Tamar Flash

Moving gracefully: quantitative theories of motor coordination

Abstract Even simple movements require the coordination of a bewildering number of muscles. How does the brain cope with this task? How can we begin to understand this extraordinarily complex behavior? One effective way is to formulate a quantitative, mathematical theory of movement control. A theory simplifies matters because complex, detailed and experimentally testable predictions can be derived from basic concepts. This article will briefly review some attempts to develop a quantitative theory of motor coordination.

Multiple shifts in the representation of a motor sequence during the acquisition of skilled performance.

When do learning-related changes in performance occur? Here we show that the knowledge of a sequence of movements evolves through several distinctive phases that depend on two critical factors: the amount of practice as well as the passage of time. Our results show the following. (i) Within a given session, large performance gains constituted a signature for motor novelty. Such gains occurred only for newly introduced conditions irrespective of the absolute level of performance. (ii) A single training session resulted in both immediate but also time-dependent, latent learning hours after the termination of practice. Time in sleep determined the time of expression of these delayed gains. Moreover, the delayed gains were sequence-specific, indicating a qualitative change in the representation of the task within 24 h posttraining. (iii) Prolonged training resulted in additional between-session gains that, unlike the effects of a single training session, were confined to the trained hand. Thus, the effects of multisession training were qualitatively different than the immediate and time-dependent effects of a single session. Altogether, our results indicate multiple time-dependent shifts in the representation of motor experience during the acquisition of skilled performance.

Arm trajectory modifications during reaching towards visual targets

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.

Motor primitives in vertebrates and invertebrates

In recent years different lines of evidence have led to the idea that motor actions and movements in both vertebrates and invertebrates are composed of elementary building blocks. The entire motor repertoire can be spanned by applying a well-defined set of operations and transformations to these primitives and by combining them in many different ways according to well-defined syntactic rules. Motor and movement primitives and modules might exist at the neural, dynamic and kinematic levels with complicated mapping among the elementary building blocks subserving these different levels of representation. Hence, while considerable progress has been made in recent years in unravelling the nature of these primitives, new experimental, computational and conceptual approaches are needed to further advance our understanding of motor compositionality.

Controlling multijoint motor behavior.

Much can be learned about the central nervous system from a study of motor coordination, but its true richness and complexity become evident only in a multiarticular system. Despite the intrinsic complexity of multiarticular actions, they offer an unparalleled opportunity to learn about the central nervous system in a quantitative and experimentally testable way. For example, the observation that unconstrained, unperturbed arm movements are coordinated in terms of hand motion shows that motor control is organized in a hierarchy of increasing levels of abstraction. These arm motions are organized as though a disembodied hand could be moved in space; the details of how this is to be achieved must then be supplied by a different level in the hierarchy. The essence of human behavior is its adaptability. Just as the true complexity of coordination is evident only in multiarticular actions, the sophistication and subtlety of adaptive behavior are evident only in dynamic, interactive tasks. A study of movement alone is not sufficient to understand this behavior. The dynamic response of the limbs becomes the overriding concern and must be controlled by the central nervous system. The dynamic response of a limb is usually associated with its posture, rather than its movement, but in a functional task such as the use of a tool, the postural dynamics are an integral part of the action. This perspective on motor behavior leads to some useful insights. Coordination is not a problem for movement alone; in a multiarticular system, even posture requires coordination and control. Muscles do not merely act reciprocally to generate forces about the joints; the net mechanical impedance of the limb may be controlled by synergistic activation of all muscles, including antagonists. Controlling dynamic behavior is a far more demanding task than controlling motion. Consequently, features of the neuromusculoskeletal system that appear to be redundant or unnecessary for movement control can play a functional role in controlling dynamic behavior. Polyarticular muscles contribute to the mechanical impedance in a unique way. Skeletal redundancies have a profound influence on all aspects of dynamic behavior, including the apparent inertia of the limbs. Redundancies are commonly perceived as a complicating factor in the control of motion, a problem that must be solved by the central nervous system. Rather than presenting a problem requiring solution, they may present a solution to a problem. Posture is not merely the outcome of a motor act; it is one of the important preparatory stages in the production of motor behavior.

Human arm stiffness characteristics during the maintenance of posture

SummaryWhen the hand is displaced from an equilibrium position, the muscles generate elastic forces to restore the original posture. In a previous study, Mussa-Ivaldi et al. (1985) have measured and characterized the field of elastic forces associated with hand posture in the horizontal plane. Hand stiffness which describes the relation between force and displacement vectors in the vicinity of equilibrium position was measured and graphically represented by an ellipse, characterized by its size, shape and orientation. The results indicated that the shape and orientation of the stiffness ellipse are strongly dependent on arm configuration. At any given hand position, however, the values of these parameters were found to remain invariant among subjects and over time. In this study we investigate the underlying causes for the observed spatial pattern of variation of the hand stiffness ellipse. Mathematically analyzing the relation between hand and joint stiffness matrices, we found that in order to produce the observed spatial variations of the stiffness ellipse, the shoulder stiffness must covary in the workspace with the stiffness component provided by the two-joint muscles. This condition was found to be satisfied by the measured joint stiffness components. Using anatomical data and considering the effects that muscle cross-sections and changes in muscle moment arms have on the joint stiffness matrix, we found that these anatomical factors are not sufficient to account for the observed pattern of variation of joint stiffness in the workspace. To examine whether the coupling between shoulder and two-joint stiffnesses results from the coactivation of muscles contributing to these stiffnesses, EMG signals were recorded from shoulder, elbow and two-joint muscles. Our results indicated that, while some muscle coactivation may indeed exist, it can be found for only some of the muscles and in only part of the workspace.

A Model of Handwriting

The research reported here is concerned with hand trajectory planning for the class of movements involved in handwriting. Previous studies show that the kinematics of human two-joint arm movements in the horizontal plane can be described by a model which is based on dynamic minimization of the square of the third derivative of hand position (jerk), integrated over the entire movement. We extend this approach to both the analysis and the synthesis of the trajectories occurring in the generation of handwritten characters. Several basic strokes are identified and possible stroke concatenation rules are suggested. Given a concise symbolic representation of a stroke shape, a simple algorithm computes the complete kinematic specification of the corresponding trajectory. A handwriting generation model based on a kinematics from shape principle and on dynamic optimization is formulated and tested. Good qualitative and quantitative agreement was found between subject recordings and trajectories generated by the model. The simple symbolic representation of hand motion suggested here may permit the central nervous system to learn, store and modify motor action plans for writing in an efficient manner.

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 Parkinsons 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.

When practice leads to co-articulation: the evolution of geometrically defined movement primitives.

The skilled generation of motor sequences involves the appropriate choice, ordering and timing of a sequence of simple, stereotyped movement elements. Nevertheless, a given movement element within a well-rehearsed sequence can be modified through interaction with its neighboring elements (co-articulation). We show that extensive training on a sequence of planar hand trajectories passing through several targets resulted in the co-articulation of movement components, and in the formation of new movement elements (primitives). Reduction in movement duration was accompanied by the gradual replacement of straight trajectories by longer curved ones, the latter affording the maximization of movement smoothness. Surprisingly, the curved trajectories were generated even when new target configurations were introduced, i.e., when target distances were scaled, movement direction reversed or when different start and end positions were used, indicating the acquisition of geometrically defined movement elements. However, the new trajectories were not shared by the untrained hand. Altogether, our results suggest that novel movement elements can be acquired through extensive training in adults.

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 ofOctopus 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.