Corrective Submovements Research Articles

Evaluation of Trajectory Planning Models for Arm-Reaching Movements Based on Energy Cost

Computational studies have suggested that many characteristics of reaching trajectories in a horizontal plane can be effectively predicted by certain models, including, the minimum end point variance model and minimum torque change model. It has also been reported that these characteristics appear to differ from those obtained by the minimum energy cost model that has been reported to explain the characteristics of locomotor patterns. Do these results imply that the human nervous system uses different strategies to resolve the redundancy problem for different tasks? In order to reexamine the optimality of reaching trajectories from a viewpoint of energy cost, we considered the corrective submovements to compensate for positional error due to signal-dependent noise in motor commands and computed the expected value of the total energy costs required to reach a target by repetition of submovements planned by each of the following models: the minimum energy cost model, minimum end point variance model, and minimum torque change model. The results revealed that when the noise is large, the total energy cost required by the minimum end point variance model and the minimum torque change model can be lower than that required by the minimum energy cost model which assumes minimizing energy cost under noise-free condition. This result indicates that the minimization of the expected value of the energy cost would be an important factor in determining the reaching trajectories.

Basal ganglia contribution to the initiation of corrective submovements

We investigated the neural processes, with a focus on subcortical circuits, which govern corrective submovements in visually targeted action. During event-related fMRI, subjects moved a cursor to capture targets presented at varying movement amplitudes. Movements were performed in a rehearsed null and a novel viscous (25% random trials) torque field. Movement error feedback was provided after each trial. The viscous field invoked a significantly larger error at the end of the primary movement. Subjects compensated by producing more corrections than they had in the null condition. Corrective submovements were appropriately scaled such that terminal error was similar between the two conditions. Parametric analysis identified two regions where the BOLD signal correlated with the number of submovements per trial: a cerebellar region similar to the one noted in the task contrast and the contralateral dorsal putamen. A separate parametric analysis identified brain regions where activity correlated with movement amplitude. This identified the same cerebellar region as above, bilateral parietal cortex, and left motor and premotor cortex. Our data indicate that the basal ganglia and cerebellum play complementary roles in regulating ongoing actions when precise updating is required. The basal ganglia have a key role in contextually-based motor decision-making, i.e. for deciding if and when to correct a given movement by initiating corrective submovements, and the cerebellum is more generally involved in amplifying and refining the command signals for movements of different amplitudes.

Submovements during pointing movements in Parkinson’s disease

Velocity irregularities frequently observed during deceleration of arm movements have usually been interpreted as corrective submovements that improve motion accuracy. This hypothesis is re-examined here in application to movements of Parkinson's disease (PD) patients in which submovements are specifically frequent. Pointing movements in patients and age-matched controls to large and small targets in three movement modes were studied. The modes were discrete (stop on the target), continuous (reverse on the target), and passing (stop after crossing the target). Two types of submovements were distinguished, gross and fine. In both groups, gross submovements were more frequent during the discrete and passing than continuous mode, specifically for large targets. This suggested that gross submovements were fluctuations accompanying motion termination (stabilization at the target) that was included in discrete and passing but not continuous movements. Gross submovements were specifically frequent in patients, suggesting that PD causes deficiency in smooth motion termination. Although in both groups fine submovements were more frequent for small than large targets, this relation was also observed in passing movements after crossing the target, i.e., when no corrections were needed. This result, together with higher jerk of the entire trajectory found for smaller targets, indicates that fine submovements may also be not corrective adjustments but rather velocity fluctuations emerging due to low speed of movements to small targets. This interpretation is consistent with the recognized inability of PD patients to promptly change generated force as well as to quickly re-plan current motion. The results suggest a need to re-examine the traditional interpretation of submovements in PD and the related theory that the production of iterative submovements is a strategy used by patients to compensate for a decreased initial force pulse.

Origins of submovements in movements of elderly adults

BackgroundSlowness is a well-recognized feature of movements in aging. One of the possible reasons for slowness suggested by previous research is production of corrective submovements that compensate for shortened primary submovement to the target. Here, we re-examine this traditional interpretation and argue that the majority of submovements in older adults may be a consequence rather than the cause of slowness.MethodsPointing movements in young and older adults were recorded. Conditions for submovement emergence were manipulated by using small and large targets and three movement modes: discrete (required stopping on the target), reciprocal (required reversal on the target), and passing (required crossing the target and stopping after that). Movements were parsed into a primary and secondary submovement based on zero-crossings of velocity (type 1 submovements), acceleration (type 2 submovements), and jerk (type 3 submovements). In the passing mode, secondary submovements were analyzed only after crossing the target to exclude that they were accuracy adjustments.ResultsConsistent with previous research, the primary submovement was shortened and total secondary submovement incidence was increased in older adults. However, comparisons across conditions suggested that many submovements were non-corrective in both groups. Type 1 submovements were non-corrective because they were more frequent for large than small targets. They predominantly emerged due to arm stabilization and energy dissipation during motion termination in the discrete and passing mode. Although type 2 and 3 submovements were more frequent for small than large targets, this trend was also observed in the passing mode, suggesting that many of these submovements were non-corrective. Rather, they could have been velocity fluctuations associated predominantly with low speed of movements to small targets.ConclusionThe results question the traditional interpretation of frequent submovements in older adults as corrective adjustments. Rather, the increased incidence of submovements in older adults is directly related to low movement speed observed in aging, whereas the relationship between submovement incidence and target size is a result of speed-accuracy trade-off. Aging-related declines in muscular control that may contribute to the disproportional increases in submovement incidence during slow movements of older adults are discussed.

Origins of submovements during pointing movements

Submovements that are frequently observed in the final portion of pointing movements have traditionally been viewed as pointing accuracy adjustments. Here we re-examine this long-lasting interpretation by developing evidence that many of submovements may be non-corrective fluctuations arising from various sources of motor output variability. In particular, non-corrective submovements may emerge during motion termination and during motion of low speed. The contribution of these factors and the factor of accuracy regulation in submovement production is investigated here by manipulating movement mode (discrete, reciprocal, and passing) and target size (small and large). The three modes provided different temporal combinations of accuracy regulation and motion termination, thus allowing us to disentangle submovements associated with each factor. The target size manipulations further emphasized the role of accuracy regulation and provided variations in movement speed. Gross and fine submovements were distinguished based on the degree of perturbation of smooth motion. It was found that gross submovements were predominantly related to motion termination and not to pointing accuracy regulation. Although fine submovements were more frequent during movements to small than to large targets, other results show that they may also be not corrective submovements but rather motion fluctuations attributed to decreases in movement speed accompanying decreases in target size. Together, the findings challenge the traditional interpretation, suggesting that the majority of submovements are fluctuations emerging from mechanical and neural sources of motion variability. The implications of the findings for the mechanisms responsible for accurate target achievement are discussed.

Action selection and refinement in subcortical loops through basal ganglia and cerebellum.

Subcortical loops through the basal ganglia and the cerebellum form computationally powerful distributed processing modules (DPMs). This paper relates the computational features of a DPM's loop through the basal ganglia to experimental results for two kinds of natural action selection. First, functional imaging during a serial order recall task was used to study human brain activity during the selection of sequential actions from working memory. Second, microelectrode recordings from monkeys trained in a step-tracking task were used to study the natural selection of corrective submovements. Our DPM-based model assisted in the interpretation of puzzling data from both of these experiments. We come to posit that the many loops through the basal ganglia each regulate the embodiment of pattern formation in a given area of cerebral cortex. This operation serves to instantiate different kinds of action (or thought) mediated by different areas of cerebral cortex. We then use our findings to formulate a model of the aetiology of schizophrenia.

Kinematic analysis of multiple constraints on a pointing task

The current experiment suggests that the speed/accuracy tradeoff is composed of two classes of constraints, effector and task. We examined the effects of movement distance, target size, orientation of the movement in the workspace, and C–D gain on the kinematics of discrete pointing movements made with computer mouse. It was found that target size influenced the shape of velocity profiles by elongating the duration of the corrective sub-movement phase, while movement distance scaled the entire velocity curve without affecting its shape. C–D gain and orientation of the movement exhibited two kinds of effects: an overall scaling of the velocity curve and a change in its shape. We conclude that target size is a task constraint and movement distance is an effector constraint, while movement orientation exhibited characteristics of both. C–D gain by itself was not a constraint, but interacted with both task and effector constrains. These results highlight the roles of biomechanical and information processing factors in the speed/accuracy tradeoff.

Deciding when and how to correct a movement: discrete submovements as a decision making process

Rapid reaching movements of human and non-human primates are often characterized by irregular multi-peaked velocity profiles. How to interpret these irregularities is still under debate. While some reports assert that these irregularities are the result of a continuous controller interacting with the environment, we and others hold that the velocity irregularities are evidence for a controller that produces discrete movement corrections. Here we analyze rapid pronation/supination wrist movements in monkey during a 1D step-tracking task, where visual perturbations of the target were randomly introduced at movement onset. We use our recently introduced algorithm (Fishbach et al. in Exp Brain Res 164:442-457, 2005) to decompose an irregular movement into a primary movement and one or more discrete, corrective submovements. We first show that the visual perturbation has almost no effect on primary movements. In contrast, this perturbation influences the type and the extent of the corrective submovements that often follow primary movements. Secondly, we show that the highly variable timing of overlapping submovements does not depend directly on the visual perturbation but rather on an estimate of the movement error and on the movement's extent-to-go at the time of correction initiation. These results are consistent with a forward-model based intermittent controller with a non-linearity that depends both on a prediction of the magnitude and direction of the movement's error and on its variance. Corrections are initiated only when the predicted error is statistically significant. A simple abstract model that implements these principles accounts for the type and timing of the corrections observed in our data.

The role of different submovement types during pointing to a target

The present study extends our previous findings in challenging the traditional interpretation of irregularities in the velocity profile of pointing movements as corrective submovements performed to improve accuracy of target achievement. The study is driven by a hypothesis that pointing includes at least two subtasks, accurate target achievement and motion termination, each of which can cause submovements (Dounskaia et al. Exp Brain Res 164:505-516, 2005). To investigate submovements associated with these subtasks, two tasks were performed in the experiment. Task 1 was used to examine the contribution of the two subtasks on submovement production by comparing submovements in discrete movements that include motion termination and in cyclic movements during which motion termination is not performed. Target size manipulations emphasized submovements related to the accuracy subtask. The results confirmed that both subtasks included in pointing cause submovements. Gross types of submovements (types 1 and 2) were associated with motion termination and fine submovements (type 3) with accuracy regulation. Task 2 further investigated sources of the accuracy-associated type 3 submovements by including only cyclic movements performed at two levels of frequency. Most (97.6%) of the submovements in task 2 were of type 3. Submovement incidence was strongly (inversely) associated with cyclic frequency, and it was independent of target size. This result questions the accuracy subtask as a primary source for type 3 submovements, and it raises the possibility that these submovements are an inherent property of low-speed movements. Together, results of the two tasks support our previous finding that gross submovements are not necessarily related to accuracy regulation. They also provide evidence that challenges the interpretation of fine submovements as corrections performed voluntarily to improve pointing accuracy. Alternative interpretations of accuracy regulation mechanisms, such as regulation of muscle stiffness and of the muscle co-contraction level are discussed in light of the present results.

Optimality of the minimum endpoint variance model based on energy consumption

It has been reported that arm trajectories for reaching movements are not planned so as to minimize the energy cost. However, from a biological point of view, saving energy consumption would be important for survival. If human brains do not apply the criterion of the minimum energy consumption to reaching movements, what is the reason? If they do, what has been unrecognized in the studies of the minimum energy model? In this study, we computed energy costs required for the reaching movements planned by the minimum energy cost model and the minimum endpoint variance model which is one of the leading models for reaching movements, respectively. In the computation we considered corrective sub-movements to compensate for the positional error due to signal-dependent noise for motor commands. The results show that the trajectories planned so as to minimize energy cost without considering the effect of noise are easily affected by noise. Therefore, when noise is large, sub-movements are required to reach the target and as a result the total energy cost becomes larger than that for the minimum endpoint variance model. These results suggest that the human arm reaching movement might be optimized on the energy cost and we should consider the effect of the noise in the analysis of the reaching movement from the view point of optimization on the energy cost.

Spatial audio target acquisition in the frontal horizontal plane: Effects of feedback, mobility, and index of difficulty

The results of an empirical study investigating the effect of feedback, mobility, and index of difficulty on a deictic spatial audio target acquisition task in the horizontal plane in front of a user are presented. Audio feedback marked display elements are found to enable usable deictic interaction that is performed with high accuracy and can be described using Fitts’ law. Feedback does not affect perceived workload or preferred walking speed compared to interaction without feedback. Without audio feedback, spatial audio is not found to support adequately the corrective submovements necessary for high selection accuracies. Interaction with the display becomes therefore highly inefficient. Mobility is found to degrade interaction speed and accuracy by 20%. Participants were able to perform deictic spatial audio target acquisition when mobile while walking at 73% of their preferred walking speed. The proposed feedback design is examined in detail and the effects of variable target widths are quantified. Deictic interaction with a spatial audio display is found to be a feasible solution for future interface designs.

Systematic changes in the duration and precision of interception in response to variation of amplitude and effector size

The results of two experiments are reported that examined how performance in a simple interceptive action (hitting a moving target) was influenced by the speed of the target, the size of the intercepting effector and the distance moved to make the interception. In Experiment 1, target speed and the width of the intercepting manipulandum (bat) were varied. The hypothesis that people make briefer movements, when the temporal accuracy and precision demands of the task are high, predicts that bat width and target speed will divisively interact in their effect on movement time (MT) and that shorter MTs will be associated with a smaller temporal variable error (VE). An alternative hypothesis that people initiate movement when the rate of expansion (ROE) of the target's image reaches a specific, fixed criterion value predicts that bat width will have no effect on MT. The results supported the first hypothesis: a statistically reliable interaction of the predicted form was obtained and the temporal VE was smaller for briefer movements. In Experiment 2, distance to move and target speed were varied. MT increased in direct proportion to distance and there was a divisive interaction between distance and speed; as in Experiment 1, temporal VE was smaller for briefer movements. The pattern of results could not be explained by the strategy of initiating movement at a fixed value of the ROE or at a fixed value of any other perceptual variable potentially available for initiating movement. It is argued that the results support pre-programming of MT with movement initiated when the target's time to arrival at the interception location reaches a criterion value that is matched to the pre-programmed MT. The data supported completely open-loop control when MT was less than between 200 and 240 ms with corrective sub-movements increasingly frequent for movements of longer duration.

Influence of biomechanical factors on substructure of pointing movements

Irregularities in the velocity profile near the end of pointing movements have been interpreted as corrective submovements whose purpose is to provide accuracy of pointing to the target. The purpose of the present study was to investigate whether two additional factors related to biomechanical properties of the arm also cause submovements. First, motion termination and stabilization of the limb in the final position required by a discrete pointing task may contribute to submovements. Second, inaccurate regulation of interactive torque at the joints may also cause submovements. To investigate the contributions of these two biomechanical factors and the traditionally considered factor of pointing accuracy, the incidence of submovements was analyzed during three types of experimental manipulations. In addition to target size manipulations (small and large targets), conditions for motion termination were manipulated by examining discrete movements (which terminated at the target) and reciprocal movements (which reversed direction without dwelling on the target). Interaction torques were varied by using targets that require different shoulder-elbow coordination patterns. Submovements were detected in 41% of all analyzed movements. Data supported influences from the accuracy and motion termination factors but not from the interactive torque regulation factor on submovement incidence. Gross submovements were associated with motion termination; fine submovements primarily with accuracy demands. These findings and the analysis of temporal movement characteristics suggest that motion termination is an extra movement component that makes control of discrete movements different to control of reciprocal movements. Implications of the findings to a noise-related interpretation of Fitts' law are discussed. The study emphasizes the influence of arm biomechanics on endpoint kinematics.

On-line motor control in patients with Parkinson's disease.

Recent models based, in part on a study of Huntington's disease, suggest that the basal ganglia are involved in on-line movement guidance. Two experiments were conducted to investigate this idea. First, we studied advanced Parkinson's disease patients performing a reaching task known to depend on on-line guidance. The task was to 'look and point' in the dark at visual targets displayed in the peripheral visual field. In some trials, the target location was slightly modified during saccadic gaze displacement (when vision is suppressed). In both patient and control groups, the target jump induced a gradual modification of the movement which diverged smoothly from its original path to reach the new target location. No deficit was found in the patients, except for an increased latency to respond to the target jump (Parkinson's disease: 243 ms; controls: 166 ms). A computational simulation indicated that this response slowing was likely to be a by-product of bradykinesia. The unexpected inconsistency between this result and previous reports was investigated in a second experiment. We hypothesized that the relevant factor was the characteristics of the corrections to be performed. To test this prediction, we investigated a task requiring corrections of the same type as investigated in Huntington's disease, namely large, consciously detected errors induced by large target jumps at hand movement onset. In contrast with the smooth adjustments observed in the first experiment, the subjects responded to the target jump by generating a discrete corrective sub-movement. While this iterative response was relatively rapid in the control subjects (220 ms), Parkinson's disease patients exhibited either dramatically late (>730 ms) or totally absent on-line corrections. When on-line corrections were absent, the initial motor response was completed before a second corrective response was initiated (the latency of the corrective response was the same as the latency of the initial response). Considered together, these results suggest that basal ganglia dependent circuits are not critical for feedback loops involving a smooth modulation of the ongoing command. These circuits may rather contribute to the generation of discrete corrective sub-movements. This deficit is in line with the general impairment of sequential and simultaneous actions in patients with basal ganglia disorders.

The emergence of movement units through learning with noisy efferent signals and delayed sensory feedback

Rapid human arm movements often have velocity profiles consisting of several bell-shaped acceleration–deceleration phases, sometimes overlapping in time and sometimes appearing separately. We show how such sub-movement sequences can emerge naturally as an optimal control policy is approximated by a reinforcement learning system in the face of uncertainty and feedback delay. The system learns to generate sequences of pulse-step commands, producing fast initial sub-movements followed by several slow corrective sub-movements that often begin before the initial sub-movement has completed. These results suggest how the nervous system might efficiently control a stochastic motor plant under uncertainty and feedback delay.

Kinematic properties of rapid hand movements in a knob turning task.

In order to understand how the central nervous system controls the kinematics of rapid finger and hand movements, we studied the motions of subjects turning a knob to light-emitting diode targets, similar to tuning a radio dial. On many trials, subjects turned the knob with a single, smooth, and regular motion as revealed by the angular position and velocity trajectories, but on others, subjects produced irregularities in the kinematics. Like many past studies, we interpreted these irregularities as discrete corrective submovements. Unlike other studies, we used a direct, objective algorithm to identify overlapping submovements, detecting appreciable inflections in the acceleration traces by examining zero crossings in their derivatives, jerk and snap. The movements without overlapping submovements on average had a near symmetric, bell-shaped velocity profile that was independent of speed, and which matched the theoretical minimum jerk velocity very closely. We proposed three plausible mechanisms for altering the shape of movement kinematics, and implemented a mass-spring model with nonlinear damping to explore the possibilities. Although there was relatively little variability in the shape and symmetry of movements across trials, there was a fair amount of variability in their amplitude. We show that subjects attempted to eliminate the need for corrective submovements by making more accurate primary movements with practice, but that the variability inherent in rapid movements dictated the need for corrective submovements. Subjects used corrective submovements to improve final endpoint accuracy while reducing endpoint variability, resulting in higher task success rates.

Rapid aimed limb movements: differential effects of practice on component submovements.

Three experiments are reported in which subjects practiced rapid aimed limb movements (arm pointing and wrist rotation) toward a visible target region. Subjects were required to minimize their movement durations while still landing in the target. The movement trajectories were examined to assess the effects of practice on separate component submovements of the limb movements. The results revealed that practice improved primarily temporal, not spatial, aspects of performance. Practice reduced the overall movement durations, but had different effects on the individual submovements. Practice allowed subjects to reduce the amount of time spent performing final corrective submovements, but actually increased slightly the time needed to produce the initial ballistic submovement. The results suggest that practice in the present task primarily enhanced the ability to use feedback information, but there was also some evidence of changes in the ballistic, preprogrammed portion of the movements. The results demonstrate that analysis of submovements can reveal important details of the underlying motor control processes.

Optimality in human motor performance: ideal control of rapid aimed movements.

A stochastic optimized-submovement model is proposed for Pitts' law, the classic logarithmic tradeoff between the duration and spatial precision of rapid aimed movements. According to the model, an aimed movement toward a specified target region involves a primary submovement and an optional secondary corrective submovement. The submovements are assumed to be programmed such that they minimize average total movement time while maintaining a high frequency of target hits. The programming process achieves this minimization by optimally adjusting the average magnitudes and durations of noisy neuromotor force pulses used to generate the submovements. Numerous results from the literature on human motor performance may be explained in these terms. Two new experiments on rapid wrist rotations yield additional support for the stochastic optimizedsubmovement model. Experiment 1 revealed that the mean durations of primary submovements and of secondary submovements, not just average total movement times, conform to a square-root approximation of Pitts' law derived from the model. Also, the spatial endpoints of primary submovements have standard deviations that increase linearly with average primary-submovement velocity, and the average primary-submovement velocity influences the relative frequencies of secondary submovements, as predicted by the model. During Experiment 2, these results were replicated and extended under conditions in which subjects made movements without concurrent visual feedback. This replication suggests that submovement optimization may be a pervasive property of movement production. The present conceptual framework provides insights into principles of motor performance, and it links the study of physical action to research on sensation, perception, and cognition, where psychologists have been concerned for some time about the degree to which mental processes incorporate rational and normative rules. An enduring issue in the study of the human mind concerns of mathematical probability theory and statistical decision thethe rationality and optimality of the mental processes that guide ory (e.g., see Edwards, 1961; Edwards, Lindman, & Savage,

Temporal Distribution of Attention During a Throwing Motion

A reaction-time measure of attention was employed during five segments of a simultaneous dart throw: premovement decision, immediately after recoil was begun, maximum recoil, immediately after forward movement was begun, and after release of the dart. Reaction time was significantly longer when the stimulus was presented during the first or second segment than during later segments. Reaction time during premovement was not consistently greater than that immediately after movement was begun, indicating that information is being sampled at a high rate after movement commences. It appears that monitoring of proprioceptive feedback after movement has begun, and initiation of corrective submovements, is necessary for skillful performance of dart throwing.

Absorption of lactose and its digestion products i the normal and malnourished Ugandan.

Natural movements are corrected in part by the generation of submovements, occurring early in a movement such that they amend an ongoing action. Submovements are associated with activity of the basal ganglia, implying a role for the structures in error correction. In parallel, the basal ganglia are linked to the generation and control of force amplitude, change, and duration. Here, we tested whether activity in human basal ganglia is associated with submovements generally, or was specific to a condition where the submovements only occurred in the face of unexpected proprioceptive error. Submovements were induced by introducing unexpected and variable viscous loads (augmenting the need for trial-specific grip forces) or by reducing target size (augmenting the need for visually guided on-line control) in a one-dimensional target-capture task. In both cases, subjects compensated for the increased task difficulty by generating corrective submovements, which were closely matched in frequency and type. Activity in the internal segment of the globus pallidus and subthalamic nucleus correlated strongly with the number of submovements during the viscous challenge but not with the target challenge. The effects could not be explained by kinematic differences, i.e., movement amplitude or average number of submovements. The results support a specific role for the basal ganglia in error correction under conditions of variable load where there is a need for the dynamic control of force within an ongoing movement.