1Department of Neuroscience and 2Department of Otolaryngology, University of Minnesota, Minneapolis, Minnesota 55455
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ABSTRACT |
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Engel, Kevin C., John H. Anderson, and John F. Soechting. Oculomotor tracking in two dimensions. Results from studies of oculomotor tracking in one dimension have indicated that saccades are driven primarily by errors in position, whereas smooth pursuit movements are driven primarily by errors in velocity. To test whether this result generalizes to two-dimensional tracking, we asked subjects to track a target that moved initially in a straight line then changed direction. We found that the general premise does indeed hold true; however, the study of oculomotor tracking in two dimensions provides additional insight. The first saccade was directed slightly in advance of target location at saccade onset. Thus its direction was related primarily to angular positional error. The direction of the smooth pursuit movement after the saccade was related linearly to the direction of target motion with an average slope of 0.8. Furthermore the magnitude and direction of smooth pursuit velocity did not change abruptly; consequently the direction of smooth pursuit appeared to rotate smoothly over time.
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INTRODUCTION |
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Tracking of a moving target with the eyes is
accomplished by smooth pursuit movements interrupted occasionally by
saccades. To a first approximation, the smooth pursuit system matches
eye velocity to target velocity, whereas the saccadic system is driven by positional error. This was first shown by Rashbass
(1961) who used a "step-ramp" paradigm in which the
target makes an initial jump away from the fixation point and then
moves at a constant speed in the opposite direction. The latency of the
smooth pursuit system is less than that of the saccades
(Rashbass 1961
), and the initial eye movement is in the
direction of target motion, away from the target's position.
Positional error then is reduced by a saccade toward the target, in the
direction opposite to the pursuit movement, and at a longer latency.
Since then, several other experimental paradigms, based on tracking
tasks in one dimension, generally have supported this scheme
(Keller and Heinen 1991
; Lisberger et al.
1987
). However, it is well known that concepts derived from
studies of one-dimensional movements do not always generalize to two or
more dimensions (Georgopoulos 1986
; Soechting and
Flanders 1991
). In fact, recent studies on oculomotor tracking in two dimensions (de'Sperati and Viviani 1997
;
Leung and Kettner 1997
) have shown that this task cannot
be decomposed into two independent one-dimensional tasks, one involving
horizontal pursuit and the other involving vertical pursuit.
The question then arises: how are the saccadic and smooth pursuit systems coordinated in tracking an object the motion of which undergoes a directional change? In particular, does the premise that the saccadic system reduces positional error while the smooth pursuit system matches eye velocity to target velocity hold true during two-dimensional pursuit tasks? To answer this question, we asked subjects to track an object that initially moved in a straight line at a constant speed and then, at a random point in time, changed direction abruptly but maintained its original speed. Specifically, the target initially moved straight down and then changed to 1 of 11 equally spaced directions.
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METHODS |
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Six normal subjects participated in this study. All subjects either did not require corrective lenses or wore eye glasses during the experiment. Subjects were seated with the head immobilized by a custom head-holder, and their right eye was 150 cm in front of a rear projection screen. They were asked to track, with their eyes, the motion of a target projected onto the screen. Each trial began with the target being extinguished from a central position directly in front of the subject's right eye and being displaced 20° upward. After a 1.5-s holding period, the target began moving downward at a constant speed, alternating between 15 and 30°/s on successive trials. We found that by simply alternating velocities on successive trials, the predictability of the target motion was reduced and smooth pursuit tracking was improved. When the target reached a random position within a region between 5° above and 10° below the horizontal plane, target motion changed abruptly to 1 of 11 directions. These 11 directions spanned 360° at 30° increments, excluding 180° (i.e., the target reversing on itself). Furthermore, those trials with no change in direction (0°), were excluded from all analysis. After assuming a new direction, the target would continue until it reached an angular displacement of either 20° to the left or right, or 20° above or below the center position of gaze. At all times, the target maintained a constant speed. Each session had 88 trials and lasted no longer than 45 min. (For subject F in Tables 1 and 2, data were collected using a target motion of only 15°/s, with 16 rather than 11 directions and 83 rather than 88 trials. The data from this subject therefore are excluded from some of the statistical analyses.) Subjects gave their informed consent to the experimental procedures, which were approved by the Institutional Review Board of the University of Minnesota.
The magnetic search-coil technique (CNC Engineering) was used to record
eye movements (Robinson 1963). An annulus was placed on
the right eye, and the target was tracked binocularly. The target
stimulus was a rear-projected red spot of light, 0.5° in diameter,
that was produced by a 5-mw helium-neon laser. The motion of the target
was generated by a two-axis, servo-controlled galvanometer mirror
system with a dynamic range >300 Hz (General Scanning). The entire
experiment was controlled by a laboratory computer, which sampled the
horizontal and vertical position of the eyes and updated the position
of the target at a rate of 1,000 Hz/channel.
Eye movement records were analyzed off-line by means of custom software. The records first were filtered digitally by means of a "notch"-type filter to remove 60 cycle noise. Eye velocity was estimated by numerically differentiating the position data and digitally smoothed using a two-sided exponential filter with a cutoff frequency of 120 Hz. Saccade onset and end were determined as the times at which the speed of the movement crossed a threshold value set at 150% of target speed. Trials were examined individually, and the times that were determined automatically could be adjusted through an interactive process. The directions of saccades and smooth pursuit segments were determined by the first and last points of the segment. The instantaneous direction of eye movements was computed from the inverse tangent of the ratio of the x and y velocities. The latency of the smooth pursuit after the target changed direction was determined from the time at which eye movements began to change direction. This was done interactively by fitting straight line segments to smooth pursuit direction over the intervals before and after the change in direction and using their intercept to define latency.
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RESULTS |
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Figure 1 shows four representative trials from three different subjects. In each case, the traces are centered around the time at which the target changed direction. The path of the target is described by the smooth bold line. The gaze position of the eye is plotted every millisecond, creating a densely dotted line during periods of smooth pursuit and a sparsely spaced dotted line during saccades. Isochronic lines connect the position of the eye and the position of the target every 50 ms after the change in target direction. The inset in Fig. 1C indicates how changes in target and pursuit angle are measured.
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Before the target motion changed direction, the subjects were generally successful at tracking the target. At the time that the target direction changed, tracking error was small (median 0.72°, 421 trials). This is apparent in Fig. 1 if one considers the first isochronic line. If tracking was perfect, this line would connect points of target and eye position equidistant from the point at which the target changed direction.
In the following, we consider three aspects of the oculomotor tracking performance in response to a change in direction of target motion: the initial saccade, the smooth pursuit phase after that saccade, and the smooth pursuit segment before the saccade.
Saccade
In each example, after the target changed direction, the eye
initially continued on its original trajectory and then smoothly changed direction. This is especially pronounced in Fig. 1,
B and C. At a latency that ranged from 191 (Fig.
1A) to 218 ms (Fig. 1B), there was a saccade that
significantly reduced the error in position. Across all subjects the
mean time for saccade initiation was 197 ± 28 (SD) ms. This is
consistent with previous results from one-dimensional tracking
(Leigh and Zee 1991) where the latency for saccades was
found to be ~200 ± 25 ms.
Two points are clear from inspection of Fig. 1. First, the saccades
were directed toward the location of the target at saccade onset or to
a location in advance of the target (Fig. 1, A and D) as can be ascertained by comparing saccade direction with
the direction of the isochronic lines. (If the saccade was directed to
the target's position at the onset of the saccade, the direction of
the saccade would parallel the nearest isochronic line.) Second, the
saccades were hypometric. To quantify this second characteristic, we
defined positional error as the distance between the position of the
eye at saccade onset and target position at one of two times: at
saccade onset (SO) and at the end of the saccade (SE). We then defined
the gain of the saccade as the saccade amplitude divided by one of
these two positional errors. For the four examples shown in Fig. 1, the
gains ranged from 0.56 (Fig. 1D) to 0.91 (Fig.
1B) if position error was defined at SO. The gains were lower if position error was computed at SE, with values ranging from
0.52 (Fig. 1D) to 0.82 (Fig. 1B). The results for
all six subjects are shown in Table 1. In
general, these results are consistent with the results described for
one-dimensional motion, in which the first saccade on average spans
90% of the positional error, with the final 10% being corrected by a
subsequent saccade (Becker and Fuchs 1969).
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As already noted, the first saccade was usually directed to a point in
advance of the target at SO. This is shown more precisely in Fig.
2, where we have plotted the difference
between saccade direction and the direction from eye position to target
position at SO (). For positive target directions, a negative error
means the saccade direction was to a point in advance of the target's location at SO, whereas the converse is true for negative target directions.
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We also tested the extent to which saccade direction was related to
directional error defined as the difference between eye position at SO
and target position at SE ( in Fig. 2). Except for the smallest
angles, this directional difference was close to zero. Furthermore, an
ANOVA analysis showed that directional errors (related to SE) did not
differ from each other significantly (P > 0.05),
except for the smallest change in target directions (±30°).
Conversely, directional errors defined at SO did show a statistical
dependence on target direction (P < 0.05). Therefore the saccades were generally "predictive."
To more precisely characterize the predictive nature of the saccades, we compared their direction with the predictions of four models. In one model, saccade direction is defined by the vector sum of a positional error signal and a signal proportional to target velocity (illustrated schematically as 1 in Fig. 3A). In the second model, saccade direction is defined by the sum of positional error and a downward bias that is related to the initial direction of the target motion (model 2 in Fig. 3A). Models 3 and 4 in Fig. 3A show the idealized cases in which saccade direction is modeled as if it headed directly toward the position of the target either at SO or to the position of the target at saccade end (SE). For the first two models, we computed the coefficient a (model 1) and d (model 2), which minimized the variance across all trials for all target directions for a given subject.
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Figure 3, bottom, shows the extent to which each of the four
models fit the data for the six subjects. Their variances have all been
normalized to the variance of the first model (1), which generally gave
the best fit. Model 3 (in which saccade direction was defined by
position error at saccade onset) had the largest error in all but
subject D. The other three models had variances that were
usually comparable in magnitude. However, statistically, model 1 was
superior to the other three models when the data for all of the
subjects were pooled together (F test, P < 0.05). In all but subject D, the coefficient a (model 1) was
positive, with values ranging from 0.015 to 0.096 s. (For subject
D, a = 0.003 s.) The average value was 0.034 s. Model
2 gave a consistent downward bias for all subjects, with an average of
0.30°. Note that in our experimental situation, a downward bias
always will lead to a direction in advance of the target (see model 2 in Fig. 3A).
Smooth pursuit after the first saccade
After the initial saccade, for some trials the average direction
of the next segment of smooth pursuit was nearly parallel with the
motion of the target. For example, the direction of eye velocity
differed from that of target motion by 4° in Fig. 1A. More
commonly (Fig. 1, B-D), eye velocity did not parallel
target velocity. In these examples, the directional change of smooth pursuit, from its original vertical trajectory, was less than the
directional change () of the target motion, i.e., the positional error actually increased during this segment of pursuit. In these cases, the angular differences between the direction of eye motion and
target motion were 10, 19, and 29°, respectively.
Figure 4 shows how the directional change
of the smooth pursuit interval following the first saccade after the
change in target direction is related to the directional change of the
target () for one subject (B). The 45° line indicates a
perfect angular match; the other two are linear regressions fitted
independently to the positive and negative target directions. For this
subject, the slopes were comparable (0.66 and 0.65) and significantly
<1. Inspection of Table 2 shows that for
all subjects, the slopes were <1 in all but one instance, with the
average slope being 0.82 ± 0.14. Figure 4 also shows that for
small directional changes of the target (±30°, ±60°) the
directional change of the first pursuit segment actually surpassed the
directional change of the target. Accordingly, the regressions for
positive and negative directions intercept zero at ±27°. As
summarized in Table 2, in almost all cases there was a positive offset
for clockwise rotations and a negative one for counterclockwise
rotations such that the directional change of the first pursuit segment
tended to surpass the directional change of the target for small
angles. Across all six subjects, the average absolute angular offset
was 15 ± 10°.
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The average speed of the eye during this pursuit segment also tended to be less than that of the target. On average, across all subjects and all directions, for targets moving at 15°/s, the average eye speed in the first postsaccadic interval was 73 ± 22% of target speed. For targets moving at 30°/s, it was 66 ± 25% of target speed. Furthermore the greater the directional change in target motion, the slower was the average speed of the smooth pursuit during this interval. A linear regression of eye speed (as a percentage of target speed) versus the angular change in target motion was performed for each subject for both positive and negative directional changes. In all instances, the slope was negative, that is, the greater the amount by which the target changed direction, the slower was the smooth pursuit eye velocity. The average change in normalized speed per degree of target direction change was 0.209 ± 0.129 (n = 12) i.e., a 21% decrement in speed per 100° of directional change in target motion. In general, the speed of eye motion during the first postsaccadic interval was not constant. Instead, after the target changed direction, there was an initial deceleration of the eye followed by a subsequent acceleration. The time course for this change in speed was as much as 350 ms for large angular changes in target direction.
Smooth pursuit before the first saccade
For the four examples shown, the latency for the smooth pursuit to
change direction ranged from 94 ms for Fig. 1B to 129 ms for
Fig. 1A. For all subjects, the average latency was 109 ± 21 ms, consistent with previous findings for oculomotor tracking in
one dimension (Carl and Gellman 1987; Leigh and
Zee 1991
; Morrow and Sharpe 1993
;
Robinson 1965
). Generally, smooth pursuit changed direction smoothly and gradually before the first saccade. This rotation is especially apparent in Fig. 1, B and
C. Both of these examples show a smooth change in direction
sweeping through intervening angles between the initial direction of
pursuit and the new direction of the target. (The degree of curvature
observed in Fig. 1, B and C, compared with Fig.
1, A and D, is primarily due both to a slightly
increased saccadic latency as well as a somewhat shorter latency for
smooth pursuit in Fig. 1, B and C).
Although we have approximated the smooth pursuit segments after the initial saccades with straight lines for the current analysis, inspection of these segments in Fig. 1, A-C, reveals that the postsaccadic segments show a slight amount of curvature. The direction as well as curvature of these segments appears to be a continuation of the rotation of smooth pursuit direction before the saccade. Furthermore Fig. 1D, although not being a typical example, illustrates a case in which multiple iterations between saccades and smooth pursuit occurred before the eye had reacquired the target. In this example, each smooth pursuit iteration further reduced the angular error between the direction of the target motion and the direction of the smooth pursuit velocity.
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DISCUSSION |
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We have shown that during two-dimensional tracking, the amplitude and direction of saccades are correlated mainly with the error between the gaze position of the eye and the target position. Furthermore we have shown that the direction of the smooth pursuit is related to the direction of the target velocity. Finally the direction and the speed of smooth pursuit change gradually over a period of several hundred milliseconds.
In the current study, the direction of the saccade was primarily toward
the target, reducing positional error. We found that the angular
difference between the direction of the saccade and the direction
defined by target location at SE was much closer to zero than the
direction defined by target location at SO. Furthermore this angular
difference did not depend on the direction of target motion (except for
the smallest angular changes) when it was defined at SE. Conversely,
there was a statistical dependence on target direction when direction
was defined by target position at SO. Both of these factors argue for
the fact that the direction of the saccade is predictive toward where
the target will be at the end of the saccade (Keller and Johnsen
1990). This predictive nature of the saccadic system suggests
that target velocity or a velocity error signal, as well as positional
error, contributes to determining the metrics of the saccade, at least
in terms of its direction.
Quantitative modeling (Fig. 3) supported this idea. A model (Fig. 3A, model 1) combining a positional error vector with a vector in the direction of target velocity gave the best fit to the data. The coefficient for the velocity term was small (~0.03 s) and positive indicating that the saccade was directed to the location of the target, on average, 30 ms in the future. A second model in which there was a constant downward bias to saccade direction (model 2) could fit the data nearly as well. In our experimental situation, such a downward bias will always lead to saccades directed in advance of the target position at saccade onset. However, this model would lead to a different interpretation of the underlying mechanisms. Such a downward bias could result if directional information did not change instantaneously, as was found for the smooth pursuit system in the present study.
We characterized saccadic gain by taking saccade amplitude and dividing
it by the positional error at SO or SE. The gain, computed by
considering SO, was comparable with that reported previously for
studies of tracking in one dimension (Becker and Fuchs
1969). However, the gain relative to the position of the target
at SE generally was reduced by another 10% over what was found for SO.
Thus the saccades were more hypometric than has been reported
previously. This difference might be explained by the following
considerations. It has been proposed that the error signal to the
saccadic system is based on target position some time between SO and
100 ms before (Ron et al. 1989
). In the step-ramp paradigm, at the time of the first saccade, the smooth pursuit velocity
is already close to target velocity (Lisberger and Westbrook 1985
; Rashbass 1961
). Thus in that paradigm, the
positional error increases only slightly between the time at which the
metrics of the saccade are specified and the time at which the saccade is initiated. In contrast, in our experiments, positional error increased appreciably before saccade initiation because the direction of pursuit was away from the target and because the speed of the eye
was less than the speed of the target. This could account for our
finding that saccades were more hypometric at SE, and it suggests that
the saccadic system is not able to compensate for the time course of
changes in positional error. This interpretation also suggests that the
processing of saccade amplitude and direction are separate, because, as
was discussed earlier, the specification of saccade direction does
appear to have a predictive component.
The results of the present study suggest that the direction of smooth
pursuit was not influenced by positional error. After the change in
direction by the target, the direction of the smooth pursuit did not
tend to decrease the positional error between the target and the gaze
(see Fig. 1). Except for small directional changes in target motion,
the directional change of the smooth pursuit was less than the
directional change of the target's motion (Fig. 4 and Table 2), i.e.,
the eye headed away from the target. The instances where the change in
the direction of smooth pursuit motion exceeded the amount by which
target motion changed direction might be taken as evidence for a
positional component in the error signal for smooth pursuit
(Noda and Warabi 1982; Pola and Wyatt 1980
). However, a closer inspection of individual trials with directional changes <90° showed that in the majority of instances (19 of 31 trials for subject B, Fig. 4), the eye moved away
from the target in these instances as well. In some cases, the
directional gain change exceeded unity even when the saccade was not
hypometric. In other cases, when the saccade was hypometric, ocular
motion crossed the target's trajectory, first approaching the target and then moving away from it without any appreciable change in direction.
Thus we conclude that positional error does not contribute
substantially to the input to the smooth pursuit system in our experimental paradigm. This is in agreement with the original finding
by Rashbass (1961). It also agrees with the results of a
recent study by Lisberger and Ferrera (1997)
. They
presented monkeys with two targets at disparate locations, moving in
different directions and found that smooth pursuit eye motion
represented a vector average of the two velocities. They concluded that
"the pursuit system is attempting to match eye and target speed and therefore has no obvious reason to care about the exact spatial position of the targets."
Of particular interest is the finding that both the change in direction
as well as the change in speed of the smooth pursuit appear to occur
gradually over time. The fact that the pursuit system does not change
speed immediately has been well established in work studying
one-dimensional tracking (Lisberger and Westbrook 1985).
However, the current study indicates that this holds true for the
direction of motion as well as for speed. The inability of smooth
pursuit velocity to change abruptly does not appear to be mechanical in
origin, for example due to inertia or viscoelastic properties of the
eye and orbit. Such a limitation may hold for limb motion, where it
also has been found that a directional change in motion requires a
finite amount of time (Georgopoulos 1986
). However, the
inertia of the eye is much less. This is demonstrated by the fact that
saccades interrupt the smooth pursuit in a direction at sharp angles to
the direction of smooth pursuit both before and after the saccade (Fig.
1). The overall behavior is consistent with the proposition that there
are neural constraints for smooth pursuit, limiting acceleration, that
do not exist for the saccadic system.
The observation that the angular gain of the smooth pursuit system
appears to be significantly less than one (Table 2) may be linked to a
gradual rotation within the smooth pursuit system from one direction to
another (de'Sperati and Viviani 1997). In addition, the
smooth pursuit speed decelerates as it changes direction, with the
amount of deceleration being proportional to the magnitude of the
directional change. Once again, the interwoven saccades make it clear
that this change in speed is not a function of the mechanical
properties of the eye.
The coincidence of the temporal profiles for the change in speed as
well as direction suggests that both speed and direction (velocity) are
controlled by the same neural mechanism. Although the neural basis for
smooth pursuit velocity coding is characterized incompletely, it is
possible that its implementation might be similar to that found for
directional coding of arm movements in primary motor cortex where
direction of motion is coded by a population vector and the same
population of neurons also codes for speed (Fu et al.
1995; Georgopoulos 1986
). It has been found that
this neural vector is incapable of changing directions instantaneously but, rather, that it rotates at a constant speed (Georgopoulos et al. 1989
).
The fact that the system appears to have a "virtual inertia" may
not be detrimental to the overall performance of the system because
objects being tracked do have a mass and therefore do not change
direction immediately. This effective inertia therefore may allow the
eye to more easily match the velocity of the object being tracked and
may in fact be beneficial in cases where the object moves behind a
momentary occlusion (Becker and Fuchs 1985) and where
retinal slip is zero (Krauzlis and Lisberger 1994
;
Robinson 1965
).
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ACKNOWLEDGMENTS |
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We thank Dr. Martha Flanders and two anonymous reviewers for helpful suggestions and comments.
This work was supported by a grant from the Human Frontiers Science Program and by National Institute of Neurological Disorders and Stroke Grants NS-15018 and NS-37211.
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FOOTNOTES |
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Address for reprint requests: K. C. Engel, Dept. of Physiology, University of Minnesota, 6-255 Millard Hall, 435 Delaware St. SE, Minneapolis, MN 55455.
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 9 November 1998; accepted in final form 29 December 1998.
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REFERENCES |
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