Learning the dynamics of reaching movements results in the modification of arm impedance and long-latency perturbation responses

 Some characteristics of arm movements that humans exhibit during learning the dynamics of reaching are consistent with a theoretical framework where training results in motor commands that are gradually modified to predict and compensate for novel forces that may act on the hand. As a first approximation, the motor control system behaves as an adapting controller that learns an internal model of the dynamics of the task. It approximates inverse dynamics and predicts motor commands that are appropriate for a desired limb trajectory. However, we had previously noted that subtle motion characteristics observed during changes in task dynamics challenged this simple model and raised the possibility that adaptation also involved sensory–motor feedback pathways. These pathways reacted to sensory feedback during the course of the movement. Here we hypothesize that adaptation to dynamics might also involve a modification of how the CNS responds to sensory feedback. We tested this through experiments that quantified how the motor system's response to errors during voluntary movements changed as it adapted to dynamics of a force field. We describe a nonlinear approach that approximates the impedance of the arm, i.e., force response as a function of arm displacement trajectory. We observe that after adaptation, the impedance function changes in a way that closely matches and counters the effect of the force field. This is particularly prominent in the long-latency (>100 ms) component of response to perturbations. Therefore, it appears that practice not only modifies the internal model with which the brain generates motor commands that initiate a movement, but also the internal model with which sensory feedback is integrated with the ongoing descending commands in order to respond to error during the movement. Received: 10 January 2001 / Accepted in revised form: 30 May 2001     

Analysis of an optimal control model of multi-joint arm movements

 In this paper, we propose a model of biological motor control for generation of goal-directed multi-joint arm movements, and study the formation of muscle control inputs and invariant kinematic features of movements. The model has a hierarchical structure that can determine the control inputs for a set of redundant muscles without any inverse computation. Calculation of motor commands is divided into two stages, each of which performs a transformation of motor commands from one coordinate system to another. At the first level, a central controller in the brain accepts instructions from higher centers, which represent the motor goal in the Cartesian space. The controller computes joint equilibrium trajectories and excitation signals according to a minimum effort criterion. At the second level, a neural network in the spinal cord translates the excitation signals and equilibrium trajectories into control commands to three pairs of antagonist muscles which are redundant for a two-joint arm. No inverse computation is required in the determination of individual muscle commands. The minimum effort controller can produce arm movements whose dynamic and kinematic features are similar to those of voluntary arm movements. For fast movements, the hand approaches a target position along a near-straight path with a smooth bell-shaped velocity. The equilibrium trajectories in X and Y show an ‘N’ shape, but the end-point equilibrium path zigzags around the hand path. Joint movements are not always smooth. Joint reversal is found in movements in some directions. The excitation signals have a triphasic (or biphasic) pulse pattern, which leads to stereotyped triphasic (or biphasic) bursts in muscle control inputs, and a dynamically modulated joint stiffness. There is a fixed sequence of muscle activation from proximal muscles to distal muscles. The order is preserved in all movements. For slow movements, it is shown that a constant joint stiffness is necessary to produce a smooth movement with a bell-shaped velocity. Scaled movements can be reproduced by varying the constraints on the maximal level of excitation signals according to the speed of movement. When the inertial parameters of the arm are altered, movement trajectories can be kept invariant by adjusting the pulse height values, showing the ability to adapt to load changes. These results agree with a wide range of experimental observations on human voluntary movements. Received: 4 December 1995 / Accepted in revised form: 17 September 1996     

Cognitive Loading Affects Motor Awareness and Movement Kinematics but Not Locomotor Trajectories during Goal-Directed Walking in a Virtual Reality Environment

The primary purpose of this study was to investigate the effects of cognitive loading on movement kinematics and trajectory formation during goal-directed walking in a virtual reality (VR) environment. The secondary objective was to measure how participants corrected their trajectories for perturbed feedback and how participants'' awareness of such perturbations changed under cognitive loading. We asked 14 healthy young adults to walk towards four different target locations in a VR environment while their movements were tracked and played back in real-time on a large projection screen. In 75% of all trials we introduced angular deviations of ±5° to ±30° between the veridical walking trajectory and the visual feedback. Participants performed a second experimental block under cognitive load (serial-7 subtraction, counter-balanced across participants). We measured walking kinematics (joint-angles, velocity profiles) and motor performance (end-point-compensation, trajectory-deviations). Motor awareness was determined by asking participants to rate the veracity of the feedback after every trial. In-line with previous findings in natural settings, participants displayed stereotypical walking trajectories in a VR environment. Our results extend these findings as they demonstrate that taxing cognitive resources did not affect trajectory formation and deviations although it interfered with the participants'' movement kinematics, in particular walking velocity. Additionally, we report that motor awareness was selectively impaired by the secondary task in trials with high perceptual uncertainty. Compared with data on eye and arm movements our findings lend support to the hypothesis that the central nervous system (CNS) uses common mechanisms to govern goal-directed movements, including locomotion. We discuss our results with respect to the use of VR methods in gait control and rehabilitation.     

The Temporal Structure of Vertical Arm Movements

The present study investigates how the CNS deals with the omnipresent force of gravity during arm motor planning. Previous studies have reported direction-dependent kinematic differences in the vertical plane; notably, acceleration duration was greater during a downward than an upward arm movement. Although the analysis of acceleration and deceleration phases has permitted to explore the integration of gravity force, further investigation is necessary to conclude whether feedforward or feedback control processes are at the origin of this incorporation. We considered that a more detailed analysis of the temporal features of vertical arm movements could provide additional information about gravity force integration into the motor planning. Eight subjects performed single joint vertical arm movements (45° rotation around the shoulder joint) in two opposite directions (upwards and downwards) and at three different speeds (slow, natural and fast). We calculated different parameters of hand acceleration profiles: movement duration (MD), duration to peak acceleration (D PA), duration from peak acceleration to peak velocity (D PA-PV), duration from peak velocity to peak deceleration (D PV-PD), duration from peak deceleration to the movement end (D PD-End), acceleration duration (AD), deceleration duration (DD), peak acceleration (PA), peak velocity (PV), and peak deceleration (PD). While movement durations and amplitudes were similar for upward and downward movements, the temporal structure of acceleration profiles differed between the two directions. More specifically, subjects performed upward movements faster than downward movements; these direction-dependent asymmetries appeared early in the movement (i.e., before PA) and lasted until the moment of PD. Additionally, PA and PV were greater for upward than downward movements. Movement speed also changed the temporal structure of acceleration profiles. The effect of speed and direction on the form of acceleration profiles is consistent with the premise that the CNS optimises motor commands with respect to both gravitational and inertial constraints.     

Modeling discrete and rhythmic movements through motor primitives: a review

Rhythmic and discrete movements are frequently considered separately in motor control, probably because different techniques are commonly used to study and model them. Yet the increasing interest in finding a comprehensive model for movement generation requires bridging the different perspectives arising from the study of those two types of movements. In this article, we consider discrete and rhythmic movements within the framework of motor primitives, i.e., of modular generation of movements. In this way we hope to gain an insight into the functional relationships between discrete and rhythmic movements and thus into a suitable representation for both of them. Within this framework we can define four possible categories of modeling for discrete and rhythmic movements depending on the required command signals and on the spinal processes involved in the generation of the movements. These categories are first discussed in terms of biological concepts such as force fields and central pattern generators and then illustrated by several mathematical models based on dynamical system theory. A discussion on the plausibility of theses models concludes the work.     

Flexible Switching of Feedback Control Mechanisms Allows for Learning of Different Task Dynamics

To produce skilled movements, the brain flexibly adapts to different task requirements and movement contexts. Two core abilities underlie this flexibility. First, depending on the task, the motor system must rapidly switch the way it produces motor commands and how it corrects movements online, i.e. it switches between different (feedback) control policies. Second, it must also adapt to environmental changes for different tasks separately. Here we show these two abilities are related. In a bimanual movement task, we show that participants can switch on a movement-by-movement basis between two feedback control policies, depending only on a static visual cue. When this cue indicates that the hands control separate objects, reactions to force field perturbations of each arm are purely unilateral. In contrast, when the visual cue indicates a commonly controlled object, reactions are shared across hands. Participants are also able to learn different force fields associated with a visual cue. This is however only the case when the visual cue is associated with different feedback control policies. These results indicate that when the motor system can flexibly switch between different control policies, it is also able to adapt separately to the dynamics of different environmental contexts. In contrast, visual cues that are not associated with different control policies are not effective for learning different task dynamics.     

The Development of Upper Limb Movements: From Fetal to Post-Natal Life

Background

The aim of this longitudinal study was to investigate how the kinematic organization of upper limb movements changes from fetal to post-natal life. By means of off-line kinematical techniques we compared the kinematics of hand-to-mouth and hand-to-eye movements, in the same individuals, during prenatal life and early postnatal life, as well as the kinematics of hand-to-mouth and reaching-toward-object movements in the later age periods.

Methodology/Principal Findings

Movements recorded at the 14^th, 18^th and 22^nd week of gestation were compared with similar movements recorded in an ecological context at 1, 2, 3, 4, 8, and 12 months after birth. The results indicate a similar kinematic organization depending on movement type (i.e., eye, mouth) for the infants at one month and for the fetuses at 22 weeks of gestation. At two and three months such differential motor planning depending on target is lost and no statistical differences emerge. Hand to eye movements were no longer observed after the fourth month of life, therefore we compared kinematics for hand to mouth with hand to object movements. Results of these analyses revealed differences in the performance of hand to mouth and reaching to object movements in the length of the deceleration phase of the movement, depending on target.

Conclusion/Significance

Data are discussed in terms of how the passage from intrauterine to extra-uterine environments modifies motor planning. These results provide novel evidence of how different types of upper extremity movements, those directed towards one’s own face and those directed to external objects, develop.     

Submovement Composition of Head Movement

Limb movement is smooth and corrections of movement trajectory and amplitude are barely noticeable midflight. This suggests that skeletomuscular motor commands are smooth in transition, such that the rate of change of acceleration (or jerk) is minimized. Here we applied the methodology of minimum-jerk submovement decomposition to a member of the skeletomuscular family, the head movement. We examined the submovement composition of three types of horizontal head movements generated by nonhuman primates: head-alone tracking, head-gaze pursuit, and eye-head combined gaze shifts. The first two types of head movements tracked a moving target, whereas the last type oriented the head with rapid gaze shifts toward a target fixed in space. During head tracking, the head movement was composed of a series of episodes, each consisting of a distinct, bell-shaped velocity profile (submovement) that rarely overlapped with each other. There was no specific magnitude order in the peak velocities of these submovements. In contrast, during eye-head combined gaze shifts, the head movement was often comprised of overlapping submovements, in which the peak velocity of the primary submovement was always higher than that of the subsequent submovement, consistent with the two-component strategy observed in goal-directed limb movements. These results extend the previous submovement composition studies from limb to head movements, suggesting that submovement composition provides a biologically plausible approach to characterizing the head motor recruitment that can vary depending on task demand.     

The discontinuous nature of motor execution II. Merging discrete and rhythmic movements in a single-joint system -- the phase entrainment effect

 Initiation of rapid discrete flexion movements is significantly altered when a secondary rhythmic movement is performed simultaneously with the same limb; the onset of a stimulus-evoked discrete movement tends to occur time-locked to the oscillation: i.e., the rhythmic movement entrains the discrete response. This nonlinear interaction may reflect a specific principle of coordination of motor tasks which are simultaneously executed with the same effector. This part II of a tripartite research report on such single-muscle multiple-task coordination investigates the contribution of the dynamic properties of the muscle and its reflex circuitry to phase entrainment. Assuming a simple threshold-linear relationship between the control signals generated by the central nervous system and the observable kinematic and electromyographic signals, a secondary rhythmic movement will cause an additional phase-dependent delay between the central “go” command and the first observable change in actual kinematics of the compound movement. Several indicators for such threshold-linear interaction are derived and tested on real data obtained in psychophysical experiments. Four healthy subjects performed rapid lateral abductions of the index finger in response to a visual “go” signal. During a portion of the experiments, subjects produced additional low-amplitude oscillatory movements before stimulus presentation with either the same finger (one-handed task), or with the index finger of the other hand (two-handed task). Results showed phase entrainment and modulation of reaction times when the cyclic and the discrete movements were simultaneously executed by the same finger. But there was no entrainment in the bimanual execution of the tasks. The model was capable of reproducing the observed effects. It is concluded that coordination of voluntary movements which are concurrently performed by the same effector involves specific discontinuous operations, which represents an essential part of the mechanism of motor coordination. Phase entrainment reflects this characteristic discontinuous behavior of the lower stages of motor execution and does not necessarily require nonlinear interaction of motor commands at higher levels of motor processing. Received: 5 September 2001 / Accepted in revised form: 19 December 2001     

Modelling the control of interceptive actions

In recent years, several phenomenological dynamical models have been formulated that describe how perceptual variables are incorporated in the control of motor variables. We call these short-route models as they do not address how perception-action patterns might be constrained by the dynamical properties of the sensory, neural and musculoskeletal subsystems of the human action system. As an alternative, we advocate a long-route modelling approach in which the dynamics of these subsystems are explicitly addressed and integrated to reproduce interceptive actions. The approach is exemplified through a discussion of a recently developed model for interceptive actions consisting of a neural network architecture for the online generation of motor outflow commands, based on time-to-contact information and information about the relative positions and velocities of hand and ball. This network is shown to be consistent with both behavioural and neurophysiological data. Finally, some problems are discussed with regard to the question of how the motor outflow commands (i.e. the intended movement) might be modulated in view of the musculoskeletal dynamics.     

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.     

American Society of Biomechanics Journal of Biomechanics Award 2018: Adaptive motor planning of center-of-mass trajectory during goal-directed walking in novel environments

To aid in the successful execution of goal-directed walking (discrete movement from a start location to an end target) the central nervous system forms a predictive motor plan. For the motor plan to be effective, it must be adapted in response to environmental changes. Despite motor planning being inherent to goal-directed walking, it is not understood how the nervous system adapts these plans to interact with changing environments. Our objective was to understand how people adapt motor plans of center of mass (COM) trajectory during goal-directed walking in response to a consistent change in environmental dynamics. Participants preformed a series of goal-directed walking trials in a novel environment created by a cable robot that applied a lateral force field to their COM. We hypothesized that participants would adapt to the environment by forming an internal model of their COM trajectory within the force field. Our findings support this hypothesis. Initially, we found COM trajectory significantly deviated in the same direction as the applied field, relative to baseline (no field) (p = 0.002). However, with practice in the field, COM trajectory adapted back to the baseline (p = 0.6). When we unexpectedly removed the field, participants demonstrated after-effects, COM trajectory deviated in the direction opposite of the field relative to baseline (p < 0.001). Our findings suggest that when performing a goal-directed walking task, people adapt a motor plan that predicts the COM trajectory that will emerge from the interaction between a specific set of motor commands and the external environment.     

Optimal control of saccades by spatial-temporal activity patterns in the monkey superior colliculus

A major challenge in computational neurobiology is to understand how populations of noisy, broadly-tuned neurons produce accurate goal-directed actions such as saccades. Saccades are high-velocity eye movements that have stereotyped, nonlinear kinematics; their duration increases with amplitude, while peak eye-velocity saturates for large saccades. Recent theories suggest that these characteristics reflect a deliberate strategy that optimizes a speed-accuracy tradeoff in the presence of signal-dependent noise in the neural control signals. Here we argue that the midbrain superior colliculus (SC), a key sensorimotor interface that contains a topographically-organized map of saccade vectors, is in an ideal position to implement such an optimization principle. Most models attribute the nonlinear saccade kinematics to saturation in the brainstem pulse generator downstream from the SC. However, there is little data to support this assumption. We now present new neurophysiological evidence for an alternative scheme, which proposes that these properties reside in the spatial-temporal dynamics of SC activity. As predicted by this scheme, we found a remarkably systematic organization in the burst properties of saccade-related neurons along the rostral-to-caudal (i.e., amplitude-coding) dimension of the SC motor map: peak firing-rates systematically decrease for cells encoding larger saccades, while burst durations and skewness increase, suggesting that this spatial gradient underlies the increase in duration and skewness of the eye velocity profiles with amplitude. We also show that all neurons in the recruited population synchronize their burst profiles, indicating that the burst-timing of each cell is determined by the planned saccade vector in which it participates, rather than by its anatomical location. Together with the observation that saccade-related SC cells indeed show signal-dependent noise, this precisely tuned organization of SC burst activity strongly supports the notion of an optimal motor-control principle embedded in the SC motor map as it fully accounts for the straight trajectories and kinematic nonlinearity of saccades.     

Peculiarities of Activation of Muscles of the Shoulder Belt in Voluntary Two-Joint Movements of the Upper Limb

We studied coordination of central motor commands (СMCs) coming to muscles of the shoulder and shoulder belt in the course of single-joint and two-joint movements including flexion and extension of the elbow and shoulder joints. Characteristics of rectified and averaged EMGs recorded from a few muscles of the upper limb were considered correlates of the CMC parameters. Special attention was paid to coordination of CMCs coming to two-joint muscles that are able to function as common flexors (m. biceps brachii, caput breve, BBcb) and common extensors (m. triceps brachii, caput longum, TBcl) of the elbow and shoulder joints. Upper limb movements used in the tests included planar shifts of the arm from one spatial point to another resulting from either simultaneous changes in the angles of the shoulder and elbow joints or isolated sequential (two-stage) changes in these joint angles. As was found, shoulder muscles providing movements of the elbow with changes in the angle of the elbow joint, i.e., BBcb and TBcl, were also intensely involved in the performance of single-joint movements in the shoulder joint. The CMCs coming to two-joint muscles in the course of two-joint movements appeared, in the first approximation, as sums of the commands received by these muscles in the course of corresponding single-joint movements in the elbow and shoulder joints. Therefore, if we interpret the isolated forearm movement performed due to a change in the angle of the elbow joint as the main motor event, while the shoulder movement is considered the accessory one, we can conclude that realization of a two-joint movement of the upper-limb distal part is based on superposition of CMCs related to basic movements (main and accessory). Neirofiziologiya/Neurophysiology, Vol. 41, No. 1, pp. 48–56, January–February, 2009.     

Neuronal correlates of kinematics-to-dynamics transformation in the supplementary motor area

It is widely acknowledged that movements are planned at the level of the kinematics. However, the central nervous system must ultimately transform kinematic plans into dynamics-related commands. How, when, and where the kinematics-to-dynamics (KD) transformation is processed represent fundamental and unanswered questions. We recorded from the supplementary motor area (SMA) of two monkeys as they executed visually instructed reaching movements. We specifically analyzed a delay period following the instruction but prior to the go signal (motor planning). During the delay, a group of neurons in the SMA progressively came to reflect the dynamics rather than the desired kinematics of the upcoming movement. This finding suggests that some neurons in the SMA participate in the KD transformation.     

Control of targeted flexor movements of the human arm at different levels of the possibility for their preprograming

Contribution of the processes of central preprograming of an equilibrium target position of the limb link was studied by testing two variants of motor task in humans. In the first variant, the tested person could obtain visual information about the target position before the movement initiation. In the second variant, such information initially was absent and was presented only in the course of the movement performance. It has been shown that in both variants the pattern of EMG activity of flexor muscles, which realize the movement (and, respectively, the pattern of motor commands, i.e., efferent activity of spinal motoneurons) demonstrated no fundamental differences. Therefore, it can be supposed that the attainment of a target level in both cases was preprogramed only to a limited extent; more probably, it was provided by successive current control of the limb link position. This control is based, first of all, on dynamic changes of the control signals. In general, data of the experiments are in agreement with the impulse—temporal hypothesis of control of targeted movements.     

Control of the Elbow Extensor Muscles in Slow Targeted Extensions of the Arm in Humans

Relations between the kinematic parameters of slow (non-ballistic) targeted extension movements in the elbow joint of humans and characteristics of the movement-related EMG activity in the two heads of the m. triceps brachii were analyzed. Test movements were performed under conditions of application of non-inertional external loadings directed toward flexion. It was shown that the movement-related EMG activity of the elbow extensors, similarly to what was observed in the flexors at flexion movements with the same parameters, demonstrates a complex structure and includes dynamic and stationary phases. In the former phase, in turn, initial and main components can be differentiated. The rising edge and decay of the main component of the dynamic extensor EMG phase could be approximated by exponential functions; this component was never split into a few subcomponents. Dependences between the amplitudes of m. triceps brachii EMG phases and the amplitude of the movement (or external loading) were, as a rule, nonlinear but monotonic. An increase in the test movement velocity led to an increase in the rate of rise of the rising edge of the dynamic EMG phase, while an increment in the amplitude was less significant. Under the used test conditions, the activity of the elbow extensors was usually accompanied by some coactivation of the antagonists (m. biceps brachii). It is concluded that motor commands coming to the elbow extensors at performance of the extension test movements differ from motor commands to the flexors at analogous flexion test movements by a simpler structure and more tonic pattern. Biomechanical specificities of fixation of the mentioned muscle groups to the arm bones (stability of the moment for application of the extensor force under conditions of changing the joint angle vs variable moment of the flexor force) are considered one of the main reasons for such specificity of the patterns of the extensor and flexor motor commands.     

Automatic versus voluntary motor imitation: effect of visual context and stimulus velocity

Automatic imitation is the tendency to reproduce observed actions involuntarily. Though this topic has been widely treated, at present little is known about the automatic imitation of the kinematic features of an observed movement. The present study was designed to understand if the kinematics of a previously seen stimulus primes the executed action, and if this effect is sensitive to the kinds of stimuli presented. We proposed a simple imitation paradigm in which a dot or a human demonstrator moved in front of the participant who was instructed either to reach the final position of the stimulus or to imitate its motion with his or her right arm. Participants' movements were automatically contaminated by stimulus velocity when it moved according to biological laws, suggesting that automatic imitation was kinematic dependent. Despite that the performance, in term of reproduced velocity, improved in a context of voluntary imitation, subjects did not replicate the observed motions exactly. These effects were not affected by the kind of stimuli used, i.e., motor responses were influenced in the same manner after dot or human observation. These findings support the existence of low-level sensory-motor matching mechanisms that work on movement planning and represent the basis for higher levels of social interaction.