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.

A note on the kinematcis of drawing movements in children.

The relationship between instantaneous tangential velocity and radius of curvature (power 1/3) that is characteristic of adult subjects was found to be already present in children 3 to 11 years old. The correlation coefficient between these two parameters increases gradually with age without apparent discontinuities. However, even at the upper limit of the age range examined, the values are still lower than in the adults.

Organization of arm movements. Motion is segmented.

A kinematic analysis of human arm trajectories which underlie the production of learned, continuous movements (such as drawing of 'figure 8s' and stars) in free space is presented. The objective of this investigation was to see if a set of rules, which had been identified previously and which are appropriate for generating circular or elliptical motion of the wrist in an arbitrary plane, also hold true for arbitrary, learned trajectories provided one additional assumption is made: that apparently continuous complex movements are composed of unit segments. The results presented in this paper are consistent with this hypothesis. Furthermore, as predicted by the hypothesis, the wrist trajectory deviates little from planar motion in each segment while the plane of motion can change abruptly from one segment to the next.

Organization of arm movements in three-dimensional space. Wrist motion is piecewise planar.

It is shown that human subjects are incapable of producing with the arm, in free space, planned or extemporaneously drawn trajectories in which the plane of wrist motion changes smoothly or continuously. The three-dimensional nature of these movements results from the fact that the plane of motion changes abruptly from one segment of the trajectory to the next, being confined to one plane during each segment (i.e. piecewise planar).

Changes in spatial scale in drawing and handwriting: kinematic contributions by proximal and distal joints.

The coordination of arm and hand motions was studied in tasks involving drawing and handwriting movements of different amplitudes. To this end, pen motion was recorded by means of a digitizing table, while the positions of different markers on the limb were monitored by the ELITE system. It was found that the amplitude of shoulder and elbow angular motions scales roughly with the size of the figure drawn or of the script, whereas the amplitude of wrist and finger motions is small, independent of size. Consequently, the larger the limb movement, the smaller the magnitude of the contributions by motions at distal joints relative to that at proximal joints. Furthermore, while shoulder and elbow motions are tightly coupled (constant phase relation), motions at distal joints are loosely coupled to those at the proximal joints (variable phase relation). On the other hand, motion at distal joints increases the accuracy of the movement, as indicated by the smaller variability of pen trajectories compared to that of wrist trajectories.

An algorithm for the generation of curvilinear wrist motion in an arbitrary plane in three-dimensional space.

The elements of an algorithm are presented which predicts for some simple forms (circles and ellipses) the kinematic and figural aspects of the trajectories of the human wrist when these are drawn in any arbitrary plane of free, three-dimensional space. The algorithm is based on theoretical considerations and experimental data and specifies in a unique way the angular motion at the shoulder and elbow joints by utilizing a coordinate transformation, which is only approximate, between the chosen extrinsic (trajectory) and intrinsic (joint angles) parameters. A way to extend the use of this algorithm to generate any arbitrary complex movement in all possible planes of space is also suggested.

Coordination of arm movements in three-dimensional space. Sensorimotor mapping during drawing movement.

In this paper data are presented concerning the motion of limb segments during drawing movements executed in different planes in free space. The technique used allows the determination of the wrist and elbow positions in space as well as the measurement of the elbow angle of extension. Other kinematic variables are determined trigonometrically. Elbow and shoulder torque is also calculated. For circles and ellipses, it was found that the motion at the wrist is sinusoidal in two orthogonal directions in the plane of motion. Angular motion, when described by a set of angles previously identified psychophysically as constituting an appropriate coordinate system, is also sinusoidal. Although the number of degrees of freedom of the arm affords many possible ways of performing the task, there is a fixed phase relation between the angles of elevation of the upper arm and forearm for naturally executed movements in all planes of space. Also, the phase of the yaw angles of the upper arm and forearm relative to the angles of elevation are related to the plane of motion and to the slant of ellipses in a fixed manner. There is a simple mapping between angular motion and intended wrist trajectory. Because this mapping is not valid for all planes of space, the actual trajectory can deviate from the intended one. However, the subject has no cognizance of the distortion. The calculated torque deviates substantially from sinusoidal and does change significantly when the same movement is executed in different planes. Results of simulations and mathematical analysis indicate that the fixed phase relationship between angles of elevation leads to a minimal distortion from sinusoidal motion at the wrist in an average sense and that the characteristic distortions observed in the sagittal plane result inevitably from this constraint on the phase relations. The results support the assumption that the topology of the sensorimotor map used for the production of the movement and for its perception is the same. The problem of invariant relationships between kinematic parameters is discussed and the suggestion is made that they represent a general constraint, leading through learning and practice to an optimal solution in an average sense.

Some factors pertinent to the organization and control of arm movements.

Trajectories of arm movement during a pointing task were shown to be unaffected by large loads. Moreover, when the effective arm length was changed, the target was still approached along a direct trajectory. It is concluded that: (1) compensation for load occurs automatically without affecting those constraints on the basis of which movements are organized; (2) that the effective lengths of body segments as well as joint angles constitute variables utilized in the organization of trajectories.

On the application of systems analysis to neurophysiological problems.

In this essay we have presented some personal viewpoints on the application of Systems. Analysis to suitable neurophysiological problems and provided reasoned reviews on selected topics (receptor and nerve cell physiology, motor control, vestibular and visual systems) in which new data and ideas were brought about in the past several years by the use of Systems Analysis. Since the nature of the paper precludes the possibility of writing a summary, we simply thank those readers who have endured up to this point. As for those prudent persons who are beginning from this summary, before deciding as to the advisability of taking-up the task, we have a simple advice which runs contrary to the rule stated by the King to Alice in Wonderland (and accepted by one of us; see p. 60): begin from the topic that you like most and eventually go on, using the same criteria, till you are tired: then stop.

Trajectory determines movement dynamics.

The relation between figural and kimematic aspects of movement was studied in handwriting and drawing. It was found that, throughout the movement, the tangential velocity. V is proportional to the radius of curvature r of the trajectory: V= kr, or, equivalently, that the angular velocity is constant: dalpha(t)/dt = K. However, the constant k generally takes several distinct values during the movement, the changes being abrupt. These changes suggest a clear segmentation of the movement into units of action which overlap but do not coincide with the figural units as defined by the discontinuities of the movement (cuspids, points of inflection). This organisational principle holds even when movements are mechanically constrained or are executed under strict visuo-motor guidance. Moreover, the segmentation of a given trajectory is invariant with respect to the total duration of the movement. A tentative interpretation of the principle is proposed which results from the assumption that the actual movement is produced as a continuous approximation to an intended movement, and that the well known relationship between movement speed and extent in rectilinear trajectories (Fitts' law) also applies to such continuous approximation.

Modulation of the myotatic reflex gain in man during intentional movements.

Human subjects were asked to perform sinusoidal tracking movements (0.5--3.0 Hz) with their forearms while external torque disturbances were applied at the elbow. The changes in angular position, velocity, and acceleration produced by these disturbances were found to be represented in the reflex changes in EMG activity of both biceps and triceps muscles. The gain of each of these reflex components varied during the tracking task, their maximal being about the same as those measured when the torque disturbances were applied in the absence of movements and the subjects attempted to maintain a constant forearm position. Such changes in gain were found to be centrally regulated since they were shown not to depend on the movement itself, being also present during force tracking, i.e. under nearly isometric conditions. Also their minima and maxima did not coincide with those of the EMG activity. These results suggest that an internal plan (or model) of the learned task is present, whereby reflex gains can be regulated independently from the motion and alpha-motoneuron activity. Such regulation effectively uncouples the reflex motor output from the intentionally controlled motion and maintains spindle sensitivity to external disturbances independent of large changes in muscle length. These conclusions are discussed in the context of the functional role of gamma-motoneurons in the control of movements.

Response to transient disturbances during intentional forearm flexion in man.

Steps of torque were applied to the human forearm during intentional flexion movements with peak velocities of 40-500 degrees/sec and during ballistically initiated flexion movements. The question asked was whether or not the motor ouput to both agonist and antagonist muscles is independent of sensory input data or is accessible and influenced by these inputs. The data obtained demonstrate unequivocally that the applied perturbation affects the motor output, irrespective of the speed of the movement. The time of onset of the reflex changes in motor output and their maxima are related to the movement's parameters. Data are presented which indicate that the source for the reflex changes observed are the muscle spindles.

Dynamic relations between natural vestibular inputs and activity of forelimb extensor muscles in the decerebrate cat. I. Motor output during sinusoidal linear accelerations.

Decerebrate cats were subjected to sinusoidal linear accelerations along the animal's horizontal and vertical axes, while recording the EMG activity of both triceps brachii muscles. This activity was found to be sinusoidally modulated in response to the accelerations and thus phase and gain relations between motor output and input acceleration could be obtained. They were found to be the same for accelerations along each of the three axes. In particular the gain dropped by 14-20 dB over a frequency range from 0.2 to 1.0 Hz and the phase of the motor output showed a lag of 40-60 degrees at 1.0 Hz. Thus, it was concluded that (1) the dynamic behavior of utricular and saccular receptors is the same, (2) the changes in motor activity observed during accelerations along the vertical axis are mostly due to the activation of saccular afferents, and (3) the motor output cannot simply result from vestibular afferent activities being relayed directly to the spinal motoneurons via the vestibulo-spinal tracts.