Stereotypical reaching movements of the octopus involve both bend propagation and arm elongation.

The bend propagation involved in the stereotypical reaching movement of the octopus arm has been extensively studied. While these studies have analyzed the kinematics of bend propagation along the arm during its extension, possible length changes have been ignored. Here, the elongation profiles of the reaching movements of Octopus vulgaris were assessed using three-dimensional reconstructions. The analysis revealed that, in addition to bend propagation, arm extension movements involve elongation of the proximal part of the arm, i.e., the section from the base of the arm to the propagating bend. The elongations are quite substantial and highly variable, ranging from an average strain along the arm of -0.12 (i.e. shortening) up to 1.8 at the end of the movement (0.57 ± 0.41, n = 64 movements, four animals). Less variability was discovered in an additional set of experiments on reaching movements (0.64 ± 0.28, n = 30 movements, two animals), where target and octopus positions were kept more stationary. Visual observation and subsequent kinematic analysis suggest that the reaching movements can be broadly segregated into two groups. The first group involves bend propagation beginning at the base of the arm and propagating towards the arm tip. In the second, the bend is formed or present more distally and reaching is achieved mainly by elongation and straightening of the segment proximal to the bend. Only in the second type of movements is elongation significantly positively correlated with the distance of the bend from the target. We suggest that reaching towards a target is generated by a combination of both propagation of a bend along the arm and arm elongation. These two motor primitives may be combined to create a broad spectrum of reaching movements. The dynamical model, which recapitulates the biomechanics of the octopus muscular hydrostatic arm, suggests that achieving the observed elongation requires an extremely low ratio of longitudinal to transverse muscle force (<0.0016 for an average strain along the arm of around 0.5). This was not observed and moreover such extremely low value does not seem to be physiologically possible. Hence the assumptions made in applying the dynamic model to behaviors such as static arm stiffening that leads to arm extension through bend propagation and the patterns of activation used to simulate such behaviors should be modified to account for movements combining bend propagation and arm elongation.

Reproduction of self-rotation duration.

The vestibular system detects the velocity of the head even in complete darkness, and thus contributes to spatial orientation. However, during vestibular estimation of linear passive self-motion distance in darkness, healthy human subjects mainly rely on time, and they replicate also stimulus duration when required to reproduce previous self-rotation. We then made the hypothesis that the perception of vestibular-sensed motion duration is embedded within encoding of motion kinetics. The ability to estimate time during passive self-motion in darkness was examined with a self-rotation reproduction paradigm. Subjects were required to replicate through self-driven transport the plateau velocity (30, 60 and 90 degrees /s) and duration (2, 3 and 4s) of the previously imposed whole-body rotation (trapezoid velocity profile) in complete darkness; the rotating chair position was recorded (500 Hz) during the whole trials. The results showed that the peak velocity, but not duration, of the plateau phase of the imposed rotation was accurately reproduced. Suspecting that the velocity instruction had impaired the duration reproduction, we added a control experiment requiring subjects to reproduce two successive identical rotations separated by a momentary motion interruption (MMI). The MMI was of identical duration to the previous plateau phase. MMI duration was fidelitously reproduced whereas that of the plateau phase was hypometric (i.e. lesser reproduced duration than plateau) suggesting that subjective time is shorter during vestibular stimulation. Furthermore, the accurate reproduction of the whole motion duration, that was not required, indicates an automatic process and confirms that vestibular duration perception is embedded within motion kinetics.

Intrinsic joint kinematic planning. II: hand-path predictions based on a Listing's plane constraint.

This study was aimed at examining the assumption that three-dimensional (3D) hand movements follow specific paths that are dictated by the operation of a Listing's law constraint at the intrinsic joint level of the arm. A kinematic model was used to simulate hand paths during 3D point-to-point movements. The model was based on the assumption that the shoulder obeys a 2D Listing's constraint and that rotations are about fixed single-axes. The elbow rotations were assumed to relate linearly to those of the shoulder. Both joints were assumed to rotate without reversals, and to start and end rotating simultaneously with zero initial and final velocities. Model predictions were compared to experimental observations made on four right-handed individuals that moved toward virtual objects in "extended arm", "radial", and "frontal plane" movement types. The results showed that the model was partially successful in accounting for the observed behavior. Best hand-path predictions were obtained for extended arm movements followed by radial ones. Frontal plane movements resulted in the largest discrepancies between the predicted and the observed paths. During such movements, the upper arm rotation vectors did not obey Listing's law and this may explain the observed discrepancies. For other movement types, small deviations from the predicted paths were observed which could be explained by the fact that single-axis rotations were not followed even though the rotation vectors remained within Listing's plane. Dynamic factors associated with movement execution, which were not taken into account in our purely kinematic approach, could also explain some of these small discrepancies. In conclusion, a kinematic model based on Listing's law can describe an intrinsic joint strategy for the control of arm orientation during pointing and reaching movements, but only in conditions in which the movements closely obey the Listing's plane assumption.

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 approximately 1.7 degrees and 4.7 degrees for the rotation vectors of the upper arm segment and approximately 2.6 degrees and 7.5 degrees 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.

Velocity and curvature in human locomotion along complex curved paths: a comparison with hand movements.

There is extensive experimental evidence linking instantaneous velocity to curvature in drawing and hand-writing movements. The empirical relationship between these characteristics of motion and path is well described by a power law in which the velocity varies in proportion to the one-third power of the radius of curvature. It was recently shown that a similar relationship can be observed during locomotion along curved elliptical paths raising the possibility that these very different motor activities might, at some level, share the same planning strategies. It has, however, been noted that the ellipse is a special case with respect to the one-third power law and therefore these previous results might not provide strong evidence that the one-third power law is a general feature of locomotion around curved paths. For this reason the experimental study of locomotion and its comparison with hand writing is extended here to non-elliptical paths. Subjects walked along predefined curved paths consisting of two complex shapes drawn on the ground: the cloverleaf and the limacon. It was found that the data always supported a close relationship between instantaneous velocity and curvature. For these more complex paths, however, the relationship is shape-dependent--although velocity and curvature can still be linked by a power law, the exponent depends on the geometrical form of the path. The results demonstrate the existence of a close relationship between instantaneous velocity and curvature in locomotion that is more general than the one-third power law. The origins of this relationship and its possible explanation in the mechanical balance of forces and in central planning are discussed.

Mental and motor switching in Parkinson's disease.

Switching difficulties in Parkinson's disease (PD) are expressed in both mental and motor tasks. The authors of the present study investigated whether those deficits coexist in the same patient and are positively correlated. They tested 8 nondemented PD patients and 6 age-matched control participants by using the modified Wisconsin Card Sorting Test and a motor switching paradigm that is based on the task of reaching toward visual targets, the location of which could unexpectedly be altered within the reaction time. In both mental and motor tasks, patients performed significantly worse than controls. There were no significant correlations between the two types of pathology in individual patients. Mental and motor switching deteriorate in PD patients, but the deficits are not necessarily of parallel severity.

Computational approaches to motor control.

New concepts and computational models that integrate behavioral and neurophysiological observations have addressed several of the most fundamental long-standing problems in motor control. These problems include the selection of particular trajectories among the large number of possibilities, the solution of inverse kinematics and dynamics problems, motor adaptation and the learning of sequential behaviors.

Control of octopus arm extension by a peripheral motor program.

For goal-directed arm movements, the nervous system generates a sequence of motor commands that bring the arm toward the target. Control of the octopus arm is especially complex because the arm can be moved in any direction, with a virtually infinite number of degrees of freedom. Here we show that arm extensions can be evoked mechanically or electrically in arms whose connection with the brain has been severed. These extensions show kinematic features that are almost identical to normal behavior, suggesting that the basic motor program for voluntary movement is embedded within the neural circuitry of the arm itself. Such peripheral motor programs represent considerable simplification in the motor control of this highly redundant appendage.

The superposition strategy for arm trajectory modification in robotic manipulators.

This work deals with the problem of end-effector trajectory modification for a robot manipulator when it must respond to unexpected changes in target location. Trajectory modification and corrections are particularly important in dealing with dynamic tasks. In this paper, we present and discuss the superposition strategy derived from the study of arm trajectory modification in human subjects. According to this strategy, the motion toward the initial target location continues unmodified as planned from its beginning to its end even after the target location has unexpectedly changed. However, a trajectory leading from the first target to the final one is added vectorially to the initial one to yield the combined modified motion. A method for choosing the temporal parameters of this trajectory modification scheme is suggested so as to minimize the total travelling time under existing kinematic constraints (including both joint and hand space constraints). Then, a variant of this strategy is presented, dealing with trajectory modification in the case that the targets (both the initial and final ones) specify the desired end-point orientation rather than position.

Motor switching abilities in Parkinson's disease and old age: temporal aspects.

OBJECTIVES: To investigate capabilities of arm trajectory modification in patients with Parkinson's disease and elderly subjects using a double step target displacement paradigm. METHODS: Nine patients with Parkinson's disease and seven age matched control subjects were instructed to move a stylus towards visual targets presented on a digitising table. Within each session, in some trials the target location was changed before initiation of movement and the subjects were to modify their movements towards the new target (switching trials). In other trials the target location was not changed (control trials). This procedure was repeated for four different target configurations, using interstimulus time intervals of six different durations. The subjects' hand trajectories were recorded and their kinematic characteristics were analysed. RESULTS: In switching trials, about 40% of the movements were aimed directly toward the final target location in both groups. When the trajectories were initially directed toward the first target and then modified toward the second, the reaction time (RT) to the second stimulus (RT2) was longer than to the first stimulus (RT1). The RT2/RT1 ratio was significantly larger in patients with Parkinson's disease than in healthy elderly subjects. CONCLUSIONS: Patients with Parkinson's disease and elderly subjects are substantially slower in responding to a required modification of their movement than in responding to the required movement initiation. Patients with Parkinson's disease have impaired capabilities in processing simultaneously the motor responses to two visual stimuli presented in rapid succession.

Patterns of arm muscle activation involved in octopus reaching movements.

The extreme flexibility of the octopus arm allows it to perform many different movements, yet octopuses reach toward a target in a stereotyped manner using a basic invariant motor structure: a bend traveling from the base of the arm toward the tip (Gutfreund et al., 1996a). To study the neuronal control of these movements, arm muscle activation [electromyogram (EMG)] was measured together with the kinematics of reaching movements. The traveling bend is associated with a propagating wave of muscle activation, with maximal muscle activation slightly preceding the traveling bend. Tonic activation was occasionally maintained afterward. Correlation of the EMG signals with the kinematic variables (velocities and accelerations) reveals that a significant part of the kinematic variability can be explained by the level of muscle activation. Furthermore, the EMG level measured during the initial stages of movement predicts the peak velocity attained toward the end of the reaching movement. These results suggest that feed-forward motor commands play an important role in the control of movement velocity and that simple adjustment of the excitation levels at the initial stages of the movement can set the velocity profile of the whole movement. A simple model of octopus arm extension is proposed in which the driving force is set initially and is then decreased in proportion to arm diameter at the bend. The model qualitatively reproduces the typical velocity profiles of octopus reaching movements, suggesting a simple control mechanism for bend propagation in the octopus arm.

Arm position constraints during pointing and reaching in 3-D space.

Arm movements in 3-D space were studied to investigate the reduction in the number of rotational degrees of freedom in the shoulder and elbow during pointing movements with the fully extended arm and during pointing movements to targets in various directions and at various distances relative to the shoulder, requiring flexion/extension in the elbow. The postures of both the upper arm and forearm can be described by rotation vectors, which represent these postures as a rotation from a reference position to the current position. The rotation vectors describing the posture of the upper arm and forearm were found to lie in a 2-D (curved) surface both for pointing with the fully extended arm and for pointing with elbow flexion. This result generalizes on previous results on the reduction of the number of degrees of freedom from three to two in the shoulder for the fully extended arm to a similar reduction in the number of degrees of freedom for the upper arm and forearm for normal arm movements involving also elbow flexion and extension. The orientation of the 2-D surface fitted to the rotation vectors describing the position of the upper arm and forearm was the same for pointing with the extended arm and for movements with flexion/extension of the elbow. The scatter in torsion of the rotation vectors describing the position of the upper arm and forearm relative to the 2-D surface was typically 3-4 degrees, which is small considering the range of approximately 180 and 360 degrees for torsional rotations of the upper arm and the forearm, respectively. Donders' law states that arm posture for pointing to a target does not depend on previous positions of the arm. The results of our experiments demonstrate that the upper arm violates Donders' law. However, the variations in torsion of the upper arm are small, typically a few degrees. These deviations from Donders' law have been overlooked in previous studies, presumably because the variations are relatively small. These variations may explain the larger scatter of the rotation vectors for arm movements (3-4 degrees) than reported for the eye (1 degree). Unlike for saccadic eye movements, joint rotations in the shoulder during aiming movements were not all single-axis rotations. On the contrary, the direction of the angular velocity vector varied during the movement in a consistent and reproducible way, depending on amplitude, direction, and starting position of the movement. These results reveal several differences between arm movements during pointing and saccadic eye movements. The implications for our understanding of the coordination of eye and arm movements and for the planning of 3-D arm movements are discussed.

Organization of octopus arm movements: a model system for studying the control of flexible arms.

Octopus arm movements provide an extreme example of controlled movements of a flexible arm with virtually unlimited degrees of freedom. This study aims to identify general principles in the organization of these movements. Video records of the movements of Octopus vulgaris performing the task of reaching toward a target were studied. The octopus extends its arm toward the target by a wave-like propagation of a bend that travels from the base of the arm toward the tip. Similar bend propagation is seen in other octopus arm movements, such as locomotion and searching. The kinematics (position and velocity) of the midpoint of the bend in three-dimensional space were extracted using the direct linear transformation algorithm. This showed that the bend tends to move within a single linear plane in a simple, slightly curved path connecting the center of the animal's body with the target location. Approximately 70% of the reaching movements demonstrated a stereotyped tangential velocity profile. An invariant profile was observed when movements were normalized for velocity and distance. Two arms, extended together in the same behavioral context, demonstrated identical velocity profiles. The stereotyped features of the movements were also observed in spontaneous arm extensions (not toward an external target). The simple and stereotypic appearance of the bend trajectory suggests that the position of the bend in space and time is the controlled variable. We propose that this strategy reduces the immense redundancy of the octopus arm movements and hence simplifies motor control.

Kinematic properties of upper limb trajectories in idiopathic torsion dystonia.

The kinematic properties of upper limb trajectories of simple reaching movements have been analysed in patients with idiopathic torsion dystonia (ITD). The velocity profiles differed from those of neurologically healthy subjects by being less symmetric. In several patients movement execution was slow due to a longer deceleration time. This phenomenon was even more conspicuous in the absence of visual feedback from the limb and was accompanied by a significant decrease in the final accuracy. These findings show that patients with ITD have deficits in central motor mechanisms beyond abnormal muscle activation patterns. Similarities between kinematic properties of patients with ITD and patients with Parkinson's disease including the deterioration of motor performance in ITD in the absence of visual feedback from the limb, suggest the existence of abnormalities in sensorimotor integration in both diseases.

Minimum-jerk, two-thirds power law, and isochrony: converging approaches to movement planning.

Two approaches to the study of movement planning were contrasted. Data on the drawing of complex two-dimensional trajectories were used to test whether the covariations of the kinematic and geometrical parameters of the movement formalized by the two-thirds power law and by the isochrony principle (P. Viviani & R. Schneider, 1991) can be derived from the minimum-jerk model hypothesis (T. Flash & N. Hogan, 1985). The convergence of the 2 approaches was satisfactory insofar as the relation between tangential velocity and curvature is concerned (two-thirds power law). Global isochrony could not be deduced from the optimal control hypothesis. Scaling of velocity within movement subunits can instead be derived from the minimum-jerk hypothesis. The implications vis-à-vis the issue of movement planning are discussed with an emphasis on the representation used by the motor control system for coding the intended trajectories.

A model of the learning of arm trajectories from spatial deviations.

Abstract Unconstrained point-to-point reaching movements performed in the horizontal plane tend to follow roughly straight hand paths with smooth, bell-shaped velocity profiles. The objective of the research reported here was to explore the hypothesis that these data reflect an underlying learning process that prefers simple paths in space. Under this hypothesis, movements are learned based only on spatial errors between the actual hand path and a desired hand path; temporally varying targets are not allowed. We designed a neural network architecture that learned to produce neural commands to a set of muscle-like actuators based only on information about spatial errors. Following repetitive executions of the reaching task, the network was able to generate point-to-point horizontal arm movements and the resulting muscle activation patterns and hand trajectories were found to be similar to those observed experimentally for human subjects. The implications of our results with respect to current theories of multijoint limb movement generation are discussed.

Kinematic analysis of upper limb trajectories in Parkinson's disease.

The purpose of this study was to analyze the kinematic properties of upper limb trajectories in Parkinson's disease (PD) patients and to investigate the role of visual feedback from the moving limb. Beyond the characteristic bradykinesia, PD patients differed from controls by generating hand trajectories with asymmetrical velocity profiles that lacked smoothness and were composed of a short initial accelerative phase, followed by a prolonged interval composed of alternating decelerative and accelerative phases. In both groups, the reaction times for movements directed away from the body were longer than for movements directed toward the body; this effect was accentuated in PD. In both groups, initial peak accelerations were significantly larger for distally as compared to proximally directed movements. In the absence of visual feedback from the limb a deterioration in the accuracy of reaching the target was observed in both control and PD patients only for distally directed movements. However, this deterioration and the effect of target location on final accuracy was substantially larger in PD. Taken together, our study suggests that in PD visual information is continuously relied upon for ongoing movement correction, therefore accentuating the bradykinesia. The deficit in final accuracy in the absence of visual feedback reflects the important role played by the basal ganglia in sensorimotor integration.

Arm trajectory modifications during reaching towards visual targets.

Abstract In this paper we study the question of how an aimed arm movement is modified in response to a sudden change in target location occurring during the reaction or movement time. Earlier monkey and human studies demonstrated that aimed arm movements can be elicited in quick succession, without appreciable delays in responding to the target displacement, beyond the normal reaction time. Nevertheless, it is not yet clear how this motor task is performed. A first guess is that when a new visual stimulus appears the old plan is aborted and a new one conceived. Upon analyzing human arm movements, however, we find that the observations can be well accounted for by a different movement modification scheme. It appears that a new plan is vectorially added to the original plan. Among the implications of this result is the possibility of parallel planning of elemental movements and further support for the idea that arm movements are internally represented in terms of hand motion through external space.