Coordinated turn-and-reach movements. I. Anticipatory compensation for self-generated coriolis and interaction torques

When reaching movements involve simultaneous trunk rotation, additional interaction torques are generated on the arm that are absent when the trunk is stable. To explore whether the CNS compensates for such self-generated interaction torques, we recorded hand trajectories in reaching tasks involving various amplitudes and velocities of arm extension and trunk rotation. Subjects pointed to three targets on a surface slightly above waist level. Two of the target locations were chosen so that a similar arm configuration relative to the trunk would be required for reaching to them, one of these targets requiring substantial trunk rotation, the other very little. Significant trunk rotation was necessary to reach the third target, but the arm's radial distance to the body remained virtually unchanged. Subjects reached at two speeds-a natural pace (slow) and rapidly (fast)-under normal lighting and in total darkness. Trunk angular velocity and finger velocity relative to the trunk were higher in the fast conditions but were not affected by the presence or absence of vision. Peak trunk velocity increased with increasing trunk rotation up to a maximum of 200 degrees /s. In slow movements, peak finger velocity relative to the trunk was smaller when trunk rotation was necessary to reach the targets. In fast movements, peak finger velocity was approximately 1.7 m/s for all targets. Finger trajectories were more curved when reaching movements involved substantial trunk rotation; however, the terminal errors and the maximal deviation of the trajectory from a straight line were comparable in slow and fast movements. This pattern indicates that the larger Coriolis, centripetal, and inertial interaction torques generated during rapid reaches were compensated by additional joint torques. Trajectory characteristics did not vary with the presence or absence of vision, indicating that visual feedback was unnecessary for anticipatory compensations. In all reaches involving trunk rotation, the finger movement generally occurred entirely during the trunk movement, indicating that the CNS did not minimize Coriolis forces incumbent on trunk rotation by sequencing the arm and trunk motions into a turn followed by a reach. A simplified model of the arm/trunk system revealed that additional interaction torques generated on the arm during voluntary turning and reaching were equivalent to < or =1.8 g (1 g = 9.81 m/s(2)) of external force at the elbow but did not degrade performance. In slow-rotation room studies involving reaching movements during passive rotation, Coriolis forces as small as 0.2 g greatly deflect movement trajectories and endpoints. We conclude that compensatory motor innervations are engaged in a predictive fashion to counteract impending self-generated interaction torques during voluntary reaching movements.     

Hand trajectory invariance in reaching movements involving the trunk

Movements of different body segments may be combined in different ways to achieve the same motor goal. How this is accomplished by the nervous system was investigated by having subjects make fast pointing movements with the arm in combination with a forward bending of the trunk that was unexpectedly blocked in some trials. Subjects moved their hand above the surface of a table without vision from an initial position near the midline of the chest to remembered targets placed within the reach of the arm in either the ipsi- or contralateral workspace. In experiment 1, subjects were instructed to make fast arm movements to the target without corrections whether or not the trunk was arrested. Only minor changes were found in the hand trajectory and velocity profile in response to the trunk arrest, and these changes were seen only late in the movement. In contrast, the patterns of the interjoint coordination substantially changed in response to the trunk arrest, suggesting the presence of compensatory arm-trunk coordination minimizing the deflections from the hand trajectory regardless of whether the trunk is recruited or mechanically blocked. Changes in the arm interjoint coordination in response to the trunk arrest could be detected kinematically at a minimal latency of 50 ms. This finding suggests a rapid reflex compensatory mechanism driven by vestibular and/or proprioceptive afferent signals. In experiment 2, subjects were required, as soon as they perceived the trunk arrest, to change the hand motion to the same direction as that of the trunk. Under this instruction, subjects were able to initiate corrections only after the hand approached or reached the final position. Thus, centrally mediated compensatory corrections triggered in response to the trunk arrest were likely to occur too late to maintain the observed invariant hand trajectory in experiment 1. In experiment 3, subjects produced similar pointing movements, but to a target that moved together with the trunk. In these body-oriented pointing movements, the hand trajectories from trials in which the trunk was moving or arrested were substantially different. The same trajectories represented in a relative frame of reference moving with the trunk were virtually identical. We conclude that hand trajectory invariance can be produced in an external spatial (experiment 1) or an internal trunk-centered (experiment 3) frame of reference. The invariance in the external frame of reference is accomplished by active compensatory changes in the arm joint angles nullifying the influence of the trunk motion on the hand trajectory. We suggest that to make a transition to the internal frame of reference, control systems suppress this compensation. One of the hypotheses opened to further experimental testing is that the integration of additional (trunk) degrees of freedom into movement is based on afferent (proprioceptive, vestibular) signals stemming from the trunk motion and transmitted to the arm muscles.     

Interjoint coordination dynamics during reaching in stroke

A technique is described that characterizes the dynamics of the interjoint coordination of arm reaching movements in healthy subjects (n=10) and in patients who had sustained a left-sided cerebrovascular accident (n=18). All participants were right-handed. Data from the affected right arm of patients with stroke were compared with those from the right arm of healthy subjects. Seated subjects made 25 pointing movements in a single session. Movements were made from an initial target located ipsilaterally to the right arm beside the body, to a final target located in front of the subject in the contralateral arm workspace. Kinematic data from the finger, wrist, elbow, both shoulders and sternum were recorded in three dimensions at 200 Hz with an optical tracking system. Analysis of interjoint coordination was based on the patterns of temporal delay between rotations at two adjacent joints (shoulder and elbow). The data were reduced to a single graph (Temporal Coordination or TC index) integrating the essential temporal characteristics of joint movement (the angular displacements, velocities and timing). TC segments, duration and amplitude, were analysed. The analysis was sensitive to the differences in interjoint coordination between healthy subjects and patients with arm motor deficits. In patients, the temporal coordination between elbow and shoulder movements was disrupted from the middle to the end of the reach. More specifically, in mid-reach, all patients had difficulty coordinating elbow flexion with shoulder horizontal adduction. In addition, patients with severe arm hemiparesis had difficulty changing elbow movement direction from flexion to extension and in coordinating this change with shoulder movement. At the end of the reach, patients with severe hemiparesis had deficits in the execution of elbow extension while all patients had impaired coordination of elbow extension and shoulder horizontal adduction. In addition, active ranges of joint motions were significantly decreased in the stroke compared to the healthy subjects. Finally, TC analysis revealed significant relationships between specific aspects of disrupted interjoint coordination and the level of motor impairment, suggesting that it may be a useful tool in the identification of specific movement coordination deficits in neurological impaired populations that can be targeted in treatment for arm motor recovery.     

Influence of movement speed on accuracy and coordination of reaching movements to memorized targets in three-dimensional space in a deafferented subject

Multiarticular reaching movements at different speeds produce differential demands for the on-line control of ongoing movements and for the predictive control of intersegmental dynamics. The aim of this study was to assess the ability of a proprioceptively deafferented patient and aged-matched control subjects to make precise and coordinated three-dimensional reaching movements at different speeds without vision during the movement. A patient with a complete loss of proprioception below the neck (C.F.) and five control subjects made reaching movements to four remembered visual targets at slow, natural, and fast speeds. All movements were performed without vision of the arm during the movements. The spatial accuracy, the movement kinematics and the interjoint coordination of these movements were analyzed. Results showed that control subjects made larger spatial errors at both slow and fast speeds than at natural speed. However, they synchronized motions at the shoulder and elbow joints and kept most movement kinematic features invariant across speed conditions. In contrast, C.F. failed to produce smooth and simultaneous motions at the shoulder and elbow joints at all speeds. Surprisingly, however, he made much larger errors than control subjects at slow and natural speeds, but not at fast speed. Analysis of patterns of interjoint coordination revealed that, when instructed to move fast, C.F. initiated arm movements by fixing the elbow while moving the shoulder joint to damp interaction torques exerted on the elbow joint from motion of the upper arm. The results demonstrated that, although proprioceptive loss disrupted normal control of multijoint movements at all speeds, when performing relatively fast three-dimensional movements, C.F. could control intersegmental dynamics by reducing the number of active joints. More importantly, the results highlight the dual role of proprioception in controlling multijoint movements; that is, to provide important cues both for the predictive control of interaction torques and for the synchronization of adjacent joints even when interactive torques are very small. These findings support the idea that proprioceptive input is used by the CNS to update an internal model of limb dynamics that adapts the motor plan according to biomechanical contexts. Electronic Publication     

Target-dependent differences between free and constrained arm movements in chronic hemiparesis

This study compares the kinematic and kinetic characteristics of constrained and free upper limb movements in eight subjects with chronic hemiparesis. Movements of the dominant and nondominant limbs were also examined in five control subjects. Rapid movements were performed in the horizontal plane from a central starting point to five targets located to require various combinations of flexion/extension rotations at the elbow and shoulder. Support of the upper limb against gravity loading was provided either by a low-friction air-bearing apparatus (constrained condition) or by voluntary generation of abduction and external rotation torques at the shoulder (free condition). Data analysis focused on the peak joint torques generated during the acceleratory phase of movement, and on the net change in joint angles at the elbow and shoulder. We found that movement parameters were broadly invariant with support condition for either limb of control subjects, as well as for the nonparetic limb of hemiparetic subjects. In contrast, support condition had a target-dependent effect on movements of the paretic limb. Relative to the constrained condition, peak torques for free arm movements were significantly reduced for distal targets requiring elbow extension and/or shoulder flexion torques. However, peak elbow flexion and shoulder extension joint torques for proximal targets were relatively unaffected by support condition. Of perhaps more functional importance, free movements were characterized by a target-dependent restriction in the hands work area that reflected a reduced range of active elbow extension, relative to constrained movements. The target-dependent effects of support condition on movements of the paretic limb are consistent with the existence of abnormal constraints on muscle activation patterns in subjects with chronic hemiparesis, namely an abnormal linkage between activation of the elbow flexors and shoulder extensors, abductors, and external rotators.     

Differences in control of limb dynamics during dominant and nondominant arm reaching

This study compares the coordination patterns employed for the left and right arms during rapid targeted reaching movements. Six right-handed subjects reached to each of three targets, designed to elicit progressively greater amplitude interaction torques at the elbow joint. All targets required the same elbow excursion (20 degrees ), but different shoulder excursions (5, 10, and 15 degrees, respectively). Movements were restricted to the shoulder and elbow and supported on a horizontal plane by a frictionless air-jet system. Subjects received visual feedback only of the final hand position with respect to the start and target locations. For motivation, points were awarded based on final position accuracy for movements completed within an interval of 400-600 ms. For all subjects, the right and left hands showed a similar time course of improvement in final position accuracy over repeated trials. After task adaptation, final position accuracy was similar for both hands; however, the hand trajectories and joint coordination patterns during the movements were systematically different. Right hand paths showed medial to lateral curvatures that were consistent in magnitude for all target directions, whereas the left hand paths had lateral to medial curvatures that increased in magnitude across the three target directions. Inverse dynamic analysis revealed substantial differences in the coordination of muscle and intersegmental torques for the left and right arms. Although left elbow muscle torque contributed largely to elbow acceleration, right arm coordination was characterized by a proximal control strategy, in which movement of both joints was primarily driven by the effects of shoulder muscles. In addition, right hand path direction changes were independent of elbow interaction torque impulse, indicating skillful coordination of muscle actions with intersegmental dynamics. In contrast, left hand path direction changes varied directly with elbow interaction torque impulse. These findings strongly suggest that distinct neural control mechanisms are employed for dominant and non dominant arm movements. However, whether interlimb differences in neural strategies are a consequence of asymmetric use of the two arms, or vice versa, is not yet understood. The implications for neural organization of voluntary movement control are discussed.     

Control of joint rotations in overarm throws of different speeds made by dominant and nondominant arms

We tested the hypothesis that dominant and nondominant overarm throws of different speeds are made by time-scaling of joint rotations, i.e., by joint rotations that have the same positions and amplitudes but that are scaled in time. Eight skilled subjects stood and made overarm throws with both their dominant and nondominant arms. Six joint rotations were computed from recordings of arm segments made with the search-coil technique. Throws made with nondominant arms were less accurate and had lower ball speeds. In contrast to the hypothesis, dominant arms showed large and consistent differences between fast and slow throws in six-dimensional angular position joint space. These same throws showed similar hand angular paths when these were time-scaled based on ball speed. Nondominant arms showed only small differences in angular position joint space in fast and slow throws. It is concluded that a joint space pattern resembling that predicted by time-scaling occurs in nondominant arm throwing when it is unskilled. However, time-scaling does not occur in dominant arm throwing, i.e., a skilled fast throw is not simply a skilled slow throw whose joint positions and amplitudes remain constant but whose joint velocities are sped-up. We hypothesize for future study that, when subjects first learn to throw at different speeds with their dominant arms, they use time-scaling of joint rotations that involves compensating for interaction torques; then as they become skilled at throwing fast, time-scaling is superseded by a more complex pattern of interjoint coordination that involves exploiting interaction torques.     

Kinetic analysis of arm reaching movements during voluntary and passive rotation of the torso

Reaching movements made to targets during exposure to passive constant velocity rotation show significant endpoint errors. By contrast, reaching movements made during voluntary rotation of the torso are accurate. In both cases, as a consequence of the simultaneous motion of the arm and the torso, Coriolis forces are generated on the arm tending to deflect its path. Our goal in the present paper was to determine whether during voluntary torso rotations arm movement accuracy is preserved by feed forward compensations for self-generated Coriolis forces. To test this hypothesis we analyzed and quantified the contribution of torso rotation and translation to arm dynamics and compared the kinematics and kinetics of pointing movements during voluntary and passive torso rotation. Coriolis torques at the shoulder increase nearly sixfold in voluntary turn and reach movements relative to reaches made without torso rotation, yet are equally accurate. Coriolis torques during voluntary turn and reach movements are more than double those produced by reaching movements during passive body rotation at 60°/s. Nevertheless, the endpoints of the reaches made during voluntary rotation are not deviated, but those of reaches made during passive rotation are deviated in the direction of the Coriolis forces generated during the movements. We conclude that there is anticipatory pre-programmed compensation for self-generated Coriolis forces during voluntary torso rotation contingent on intended torso motion and arm trajectory.     

Kinematic and dynamic synergies of human precision-grip movements

We analyzed the adaptability of human thumb and index finger movement kinematics and dynamics to variations of precision grip aperture and movement velocity. Six subjects performed precision grip opening and closing movements under different conditions of movement velocity and movement aperture (thumb and index finger tip-to-tip distance). Angular motion of the thumb and index finger joints was recorded with a CyberGlove and a three-dimensional biomechanical model was used for solving the inverse dynamics problem during precision grip movements, i.e., for calculating joint torques from experimentally obtained angular variations. The time-varying joint angles and joint torques were analyzed by principal-component analysis to quantify the contributions of individual joints in kinematic and dynamic synergies. At the level of movement kinematics, we found subject-specific angular contributions. However, the adaptation to large aperture, achieved by an increase of the relative contribution of the proximal joints, was subject-invariant. At the level of movement dynamics, the adaptation of thumb-index finger movements to task constraints was similar among all subjects and required the linear scaling of joint torques, the synchronization of joint torques under high velocity conditions, and a flexible redistribution of joint torques between the proximal joint of the thumb and that of the index finger. This work represents one of the first attempts at calculating the joint torques during human precision-grip movements and indicates that the dynamic synergies seem to be remarkably simple compared with the synergies found for movement kinematics.     

Torque response to external perturbation during unconstrained goal-directed arm movements

It is unclear to what extent control strategies of 2D reaching movements of the upper limbs also apply to movements with the full seven degrees of freedom (DoFs) including rotation of the forearm. An increase in DoFs may result in increased movement complexity and instability. This study investigates the trajectories of unconstrained reaching movements and their stability against perturbations of the upper arm. Reaching movements were measured using an ultrasound marker system, and the method of inverse dynamics was applied to compute the time courses of joint torques. In full DoF reaching movements, the velocity of some joint angles showed multiple peaks, while the bell-shaped profile of the tangential hand velocity was preserved. This result supports previous evidence that tangential hand velocity is an essential part of the movement plan. Further, torque responses elicited by external perturbation started shortly after perturbation, almost simultaneously with the perturbation-induced displacement of the arm, and were mainly observed in the same joint angles as the perturbation torques, with similar shapes but opposite signs. These results indicate that these torque responses were compensatory and contributed to system stabilization.     

Motor planning of arm movements is direction-dependent in the gravity field

In the present study we analyzed kinematic and dynamic features of arm movements in order to better elucidate how the motor system integrates environmental constraints (gravity) into motor planning and control processes. To reach this aim, we experimentally manipulated the mechanical effects of gravity on the arm while maintaining arm inertia constant (i.e. the distribution of the mass around the shoulder joint). Six subjects performed single-joint arm movements (rotation around the shoulder joint) in both sagittal (upward, U, versus downward, D) and horizontal (left, L, versus right, R) planes, at different amplitudes and from different initial positions. Under these conditions, shoulder gravitational torques (SGTs) significantly varied when arm movements were performed in the sagittal but not in the horizontal plane. Contrary to SGTs, arm inertia remained constant and similar for both horizontal and sagittal planes since subjects performed arm movements with only one degree of freedom. All subjects, whatever the movement direction, appropriately scaled shoulder joint kinematic parameters according to movement amplitude. Furthermore, peak velocity and movement duration were equivalent for both horizontal and sagittal planes. Interestingly, some kinematic parameters significantly differed according to U/D but not L/R directions. Specifically, acceleration duration was greater for D than U movements, while the opposite was true for peak acceleration. Consequently, although vertical and horizontal arm movements shared a general common strategy (i.e. scaling law), the kinematic asymmetries between U and D arm movements, especially those that reflect central planning process (i.e. peak acceleration), indicated different motor intentions regarding the direction of the upcoming movement. These findings indicate that the interaction of the arm with the dynamics of the environment is internally represented during the generation of arm trajectories.     

Intrinsic joint kinematic planning. I: Reassessing the Listing’s law constraint in the control of three-dimensional arm movements

This study tested the validity of the assumption that intrinsic kinematic constraints, such as Listing’s law, can account for the geometric features of three-dimensional arm movements. In principle, if the arm joints follow a Listing’s constraint, the hand paths may be predicted. Four individuals performed ‘extended arm’, ‘radial’, ‘frontal plane’, and ‘random mixed’ movements to visual targets to test Listing’s law assumption. Three-dimensional rotation vectors of the upper arm and forearm were calculated from three-dimensional marker data. Data fitting techniques were used to test Donders’ and Listing’s laws. The coefficient values obtained from fitting rotation vectors to the surfaces described by a second-order equation were analyzed. The results showed that the coefficients that represent curvature and twist of the surfaces were often not significantly different from zero, particularly not during randomly mixed and extended arm movements. These coefficients for forearm rotations were larger compared to those for the upper arm segment rotations. The mean thickness of the rotation surfaces ranged between ≈1.7° and 4.7° for the rotation vectors of the upper arm segment and ≈2.6° and 7.5° for those of the forearm. During frontal plane movements, forearm rotations showed large twist scores while upper arm segment rotations showed large curvatures, although the thickness of the surfaces remained low. The curvatures, but not the thicknesses of the surfaces, were larger for large versus small amplitude radial movements. In conclusion, when examining the surfaces obtained for the different movement types, the rotation vectors may lie within manifolds that are anywhere between curved or twisted manifolds. However, a two-dimensional thick surface may roughly represent a global arm constraint. Our findings suggest that Listing’s law is implemented for some types of arm movement, such as pointing to targets with the extended arm and during radial reaching movements.     

Superposition of independent units of coordination during pointing movements involving the trunk with and without visual feedback

Previous studies addressing the problem of the control of multiple degrees of freedom have examined the influence of trunk movement on pointing movements within the arm's reach. Such movements may be controlled by two functionally independent units of coordination (synergies): one involving only arm joints and producing the hand trajectory to the target (the transport synergy), and the other coordinating trunk and arm movements leaving the hand trajectory unchanged (the compensatory synergy). The question of whether or not this functional subdivision depends on visual feedback was addressed in the present study. We also tested whether or not the motor effects of different synergies are summated as independent components, a control strategy called "superposition." Finally, we investigated whether or not the relationship between different degrees of freedom within each synergy could be considered linear resulting in proportional changes in different joint angles. Seated subjects produced fast, uncorrected arm movements to an ipsi- or a contralateral target in the direction of +/-45 degrees to the sagittal midline of the trunk. Targets could be reached using the arm alone (control trials) or by combining the arm motion with a forward or backward trunk motion produced by hip flexion or extension (test trials), with and without visual feedback. The shape of the hand trajectory, its direction and tangential velocity, movement precision, joint angles and the sequence of the trunk and hand recruitment and de-recruitment were measured. In both visual conditions, the direction of the hand trajectory observed in control trials was generally preserved in test trials. In terms of sequencing, even in the absence of vision, the trunk movement was initiated before the onset of and outlasted the hand shift, indicating that the potential influence of the trunk on the hand movement was compensated by rotations in the elbow and shoulder joint. The analysis of other variables also implied that the effects of trunk recruitment on the hand trajectory were minor compared to those which could be observed if these effects were not compensated by appropriate changes in the arm joint angles. It was concluded that an arm-trunk compensatory synergy is present in pointing movements regardless of visual feedback. Principal component analysis showed that the relationship between elbow, shoulder and hip joint angles in individual arm and combined arm-trunk movements cannot be considered linear, implying that this relationship is adjusted according to the changing arm geometry. The changes in each arm joint angle (elbow, shoulder) elicited by a forward trunk bending in one block of trials were compared with those elicited by a backward bending in another block, whereas the hand moved to the same target in both blocks. These changes were opposite but of similar magnitude. As a result, for each moment of movement, the mean joint angle obtained by averaging across two directions of trunk motion was practically identical to that in control trials in which the trunk was motionless. It is concluded that the transport and arm-trunk compensatory synergies are combined as independent units, according to the principle of superposition. This principle may simplify the control of the coordination of a redundant number of degrees of freedom.     

Control of 3D limb dynamics in unconstrained overarm throws of different speeds performed by skilled baseball players

This study investigated how the human CNS organizes complex three-dimensional (3D) ball-throwing movements that require both speed and accuracy. Skilled baseball players threw a baseball to a target at three different speeds. Kinematic analysis revealed that the fingertip speed at ball release was mainly produced by trunk leftward rotation, shoulder internal rotation, elbow extension, and wrist flexion in all speed conditions. The study participants adjusted the angular velocities of these four motions to throw the balls at three different speeds. We also analyzed the dynamics of the 3D multijoint movements using a recently developed method called "nonorthogonal torque decomposition" that can clarify how angular acceleration about a joint coordinate axis (e.g., shoulder internal rotation) is generated by the muscle, gravity, and interaction torques. We found that the study participants utilized the interaction torque to generate larger angular velocities of the shoulder internal rotation, elbow extension, and wrist flexion. To increase the interaction torque acting at these joints, the ball throwers increased muscle torque at the shoulder and trunk but not at the elbow and wrist. These results indicates that skilled ball throwers adopted a hierarchical control in which the proximal muscle torques created a dynamic foundation for the entire limb motion and beneficial interaction torques for distal joint rotations.     

Coordination of multi-joint arm movements in cerebellar ataxia: Analysis of hand and angular kinematics

Kinematic abnormalities of fast multijoint movements in cerebellar ataxia include abnormally increased curvature of hand trajectories and an increased hand path and are thought to originate from an impairment in generating appropriate levels of muscle torques to support normal coordination between shoulder and elbow joints. Such a mechanism predicts that kinematic abnormalities are pronounced when fast movements are performed and large muscular torques are required. Experimental evidence that systematically explores the effects of increasing movement velocities on movement kinematics in cerebellar multijoint movements is limited and to some extent contradictory. We, therefore, investigated angular and hand kinematics of natural multijoint pointing movements in patients with cerebellar degenerative disorders and healthy controls. Subjects performed self-paced vertical pointing movements with their right arms at three different target velocities. Limb movements were recorded in three-dimensional space using a two-camera infrared tracking system. Differences between patients and healthy subjects were most prominent when the subjects performed fast movements. Peak hand acceleration and deceleration were similar to normals during slow and moderate velocity movements but were smaller for fast movements. While altering movement velocities had little or no effect on the length of the hand path and angular motion of elbow and shoulder joints in normal subjects, the patients exhibited overshooting motions (hypermetria) of the hand and at both joints as movement velocity increased. Hypermetria at one joint always accompanied hypermetria at the neighboring joint. Peak elbow angular deceleration was markedly delayed in patients compared with normals. Other temporal movement variables such as the relative timing of shoulder and elbow joint motion onsets were normal in patients. Kinematic abnormalities of multijoint arm movements in cerebellar ataxia include hypermetria at both the elbow and the shoulder joint and, as a consequence, irregular and enlarged paths of the hand, and they are marked with fast but not with slow movements. Our findings suggest that kinematic movement abnormalities that characterize cerebellar limb ataxia are related to an impairment in scaling movement variables such as joint acceleration and deceleration normally with movement speed. Most likely, increased hand paths and decomposition of movement during slow movements, as described earlier, result from compensatory mechanisms the patients may employ if maximum movement accuracy is required.     

Axial synergies during human upper trunk bending

Upper trunk bending movements were accompanied by opposite movements of the lower body segments. These axial kinematic synergies maintained equilibrium during the movement performance by stabilizing the center of gravity (CG), which shifted on average across all the subjects by 1±4 cm in the anteroposterior direction and thus always remained within the support area. The aim of the present investigation was to provide an insight into the central control responsible for the performance of these synergies. The kinematic analysis was performed by the method of principal components (PC) analysis applied to the covariation between ankle, knee and hip joint angles and compared with CG shifts during upper trunk bending. Subjects were asked to perform backward or forward upper trunk bending in response to a tone. They were instructed to move as fast as possible or slowly (2 s), with high or low movement amplitudes. PC analysis showed a strong correlation between hip, knee and ankle joint changes. The first principal component (PC1) representing a multijoint movement with fixed ratios between joint angular changes, accounted, on average, for 99.7%±0.2% of the total angular variance in the forward trunk movements and for 98.4%±1.4% in the backward movements. The instructed voluntary regulation of the amplitude and velocity of the movement was achieved by adapting the bell-shaped profile of the velocity time course without changes in interjoint angular relations. Fixed ratios between changes in joint angles, represented by PC1, ensured localization of the CG within the support area during trunk bending. The ratios given by PC1 showed highly significant dependence on subjects, suggesting the adaptability of the central control to each subject’s biomechanical peculiarities. Subject’s intertrial variability of PC1 ratios was small, suggesting a stereotyped automatic interjoint coordination. When changing velocity and amplitude of the movement, the ratios remained the same in about half the subjects while in others slight variations were observed. A weak second principal component (PC2) was shown only for fast movements. In forward movements PC2 reflected the early knee flexion that seems related to the disturbances caused by the passive interaction between body segments, rather than to the effect of a central command. In fast backward movements, PC2 reflected the delay in hip extension relative to the movement onset in the ankle and knee that mirrors intersubject differences in the initiation process of the axial synergy. The results suggest that PC1 reflects the centrally controlled multijoint movement, defining the time course and amplitude of the movement and fixing the ratios between changes in joint angles. They support the hypothesis that the axial kinematic synergies result from a central automatic control that stabilizes the CG shift in the anteroposterior direction while performing the upper trunk bending. Received: 8 August 1996 / Accepted: 7 July 1997     

Multijoint arm movements in cerebellar ataxia: Abnormal control of movement dynamics

In cerebellar ataxia, kinematic aberrations of multijoint movements are thought to originate from deficiencies in generating muscular torques that are adequate to control the mechanical consequences of dynamic interaction forces. At this point the exact mechanisms that lead to an abnormal control of interaction torques are not known. In principle, the generation of inadequate muscular torques may result from an impairment in generating sufficient levels of torques or from an inaccurate assessment and prediction of the mechanical consequences of movements of one limb segment on adjacent joints. We sought to differentiate the relative contribution of these two mechanisms and, therefore, analyzed intersegmental dynamics of multijoint pointing movements in healthy subjects and in patients with cerebellar degeneration. Unrestrained vertical arm movements were performed at three different target movement velocities and recorded using an optoelectronic tracking system. An inverse dynamics approach was employed to compute net joint torques, muscular torques, dynamic interaction torques and gravitational torques acting at the elbow and shoulder joint. In both groups, peak dynamic interaction forces and peak muscular forces were largest during fast movements. In contrast to normal subjects, patients produced hypermetric movements when executing fast movements. Hypermetric movements were associated with smaller peak muscular torques and smaller rates of torque change at elbow and shoulder joints. The patients’ deficit in generating appropriate levels of muscular force were prominent during two different phases of the pointing movement. Peak muscular forces at the elbow were reduced during the initial phase of the movement when simultaneous shoulder joint flexion generated an extensor influence upon the elbow joint. When attempting to terminate the movement, gravitational and dynamic interaction forces caused overshooting extension at the elbow joint. In normal subjects, muscular torque patterns at shoulder and elbow joint were synchronized in that peak flexor and extensor muscular torques occurred simultaneously at both joints. This temporal pattern of muscular torque generation at shoulder and elbow joint was preserved in patients. Our data suggest that an impairment in generating sufficient levels of phasic muscular torques significantly contributes to the patients’ difficulties in controlling the mechanical consequences of dynamic interaction forces during multijoint movements. Received: 28 October 1996 / Accepted: 30 September 1997     

Prediction and compensation by an internal model for back forces during finger opening in an overarm throw.

Previous studies have indicated that timing of finger opening in an overarm throw is likely controlled centrally, possibly by means of an internal model of hand trajectory. The present objective was to extend the study of throwing to an examination of the dynamics of finger opening. Throwing a heavy ball and throwing a light ball presumably require different neural commands, because the weight of the ball affects the mechanics of the arm, and particularly, the mechanics of the finger. Yet finger control is critical to the accuracy of an overarm throw. We hypothesized that finger opening in an overarm throw is controlled by a central mechanism that uses an internal model to predict and compensate for movement-dependent back forces on the fingers. To test this idea we determined whether finger motion is affected by back forces, i.e., whether larger back forces cause larger finger extensions. Back forces were varied by having subjects throw, at the same fast speed, tennis-sized balls of different weights (14, 55, and 196 g). Arm- and finger-joint rotations were recorded with the search-coil technique; forces on the middle finger were measured with force transducers. Recordings showed that during ball release, the middle finger experienced larger back forces in throws with heavier balls. Nevertheless, most subjects showed proximal interphalangeal joint extensions that were unchanged or actually smaller with the heavier balls. This was the case for the first throw and for all subsequent throws with a ball of a new weight. This suggests that the finger flexors compensated for the larger back forces by exerting larger torques during finger extension. Supporting this view, at the moment of ball release, all finger joints flexed abruptly due to the now unopposed torques of the finger flexors, and the amplitude of this flexion was proportional to ball weight. We conclude that in overarm throws made with balls of different weights, the CNS predicts the different back forces from the balls and adjusts finger flexor torques accordingly. This is consistent with the view that finger opening in overarm throws is controlled by means of an internal model of the motor apparatus and the external load.     

Quantitative examinations of internal representations for arm trajectory planning: minimum commanded torque change model.

Quantitative examinations of internal representations for arm trajectory planning: minimum commanded torque change model. A number of invariant features of multijoint planar reaching movements have been observed in measured hand trajectories. These features include roughly straight hand paths and bell-shaped speed profiles where the trajectory curvatures between transverse and radial movements have been found to be different. For quantitative and statistical investigations, we obtained a large amount of trajectory data within a wide range of the workspace in the horizontal and sagittal planes (400 trajectories for each subject). A pair of movements within the horizontal and sagittal planes was set to be equivalent in the elbow and shoulder flexion/extension. The trajectory curvatures of the corresponding pair in these planes were almost the same. Moreover, these curvatures can be accurately reproduced with a linear regression from the summation of rotations in the elbow and shoulder joints. This means that trajectory curvatures systematically depend on the movement location and direction represented in the intrinsic body coordinates. We then examined the following four candidates as planning spaces and the four corresponding computational models for trajectory planning. The candidates were as follows: the minimum hand jerk model in an extrinsic-kinematic space, the minimum angle jerk model in an intrinsic-kinematic space, the minimum torque change model in an intrinsic-dynamic-mechanical space, and the minimum commanded torque change model in an intrinsic-dynamic-neural space. The minimum commanded torque change model, which is proposed here as a computable version of the minimum motor command change model, reproduced actual trajectories best for curvature, position, velocity, acceleration, and torque. The model's prediction that the longer the duration of the movement the larger the trajectory curvature was also confirmed. Movements passing through via-points in the horizontal plane were also measured, and they converged to those predicted by the minimum commanded torque change model with training. Our results indicated that the brain may plan, and learn to plan, the optimal trajectory in the intrinsic coordinates considering arm and muscle dynamics and using representations for motor commands controlling muscle tensions.