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.     

Rate effects on timing, key velocity, and finger kinematics in piano performance

We examined the effect of rate on finger kinematics in goal-directed actions of pianists. In addition, we evaluated whether movement kinematics can be treated as an indicator of personal identity. Pianists' finger movements were recorded with a motion capture system while they performed melodies from memory at different rates. Pianists' peak finger heights above the keys preceding keystrokes increased as tempo increased, and were attained about one tone before keypress. These rate effects were not simply due to a strategy to increase key velocity (associated with tone intensity) of the corresponding keystroke. Greater finger heights may compensate via greater tactile feedback for a speed-accuracy tradeoff that underlies the tendency toward larger temporal variability at faster tempi. This would allow pianists to maintain high temporal accuracy when playing at fast rates. In addition, finger velocity and accelerations as pianists' fingers approached keys were sufficiently unique to allow pianists' identification with a neural-network classifier. Classification success was higher in pianists with more extensive musical training. Pianists' movement "signatures" may reflect unique goal-directed movement kinematic patterns, leading to individualistic sound.     

Trajectory formation and speed-accuracy trade-off in aiming movements

The trade-off between speed and accuracy and the patterning of movement kinematics have been central issues for theories of human movement for almost a century. In the present contribution experimentally obtained kinematics of reciprocal aiming movements, performed under different task conditions, are modelled as resulting from a single non-linear dynamical system whose parameters vary so as to respond to the task demands. Providing a unified account of speed-accuracy trade-off and trajectory formation phenomena, the model offers a theoretical framework in which both discrete and continuous movements, performed along one or more dimensions can be understood.     

Tracking Second Thoughts: Continuous and Discrete Revision Processes during Visual Lexical Decision

We studied the dynamics of lexical decisions by asking participants to categorize lexical and nonlexical stimuli and recording their mouse movements toward response buttons during the choice. In a previous report we revealed greater trajectory curvature and attraction to competitors for Low Frequency words and Pseudowords. This analysis did not clarify whether the trajectory curvature in the two conditions was due to a continuous dynamic competition between the response alternatives or if a discrete revision process (a "change of mind") took place during the choice from an initially selected response to the opposite one. To disentangle these two possibilities, here we analyse the velocity and acceleration profiles of mouse movements during the choice. Pseudowords'' peak movement velocity occurred with 100ms delay with respect to words and Letters Strings. Acceleration profile for High and Low Frequency words and Letters Strings exhibited a butterfly plot with one acceleration peak at 400ms and one deceleration peak at 650ms. Differently, Pseudowords'' acceleration profile had double positive peaks (at 400 and 600ms) followed by movement deceleration, in correspondence with changes in the decision from lexical to nonlexical response buttons. These results speak to different online processes during the categorization of Low Frequency words and Pseudowords, with a continuous competition process for the former and a discrete revision process for the latter.     

A comparison of the effects of agonist and antagonist muscle fatigue on performance of rapid movements

The aim of this study was to investigate the effects of agonist and antagonist muscle fatigue on the performance of rapid, self-terminating movements. Six subjects performed rapid, consecutive elbow flexion and extension movements between two targets prior to and after fatiguing either the elbow flexor or elbow extensor muscles. The experiments demonstrated consistent results. Agonist muscle fatigue was associated with a decrease in peak velocity and peak deceleration, while a decrease in peak acceleration was particularly prominent. Antagonist muscle fatigue, however, was associated with a decrease in peak deceleration, while a decrease in both the peak velocity and peak acceleration was modest and, in some tests, non-significant. The relative acceleration time (i.e. acceleration time as a proportion of the total movement time) increased when agonists were fatigued, but decreased when antagonists were fatigued. Taken together, these results emphasize the mechanical roles of the agonist and antagonist muscles; namely, the fatigue of each muscle group particularly affected the movement phase in which that group accelerated a limb, while changes of the movement kinematics pattern provided more time for action of the fatigued muscles. In addition, the results presented suggest that agonist muscle fatigue affects movement velocity more than antagonist muscle fatigue, even in movements that demonstrate prominently both mechanical and myoelectric activity of the antagonist muscles, such as rapid, self-terminating movements. Accepted: 11 February 1997     

Kinematic invariants during cyclical arm movements

It has been observed that the motion of the arm end-point (the hand, fingertip or the tip of a pen) is characterized by a number of regularities (kinematic invariants). Trajectory is usually straight, and the velocity profile has a bell shape during point-to-point movements. During drawing movements, a two-thirds power law predicts the dependence of the end-point velocity on the trajectory curvature. Although various principles of movement organization have been discussed as possible origins of these kinematic invariants, the nature of these movement trajectory characteristics remains an open question. A kinematic model of cyclical arm movements derived in the present study analytically demonstrates that all three kinematic invariants can be predicted from a two-joint approximation of the kinematic structure of the arm and from sinusoidal joint motions. With this approach, explicit expressions for two kinematic invariants, the two-thirds power law during drawing movements and the velocity profile during point-to-point movements are obtained as functions of arm segment lengths and joint motion parameters. Additionally, less recognized kinematic invariants are also derived from the model. The obtained analytical expressions are further validated with experimental data. The high accuracy of the predictions confirms practical utility of the model, showing that the model is relevant to human performance over a wide range of movements. The results create a basis for the consolidation of various existing interpretations of kinematic invariants. In particular, optimal control is discussed as a plausible source of invariant characteristics of joint motions and movement trajectories.     

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

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

Kinematic study of reaching-grasping movements in the monkey]

Kinematics of reaching-grasping movement towards stimuli of three different sizes located at two different distances were studied in one monkey (Macaca nemestrina). Transport and manipulation components were analyzed using the ELITE system. Transport time, peak velocity and deceleration phase of velocity were influenced by stimulus size, whilst acceleration phase remained unmodified. Peak velocity clearly increased with distance, while transport time remained constant (isochrony ). The main parameters of manipulation component were all influenced by stimulus size but they did not vary with distance. A comparison with kinematic data obtained from human subjects was made.     

Basic functions of variability of simple pre-planned movements

A model of a pre-planned single joint movements performed without feedback is considered. Modifications of this movement result from transformation of a trajectory pattern f(t) in space and time. The control system adjusts the movement to concrete external conditions specifying values of the transform parameters before the movement performance. The preplanned movement is considered to be simple one, if the transform can be approximated by an affine transform of the movement space and time. In this case, the trajectory of the movement is x(t) = Af(t/ + s) +p, were A and 1/ are space and time scales, s and p are translations. The variability of movements is described by time profiles of variances and covariances of the trajectory x(t), velocity v(t), and acceleration a(t). It is assumed that the variability is defined only by parameters variations. From this assumption follows the main finding of this work: the variability time profiles can be expanded on a special system of basic functions corresponding to established movement parameters. Particularly, basic functions of variance time profiles, reflecting spatial and temporal scaling, are x ²(t) and t ² v ²(t) for trajectory, v ²(t) and (v(t) + t · a(t))² for velocity, and a ²(t) and (2a(t) +t · j(t))², where j(t) = d³ x(t)/dt ³, for acceleration. The variability of a model of a reaching movement was studied analytically. The model predicts certain peculiarities of the form of time profiles (e.g., the variance time profile of velocity is bi-modal, the one of acceleration is tri-modal, etc.). Experimental measurements confirmed predictions. Their consistence allows them to be considered invariant properties of reaching movement. A conclusion can be made, that reaching movement belongs to the type of simple preplanned movements. For a more complex movement, time profiles of variability are also measured and explained by the model of movements of this type. Thus, a movement can be attributed to the type of simple pre-planned ones by testing its variability.     

Analysis of kinematic invariances of multijoint reaching movement

 There is a no unique relationship between the trajectory of the hand, represented in cartesian or extrinsic space, and its trajectory in joint angle or intrinsic space in the general condition of joint redundancy. The goal of this work is to analyze the relation between planning the trajectory of a multijoint movement in these two coordinate systems. We show that the cartesian trajectory can be planned based on the task parameters (target coordinates, etc.) prior to and independently of angular trajectories. Angular time profiles are calculated from the cartesian trajectory to serve as a basis for muscle control commands. A unified differential equation that allows planning trajectories in cartesian and angular spaces simultaneously is proposed. Due to joint redundancy, each cartesian trajectory corresponds to a family of angular trajectories which can account for the substantial variability of the latter. A set of strategies for multijoint motor control following from this model is considered; one of them coincides with the frog wiping reflex model and resolves the kinematic inverse problem without inversion. The model trajectories exhibit certain properties observed in human multijoint reaching movements such as movement equifinality, straight end-point paths, bell-shaped tangential velocity profiles, speed-sensitive and speed-insensitive movement strategies, peculiarities of the response to double-step targets, and variations of angular trajectory without variations of the limb end-point trajectory in cartesian space. In humans, those properties are almost independent of limb configuration, target location, movement duration, and load. In the model, these properties are invariant to an affine transform of cartesian space. This implies that these properties are not a special goal of the motor control system but emerge from movement kinematics that reflect limb geometry, dynamics, and elementary principles of motor control used in planning. All the results are given analytically and, in order to compare the model with experimental results, by computer simulations. Received: 6 April 1994/Accepted in revised form: 25 April 1995     

Pointing movement in short and long-term exposure to hypoxia.

Kinematics variables of pointing movements where assessed in five adult subjects exposed acutely (30 min) and chronically (10 days) to a low O2 mixture (13.5% O2 in N2). Amplitude of displacement did not vary in both experimental conditions but movement duration markedly increased compared to pre and post exposure conditions. While in acute hypoxia the times of acceleration and deceleration are almost equal, in chronic hypoxia deceleration time exceeded of 100 ms the time of acceleration. The time from the peak acceleration to the peak of deceleration ("switch" time) increased in both experimental conditions and was about 50% of the movement duration. This time lengthening at hypoxia may be explained either by alteration of propioceptive loops or by a different strategy elaborated by the CNS to generally slow accurate movements.     

Conclusions on motor control depend on the type of model used to represent the periphery

Within the field of motor control, there is no consensus on which kinematic and kinetic aspects of movements are planned or controlled. Perturbing goal-directed movements is a frequently used tool to answer this question. To be able to draw conclusions about motor control from kinematic responses to perturbations, a model of the periphery (i.e., the skeleton, muscle–tendon complexes, and spinal reflex circuitry) is required. The purpose of the present study was to determine to what extent such conclusions depend on the level of simplification with which the dynamical properties of the periphery are modeled. For this purpose, we simulated fast goal-directed single-joint movement with four existing types of models. We tested how three types of perturbations affected movement trajectory if motor commands remained unchanged. We found that the four types of models of the periphery showed different robustness to the perturbations, leading to different predictions on how accurate motor commands need to be, i.e., how accurate the knowledge of external conditions needs to be. This means that when interpreting kinematic responses obtained in perturbation experiments the level of error correction attributed to adaptation of motor commands depends on the type of model used to describe the periphery.     

An equilibrium-point model of electromyographic patterns during single-joint movements based on experimentally reconstructed control signals

The purpose of this work has been to develop a model of electromyographic (EMG) patterns during single-joint movements based on a version of the equilibrium-point hypothesis, a method for experimental reconstruction of the joint compliant characteristics, the dual-strategy hypothesis, and a kinematic model of movement trajectory. EMG patterns are considered emergent properties of hypothetical control patterns that are equally affected by the control signals and peripheral feedback reflecting actual movement trajectory. A computer model generated the EMG patterns based on simulated movement kinematics and hypothetical control signals derived from the reconstructed joint compliant characteristics. The model predictions have been compared to published recordings of movement kinematics and EMG patterns in a variety of movement conditions, including movements over different distances, at different speeds, against different-known inertial loads, and in conditions of possible unexpected decrease in the inertial load. Changes in task parameters within the model led to simulated EMG patterns qualitatively similar to the experimentally recorded EMG patterns. The model's predictive power compares it favourably to the existing models of the EMG patterns.     

The Main Sequence of Saccades Optimizes Speed-accuracy Trade-off

In primates, it is well known that there is a consistent relationship between the duration, peak velocity and amplitude of saccadic eye movements, known as the ‘main sequence’. The reason why such a stereotyped relationship evolved is unknown. We propose that a fundamental constraint on the deployment of foveal vision lies in the motor system that is perturbed by signal-dependent noise (proportional noise) on the motor command. This noise imposes a compromise between the speed and accuracy of an eye movement. We propose that saccade trajectories have evolved to optimize a trade-off between the accuracy and duration of the movement. Taking a semi-analytical approach we use Pontryagin’s minimum principle to show that there is an optimal trajectory for a given amplitude and duration; and that there is an optimal duration for a given amplitude. It follows that the peak velocity is also fixed for a given amplitude. These predictions are in good agreement with observed saccade trajectories and the main sequence. Moreover, this model predicts a small saccadic dead-zone in which it is better to stay eccentric of target than make a saccade onto target. We conclude that the main sequence has evolved as a strategy to optimize the trade-off between accuracy and speed.     

Kinematics of the Coordination of Pointing during Locomotion

In natural motor behaviour arm movements, such as pointing or reaching, often need to be coordinated with locomotion. The underlying coordination patterns are largely unexplored, and require the integration of both rhythmic and discrete movement primitives. For the systematic and controlled study of such coordination patterns we have developed a paradigm that combines locomotion on a treadmill with time-controlled pointing to targets in the three-dimensional space, exploiting a virtual reality setup. Participants had to walk at a constant velocity on a treadmill. Synchronized with specific foot events, visual target stimuli were presented that appeared at different spatial locations in front of them. Participants were asked to reach these stimuli within a short time interval after a “go” signal. We analysed the variability patterns of the most relevant joint angles, as well as the time coupling between the time of pointing and different critical timing events in the foot movements. In addition, we applied a new technique for the extraction of movement primitives from kinematic data based on anechoic demixing. We found a modification of the walking pattern as consequence of the arm movement, as well as a modulation of the duration of the reaching movement in dependence of specific foot events. The extraction of kinematic movement primitives from the joint angle trajectories exploiting the new algorithm revealed the existence of two distinct main components accounting, respectively, for the rhythmic and discrete components of the coordinated movement pattern. Summarizing, our study shows a reciprocal pattern of influences between the coordination patterns of reaching and walking. This pattern might be explained by the dynamic interactions between central pattern generators that initiate rhythmic and discrete movements of the lower and upper limbs, and biomechanical factors such as the dynamic gait stability.     

A kinematic theory of rapid human movement. Part IV: a formal mathematical proof and new insights

A few years ago a kinematic theory was proposed to study and analyze rapid human movements. The theory relies on a model of a synergy made up of two neuromuscular systems, one agonist and the other antagonist to the movement. Representing these systems with lognormal impulse responses, it is predicted that the velocity profile of a fast movement will be described by a delta-lognormal equation. So far, many studies have been conducted to test and empirically validate the theory. This paper presents an extended mathematical proof of the model. The proof is based on the Central Limit Theorem under the assumption that a law of proportionate effect governs the cumulative time delays of a sequence of dependent subprocesses constituting a neuromuscular system. Furthermore, a detailed interpretation of the parameters of the delta-lognormal equation, in terms of movement time and amplitude, response time and time delays, is discussed, providing new insights into the properties of the model with respect to neuromuscular system activity and movement generation.     

Anticipatory postural adjustments during sitting reach movement in post-stroke subjects

The study assessed the effect of velocity of arm movement on anticipatory postural adjustments (APAs) generation in the contralateral and ipsilateral muscles of individuals with stroke in seating. Ten healthy and eight post-stroke subjects were studied in sitting. The task consisted in reaching an object placed at scapular plane and mid-sternum height at self-selected and fast velocities. Electromyography was recorded from anterior deltoid (AD), upper (UT) and lower trapezius (LT) and latissimus dorsi (LD). While kinematic analysis was used to assess peak velocity and trunk displacement. Differences were found between the timing of APAs on ipsi and contralateral LD and LT in both movement speeds and in ipsilateral UT during movement of the non-affected arm at a self-selected velocity. A delay on the contralateral LD to reach movement with the non-affected arm at fast velocity was also observed. The trunk displacement was greater in post-stroke subjects. Individuals with stroke demonstrated a delay of APAs in the muscles on both sides of the body compared to healthy subjects. The delay was observed during performance of the reaching task with the fast and self-selected velocity.