

Di Ao School of Engineering, Sun Yat-sen University, Guangzhou, Guang Dong, P. R. China Key Laboratory of Sensing Technology and Biomedical Instrument of GuangDong province, Guangzhou, Guang Dong, P. R. China
Rong Song School of Engineering, Sun Yat-sen University, Guangzhou, Guang Dong, P. R. China Key Laboratory of Sensing Technology and Biomedical Instrument of GuangDong province, Guangzhou, Guang Dong, P. R. China
Kai-yu Tong Division of Biomedical Engineering, Department of Electronic Engineering, the Chinese University of Hong Kong, Hong Kong, China

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A multi-level approach to investigate the control of an input device: application to a realistic pointing task

This study investigates the subjects' performance during realistic conditions of control of a joystick. An adapted reciprocal aiming task consisting in driving a virtual vehicle along a slalom course as fast as possible was performed while accuracy constraints were manipulated. Realistic dynamical Interface Screen Relationship between the joystick displacements and the displacements of the vehicle was simulated. Vehicle displacements and motor activity (muscle activity and joint kinematics) were recorded. The results highlighted the applicability of the Fitts' law to more realistic conditions where the use of an input device is performed in an intensive control situation. Besides, biomechanical results suggested that neuromuscular responses were different regarding the direction of movement, whereas the performance at a behavioural level were not affected. Thus, this study demonstrates the interest in considering two different aspects of the user's performance (behavioural and biomechanical ones) to make a better agreement between the device design and users' needs.

PRACTITIONER SUMMARY

This study considered two different aspects of the subject’s performance in a realistic situation of speed–accuracy trade-off: the behavioural and motor activity. The necessity for the design of the future ergonomics pointing devices to meet the expectations of the neuromuscular system in order to facilitate their uses is highlighted.

The trade-off between spatial and temporal variabilities in reciprocal upper-limb aiming movements of different durations

The spatial and temporal aspects of movement variability have typically been studied separately. As a result the relationship between spatial and temporal variabilities remains largely unknown. In two experiments we examined the evolution and covariation of spatial and temporal variabilities over variations in the duration of reciprocal aiming movements. Experiments differed in settings: In Experiment 1 participants moved unperturbed whereas in Experiment 2 they were confronted with an elastic force field. Different movement durations—for a constant inter-target distance—were either evoked by imposing spatial accuracy constraints while requiring participants to move as fast as possible, or prescribed by means of an auditory metronome while requiring participants to maximize spatial accuracy. Analyses focused on absolute and relative variabilities, respectively captured by the standard deviation (SD) and the coefficient of variation (CV = SD/mean). Spatial variability (both SDspace and CVspace) decreased with movement duration, while temporal variability (both SDtime and CVtime) increased with movement duration. We found strong negative correlations between spatial and temporal variabilities over variations in movement duration, whether the variability examined was absolute or relative. These findings observed at the level of the full movement contrasted with the findings observed at the level of the separate acceleration and deceleration phases of movement. During the separate acceleration and deceleration phases both spatial and temporal variabilities (SD and CV) were found to increase with their respective durations, leading to positive correlations between them. Moreover, variability was generally larger at the level of the constituent movement phases than at the level of the full movement. The general pattern of results was robust, as it emerged in both tasks in each of the two experiments. We conclude that feedback mechanisms operating to maximize task performance are subjected to a form of competition between spatial and temporal variabilities.

Influence of task constraints and device properties on motor patterns in a realistic control situation

The influences of task difficulty (index difficulty: 2-4), input device of different length, range of motion and mode of resistance (joystick or rotorcraft stick), and directions of movement (leftward rightward) on motor patterns in a realistic control situation were examined with a multilevel analysis (joint kinematics and muscular variables, and global task performance). Eight subjects controlled the displacements of a virtual object during a slalom task characterized by a realistic inertial model. Pilots adapted the endpoint kinematic organization to increasing accuracy constraints to preserve task success whatever the device and the direction. However, the rotorcraft stick manipulation remains highly complex in comparison to the joystick due to poorer proprioceptive information, higher inertial constraints, and an asymmetrical muscle control.

Spatial accuracy of a rapid defense behavior in caterpillars

Aimed movements require that an animal accurately locates the target and correctly reaches that location. One such behavior is the defensive strike seen in Manduca sexta larva. These caterpillars respond to noxious mechanical stimuli applied to their abdomen with a strike of the mandibles towards the location of the stimulus. The accuracy with which the first strike movement reaches the stimulus site depends on the location of the stimulus. Reponses to dorsal stimuli are less accurate than those to ventral stimuli and the mandibles generally land ventral to the stimulus site. Responses to stimuli applied to anterior abdominal segments are less accurate than responses to stimuli applied to more posterior segments and the mandibles generally land posterior to the stimulus site. A trade-off between duration of the strike and radial accuracy is only seen in the anterior stimulus location (body segment A4). The lower accuracy of the responses to anterior and dorsal stimuli can be explained by the morphology of the animal; to reach these areas the caterpillar needs to move its body into a tight curve. Nevertheless, the accuracy is not exact in locations that the animal has shown it can reach, which suggests that consistently aiming more ventral and posterior of the stimulation site might be a defense strategy.

Movement duration, Fitts's law, and an infinite-horizon optimal feedback control model for biological motor systems

Optimization models explain many aspects of biological goal-directed movements. However, most such models use a finite-horizon formulation, which requires a prefixed movement duration to define a cost function and solve the optimization problem. To predict movement duration, these models have to be run multiple times with different prefixed durations until an appropriate duration is found by trial and error. The constrained minimum time model directly predicts movement duration; however, it does not consider sensory feedback and is thus applicable only to open-loop movements. To address these problems, we analyzed and simulated an infinite-horizon optimal feedback control model, with linear plants, that contains both control-dependent and control-independent noise and optimizes steady-state accuracy and energetic costs per unit time. The model applies the steady-state estimator and controller continuously to guide an effector to, and keep it at, target position. As such, it integrates movement control and posture maintenance without artificially dividing them with a precise, prefixed time boundary. Movement pace is determined by the model parameters, and the duration is an emergent property with trial-to-trial variability. By considering the mean duration, we derived both the log and power forms of Fitts's law as different approximations of the model. Moreover, the model reproduces typically observed velocity profiles and occasional transient overshoots. For unbiased sensory feedback, the effector reaches the target without bias, in contrast to finite-horizon models that systematically undershoot target when energetic cost is considered. Finally, the model does not involve backward and forward sweeps in time, its stability is easily checked, and the same solution applies to movements of different initial conditions and distances. We argue that biological systems could use steady-state solutions as default control mechanisms and might seek additional optimization of transient costs when justified or demanded by task or context.

Agonistic and antagonistic interaction in speed/accuracy tradeoff: a delta-lognormal perspective

This paper reports the results of a model-based analysis of movements gathered in a 4×4 experimental design of speed/accuracy tradeoffs with variable target distances and width. Our study was performed on a large (120 participants) and varied sample (both genders, wide age range, various health conditions). The delta-lognormal equation was used for data modeling to investigate the interaction between the output of the agonist and the antagonist neuromuscular systems. Empirical observations show that the subjects must correlate more tightly the impulse commands sent to both neuromuscular systems in order to achieve good performances as the difficulty of the task increases whereas the correlation in the timing of the neuromuscular action co-varies with the size of the geometrical properties of the task. These new phenomena are discussed under the paradigm provided by the Kinematic Theory and new research hypotheses are proposed for further investigation of the speed/accuracy tradeoffs.

A model of reward- and effort-based optimal decision making and motor control

Costs (e.g. energetic expenditure) and benefits (e.g. food) are central determinants of behavior. In ecology and economics, they are combined to form a utility function which is maximized to guide choices. This principle is widely used in neuroscience as a normative model of decision and action, but current versions of this model fail to consider how decisions are actually converted into actions (i.e. the formation of trajectories). Here, we describe an approach where decision making and motor control are optimal, iterative processes derived from the maximization of the discounted, weighted difference between expected rewards and foreseeable motor efforts. The model accounts for decision making in cost/benefit situations, and detailed characteristics of control and goal tracking in realistic motor tasks. As a normative construction, the model is relevant to address the neural bases and pathological aspects of decision making and motor control.

A globally optimal estimator for the delta-lognormal modeling of fast reaching movements

Fast reaching movements are an important component of our daily interaction with the world and are consequently under investigation in many fields of science and engineering. Today, useful models are available for such studies, with tools for solving the inverse dynamics problem involved by these analyses. These tools generally provide a set of model parameters that allows an accurate and locally optimal reconstruction of the original movements. Although the solutions that they generate may provide a data curve fitting that is sufficient for some pattern recognition applications, the best possible solution is often necessary in others, particularly those involving neuroscience and biomedical signal processing. To generate these solutions, we present a globally optimal parameter extractor for the delta-lognormal modeling of reaching movements based on the branch-and-bound strategy. This algorithm is used to test the impact of white noise on the delta-lognormal modeling of reaching movements and to benchmark the state-of-the-art locally optimal algorithm. Our study shows that, even with globally optimal solutions, parameter averaging is important for obtaining reliable figures. It concludes that physiologically derived rules are necessary, in addition to global optimality, to achieve meaningful ∆Λ extractions which can be used to investigate the control patterns of these movement primitives.

Passive motion paradigm: an alternative to optimal control

IN THE LAST YEARS, OPTIMAL CONTROL THEORY (OCT) HAS EMERGED AS THE LEADING APPROACH FOR INVESTIGATING NEURAL CONTROL OF MOVEMENT AND MOTOR COGNITION FOR TWO COMPLEMENTARY RESEARCH LINES: behavioral neuroscience and humanoid robotics. In both cases, there are general problems that need to be addressed, such as the "degrees of freedom (DoFs) problem," the common core of production, observation, reasoning, and learning of "actions." OCT, directly derived from engineering design techniques of control systems quantifies task goals as "cost functions" and uses the sophisticated formal tools of optimal control to obtain desired behavior (and predictions). We propose an alternative "softer" approach passive motion paradigm (PMP) that we believe is closer to the biomechanics and cybernetics of action. The basic idea is that actions (overt as well as covert) are the consequences of an internal simulation process that "animates" the body schema with the attractor dynamics of force fields induced by the goal and task-specific constraints. This internal simulation offers the brain a way to dynamically link motor redundancy with task-oriented constraints "at runtime," hence solving the "DoFs problem" without explicit kinematic inversion and cost function computation. We argue that the function of such computational machinery is not only restricted to shaping motor output during action execution but also to provide the self with information on the feasibility, consequence, understanding and meaning of "potential actions." In this sense, taking into account recent developments in neuroscience (motor imagery, simulation theory of covert actions, mirror neuron system) and in embodied robotics, PMP offers a novel framework for understanding motor cognition that goes beyond the engineering control paradigm provided by OCT. Therefore, the paper is at the same time a review of the PMP rationale, as a computational theory, and a perspective presentation of how to develop it for designing better cognitive architectures.

Moving faster while preserving accuracy

Achieving movements with accuracy despite the inevitable variability of the neuromuscular mechanisms is an important everyday life problem, which has to be solved for the production of any adapted motor act, such as walking, writing, catching, or pointing. To solve this problem when we have to make goal-directed movements as fast as possible, we systematically increase movement time when accuracy requirements increase, a ubiquitous phenomenon qualified as speed-accuracy trade-off. It has been proposed that this speed-accuracy trade-off reflects an optimal compromise between speed and accuracy in the presence of biological noise and that increasing movement speed inevitably leads to decreased motor accuracy. However, the recent finding that muscle cocontraction improves movement accuracy may challenge this view and begs the question of how movement speed control and cocontraction control coexist. Here, we show that humans are in fact able to move faster while preserving movement accuracy, by using a strategy where muscles are cocontracted around the joint. As this energetically costly cocontraction strategy was not naturally used, this result has two important implications. It first demonstrates that a speed modulation strategy is preferred to a cocontraction strategy for fast, accurate movements, and it also suggests that energy economy prevents us to execute accurate movements as fast as we could do. Consequently, we propose that the mechanisms underlying the speed-accuracy trade-off are more complex than previously thought, and suggest the existence of a previously unknown speed-energy-accuracy trade-off for goal-directed movements.

Bayesian action-perception computational model: interaction of production and recognition of cursive letters

In this paper, we study the collaboration of perception and action representations involved in cursive letter recognition and production. We propose a mathematical formulation for the whole perception-action loop, based on probabilistic modeling and bayesian inference, which we call the Bayesian Action-Perception (BAP) model. Being a model of both perception and action processes, the purpose of this model is to study the interaction of these processes. More precisely, the model includes a feedback loop from motor production, which implements an internal simulation of movement. Motor knowledge can therefore be involved during perception tasks. In this paper, we formally define the BAP model and show how it solves the following six varied cognitive tasks using bayesian inference: i) letter recognition (purely sensory), ii) writer recognition, iii) letter production (with different effectors), iv) copying of trajectories, v) copying of letters, and vi) letter recognition (with internal simulation of movements). We present computer simulations of each of these cognitive tasks, and discuss experimental predictions and theoretical developments.

Experimenting with theoretical motor neuroscience

Motor neuroscience is well over 100 years old, with seminal work such as G. T. Fritz and E. Hitzig's discovery of motor cortex occurring in 1870. Theoretical motor neuroscience has been ongoing for at least the last 50 years. How mature a scientific discipline is motor neuroscience? Are experimentalists and theoreticians working together productively to help the field progress? This article addresses these questions by advancing the following theses. Motor neuroscience remains at a descriptive stage due to the incredible complexity of the problem to be solved. The proliferation of models--and distinct modeling camps--stems from the absence of unifying conceptual constructs. To advance the field, theoreticians must rely more heavily on the concept of falsification by producing models that lend themselves to clear experimental testing.

Risk-sensitivity in sensorimotor control

Recent advances in theoretical neuroscience suggest that motor control can be considered as a continuous decision-making process in which uncertainty plays a key role. Decision-makers can be risk-sensitive with respect to this uncertainty in that they may not only consider the average payoff of an outcome, but also consider the variability of the payoffs. Although such risk-sensitivity is a well-established phenomenon in psychology and economics, it has been much less studied in motor control. In fact, leading theories of motor control, such as optimal feedback control, assume that motor behaviors can be explained as the optimization of a given expected payoff or cost. Here we review evidence that humans exhibit risk-sensitivity in their motor behaviors, thereby demonstrating sensitivity to the variability of "motor costs." Furthermore, we discuss how risk-sensitivity can be incorporated into optimal feedback control models of motor control. We conclude that risk-sensitivity is an important concept in understanding individual motor behavior under uncertainty.

Active Control of Bias for the Control of Posture and Movement

Posture and movement are fundamental, intermixed components of motor coordination. Current approaches consider either that 1) movement is an active, anticipatory process and posture is a passive feedback process or 2) movement and posture result from a common passive process. In both cases, the presence of a passive component renders control scarcely robust and stable in the face of transmission delays and low feedback gains. Here we show in a model that posture and movement could result from the same active process: an optimal feedback control that drives the body from its estimated state to its goal in a given (planning) time by acting through muscles on the insertion position (bias) of compliant linkages (tendons). Computer simulations show that iteration of this process in the presence of noise indifferently produces realistic postural sway, fast goal-directed movements, and natural transitions between posture and movement.

Training grip control with a Fitts' paradigm: a pilot study in chronic stroke

STUDY DESIGN

A clinical measurement study.

PURPOSE

To test the applicability of Fitts' paradigm to grasping tasks in individuals with chronic stroke.

INTRODUCTION

Fitts' Law relates the time of target achievement to task difficulty in repetitive motor tasks.

METHODS

Six male chronic stroke patients performed repetitive actuation of a grip force dynamometer with their affected hands for 12 sessions over four to six weeks.

RESULTS

Movement times followed Fitts' behavior with correlations of R(2)>0.8 for all subjects. Grasp control improved during training, as indicated by an average decrease in Fitts' slope of 26% at high difficulty levels (p<0.05), and decreases in the number of force corrections and in jerkiness, both at p<0.001 level.

CONCLUSIONS

The Fitts' grip force targeting protocol provides an objective standardized instrument for grasp proficiency quantification and a potentially efficacious platform for hand training for persons with stroke.

LEVEL OF EVIDENCE

N/A.

Long-Latency Responses During Reaching Account for the Mechanical Interaction Between the Shoulder and Elbow Joints

Although considerable research indicates that reaching movements rely on knowledge of the arm's mechanical properties and environment to anticipate and counter predictable loads, far less research has examined whether this degree of sophistication is present for on-line corrections during reaching. Here we examine the R2/3 response to mechanical perturbations (45–100 ms, also called the long-latency reflex), which is highly flexible and includes the fastest possible contribution from primary motor cortex, a key neural substrate for self-initiated action. Torque perturbations were occasionally and unexpectedly applied to the subject's shoulder and/or elbow in the course of performing reaching movements. Critically, these perturbations would evoke different patterns of feedback corrections from a shoulder extensor muscle if it countered only the local shoulder displacement relative to unperturbed motion or accounted for the mechanical interactions between the shoulder and elbow joints and countered the underlying shoulder torque. Our results show that the earliest response (R1: 20–45 ms) reflected local shoulder displacement, whereas the R2/3 response (45–100 ms) reflected knowledge of multijoint dynamics. Moreover, the same pattern of feedback occurred whether the shoulder muscle helped initiate the movement (during its agonist phase) or helped terminate the movement (during its antagonist phase). These results contribute to the accumulating evidence that highly sophisticated feedback control underlies motor behavior and are consistent with a shared neural substrate, such as primary motor cortex, for feedforward and feedback control.

A parietal-premotor network for movement intention and motor awareness

It is commonly assumed that we are conscious of our movements mainly because we can sense ourselves moving as ongoing peripheral information coming from our muscles and retina reaches the brain. Recent evidence, however, suggests that, contrary to common beliefs, conscious intention to move is independent of movement execution per se. We propose that during movement execution it is our initial intentions that we are mainly aware of. Furthermore, the experience of moving as a conscious act is associated with increased activity in a specific brain region: the posterior parietal cortex. We speculate that movement intention and awareness are generated and monitored in this region. We put forward a general framework of the cognitive and neural processes involved in movement intention and motor awareness.

Modulation of internal model formation during force field-induced motor learning by anodal transcranial direct current stimulation of primary motor cortex

Human subjects can quickly adapt and maintain performance of arm reaching when experiencing novel physical environments such as robot-induced velocity-dependent force fields. Using anodal transcranial direct current stimulation (tDCS) this study showed that the primary motor cortex may play a role in motor adaptation of this sort. Subjects performed arm reaching movement trials in three phases: in a null force field (baseline), in a velocity-dependent force field (adaptation; 25 N s m(-1)) and once again in a null force field (de-adaptation). Active or sham tDCS was directed to the motor cortex representation of biceps brachii muscle during the adaptation phase of the motor learning protocol. During the adaptation phase, the global error in arm reaching (summed error from an ideal trajectory) was similar in both tDCS conditions. However, active tDCS induced a significantly greater global reaching (overshoot) error during the early stage of de-adaptation compared to the sham tDCS condition. The overshoot error may be representative of the development of a greater predictive movement to overcome the expected imposed force. An estimate of the predictive, initial movement trajectory (signed error in the first 150 ms of movement) was significantly augmented during the adaptation phase with active tDCS compared to sham tDCS. Furthermore, this increase was linearly related to the change of the overshoot summed error in the de-adaptation process. Together the results suggest that anodal tDCS augments the development of an internal model of the novel adapted movement and suggests that the primary motor cortex is involved in adaptation of reaching movements of healthy human subjects.

Adaptation of motor behavior to preserve task success in the presence of muscle fatigue

To achieve task goals in the various contexts of everyday life, the CNS has to adapt to short time scale changes in the properties of the neuromuscular system, such as those induced by fatigue. Here we investigated how humans preserve task success despite fatigue-induced changes within the neuromuscular system, when they have to aim at a target as fast and as accurately as possible. In such a task, subjects generally choose a compromise between speed and accuracy that has been formalized as Fitts's law. We first characterized the effect of fatigue on Fitts's law in an experiment where participants had to perform fast but accurate elbow movements aimed at targets of different sizes, before and after a fatiguing exercise that reduced maximal voluntary force by approximately 30%. We found that movements were slower to guarantee task success in the presence of fatigue. We then used an optimal control model to determine how fatigue-induced changes in variables such as noise in motor commands, muscle contraction and relaxation times, and the gain between neural activation and muscle force may contribute to changes in Fitts's law with fatigue. We concluded that the observed behavior was not due to the lack of available force, but very likely reflected the fact that the CNS uses the same optimal strategy with a fatigued neuromuscular plant that notably exhibits increased signal-dependent noise in motor commands. This strategy appears necessary to preserve task success in the presence of acute changes in the neuromuscular system.

Muscular fatigue increases signal-dependent noise during isometric force production

This study was designed to characterize the effect of fatigue on the relationship between muscular force and its variability over a broad range of submaximal forces. Eight participants had to match 4 levels of isometric force from 7 to 53% of their maximal capabilities. This task was repeated before and after a fatigue protocol that induced a loss of maximal force of approximately 31%. We found that, despite an increase in force variability that was proportional to the force level, the linear scaling of force variability with mean force was preserved during fatigue. Because this linear scaling is a prerequisite for optimal sensorimotor control models, our results broaden the explanatory power of these models to the fatigue case, while at the same time offering new routes towards understanding how the central nervous system adapts to fatigue.