INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Smooth pursuit eye movements are used by primates to track small moving targets. Step-ramp target trajectories, consisting of a step in target position concurrent with the onset of target motion, have become a standard approach for analyzing nonpredictive features of pursuit (Lisberger and Westbrook 1985; Rashbass 1961). Shortly after the onset of target motion, the eye accelerates rapidly toward target velocity. Following this rapid acceleration, eye velocity settles near target velocity. Pursuit of step-ramp targets is thus often described as having "initiation" and "maintenance" phases.

While dividing the response into initiation and maintenance phases is descriptively useful, there is no evidence that the pursuit system makes an active transition from one phase to the other, or that its responsiveness differs between the two states. Instead, analysis of pursuit has revealed two functional mechanisms that do not map directly onto the two phases of pursuit initiation and maintenance. One mechanism, called "visuo-motor drive," relies on visual motion inputs represented in a population code in the middle temporal area of extra-striate visual cortex (area MT), and transforms that code into commands for smooth eye acceleration (Dursteler et al. 1987; Groh et al. 1997; Morris and Lisberger 1987; Newsome et al. 1985). The other mechanism, called "eye velocity memory," converts commands for eye acceleration into signals for desired smooth eye velocity and ensures that eye velocity will decay only slowly from its current value in the absence of image motion (Morris and Lisberger 1987; Robinson 1971; Robinson et al. 1986; Young et al. 1968). Acting as an acceleration to velocity integrator, eye velocity memory is conceptually similar to, but functionally distinct from, the well-known "neural integrator" that converts commands for eye velocity into commands for eye position (Robinson 1989). Visuo-motor drive and eye velocity memory are both active during both the initiation and maintenance of pursuit. However, for step ramp targets, changes in pursuit initiation can typically be attributed to changes in visuo-motor drive, assuming that the status of eye velocity memory remains constant. Likewise, the analysis of maintenance can be used to evaluate the status of eye velocity memory, assuming that visuo-motor drive is sufficient to drive the eye to the constant target velocity.

Recent reports from our laboratory have emphasized a third mechanism that we have previously called a "pursuit switch" or "on-line gain control" and that we will refer to here as the "engagement" of pursuit. The existence of different levels of engagement of pursuit was previously demonstrated using brief perturbations of target motion to probe the gain of visuo-motor drive (Goldreich et al. 1992; Schwartz and Lisberger 1994). The gain of the evoked pursuit response depended on whether the monkey was fixating or tracking when the probe was presented, and on the ongoing eye/target velocity during pursuit maintenance. These experiments demonstrate that the pursuit system is engaged to differing degrees during fixation and ongoing pursuit. A deficit in engagement of pursuit was also proposed as an explanation for a number of deficits in sustained eye velocity during the maintenance of pursuit (Grasse and Lisberger 1992; Kiorpes et al. 1996). We have thus assumed that both visuo-motor drive and eye-velocity memory are modulated by the state of engagement of the pursuit system. That the engagement of pursuit influences eye velocity memory was first suggested by Robinson (Luebke and Robinson 1988; Robinson et al. 1986), and is assumed by the pursuit model of Krauzlis and Lisberger (1994). Visual motion thus serves a dual role in pursuit. It is the primary input for the visuo-motor drive of eye acceleration during pursuit, but is also necessary to engage pursuit in the first place.

One approach to understanding the perception and neural processing of visual motion has been to degrade the quality of motion using "apparent motion" stimuli, consisting of flashes of a target at a sequence of positions. Studies of human perception using different types of targets have revealed very different spatial limits for "short-range" and "long-range" perception of motion (Barlow and Levick 1965; Braddick 1980; Newsome et al. 1986; Tyler 1973). Parallel analysis of human motion perception and neuronal responses in awake monkeys have revealed a broad similarity in the spatial limit of motion perception and the spatial limit of direction selectivity for MT neurons (Mikami et al. 1986; Newsome et al. 1986). Previous studies of pursuit eye movements using apparent motion along periodic trajectories have revealed tracking deficits when the flash separation was increased past 80-150 ms (Fetter and Buettner 1990; Morgan and Turnbull 1978; Schor et al. 1984; Van der Steen et al. 1983). However, the continuous nature of the target trajectories used in these prior studies makes it difficult to determine whether the deficits arose because the degraded motion failed to support normal visuo-motor drive of eye acceleration, or because the degraded motion was insufficiently convincing to fully engage pursuit.

We now report the pursuit evoked by step-ramp target trajectories consisting of apparent motion with a range of spatial and temporal separations of the flashes. Our data reveal separable effects of apparent motion on both visuo-motor drive and eye velocity memory. Effects on visuo-motor drive were manifested as changes in the latency and magnitude of eye acceleration at the initiation of pursuit, including a paradoxical facilitation of eye acceleration over a narrow range of parameters. Effects on eye-velocity memory were manifested as sustained maintenance phase eye velocities much lower than target velocity. We interpret eye-velocity memory deficits as resulting from a failure of the visual stimulus to provide a sufficiently convincing motion signal to fully engage pursuit. Our data indicate that the engagement and subsequent visuo-motor guidance of pursuit eye movements both depend on the quality of the visual motion. We suggest that the motion signals governing engagement may not be the same as those driving eye acceleration. While deficits in visuo-motor drive were independent of extra-retinal factors such as eye and target velocity, deficits in eye velocity memory were not.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Parameterizing apparent motion stimuli

The solid line in Fig. 1A illustrates the spatio-temporal trajectory of a horizontally moving point. As time passes, the point moves rightward. The filled circles along this line illustrate the trajectory of an apparently moving spot, with spatial and temporal separations x and t, respectively. The apparent velocity is given by x/t. Smooth and apparent motion may also be represented in the frequency domain. The transform of a single spot contains a broad range of spatial frequencies. For a smoothly moving spot, each spatial frequency is associated with a different temporal frequency, where velocity = temporal frequency/spatial frequency (Adelsen and Bergen 1985; Watson and Ahumada 1985). The solid diagonal line in Fig. 1B illustrates this relationship. Apparent motion is equivalent to sampling a smoothly moving stimulus and produces aliasing. In the frequency domain aliasing produces "replicas" of the original spatio-temporal frequency content, as shown by the dashed lines in Fig. 1B.

View larger version (9K): [in this window] [in a new window]   Fig. 1. Representation of smooth and apparent motion in the space-time domain (A), and the frequency domain (B). A: time is shown on the y-axis, with downward movement along the axis reflecting the passing of time. Horizontal position is plotted on the x-axis. B: frequency domain representation of the same target motion as in A. Spatial and temporal frequency are plotted on the x- and y-axis with positive values plotted rightward and upward, respectively. The oblique solid line shows the relationship for real target motion at a given speed, while the 2 dashed oblique lines show "replicas" that appear during sampled, or apparent, motion.

The range over which apparent motion effectively emulates real motion can be described in the space-time domain in terms of the effective combinations of x and t. The same range can also be described in the frequency domain by outlining the "window of visibility": the range of temporal and spatial frequencies to which the system of interest is sensitive. Apparent motion becomes noticeably un-smooth when the replicas produced by aliasing enter this window of visibility. We choose to describe our stimuli and the effective range of apparent motion in the space-time domain for two reasons. First, the spots we used are simply and intuitively described in the space-time domain. Second, because our stimuli were actually spots, not sine wave gratings, linearity becomes an issue when one attempts to describe the response of either pursuit or of neural motion sensors in terms of the responses to individual frequency components. As an example, some of the components of an apparently rightward moving spot are in fact moving leftward (those aliasing components in the bottom right quadrant of Fig. 1B). A leftward tuned motion sensor would, if linear, respond to these components just as surely as if the stimulus had actually been a leftward moving grating. If nonlinear, the sensor might or might not be expected to respond. Unpublished experiments from this laboratory indicate that many MT cells fail to respond in the way expected given the assumptions of linearity. We therefore choose to describe the limits of apparent motion in terms of maximum x and t, and not in terms of the border of the window of visibility. This is not to deny that the latter description could be constructed, provided that the relevant nonlinearities were understood and accounted for. Such a description is, however, outside the scope of this paper, the goal of which is to parameterize the limits of apparent motion for pursuit in a simple descriptive manner that might then be compared with a similar description of the effects of apparent motion on the response of the population of MT neurons.

Surgical procedures

Experiments were performed on six adult male rhesus monkeys that had been trained to pursue single moving targets. Our basic experimental methods have been presented before (e.g., Lisberger and Westbrook 1985). Briefly, monkeys were trained to track visual targets and were rewarded with drops of water or Tang. Eye movements were monitored using scleral search coils that had been implanted with the technique of Judge et al. (1980), using sterile procedure while the monkey was anesthetized with Isofluorane. Postsurgical analgesia was provided for a minimum of 2 days with Buprenorphine (0.01 mg/kg every 12 h). During experiments, monkeys sat in a primate chair with their heads affixed to the ceiling of the chair using a dental acrylic fixture that had been implanted at the same time as the eye coil. Experiments lasted 2-3 h. Methods had been approved in advance by the Institutional Animal Care and Use Committee at the University of California, San Francisco.

Visual stimuli and presentation of targets

Stimuli were presented on a 12-in. diagonal analog oscilloscope (Hewlett Packard model 1304, P4 phosphor) driven by the D/A converter outputs from a digital-signal-processing board in a pentium PC computer. This system provided us with a spatial resolution of 65,536 by 65,536 pixels and a maximum temporal resolution of 4 ms (2 ms in a few later experiments). We positioned the display 30 cm from the monkey so that it subtended a vertical visual angle of 40° and a horizontal visual angle of 50°.

Stimuli were sequences of flashes with a wide range of temporal flash separations (t) and spatial flash separations (x), which were systematically varied. When t and x were small, the series of flashes produced the perception of a smoothly moving target (Newsome et al. 1986). Thus we will refer to the series of flashes as a target, with a given t, x, and apparent velocity. As the apparent velocity of a target is given by x/t, the stimulus is fully defined by any two of these three parameters. To maintain a constant mean luminance of the target, the luminance of each flash was varied linearly with the time between flashes (e.g., if t was doubled, so was the luminance of each flash). We adopted this approach instead of the alternative (keeping individual flash luminance constant) because it rendered pursuit targets that appeared to have similar brightness regardless of t, and because we anticipated it would avoid changes in pursuit latency that would be a function of luminance rather than of the parameters of the apparent motion itself.

Each individual target flash was very brief. The duration increased with t, due to the extra time necessary to increase the luminance. For a t of 4 ms each flash lasted approximately 160 µs. Each doubling of t doubled this duration, so that for a t of 64 ms each flash lasted approximately 2,560 µs. The specifications of the display oscilloscope indicated that the phosphor will decay to 10% of its maximal level in 10 µs to 1 ms. The tracking target was brighter than the fixation point (see next paragraph for description of these targets). Photometer measurements revealed that the fixation target and tracking target had net luminances of approximately 1.6 and 25 cd/m², respectively. Because targets were small, roughly 0.2° across, these luminances were bright but not dazzling. Experiments were performed in a dimly lit room. Due to the dark screen of the display, background luminance was beneath the threshold of the photometer, less than 1 mcd/m². Subsequent to an earlier review of this paper, an error was found in the program controlling the visual stimuli. The timing of the second flash in the sequence was often erroneous: the first two flashes would occur immediately following one another, with the specified t occurring only between subsequent flashes. This error was not visible to the naked eye, but could certainly have influenced some of our measurements of the effect of apparent motion on the initiation of pursuit, perhaps reducing the size of the observed deficits. All experiments were replicated following correction of the error, using monkeys Na, Ka, and Mo. As all the same effects were observed, we have retained the original data and added the new data to our presentation.

Targets were presented in individual trials that began with the appearance of a fixation point 10° to either the right or left of straight-ahead gaze. The fixation point always had a t of 4 ms. The monkey was required to fixate this spot within 600 ms after its appearance and to maintain fixation within a 2° window of target position for 700-1,100 ms. The fixation point was then extinguished and replaced 4 ms later with a tracking target that appeared eccentric relative to the fixation point and immediately began to move toward the position of fixation (Rashbass 1961). For example, a given trial might begin with the appearance of a fixation point to the left of center. When the fixation point disappeared, the target would appear to its left and move rightward. Because of the initial 10° offset of the fixation point, targets were able to traverse up to 35° before reaching the edge of the monitor. The duration of target motion varied from 700 to 2,400 ms, depending on the speed of the target. Quickly moving targets were extinguished when they neared the edge of the screen. In some later experiments, and for velocities faster than 16°/s, the target was not extinguished at the end of its trajectory. Instead, it stepped forward 2-4° and remained stationary for 600-1,000 ms before being extinguished. This helped to minimize the decrease in sustained eye velocity that often occurred near the end of a trial.

Most experiments also included "control trials," in which the tracking target appeared eccentric to the fixation spot and moved away from the fixation point toward the edge of the monitor that was closest to the fixation point. For all but the slowest velocities, the target neared the edge of the monitor quickly, at which point it stopped and fixation was enforced for up to 1,000 ms. These trials were not analyzed, but were intended to prevent the monkey from predicting the direction of target motion. In some later experiments, control trials were omitted. This had no discernable effect on pursuit within that experimental session, and no anticipatory eye acceleration was observed before the normal onset of pursuit.

Following the onset of target motion, the monkey was given 450 ms to bring his eyes from the initial point of fixation to the target, and was required to track the target with an accuracy of 3°. If the monkey maintained the required fixation and tracking throughout the trial, he was rewarded with a drop of juice. If fixation requirements were not met during a trial, the trial was immediately aborted. For some trials, particularly those with large values of x, the size of the fixation window was increased to as large as 9°, to allow the monkey to complete most trials successfully. Each experiment consisted of multiple repeats of a list of up to 132 types of trials, where each trial type presented a different stimulus. The trials were sequenced by shuffling the list and requiring the monkey to complete each trial successfully once. If he failed a trial, it was placed at the end of the list and presented again after all the other trials had been completed. After all trials had been completed once, the list was shuffled and presented again. Monkeys were allowed to work as long as they continued to complete most trials successfully, usually for 2,000-4,000 trials.

The wide range of possible parameters of apparent motion made it impossible to evaluate all parameters within a single experimental session. Instead, we varied different parameters on different days, in experiments designed to be complete along selected axes of the possible parameter space. Because each experiment type required slightly different methods for design and data analysis, we outline separately the five basic classes of experiment reported here.

	1
	Experiments using a single target velocity and varying flash separation. All trials had the same target velocity of 18°/s, and up to eight different values of t were used. In one later experiment we repeated this experimental design using a target velocity of 3°/s. The goal of this design was to collect large numbers of responses for each flash separation to allow the quantitative analysis of pursuit initiation shown in Fig. 5. In some early experiments additional "catch" trials were run at different velocities, but were not analyzed. Catch trials appear to have no influence on the effects we observed and were not included in all experiments. The initial step of target position relative to the fixation point was set so as to increase the latency of the first saccade (Rashbass 1961). On each experimental day, prior to collection of data, step size was optimized so that saccades were rare during the first 400 ms of pursuit. Depending on the monkey, a step between 2 and 3° was ideal for target speeds of 18°/s. The absence of saccades during the rising phase of pursuit was crucial for the analysis of initial eye acceleration, described below. A drawback of this design is that for a constant apparent velocity, t and x vary together. It is thus not possible to determine whether changes in pursuit initiation result from an excessive spatial separation or an excessive temporal separation.
	2
	Experiments using a single target velocity in which both target eccentricity and flash separation varied. These experiments were similar to those in 1) above, except we varied the size of the initial step of target position and observed the interaction of retinal eccentricity with the effects of flash separation. Within each experiment, the size of the step was randomly varied among 0.5, 3, and 7°. For steps of 0.5 and 7°, saccades were common during the first 400 ms of pursuit. When deficits were absent or small, the majority of responses nonetheless exhibited considerable presaccadic pursuit, with the first saccade occurring near the end of the rising phase of eye acceleration.
	3
	Experiments varying both target velocity and flash separation. Both apparent target velocity and t (and thus x also) were varied systematically. The goal of these experiments was to describe the combinations of x and t that produced normal initiation of pursuit, and if possible, to isolate independent temporal and spatial limits. The temporal limit would be defined as the maximum t for which normal pursuit is evoked, regardless of how small x is, and the spatial limit as the maximum x, regardless of t. As in 1) above, we attempted to optimize the initial step of target position so as to largely eliminate saccades during the rising phase of initiation. Unfortunately, the optimal step size depended strongly on target velocity. It was thus not possible to eliminate early saccades at all velocities without introducing confounding effects from varying the step size. In early experiments (those using monkeys Da and Fi), we used the same starting eccentricity for all target velocities; the tracking target always appeared 3° to one side of the fixation spot. Because targets moving at faster speeds became less eccentric more quickly, the mean eccentricity in the first 100 ms of target motion was different for different target velocities, as was the chance of early saccades. For all later experiments, we set the size of each target step so that mean image eccentricity during the first 100 ms of target motion was 1° on the same side of the fixation spot as the initial position of the moving target. Thus more swiftly moving targets started further eccentric. Both methods of determining starting position provided similar results. The latter method used initial positions that reduced the occurrence of early saccades to some degree, although not nearly as much as if eccentricity had been optimized explicitly to do so. Although these experiments were designed to study pursuit initiation, deficits in pursuit maintenance were also sometimes observed, and we took advantage of these data to examine how the maintenance deficits seen at a given t change with target velocity.
	4
	Experiments presenting two steps of target velocity. These experiments were designed to compare pursuit responses to a given apparent image motion presented either during fixation or during ongoing pursuit. These experiments included a) control trials in which we recorded the initiation of pursuit for apparent target motion that started at the position of fixation (with no position step) and b) experimental trials in which apparent target velocity changed after pursuit initiation. For the experimental trials, the initial target motion had a t of 4 ms so that stable sustained eye velocity was achieved within 400 ms after the onset of target motion. At 480 ms after the onset of target motion, the velocity of apparent target motion increased abruptly without any step of target position and, for most trials, t was also changed. Control trials used the same range of t as did experimental trials. Thus the single target velocity step of control trials and the second target velocity step of experimental trials produce nearly identical retinal image motions. In both, the target velocity step occurred at a time when the target image had been nearly stationary on the retina with a t of 4 ms. In both, the step produced a moving retinal image with a given apparent velocity, t, and x. Due to the lack of target position step, saccades before the end of the rising phase of pursuit were common for these experiments, although considerable presaccadic pursuit was nonetheless seen. A modification of this experiment was used to study sustained eye velocity during pursuit maintenance. For this modification only, a step of apparent target velocity at a given t was followed 480 ms later by a second step of the same size, with t held constant after the first step.
	5
	Experiments in which t was increased during the maintenance of pursuit. The goal of these experiments was to study the effect of t on pursuit maintenance after eye velocity had reached target velocity. Pursuit was evoked with steps of apparent target velocity. In experimental trials, t was initially 4 ms but increased to a larger value after stable tracking had been achieved. In control trials, t was set to the same value when the target first began to move.

Data acquisition

Experiments were controlled and data were acquired by computer programs running on a UNIX workstation and a Pentium PC. The workstation provided a graphical user interface for the design and control of the experiment, and the PC acted as a data-server and streamed the data over the local area network for storage on the UNIX file system. We obtained voltages proportional to eye velocity by analog differentiation of the eye position outputs from the search coil electronics (DC-25 Hz, 20 dB/decade), and we sampled voltages proportional to horizontal and vertical eye position and eye velocity at rates of 1,000 samples/s per channel. In each file, we also recorded a series of codes to indicate the target motions we commanded, and we used these codes in the data analysis program to reconstruct horizontal and vertical target position and velocity.

Data analysis for the initiation of pursuit

Pursuit initiation was analyzed for experiment types 1) through 4) above. Eye velocity and position traces were initially viewed on a computer monitor and screened according to criteria that depended on the exact analysis to be done. The changes in pursuit initiation produced by apparent motion are illustrated using averages of the eye velocity response, often with eye velocity traces from individual trials superimposed. Our methods of averaging are described in more detail in a later section. Further quantification of the changes in pursuit initiation depended on the type of experiment and the prevalence of early saccades. For experiments of type 1), the great majority of saccades were delayed until after the initiation of pursuit was over. This afforded the opportunity to observe the effects of apparent motion on both peak initial eye acceleration and the latency of initial eye acceleration. For this analysis only, we smoothed the individual eye velocity traces by convolving them with a Gaussian having a standard deviation of 20 ms. For each trial we then differentiated, measured the peak eye acceleration, and estimated a value that we call "acceleration latency": the time when eye acceleration reached 63% of its peak value. For the vigorous eye accelerations evoked by fast target velocities, measurements made using the 63% criterion were typically slightly more robust than similar measurement using the time-to-peak eye acceleration. In practice, we were interested in changes in latency, and these differed only slightly whether calculated using the peak of eye acceleration, or using the 63% point. In one experiment, when target velocity was 3°/s, we did in fact use the time-to-peak eye acceleration to calculate latency, as this measure was more robust in the presence of a low signal-to-noise ratio. We chose not to use the time of the actual onset of pursuit (when initial eye acceleration first began) as a dependent variable. Estimates of the actual onset of pursuit can be made reliably by human observers for target motions that evoke sufficiently crisp initiation of pursuit that eye velocity quickly exceeds measurement noise. However, human observers cannot make such reliable estimates for low target velocities or for parameters of apparent motion that evoke lower initial pursuit eye accelerations. Numerical algorithms suffer related drawbacks. Moreover, as we shall see, a consistent effect of apparent motion was to increase the latency to normal acceleration. Effects on absolute latency were less consistent.

For all other experiments concerning the initiation of pursuit (2-4 above), saccades during the rising phase of pursuit were common. It was therefore impossible to make the acceleration based measurements, as peak acceleration was potentially obscured by a saccade. However, at least when t was small, and deficits absent to moderate, most early saccades occurred near the end of the rising phase of pursuit, at least 50-100 ms after initiation. We therefore chose to assess initiation by measuring eye velocity at a fixed time, after normal pursuit onset but before saccades occurred. We defined the "normal" time of pursuit onset using the average eye velocity when t was 4 ms. For all trial types we then measured eye velocity at a fixed time following the normal onset. This method is illustrated in Fig. 6. The measurement time was selected to fall during the rising phase of pursuit, as close as possible to the end of the open loop interval, and before the time of most saccades. The exact time ranged from 50 to 70 ms and depended on the duration of the open loop interval of the monkey being studied. Minor errors in estimating either the duration of the open loop interval or the time of the onset of pursuit would not have had a major impact on this analysis, as the same measurement time was used for all values of t at a given apparent target velocity.

We discussed above three scalar measures of pursuit initiation: peak acceleration, acceleration latency, and eye velocity at a fixed time. When a given measure was made, it was made for each individual trial of a given type. Averages and standard errors were then calculated. For experiments of type 3) above, responses to target velocities below approximately 4°/s suffered from a signal-to-noise problem. Large numbers of trials (at least 20-50) were needed to make accurate measurements of eye velocity at a fixed time. As these experiments employed a range of velocities and many trial types, it was often not possible to collect more than 20 trials of each type (some of which would have to be excluded because of early saccades, as described below). Measurements at low velocities were therefore sometimes quite variable, preventing us from analyzing pursuit for target speeds slower than 2°/s.

In examining the initiation of pursuit, we were primarily interested in changes in the pursuit trajectory, rather than in the absolute values of latency, eye velocity, or eye acceleration. Thus the three measures described above are expressed in normalized form. Peak acceleration is expressed as the proportion of the average peak acceleration seen for the same target velocity when t was 4 ms. The eye velocity measure is normalized by the average eye velocity at the same fixed time when t was 4 ms. Acceleration latency is expressed as the time shift relative to the average acceleration latency measured when t was 4 ms. An assumption of much of our analysis is that a t of 4 ms produces normal pursuit, and that the pursuit response to such targets would not have changed had we been able to decrease the temporal separation further. This appears likely for two reasons. First, with the exception of the highest apparent target velocities (32-45°/s), pursuit performance was not altered by doubling the temporal separation to 8 ms. For the highest target velocity of 45°/s, a t of 4 ms is probably only just acceptable, as doubling t to 8 ms does produce a small deficit. Second, in some later experiments, we were able to test performance at a t of 2 ms, revealing that it was identical to performance when t was 4 ms, even for target motion at 45°/s.

For all analyses, the onset of target motion was defined to be coincident with the first flash of the tracking target. However, no directional information is available until after the second flash. It might therefore appear that the onset of target motion should be defined as the time of the second flash, and that effects of varying t should be assessed after aligning the responses at this time. However, a simple example illustrates how aligning the data on the second flash would introduce artifacts. At many target velocities, pursuit initiation was identical when t was 4 and 16 ms. If we had aligned these responses on the second flash by shifting the response 12 ms left when t was 16 ms, then we would have found that pursuit initiation was earlier when t was 16 ms than when t was 4 ms. We thus opted not to shift the timing of the responses, even though it is to be expected that initiation deficits at large values of t will be due at least partially to the delay in motion information until after the second flash.

Exclusion of trials with early saccades for analysis of the initiation of pursuit

In all analyses of pursuit initiation, some trials inevitably contained saccades that made the chosen measurement impossible. The analysis of acceleration described above was employed when saccades were rarely observed during the rising phase. However, the occasional saccade still fell within the rising phase. Similarly, the analysis of eye velocity at a fixed time was occasionally confounded by a saccade at or before that time. In such cases the trial was typically excluded from analysis. A sole exception was made in the analysis of acceleration. Some longer values of t produced initiation so delayed and slow that there were often saccades during the rising phase. Such trials were included (after interpolation of saccades, see next section) so long as saccades were delayed by at least 400 ms following target motion onset. To the degree that linear interpolation of saccades is imperfect, measurements of the precise size of large initiation deficits will be imperfect.

Trials with saccades before or during the measurement interval were excluded not only because saccades obscure pursuit eye velocity, but also because saccades are known to enhance subsequent pursuit (Lisberger 1998). If we had included measures made after the first saccade in our analyses of the initiation of pursuit, then postsaccadic enhancement of pursuit might have created effects that resulted indirectly from the relationship between different targets and the latency of the first saccade. However, exclusion of trials with early saccades raises the concern that early saccades occurred primarily when pursuit was deficient, and that the exclusion of trials with early saccades might therefore reduce the visibility of deficits. We spot-checked a handful of cases in which early saccades were common, comparing presaccadic pursuit when saccades were early in initiation to that when saccades were late. The magnitude of presaccadic eye acceleration was uninfluenced by the timing of subsequent saccades, and no consistent or statistically significant effects were seen.

In instances when the majority of responses contained early saccades, we did not attempt to analyze the data. For experiments using a range of apparent target velocities and values of t, the leftward pursuit of two monkeys (Fi and Ka) had to be discarded because early saccades were very common at slower apparent velocities. For experiments that varied the eccentricity of the moving targets, monkeys El and Da were unable to provide sufficient usable responses. Some monkeys had very few early saccades (Mo and Na in both directions, and Ka in the rightward direction) and were particularly useful in experiments in which eccentricity could not be optimized. We realize that the prevalence and latency of early saccades in response to step-ramp targets varies among publications from different laboratories, and we attribute the delayed saccades and excellent presaccadic pursuit in many of our monkeys to the extensive experience they have with targets that could be tracked successfully with very few saccades.

Data analysis for the maintenance of pursuit

For analysis of the maintenance of pursuit, saccades were excised from each individual eye velocity trace, either by a user-supervised and verified semi-automatic algorithm or by using a cursor to point out the start and end of each rapid deflection of eye velocity. Each rapid deflection was replaced with a line segment that connected the eye velocities before and after the excision. Eye velocity traces then were aligned on the onset of target motion, averaged, and filtered with a 25-Hz digital filter. This cutoff frequency reduced noise with no noticeable effects on the basic trajectory of either the initiation or maintenance of pursuit. For the maintenance of pursuit, our main documentation of the effects of changing the parameters of apparent motion consists of averages of eye velocity as a function of time. However, we will also show that average eye velocity traces are representative of single trial performance during both the initiation and maintenance of pursuit.

The analysis of pursuit maintenance necessarily includes epochs of pursuit that contain saccades. Nearly every pursuit response contained at least one saccade during maintenance. Experimental manipulations that impair pursuit maintenance further increase the prevalence of saccades, both in prior studies (Dursteler and Wurtz 1988; Dursteler et al. 1987) and in our data. It was thus necessary to analyze pursuit in a way that preserved as best as possible the eye velocity component produced by the pursuit system, but ignored the eye velocity component produced by the saccadic system. Inspection of our data showed relatively little change in smooth eye velocity before and after saccades during the maintenance of pursuit, implying that linear interpolation across the excised saccadic eye velocity is valid during the maintenance of pursuit. Saccades sometimes facilitated eye velocity during maintenance, but this effect was small. Another workable method is to excise each saccade, but to treat the missing time points as missing data during averaging. This approach essentially replaces each saccade with averaged data from other trials that do not have a saccade at that time. This approach only appears to avoid the necessity of interpolation. The replacement data may or may not be a good estimate of the saccade-obscured pursuit for that particular trial. Averages of excised data are particularly unlikely to provide a good estimate of the excised pursuit if maintained pursuit eye velocity varies from trial to trial, as was often the case when maintenance was impaired. In fact, both methods in practice provide very similar results during maintenance. Still, the method of saccade replacement by linear interpolation seemed better suited to our purposes. It should be noted that the maintenance deficits we observe below are large and could be neither produced nor obscured by any reasonable method of dealing with saccades.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Figure 2 shows a typical pursuit response for a target that moved with an apparent velocity of 22°/s and a t of 16 ms. Although the stimulus consisted of sequential flashes of a stationary target at the times indicated by dots, both the eye position and velocity profiles appear normal (e.g., Lisberger and Westbrook 1985). Pursuit began about 100 ms after the onset of target motion: the eye accelerated rapidly toward target velocity, and maintained eye velocity settled near target velocity with only small fluctuations. The first saccade (arrows on the eye position and velocity traces) occurred more than 200 ms after the initiation of pursuit, after the end of the initial rising phase.

View larger version (17K): [in this window] [in a new window]   Fig. 2. Single trial record showing a representative response to target motion at an apparent velocity of 22°/s, with a t of 16 ms. The top and bottom pairs of traces superimpose target (T) and eye (E) velocity and position, respectively. The dots on the target position trace indicate the time and position of each flash of the apparent motion target. The arrow on the eye position trace points out a saccade. The arrow on the eye velocity trace points out the (truncated) rapid upward deflection caused by the saccade. The traces begin 100 ms before the step-ramp of target motion, and about 1,000 ms after the onset of the trial. Upward deflections of the traces indicate rightward motion.

Pursuit initiation shows changes with increasing flash separation

In the first part of the paper, we analyze deficits in the presaccadic initiation of pursuit. In so doing, we explicitly avoid showing examples of deficits in the maintenance of pursuit, which are analyzed in the second part of the paper. Apparent motion had effects of three types on pursuit initiation: 1) increases in the latency to peak eye acceleration, 2) decreases in peak eye acceleration, and 3) unexpected increases in peak eye acceleration. The left column of Fig. 3 illustrates an effect of the first type. Figure 3A shows 10 single trial responses (thin traces) of monkey Ka to target motion with an apparent velocity of 16°/s and t of 4 ms. These traces are superimposed on the average response for all trials of this type (bold trace). Figure 3B shows a similar plot for target motion at the same apparent velocity but with a (longer) t of 32 ms. The average responses in Fig. 3, A and B, are similar in that both exhibit crisp initial eye acceleration, a small overshoot of target velocity, and a steady-state gain of near unity. Comparison of the averaged and individual traces shows that the individual traces are well represented by the averages. Superposition of the two averages of eye velocity (Fig. 3C) reveals that peak initial eye acceleration was delayed when t was 32 ms, although the magnitude of peak eye acceleration appears similar. Note that the latency to the onset of pursuit appears little affected: it is the latency to normal eye acceleration that increased. Subsequent figures show examples where the onset of pursuit was also delayed. Effects of apparent motion on the latency of the onset of pursuit were generally less consistent than the effects on the latency to peak eye acceleration. We term this latter measure "acceleration latency."

View larger version (31K): [in this window] [in a new window]   Fig. 3. Effect of varying t on the time course of the initiation of pursuit in one monkey. In A, B, D, and E, the fine and bold traces show 10 subsequent individual responses and averages of all 17-20 responses, respectively. A: responses to apparent target velocity of 16°/s when t was 4 ms. B: responses to apparent target velocity of 16°/s when t was 32 ms. C: the average responses from A and B are shown superimposed for comparison. Numbers next to each trace indicate the value of t used to obtain that average. D: responses to apparent target velocity of 32°/s when t was 4 ms. E: responses to apparent target velocity of 32°/s when t was 48 ms. F: the average responses from D and E are shown superimposed for comparison, along with the average response when t was 24 ms. All traces begin at the onset of target motion. Traces for individual responses are interrupted during saccades. Both target motion and the pursuit response continued for 500-1,000 ms after the portion of the response shown. These examples were drawn from experiments using multiple target velocities in monkey Ka, and not from the experiments shown in Figs. 4 or 5. Although flash separation is indicated in terms of t, x and t change together for target motion at a constant speed.

In addition to producing increases in the acceleration latency, increases in t often produced decreases in peak eye acceleration. For example, Fig. 3D shows responses of monkey Ka to target motion at an apparent velocity of 32°/s and t of 4 ms. Figure 3E shows a similar plot for data obtained when t was increased to 48 ms. Superposition of the average eye velocity traces for different values of t reveals a clear progression of deficits (Fig. 3F). Increasing t from 4 to 24 ms caused an increase in acceleration latency accompanied by a small decrement in initial eye acceleration. A further increase of t to 48 ms (dashed trace) caused a larger increase in acceleration latency and a clear decrement in initial eye acceleration. For all three values of t, eye velocity eventually reached a sustained value that was close to target velocity. Note in Fig. 3, D and E, that the averages made after linear interpolation across excised saccades provide a reasonable estimate of pursuit eye velocity during the period obscured by the saccades. Of course, there is no way of directly observing the underlying pursuit eye velocity during this period. Therefore all subsequent quantitative analysis of pursuit initiation is limited to time periods that were saccade free.

Analysis over a finer grain of values for t revealed that as t was increased, initial eye acceleration at first increased and began to decrease only for still larger values of t. These effects are illustrated in Fig. 4 using averages of eye velocity and acceleration. For the experiment summarized in Fig. 4A, an increase in t from 4 ms (bold traces) to 32 ms (fine traces) caused an increase both in acceleration latency and in peak eye acceleration. Further increases in t to 48 ms (dashed traces) caused the expected decrease in peak eye acceleration. For the experiment summarized in Fig. 4B, peak eye acceleration increased as t was increased from 4 to 16 ms. Peak eye acceleration remained above normal at a t of 20 ms and was reduced when t was 32 ms. The latency to peak acceleration increased when t was 20 ms or larger.

View larger version (19K): [in this window] [in a new window]   Fig. 4. Effect of varying t on the time course of average eye velocity and acceleration. Top and bottom groups of superimposed traces show average eye velocity and acceleration for multiple values of t. A: responses of monkey Ka to an apparent target velocity of 16°/s. Numbers next to the eye velocity traces indicate the value of t. Data were taken from an experiment using a range of velocities. B: responses of monkey Na to an apparent target velocity of 18°/s. Data were taken from an experiment using only one target velocity. For the data shown in both A and B, saccades occurred well after the peak of eye acceleration except for the longest values of t when they occurred just following the peak. Traces begin at the onset of target motion.

The increases in peak eye acceleration were not due to any effects of saccades, as all the above described data were collected under conditions that produced few saccades during the initiation of pursuit, and rare trials with saccades before the peak of acceleration were excluded from the analysis. Neither do the increases in peak eye acceleration result from any compensation for the longer latency of pursuit. This explanation assumes the pursuit system knows it is "behind," and compensates to "catch up." This is unlikely, as the increase in acceleration was regularly observed within the open loop interval (60-80 ms), before visual feedback could have any impact. Further, the increase in acceleration cannot result from compensation for increased latency, as it occurred even when pursuit initiation was not delayed (e.g., Fig. 4B and Fig. 5, monkeys Mo and Na). We therefore postulate that the increase in initial eye acceleration results because the relevant flash separations produce a larger than normal image velocity signal. This explanation is developed further in the discussion.

View larger version (25K): [in this window] [in a new window]   Fig. 5. Separate effects of varying t on peak eye acceleration and acceleration latency for 4 monkeys. , peak eye acceleration; , acceleration latency as a function of t. Apparent target velocity was 18°/s for monkeys Mo, Na, and Ka and 16°/s for monkey El. Acceleration was normalized by the average value when t was 4 ms and is plotted relative to the left-hand vertical axis. Latency is shown as the time shift from the average value when t was 4 ms and is plotted against the right-hand vertical axis. Values below the dashed line indicate decreases in acceleration and increases in latency. Error bars show the standard error of the mean and are omitted when smaller than the symbol. Asterisks indicate significant changes from the values at 4 ms (2-tailed t-test, P < 0.05). Graphs for monkeys Mo, Na, and Ka show responses to rightward target motion taken from experiments using a single apparent target velocity. Both directions are shown for monkey El, who exhibited an exceptional pattern of deficits in his rightward pursuit only.

As t increased, changes in acceleration latency and peak eye acceleration followed different trajectories. We measured peak eye acceleration and the acceleration latency for each individual trial, as described in METHODS. The graphs in Fig. 5 compare the progression of changes in these two measures as a function of t. Target velocity is held constant within each graph. Data are shown for four monkeys. Average peak eye acceleration () is plotted as a fraction of that obtained when t was 4 ms. Average acceleration latency () is plotted as the time shift from when t was 4 ms. Sign conventions were chosen so that the horizontal dashed line shows normal performance and deficits are plotted as decreases on either y-axis. In the three examples in the left column, latency began to increase when t exceeded 16 ms and increased progressively as a function of t. Peak eye acceleration first increased, starting with values of t as low as 12 ms, and then declined below normal only for relatively large values of t. Statistically significant latency increases, peak acceleration increases, and peak acceleration decreases were observed in the experiments using Mo, Na, and Ka. The responses of monkey El are discussed below.

The three experiments shown in the left column of Fig. 5 were designed to reveal the typically small increase in eye acceleration that occurs over a narrow range of flash separations. These experiments also illustrate a more general finding. As t was increased, deficits in acceleration latency were produced prior to the production of deficits in the magnitude of eye acceleration (although not necessarily before the production of increases in eye acceleration). For the plots in the left column, the open symbols denoting acceleration latency are always below the filled symbols denoting peak acceleration. This pattern was consistently observed for all experiments and all monkeys, with a single exception, illustrated in the bottom right panel. For rightward moving targets, monkey El showed the inverse pattern: as t increased, eye acceleration was significantly reduced at values of t that did not cause any increase in acceleration latency. We do not know why the changes observed in the rightward pursuit of monkey El are so atypical. However, the rightward pursuit of monkey El was unusual in a number of other respects and had an onset latency of 130 ms, nearly twice that of most monkeys and of monkey El's own leftward pursuit. The leftward pursuit of monkey El shows the more typical pattern: deficits are observed in acceleration latency before any deficits are observed in peak eye acceleration. For the leftward pursuit of monkey El, the lack of statistically significant increases or decreases in eye acceleration were probably due to an insufficient number of trials and to the limited range of values of t employed, as both effects were observed in other experiments using the same monkey (data not shown).

Spatial and temporal limits on the initiation of pursuit

The above-described results reveal that apparent motion causes consistent deficits in pursuit, but do not reveal the cause of the deficits. At a given target velocity, t and x increase together. To ask whether the spatial or temporal separation between flashes is the limiting factor, we observed the effect of a given t at multiple target velocities. The same t is associated with large values of x at high velocities and small values of x at low velocities. Figure 6 shows the time course of average eye velocity during the initiation of pursuit at three apparent target velocities and three values of t. For a target speed of 32°/s (Fig. 6A), deficits in the initiation of pursuit were present at values of t as low as 16 ms and became severe when t was increased to 32 ms. As target speed was lowered, the deficit associated with each value of t was reduced. For a target speed of 16°/s (Fig. 6B), a deficit was visible only when t was 32 ms (dashed trace). For a target speed of 8°/s (Fig. 6C), the deficit was mild even when t was 32 ms. That the deficits associated with a given t are diminished as target velocity decreases indicates that they are related to the decreasing spatial separation.

View larger version (13K): [in this window] [in a new window]   Fig. 6. Average eye velocity traces showing how the effect of varying t depends on the apparent target velocity. Apparent target velocities were 32°/s (A), 16°/s (B), and 8°/s (C). The different trace types show responses for different values of t: bold, 4 ms; fine, 16 ms; short dashes, 32 ms. Traces begin at the onset of target motion. To allow comparison of deficits, responses are scaled relative to the target velocity that evoked them. The vertical dashed line was placed 50 ms after the onset of pursuit when t was 4 ms and illustrates how we selected a measurement time that was used to extract the eye velocity measure used in later figures. Data were obtained from monkey Mo in an experiment that used only 3 target velocities. Each average was constructed from at least 45 individual traces.

These effects are quantified in Fig. 7, which shows the effect of target speed on the magnitude of deficits in the initiation of pursuit for two values of t in three monkeys. In these experiments, it was not possible to optimize all trial types so as to minimize early saccades while maintaining the same starting eccentricity across velocities (see METHODS). As a result, peak eye acceleration often was obscured by saccades, especially for flash separations that produced increases in latency. To circumvent these problems, we measured average eye velocity at a fixed presaccadic time during the rising phase of pursuit (vertical dashed line in Fig. 6) and normalized by the average eye velocity evoked at the same time, by the same target velocity, when t was 4 ms. Normalized eye velocities less than one indicate initiation deficits. This metric does confound the effects of increases in acceleration latency and decreases in eye acceleration and indicates only the degree to which pursuit initiation is normal or abnormal without indicating the nature of the underlying deficit. However, small to moderate decreases in normalized eye velocity were caused primarily by latency deficits, as these appeared first.

View larger version (21K): [in this window] [in a new window]   Fig. 7. Effect of varying apparent target velocity on the initiation of pursuit at 2 values of t. The y-axis plots normalized average eye velocity measured 50 ms after the initiation of normal pursuit. The time of initiation of normal pursuit was measured when t was 4 ms and was measured separately for each apparent velocity. The average eye velocity for a given t is normalized by the average eye velocity for normal pursuit; i.e., when t was 4 ms. The horizontal dashed line shows a normalized eye velocity of one, which would indicate that eye velocity was the same as when t was 4 ms. Values below the dashed line indicate deficits. Open and filled symbols show responses when t was 16 and 64 ms. Different symbol shapes show data for monkeys Mo (triangles), Na (squares), and Ka (circles). Error bars show the standard error of the mean. Overlapping error bars have been suppressed.

Inspection of the data in Fig. 7 reveals both spatial and temporal limits on the presaccadic initiation of pursuit. When t was 16 ms (open symbols), eye velocity was normal for target speeds up to 12-16°/s and then declined steeply. Because t was fixed at 16 ms, the deficits at higher target speeds must be due to an excessive x. In contrast, when t was 64 ms (filled symbols), eye velocity was not normal even for the lowest target speeds. For such slow target speeds, the values of x associated with a t of 64 ms were sufficiently small to have evoked normal pursuit initiation when t was 16 ms. For example, x was identical when t was 64 ms at 2°/s and when t was 16 ms at 8°/s. Yet eye velocity is normal for the latter parameters and about half normal for the former. We therefore argue that the deficit in the former case cannot be due to x and must be due to the fact that t was 64 ms. In summary, although in all figures we express the flash separation in terms of t, the temporal separation is the limiting factor only for slow target velocities. For faster target velocities, deficits are actually produced by the associated x.

For values of t < 32 ms, the disappearance of deficits when the target is slowed rules out a tempting explanation for these deficits: that they result from the delay in motion information until after the second flash. This explanation is unlikely for another reason. Latency deficits are often too large to be explained by the separation of the first two flashes. In Fig. 6B, for example, a 16-ms increase in t, from 16 to 32 ms, delayed the initiation of pursuit by nearly 40 ms. In each of the graphs in the left column of Fig. 5, the rate of increase in acceleration latency at high values of t exceeds the rate of increase in t.

To visualize simultaneously the spatial and temporal limits governing pursuit initiation, we measured eye velocity during the initiation of pursuit for a range of combinations of t and x, where apparent velocity is x/t. The symbols in Fig. 8 plot normalized eye velocity as a function of t and x. The magnitude of initial eye velocity is indicated by the size of the symbol, with filled symbols denoting eye velocities within 90% of normal. Although the plots from different monkeys are quantitatively different, there is a broad qualitative pattern. In each graph, the filled symbols denoting normal or nearly normal pursuit cluster in the bottom left corner. The range of parameters that evoked nearly normal eye velocities can be exited by traveling either vertically or horizontally, indicating that normal initiation is bounded by both a spatial and a temporal limit. Traveling vertically within a graph keeps t constant, as in Fig. 7, while traveling horizontally keeps x constant. Target velocity remains constant along the diagonal lines, at values indicated by the numbers along the top and right sides of each graph. All four monkeys tested with target speeds up to 45°/s showed a limit on pursuit initiation expressed primarily in terms of x (Fig. 8, C-F). At lower target velocities, pursuit faltered before this spatial limit was reached, indicating that pursuit initiation is also limited by t. The temporal limit is particularly clear in Fig. 8B. Defined as the point at which eye velocity falls below 90% of normal, the spatial limit lay between 0.2 and 0.4° for five monkeys, and between 0.5 and 1° for the sixth (Fi). The temporal limit lay between 32 and 64 ms. The plots are somewhat noisy, especially at low target velocities, because of the large number of trial types used in these experiments.

View larger version (37K): [in this window] [in a new window]   Fig. 8. Temporal and spatial limits of apparent motion for the initiation of normal pursuit. Each graph contains one symbol for each combination of temporal separation (t) and spatial separation (x). The symbol type expresses mean eye velocity as a percentage of that evoked by targets of the same apparent velocity but with a t of 4 ms: large solid circles, eye velocity within 90% of normal; large open circles, eye velocity within 80-90% of normal; progressively smaller circles indicate progressively slower eye velocities as defined by the key in B. The diagonal lines correspond to fixed values of apparent target velocity, indicated by the numbers along the top and right edges of each panel. A and B: experiments designed to tile a large range of possible values of t and x (monkeys Da and Fi). C-F: experiments using a closer spacing of values of t and x over a more limited range, to allow a more complete sampling of the range where pursuit initiation becomes impaired (monkeys El, Mo, Na, and Ka). Each point is based on the mean eye velocity in a 20-ms interval centered 70 ms after the initiation of normal pursuit for monkeys Da, Fi, and El, and centered 50 ms after the initiation of pursuit for monkeys Mo, Na, and Ka.

Deficits observed when x becomes too large are assumed to arise because the spatial integration ability of neural motion sensors is exceeded. Are the deficits observed when t becomes too large related to the temporal integration time of neural motion sensors? We concluded above that deficits seen when t was 32 ms or less were not due to the delay in motion information until the second flash, as they disappeared when the target was slowed. However, this conclusion does not apply to the deficits observed when t is large, which persist at slow target velocities. In the extreme, delays in the arrival of motion information obviously must contribute: a monkey with a pursuit latency of 80 ms could not initiate normal pursuit when t is 96 ms. Still, there is some reason to believe that initiation deficits seen when t is large result in part from a failure of neural motion sensors. Figure 9 plots peak eye acceleration and acceleration latency as a function of t for monkey Ka at a target velocity of 3°/s. Little or no deficit is observed when t is 32 ms, while a large latency deficit is observed when t is 64 ms. Latency increased 55 ms, while t increased only 32 ms. The deficit is 23 ms larger than expected if the latency increase were due solely to the additional 32-ms delay between the first and second flash. As