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.     

Kinematic study of reaching-grasping movements

The experiment was conducted to investigate, by using kinematic parameters, the influence of the type of prehension on the transportation component in reaching-grasping movements. The main question was whether the transportation component is influenced by the type of prehension besides the distance of the object. The experiment was carried out on eight subjects who performed reaching-grasping movements toward objects located at different distances. Two types of prehension were examined: whole hand prehension and precision grip. The following kinematic parameters of the transportation component (wrist movement) were studied: movement times, profiles of velocity and accelerations. Our results have shown that the transportation component is affected by the two factors. However the kinematic parameters were influenced differently by the distance and the type of prehension. Our conclusion is that, although distance and type of prehension affect the transportation component, they are computed separately in programming this component.     

Motor control of voluntary arm movements

The motor control of pointing and reaching-to-grasp movements was investigated using two different approaches (kinematic and modelling) in order to establish whether the type of control varies according to modifications of arm kinematics. Kinematic analysis of arm movements was performed on subjects' hand trajectories directed to large and small stimuli located at two different distances. The subjects were required either to grasp and to point to each stimulus. The kinematics of the subsequent movement, during which subject's hand came back to the starting position, were also studied. For both movements, kinematic analysis was performed on hand linear trajectories as well as on joint angular trajectories of shoulder and elbow. The second approach consisted in the parametric identification of the black box (ARMAX) model of the controller driving the arm movement. Such controller is hypothesized to work for the correct execution of the motor act. The order of the controller ARMAX model was analyzed with respect to the different experimental conditions (distal task, stimulus size and distance). Results from kinematic analysis showed that target distance and size influenced kinematic parameters both of angular and linear displacements. Nevertheless, the structure of the motor program was found to remain constant with distane and distal task, while it varied with precision requirements due to stimulus size. The estimated model order of the controller confirmed the invariance of the control law with regard to movement amplitude, whereas it was sensitive to target size.     

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.     

Simplified dynamics model of planar two-joint arm movements

A theoretical framework is presented that describes a way in which the inverse dynamics equations of motion of planar two-joint arm movements (EX-model) are reformulated in a simple form. A single point was assumed to define both the wrist and elbow joint centers, and thus the motion of two points in extrinsic space was represented by second-order differential equations to provide the variables in the reformulation (RE-) model. Through an analytical processes, it was shown that the RE-model for reproducing the shoulder joint torque consists of the linearly scaled moment per unit mass responsible for accelerating the wrist and elbow points about the shoulder joint, while that for reproducing the elbow joint torque consists of the linearly scaled moment per unit mass responsible for accelerating the wrist point about the elbow. The scaling factors for variables in the RE-model were based solely on the values for segment lengths, while in the EX-model the inertial parameter data for the segments are involved in its representation. The inertial parameter data of six-arm specimens from the cadaver experiment of Chandler et al. (1975, AMRL Technical Report, Wright-Patterson Air Force Base, OH) were used to develop and verify the numeric solutions of the RE-model. The adequacy of the model varied somewhat among subjects, but minor changes of the physical parameters of the arm segments enabled perfect reformulation, regardless of the specimens. The potential abilities of the RE-model to deal with the complexities in motor control with more simple control schemes are discussed.     

The influence of microgravity on memorized arm movements

To investigate sensory and motor functions in microgravity, goal-oriented arm movements were performed by 9 cosmonauts in weightlessness. The ability to reproduce predefined motor patterns was examined pre-, in-, and post-flight under two different paradigms: In a first test, the cosmonaut had to reproduce passively learned movements with eyes closed, while in the second test, the cosmonaut learned the pattern with eyes open. The different learning paradigms effected the metric parameters of the memorized stimulus pattern while the influence of the different gravity levels resulted in significant offsets and torsions of the reproduced figures. In comparing the inflight condition with preflight, intact proprioceptive afference seemed to play an important role for reproducing movements from motor short-time memory correctly.     

Stability and motor adaptation in human arm movements

In control, stability captures the reproducibility of motions and the robustness to environmental and internal perturbations. This paper examines how stability can be evaluated in human movements, and possible mechanisms by which humans ensure stability. First, a measure of stability is introduced, which is simple to apply to human movements and corresponds to Lyapunov exponents. Its application to real data shows that it is able to distinguish effectively between stable and unstable dynamics. A computational model is then used to investigate stability in human arm movements, which takes into account motor output variability and computes the force to perform a task according to an inverse dynamics model. Simulation results suggest that even a large time delay does not affect movement stability as long as the reflex feedback is small relative to muscle elasticity. Simulations are also used to demonstrate that existing learning schemes, using a monotonic antisymmetric update law, cannot compensate for unstable dynamics. An impedance compensation algorithm is introduced to learn unstable dynamics, which produces similar adaptation responses to those found in experiments.     

Principles for learning horizontal-planar arm movements with reversal

PurposeThis study tested the hypothesis that muscle and interaction torques can be altered independently in order to improve in specific kinematics performance observed following practice. We also tested the hypothesis that a simple set of rules of EMG-control and kinetic-control models could explain the EMG and kinetic changes due to practice of movements with reversal.ScopeKinematics of the upper arm with reversal, performed over three distances, was reconstructed using motion analysis. The muscle and interaction torques were calculated using inverse-dynamics. EMG activities of the major arm muscles were also recorded. The results demonstrate that improved performance is facilitated by an increase in muscle torque (and therefore acceleration) at the proximal joint (shoulder) and by an increase in the interaction torque at the distal joint (elbow). No changes were observed in the amount of muscle activity underlying these kinetic modifications, except for a decrease in the shoulder antagonist latency.ConclusionThe results confirm Bernstein’s idea that the central nervous system takes advantage of the passive-interactive properties of the moving system. Also the modulation of the EMG patterns should be explained taking in account the reactive forces and the dual functions (maintenance of posture and generation of movement) of the muscles.     

Changes in limb dynamics during the practice of rapid arm movements

In our study we examined Bernstein's hypothesis that practice alters the motor coordination among the muscular and passive joint moments. In particular, we conducted dynamical analyses of a human multisegmental movement during the practice of a task involving the upper extremity. Seven male human volunteers performed maximal-speed, unrestrained vertical arm movements whose upward and downward trajectories between two target endpoints required the hand to round a barrier, resulting in complex shoulder, elbow, and wrist joint movements. These movements were recorded by high-speed ciné film, and myopotentials from selected upper-extremity muscles were recorded. The arm was modeled as interconnected rigid bodies, so that dynamical interactions among the upper arm, forearm, and hand could be calculated. With practice, subjects achieved significantly shorter movement times. As movement times decreased, all joint-moment components (except gravity) increased, and the moment-time and EMG profiles were changed significantly. Particularly during reversals in movement direction, the changes in moment-time and EMG profiles were consistent with Bernstein's hypothesis relating practice effects and intralimb coordination: with practice, motor coordination was altered so that individuals employed reactive phenomena in such a way as to use muscular moments to counterbalance passive-interactive moments created by segment movements.     

Sensorimotor transformations underlying the organization of arm movements in three-dimensional space

Coordinated movements in three-dimensional space involve sensorimotor transformations between extrinsic and intrinsic coordinates. It is hypothesized that a key aspect underlying the organization of such movements is the need to simplify these transformations by means of suitable approximations and the imposition of constraints. Motor tasks involving the drawing of circles and ellipses in different planes were analyzed from this perspective, and some rules are presented whereby the plane of motion and the slant of an ellipse can be specified in a simple way in terms of intrinsic parameters. It is shown that these rules can be generalized to hold for more complicated wrist motions if one assumes that they consist of segments of elliptical arcs.     

Simulation of human arm movements controlled by peripheral feedback

A model of the human arm, suitable for simulation purposes, is presented in order to investigate whether it is possible that peripheral feedback can play an important role during fast arm movements. In spite of factors such as the inertia of the system, the slow regulation of muscle tension, and efferent and afferent conduction delays between the muscles and the motorneuronal pools, it appears from the simulations that peripheral feedback of proprioceptive information could indeed be effective even during fast movements.     

Influence of fingertip contact on illusory arm movements.

Recent evidence suggests that reaching movements are more accurate when end point contact occurs, suggesting that fingertip contact contributes to a final estimation of arm position. In the present study we tested two hypotheses: 1). that fingertip contact influences illusions of arm movement produced by muscle vibration and 2). that this influence depends on the a priori context of the stability of the contact surface. Subjects sat with their elbows on a table and eyes closed. They demonstrated the perceived orientation of the left (cue) arm by mirroring the location with the right (report) arm. We manipulated deep proprioceptive cues by vibrating the left biceps brachia, causing illusions of elbow extension, and tested whether these illusions were altered when the fingertip remained in contact with a stable external surface. The context at this point represents a prior assumption that the external contact surface is stable. Midway through the experiment, the context was changed by challenging the prior assumption that the contact surface was stable by demonstrating that it could move. Unbeknownst to the subject, the external contact surface remained stable during data collection throughout the experiment. As expected, without tactile cues, biceps vibration caused illusory elbow extension. Conditions with fingertip contact and biceps vibration in the stable context demonstrated that contact largely eliminated the overestimation of cue arm elbow angle. However, in the context of a possibly unstable (movable) contact surface, the reports of elbow extension returned. Thus a priori notions about the stability context of an external contact surface influence how this tactile cue is integrated with proprioceptive sensory modalities to generate an estimate of arm location in space. These findings support the notion that tactile cues are used to calibrate proprioception against external spatial frameworks.     

Formation and control of optimal trajectory in human multijoint arm movement

In this paper, we study trajectory planning and control in voluntary, human arm movements. When a hand is moved to a target, the central nervous system must select one specific trajectory among an infinite number of possible trajectories that lead to the target position. First, we discuss what criterion is adopted for trajectory determination. Several researchers measured the hand trajectories of skilled movements and found common invariant features. For example, when moving the hand between a pair of targets, subjects tended to generate roughly straight hand paths with bell-shaped speed profiles. On the basis of these observations and dynamic optimization theory, we propose a mathematical model which accounts for formation of hand trajectories. This model is formulated by defining an objective function, a measure of performance for any possible movement: square of the rate of change of torque integrated over the entire movement. That is, the objective function CT is defined as follows: (formula; see text) We overcome this difficult by developing an iterative scheme, with which the optimal trajectory and the associated motor command are simultaneously computed. To evaluate our model, human hand trajectories were experimentally measured under various behavioral situations. These results supported the idea that the human hand trajectory is planned and controlled in accordance with the minimum torque-change criterion.     

Using voluntary motor commands to inhibit involuntary arm movements

A hallmark of voluntary motor control is the ability to stop an ongoing movement. Is voluntary motor inhibition a general neural mechanism that can be focused on any movement, including involuntary movements, or is it mere termination of a positive voluntary motor command? The involuntary arm lift, or ‘floating arm trick’, is a distinctive long-lasting reflex of the deltoid muscle. We investigated how a voluntary motor network inhibits this form of involuntary motor control. Transcranial magnetic stimulation of the motor cortex during the floating arm trick produced a silent period in the reflexively contracting deltoid muscle, followed by a rebound of muscle activity. This pattern suggests a persistent generator of involuntary motor commands. Instructions to bring the arm down voluntarily reduced activity of deltoid muscle. When this voluntary effort was withdrawn, the involuntary arm lift resumed. Further, voluntary motor inhibition produced a strange illusion of physical resistance to bringing the arm down, as if ongoing involuntarily generated commands were located in a ‘sensory blind-spot’, inaccessible to conscious perception. Our results suggest that voluntary motor inhibition may be a specific neural function, distinct from absence of positive voluntary motor commands.     

The representation of arm movements in postcentral and parietal cortex

Considerable experimental evidence supports the hypothesis that the neocortical processes underlying kinesthetic sensation form a hierarchical series of cells signalling increasingly complex patterns of movement of the body. However, this view has been criticized and the data lack quantitative verification under controlled conditions. These studies have also typically used one-dimensional (reciprocal) movements, even of multiple degree-of-freedom joints such as the wrist or shoulder, and have been restricted to passive movements. This latter limitation is particularly critical, since the response of many muscle receptors is affected by fusimotor activity while that of many articular receptors is sensitive to the level of muscle contractile activity. Both factors introduce significant kinesthetic ambiguity to the signals arising from these receptors during active movement. This ambiguity is evident in the discharge of primary somatosensory cortex proprioceptive cells. Studies in area 5 show that single cells signal shoulder joint movements in the form of broad directional tuning curves. The pattern of activity of the entire population encodes movement direction. The cells appear to encode spatial aspects of movement unambiguously, since their discharge is relatively insensitive to the changes in muscle activity required to produce the same movements under different load conditions. It is not yet certain whether the somesthetic activity in area 5 is a kinesthetic representation that is sequential to and hierarchically superior to that in SI, or whether it is a parallel representation with separate and distinct function.     

A model of force and impedance in human arm movements

This paper describes a simple computational model of joint torque and impedance in human arm movements that can be used to simulate three-dimensional movements of the (redundant) arm or leg and to design the control of robots and human-machine interfaces. This model, based on recent physiological findings, assumes that (1) the central nervous system learns the force and impedance to perform a task successfully in a given stable or unstable dynamic environment and (2) stiffness is linearly related to the magnitude of the joint torque and increased to compensate for environment instability. Comparison with existing data shows that this simple model is able to predict impedance geometry well.     

Compositionality of arm movements can be realized by propagating synchrony

We present a biologically plausible spiking neuronal network model of free monkey scribbling that reproduces experimental findings on cortical activity and the properties of the scribbling trajectory. The model is based on the idea that synfire chains can encode movement primitives. Here, we map the propagation of activity in a chain to a linearly evolving preferred velocity, which results in parabolic segments that fulfill the two-thirds power law. Connections between chains that match the final velocity of one encoded primitive to the initial velocity of the next allow the composition of random sequences of primitives with smooth transitions. The model provides an explanation for the segmentation of the trajectory and the experimentally observed deviations of the trajectory from the parabolic shape at primitive transition sites. Furthermore, the model predicts low frequency oscillations (<10 Hz) of the motor cortex local field potential during ongoing movements and increasing firing rates of non-specific motor cortex neurons before movement onset.     

Kinematic description of variability of fast movements: analytical and experimental approaches

Analysis of variability of fast aimed movements predicts the properties of trajectory variance. The analysis is based on a kinematic model with nonlinear changes in “internal time”. The purpose of the work was to identify different sources of variability and their influence on the trajectory variance. An analytical expression for the speed-accuracy trade-off is introduced. Experiments were performed with subjects making single-joint elbow flexion movements over different distances as fast as possible with their eyes closed to memorized targets. Standard deviation of movement trajectory increased during the first part of the movement and subsequently decreased. The variance peaked after the time of peak velocity, close to the time of peak deceleration. A dependence of the trajectory variance on movement distance (speed-accuracy trade-off) was seen during the movement (at times of peak velocity and peak deceleration) but not after the movement termination. We conclude that the previously reported drop in the variability of movement trajectory during the deceleration phase does not necessarily mean a compensation by the control system but may result from purely kinematic properties of the movement. The importance of the time of measurement for analysis of the speed-accuracy trade-offs is emphasized.