Smooth pursuit tracking of an abrupt change in target direction: vector superposition of discrete responses

When intercepting moving targets, mid-movement error corrections reflect distinct responses to visual and haptic perturbations

We examined a key aspect of sensorimotor skill: the capability to correct performance errors that arise mid-movement. Participants grasped the handle of a robot that imposed a nominal viscous resistance to hand movement. They watched a target move pseudo-randomly just above the horizontal plane of hand motion and initiated quick interception movements when cued. On some trials, the robot's viscosity or the target's speed changed without warning coincident with the GO cue. We fit a sum-of-Gaussians model to mechanical power measured at the handle to determine the number, magnitude, and relative timing of submovements occurring in each interception attempt. When a single submovement successfully intercepted the target, capture times averaged 410 ms. Sometimes, two or more submovements were required. Initial error corrections typically occurred before feedback could indicate the target had been captured or missed. Error corrections occurred sooner after movement onset in response to mechanical viscosity increases (at 154 ms) than to unprovoked errors on control trials (215 ms). Corrections occurred later (272 ms) in response to viscosity decreases. The latency of corrections for target speed changes did not differ from those in control trials. Remarkably, these early error corrections accommodated the altered testing conditions; speed/viscosity increases elicited more vigorous corrections than in control trials with unprovoked errors; speed/viscosity decreases elicited less vigorous corrections. These results suggest that the brain monitors and predicts the outcome of evolving movements, rapidly infers causes of mid-movement errors, and plans and executes corrections-all within 300 ms of movement onset.

Predictive Smooth Pursuit Eye Movements

Smooth pursuit eye movements maintain the line of sight on smoothly moving targets. Although often studied as a response to sensory motion, pursuit anticipates changes in motion trajectories, thus reducing harmful consequences due to sensorimotor processing delays. Evidence for predictive pursuit includes (a) anticipatory smooth eye movements (ASEM) in the direction of expected future target motion that can be evoked by perceptual cues or by memory for recent motion, (b) pursuit during periods of target occlusion, and (c) improved accuracy of pursuit with self-generated or biologically realistic target motions. Predictive pursuit has been linked to neural activity in the frontal cortex and in sensory motion areas. As behavioral and neural evidence for predictive pursuit grows and statistically based models augment or replace linear systems approaches, pursuit is being regarded less as a reaction to immediate sensory motion and more as a predictive response, with retinal motion serving as one of a number of contributing cues.

Quick phases control ocular torsion during smooth pursuit

One of the open questions in oculomotor control of visually guided eye movements is whether it is possible to smoothly track a target along a curvilinear path across the visual field without changing the torsional stance of the eye. We show in an experimental study of three-dimensional eye movements in subhuman primates (Macaca mulatta) that although the pursuit system is able to smoothly change the orbital orientation of the eye's rotation axis, the smooth ocular motion was interrupted every few hundred milliseconds by a small quick phase with amplitude <1.5° while the animal tracked a target along a circle or ellipse. Specifically, during circular pursuit of targets moving at different angular eccentricities (5°, 10°, and 15°) relative to straight ahead at spatial frequencies of 0.067 and 0.1 Hz, the torsional amplitude of the intervening quick phases was typically around 1° or smaller and changed direction for clockwise vs. counterclockwise tracking. Reverse computations of the eye rotation based on the recorded angular eye velocity showed that the quick phases facilitate the overall control of ocular orientation in the roll plane, thereby minimizing torsional disturbances of the visual field. On the basis of a detailed kinematic analysis, we suggest that quick phases during curvilinear smooth tracking serve to minimize deviations from Donders' law, which are inevitable due to the spherical configuration space of smooth eye movements.

Spatial and temporal aspects of cognitive influences on smooth pursuit

It is well known that prediction is used to overcome processing delays within the motor system and ocular control is no exception. Motion extrapolation is one mechanism that can be used to overcome the visual processing delay. Expectations based on previous experience or cognitive cues are also capable of overcoming this delay. The present experiment was designed to examine how smooth pursuit is altered by cognitive information about the time and/or direction of an upcoming change in target direction. Subjects visually tracked a cursor as it moved at a constant velocity on a computer screen. The target initially moved from left to right and then abruptly reversed horizontal direction and traveled along one of seven possible oblique paths. In half of the trials, a cue was present throughout the trial to signal the position (as well as the time), and/or the direction of the upcoming change. Whenever a position cue (which will be referred to as a timing cue throughout the paper) was present, there were clear anticipatory adjustments to the horizontal velocity component of smooth pursuit. In the presence of a timing cue, a directional cue also led to anticipatory adjustments in the vertical velocity, and hence the direction of smooth pursuit. However, without the timing cue, a directional cue alone produced no anticipation. Thus, in this task, a cognitive spatial cue about the new direction could not be used unless it was made explicit in the time domain.

Incorporating prediction in models for two-dimensional smooth pursuit

A predictive component can contribute to the command signal for smooth pursuit. This is readily demonstrated by the fact that low frequency sinusoidal target motion can be tracked with zero time delay or even with a small lead. The objective of this study was to characterize the predictive contributions to pursuit tracking more precisely by developing analytical models for predictive smooth pursuit. Subjects tracked a small target moving in two dimensions. In the simplest case, the periodic target motion was composed of the sums of two sinusoidal motions (SS), along both the horizontal and the vertical axes. Motions following the same or similar paths, but having a richer spectral composition, were produced by having the target follow the same path but at a constant speed (CS), and by combining the horizontal SS velocity with the vertical CS velocity and vice versa. Several different quantitative models were evaluated. The predictive contribution to the eye tracking command signal could be modeled as a low-pass filtered target acceleration signal with a time delay. This predictive signal, when combined with retinal image velocity at the same time delay, as in classical models for the initiation of pursuit, gave a good fit to the data. The weighting of the predictive acceleration component was different in different experimental conditions, being largest when target motion was simplest, following the SS velocity profiles.

Causality attribution biases oculomotor responses

When viewing one object move after being struck by another, humans perceive that the action of the first object "caused" the motion of the second, not that the two events occurred independently. Although established as a perceptual and linguistic concept, it is not yet known whether the notion of causality exists as a fundamental, preattentional "Gestalt" that can influence predictive motor processes. Therefore, eye movements of human observers were measured while viewing a display in which a launcher impacted a tool to trigger the motion of a second "reaction" target. The reaction target could move either in the direction predicted by transfer of momentum after the collision ("causal") or in a different direction ("noncausal"), with equal probability. Control trials were also performed with identical target motion, either with a 100 ms time delay between the collision and reactive motion, or without the interposed tool. Subjects made significantly more predictive movements (smooth pursuit and saccades) in the causal direction during standard trials, and smooth pursuit latencies were also shorter overall. These trends were reduced or absent in control trials. In addition, pursuit latencies in the noncausal direction were longer during standard trials than during control trials. The results show that causal context has a strong influence on predictive movements.

Models for the extrapolation of target motion for manual interception

Intercepting a moving target requires a prediction of the target's future motion. This extrapolation could be achieved using sensed parameters of the target motion, e.g., its position and velocity. However, the accuracy of the prediction would be improved if subjects were also able to incorporate the statistical properties of the target's motion, accumulated as they watched the target move. The present experiments were designed to test for this possibility. Subjects intercepted a target moving on the screen of a computer monitor by sliding their extended finger along the monitor's surface. Along any of the six possible target paths, target speed could be governed by one of three possible rules: constant speed, a power law relation between speed and curvature, or the trajectory resulting from a sum of sinusoids. A go signal was given to initiate interception and was always presented when the target had the same speed, irrespective of the law of motion. The dependence of the initial direction of finger motion on the target's law of motion was examined. This direction did not depend on the speed profile of the target, contrary to the hypothesis. However, finger direction could be well predicted by assuming that target location was extrapolated using target velocity and that the amount of extrapolation depended on the distance from the finger to the target. Subsequent analysis showed that the same model of target motion was also used for on-line, visually mediated corrections of finger movement when the motion was initially misdirected.

Extrapolation of visual motion for manual interception

A frequent goal of hand movement is to touch a moving target or to make contact with a stationary object that is in motion relative to the moving head and body. This process requires a prediction of the target's motion, since the initial direction of the hand movement anticipates target motion. This experiment was designed to define the visual motion parameters that are incorporated in this prediction of target motion. On seeing a go signal (a change in target color), human subjects slid the right index finger along a touch-sensitive computer monitor to intercept a target moving along an unseen circular or oval path. The analysis focused on the initial direction of the interception movement, which was found to be influenced by the time required to intercept the target and the target's distance from the finger's starting location. Initial direction also depended on the curvature of the target's trajectory in a manner that suggested that this parameter was underestimated during the process of extrapolation. The pattern of smooth pursuit eye movements suggests that the extrapolation of visual target motion was based on local motion cues around the time of the onset of hand movement, rather than on a cognitive synthesis of the target's pattern of motion.

Target interception: hand-eye coordination and strategies

This study was designed to define the characteristics of eye-hand coordination in a task requiring the interception of a moving target. It also assessed the extent to which the motion of the target was predicted and the strategies subjects used to determine when to initiate target interception. Target trajectories were constructed from sums of sines in the horizontal and vertical dimensions. Subjects intercepted these trajectories by moving their index finger along the surface of a display monitor. They were free to initiate the interception at any time, and on successful interception, the target disappeared. Although they were not explicitly instructed to do so, subjects tracked target motion with normal, high-gain smooth-pursuit eye movements right up until the target was intercepted. However, the probability of catch-up saccades was substantially depressed shortly after the onset of manual interception. The initial direction of the finger movement anticipated the motion of the target by approximately 150 ms. For any given trajectory, subjects tended to initiate interception at predictable times that depended on the characteristics of the target trajectories [i.e., when the curvature (or angular velocity) of the target was small and when the target was moving toward the finger]. The relative weighting of various parameters that influenced the decision to initiate interception varied from subject to subject and was not accounted for by a model based on the short-range predictability of target motion.

Anisotropies in the gain of smooth pursuit during two-dimensional tracking as probed by brief perturbations

Previous investigations suggest the gain of smooth pursuit is directionally anisotropic and is regulated in a task-dependent manner. Smooth pursuit is also known to be influenced by expectations concerning the target's motion, but the role of such expectations in modulating feedback gain is not known. In the present work, the gain of smooth pursuit was probed by applying brief perturbations to quasi-predictable two-dimensional target motion at multiple time points. The target initially moved in a straight line, then followed the circumference of a circle for distances ranging between 180 degrees and 270 degrees . Finally, the path reverted to linear motion. Perturbations consisted of a pulse of velocity 50 or 100 ms in duration, applied in one of eight possible directions. They were applied at the onset of the curve or after the target had traversed an arc of 45 degrees or 90 degrees . Pursuit gain was measured by computing the average amplitude of the response in smooth pursuit velocity over a 100 ms interval. To do so we used a coordinate system defined by the motion of the target at the onset of the perturbation, with directions tangential and normal to the path. Responses to the perturbations had two components: one that was modulated with the direction of the perturbation and one that was directionally nonspecific. For the directional response, on average the gain in the normal direction was slightly larger than the gain in the tangential direction, with a ratio ranging from 1.0 to 1.3. The directionally nonspecific response, which was more prominent for perturbations at curve onset or at 90 degrees , consisted of a transient decrease in pursuit speed. Perturbations applied at curve onset also delayed the tracking of the curved target motion.

Saccades exert spatial control of motion processing for smooth pursuit eye movements

Saccades modulate the relationship between visual motion and smooth eye movement. Before a saccade, pursuit eye movements reflect a vector average of motion across the visual field. After a saccade, pursuit primarily reflects the motion of the target closest to the endpoint of the saccade. We tested the hypothesis that the saccade produces a spatial weighting of motion around the endpoint of the saccade. Using a moving pursuit stimulus that stepped to a new spatial location just before a targeting saccade, we controlled the distance between the endpoint of the saccade and the position of the moving target. We demonstrate that the smooth eye velocity following the targeting saccade weights the presaccadic visual motion inputs by the distance from their location in space to the endpoint of the saccade, defining the extent of a spatiotemporal filter for driving the eyes. The center of the filter is located at the endpoint of the saccade in space, not at the position of the fovea. The filter is stable in the face of a distracter target, is present for saccades to stationary and moving targets, and affects both the speed and direction of the postsaccadic eye movement. The spatial filter can explain the target-selecting gain change in postsaccadic pursuit, and has intriguing parallels to the process by which perceptual decisions about a restricted region of space are enhanced by attention. The effect of the spatial saccade plan on the pursuit response to a given retinal motion describes the dynamics of a coordinate transformation.

Oculomotor responses to gradual changes in target direction

Smooth pursuit tracking of targets moving linearly (in one dimension) is well characterized by a model where retinal image motion drives eye acceleration. However, previous findings suggest that this model cannot be simply extended to two-dimensional (2D) tracking. To examine 2D pursuit, in the present study, human subjects tracked a target that moved linearly and then followed the arc of a circle. The subjects' gaze angular velocity accurately matched target angular velocity, but the direction of smooth pursuit always lagged behind the current target direction. Pursuit speed slowly declined after the onset of the curve (for about 500 ms), even though the target speed was constant. In a second experiment, brief perturbations were presented immediately prior to the beginning of the change in direction. The subjects' responses to these perturbations consisted of two components: (1) a response specific to the parameters of the perturbation and (2) a nonspecific response that always consisted of a transient decrease in gaze velocity. With the exception of this nonspecific response, pursuit behavior in response to the gradual changes in direction and to the perturbations could be explained by using retinal slip (image velocity) as the input signal. The retinal slip was parallel and perpendicular to the instantaneous direction of pursuit ultimately resulted in changes in gaze velocity (via gaze acceleration). Perhaps due to the subjects' expectations that the target will curve, the sensitivity to the image motion in the direction of pursuit was not as strong as the sensitivity to image motion perpendicular to gaze velocity.