January 2006
Volume 47, Issue 1
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Eye Movements, Strabismus, Amblyopia and Neuro-ophthalmology  |   January 2006
Oculomotor Tracking Strategy in Normal Subjects with and without Simulated Scotoma
Author Affiliations
  • Peter E. Pidcoe
    From the Departments of Physical Therapy and
  • Paul A. Wetzel
    Bioengineering, Virginia Commonwealth University, Richmond, Virginia.
Investigative Ophthalmology & Visual Science January 2006, Vol.47, 169-178. doi:10.1167/iovs.04-0564
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      Peter E. Pidcoe, Paul A. Wetzel; Oculomotor Tracking Strategy in Normal Subjects with and without Simulated Scotoma. Invest. Ophthalmol. Vis. Sci. 2006;47(1):169-178. doi: 10.1167/iovs.04-0564.

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      © ARVO (1962-2015); The Authors (2016-present)

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Abstract

purpose. Experiments were conducted on five subjects with no visual impairment to assess tracking strategy differences in subjects with and without a simulated central scotoma.

methods. Subjects were asked to visually track horizontally moving periodic and nonperiodic sinusoidal stimuli through a ±5° range. Scotoma simulation was achieved electronically with a closed-loop feedback system using horizontal eye movement measurements from a monocular limbus eye tracker updated at a rate of 500 Hz. The scotoma was centrally located and had defined horizontal half widths of 1, 2, and 3°. Vertical eye position measurements from a video-based dark-pupil tracker were used to identify and remove trials in which extreme vertical eye position deviations reduced the effectiveness of the simulation.

results. All subjects developed a preferred retinal locus (PRL) in the left visual field and demonstrated a tendency for saccadic redirection to this area. Saccadic endpoints into the PRL outnumbered foveally directed saccades by a factor of 2:1. The PRL was located outside the compromised central vision region, typically near the edge of the scotoma boundary, for all subjects except one. This subject had a PRL within the simulated scotoma under two conditions, but the percentage of total time spent at the “compromised” PRL was less than for other subjects.

conclusions. Subjects with no visual impairment confronted with a central scotoma develop a preferred retinal locus to replace the nonfunctional fovea and appear to suppress normal refoveating saccadic behavior in favor of this location.

When asked to attend to a visual target, subjects who are visually unimpaired will typically foveate that target to use the area of highest retinal acuity 1 . Patients with central (or macular) scotoma, however, would lose sight of the target if they used the same strategy and instead use peripheral retina at the expense of acuity and contrast sensitivity. This eccentric viewing strategy can be accomplished by foveally aiming the point of gaze with an intentional offset, directing the image of interest onto functional peripheral retina, 2 or by developing a new preferred retinal location to direct the point of gaze. 3 4 5 The result is eccentric viewing, redirecting an image from the compromised fovea to an area of functioning peripheral retina. Patients with central scotoma have been observed to develop an eccentric area of fixation, commonly referred to as a preferred retinal locus (PRL). 6 Patients often have the ability to perform smooth pursuit and saccadic movements using this retinal location as a reference. 5 7 8  
Initial research on central scotoma assumed that most patients developed one well-defined PRL. 3 9 More recent work suggests that some patients develop multiple preferred retinal loci. 2 These preferred retinal loci have been identified as task specific based on target size 10 and illumination. 11 Some researchers are attempting to exploit this oculomotor behavior to train strategies and improve reading rates in patients with macular degeneration. 12 13  
Macular degeneration or scotoma results in a reduction in visual performance during reading and tracking tasks in both patients with a real scotoma and healthy subjects with a simulated scotoma. 14 15 16 17 Reading rates have been shown to decrease as a function of increased scotoma size. 9 18 The reasons for this include the forced use of the peripheral retina and the inherent loss of acuity this entails compared to foveal vision. When the sizes of peripherally positioned targets are magnified to compensate for lower peripheral acuity, target recognition improves. 19 Similarly, magnified image experiments have been shown to improve reading rate performance in subjects with macular scotomas. 3 These reading experiments also suggest the development and use of a nonfoveal retinal location during the task. In fixation experiments, the use of nonfoveal retinal locations or preferred retinal loci has also been observed in patients with bilateral scotomas. 20  
Also contributing to a reduction in visual performance in patients with macular scotoma is inadequate eye movement control. Saccadic eye movements are responsible for correcting positional errors in the location of targets on the retina relative to the fovea. 1 If this system remains unchanged in patients with macular scotoma, then the execution of foveating saccades would severely reduce the ability of these subjects to accurately track a target. Such movements would result in target disappearance. Previous fixation studies have suggested that the saccadic system does adapt to deficits in the oculomotor environment. Reports of consistent target imaging on the same retinal area using refixation saccades, and in some cases the complete absence of foveating saccades, illustrate this fact. 20 The refixation saccades or saccades that reorient the image to the PRL do not acquire the properties of foveating saccades. They continue to have the latency and dynamic characteristics of nonfoveating saccades, again suggesting that patients with macular scotoma suppress the foveating saccade mechanism. 5 The absence of a centripetal drift tendency with eccentric fixation has also been reported in patients with scotoma and healthy subjects with simulated scotoma. 2  
A scotoma can be simulated in subjects who are visually unimpaired by using eye position measurements as feedback to control the on/off state of a displayed target. This technique was used to generate a horizontally limited central scotoma in subjects with normal vision. The eye position responses to periodic and nonperiodic horizontally moving targets were recorded and used to assess tracking strategy differences for scotoma sizes of 0°, ±1°, ±2°, and ±3°. Preferred retinal lociwere identified based on “constant error” smooth pursuit tracking responses. Qualitative and quantitative descriptions of tracking responses for horizontal periodic and nonperiodic stimuli are presented. The simulation of a retinal scotoma in subjects with normal vision allows visual impairment to be analyzed without the additional complications usually associated with retinal disease. 
Methods
Subjects
This research was performed with adherence to the Declaration of Helsinki. Five subjects with no visual impairment (3 males and 2 females) were asked to track periodic and nonperiodic horizontal target movements. Subjects ranged in age from 28 to 37, with a mean age of 33. They had no known visual abnormalities and were in good health. Subjects had visual acuity of 20/20 corrected, measured via Snellen chart. 
Setup and Instrumentation
During each experimental session, the subject was seated comfortably on a chair at the end of an optics bench. The subject’s head was stabilized with a padded rigid frame that provided support at the forehead and chin. A custom bite bar was prepared with dental impression wax molded onto a metal mounting plate. The bite bar was then fixed into the head-supporting framework, providing additional head stability. The stimulus target was presented on a display 100 cm in front of the subject. 
Subjects were instructed to visually track the displayed target without head movement. A limbus eye tracker was used to monitor the horizontal movement of the left eye during the binocular tracking tasks. 21 The limbus eye tracker was custom built and used a central infrared source and a pair of infrared-sensitive photodiodes. This system was tested and found to provide a linear horizontal tracking range of ±15° with a resolution of 0.1°. Analog data from the limbus tracker were low-pass filtered using an active low-pass filter with a cutoff frequency of 100 Hz (Model 3362; Krohn-Hite, Brockton, MA) then sampled at 500 samples/s using a 12-bit resolution analog-to-digital converter board (DT-2801A; Data Translation Inc., Marlboro, MA). Position feedback from the limbus tracker allowed a horizontally limited computer-generated scotoma to be applied to subjects otherwise visually intact. This was accomplished by continuously computing the error between horizontal eye position and target position. If this error was less than the desired scotoma size, the target was extinguished. The target would reappear only when outside the defined scotoma boundaries. The display phosphor was P48 (Xytron International, Makati City, Philippines) with a time constant of 0.12 ms. Using this technique, the subjects had no positive perception of the artificially generated scotoma. 
The vertical position of the right eye was remotely measured using a video-based dark-pupil eye tracker (RK426-PC; ISCAN, Burlington, VA). The video camera of the ISCAN was positioned 19 cm in front of the eye and below the line of sight. The camera image of the eye was magnified by a +4 lens to maximize the smallest detectable change in movement. The vertical eye position measurement was digitized by the ISCAN system into one of 256 levels or 8 bits of resolution. The digitized signal was then converted back to an analog output voltage which ranged from 0 to 5 V. In this configuration, a 10° vertical eye movement produced an output change of 0.6 V. The resulting smallest detectable change in vertical eye movement was 0.32°. The ISCAN data were used in postprocessing to identify and remove trials in which horizontal position data was compromised due to excessive vertical eye movement. 
Stimulus Files and Data-Collection Paradigm
All stimulus files generated movement along a single centrally located horizontal axis. There were two basic stimulus patterns: periodic single-frequency sinusoids and a nonperiodic sum of sinusoids. The periodic sinusoids used were 0.2, 0.4, 0.6, and 0.8 Hz. The nonperiodic sum of sinusoids contained the nonharmonically related frequencies of 0.12, 0.35, 0.65, 0.8, and 1.0 Hz. Stimulus file characteristics are shown in Table 1
The stimulus files were designed to drive the target (a 0.28° × 0.28° plus sign [+]) through approximately 10° of visual angle. Peak velocities were computed by applying a first central difference algorithm to the stimulus position files:  
\[(vel_{i}{=}\ \frac{(pos_{i{+}1}{-}pos_{i{-}1})}{2{\Delta}t})\]
These increase as a function of frequency in the periodic files. The peak velocity of the nonperiodic sum of sinusoids file fell between those of the 0.6- the 0.8-Hz periodic files. All peak velocities were kept below 30°/s to promote smooth eye tracking. 22 For each stimulus frequency, there were two stimulus files, one starting to the left and one starting to the right. The directional starts were presented randomly so that the subject could not predict initial target direction. The order of the stimulus frequency presentation was also randomized. The target starting and stopping location was always at 0° of visual angle. Eye position was monitored to ensure a 0° starting position at the beginning of each data collection. For the scotoma trials, this resulted in immediate target blanking. The target would reappear only when outside the scotoma boundaries as a result of target movement or subject eye movement. Each stimulus file was 32 seconds long. During the first 30 seconds, there was a moving target. For the last 2 seconds, there was a stationary target positioned at 0°. A 15-second section of each stimulus file is presented in Figure 1
Calibration files were presented to the subjects before each stimulus file to compute the gain and offset of the limbus (feedback) system. During this process, subjects were asked to fixate a target presented successively in five discrete display locations (0°, ±5°, and ±10°). A first-order linear regression curve fit through the collected data provided gain and offset calibration values for that specific trial. In the artificial scotoma trials, each calibration was used to determine the preselected boundaries of the scotoma in the subsequent stimulus file. The subjects were instructed on the importance of remaining still, especially between the calibration- and stimulus-file target presentations. Calibration and stimulus files were presented alternately throughout the experiment. 
Data were collected in four 1-hour sessions. Each session contained 20 stimulus files, separated into four 5-file trials. Each trial used a single simulated scotoma size. The scotomas had horizontal half-widths of 0°, 1°, 2°, and 3°. Each subject completed the four sessions within a period of 2 weeks. Subjects were allowed to practice on the no-scotoma files only before data collection. 
All subjects were told that a horizontally moving visual target would be presented on the display and that they were to “track that target as accurately as possible.” Before the simulated scotoma trials, subjects were educated on the effects of scotoma. They were told what to expect visually, but were not instructed on compensatory tracking strategies. They were not encouraged to develop peripheral retinal loci, nor were they told to show a visual field preference. Preceding the simulated scotoma sessions, subjects were given an additional instruction to “keep the target on as much as possible.” The second instruction was included to avoid any interpretational biases with respect to the first instruction. Pilot experiments showed that without this second instruction, two interpretations existed. Using the first interpretation, the subject would continue to refoveate the target, causing it to disappear. Accurate tracking would cease until the target reappeared. Using the second interpretation, the subject would eccentrically view the target without active tracking. The combination of the two instructions was found to provide the most clarity. 
During the simulated scotoma sessions, the subjects were asked to constrain their vertical tracking to the display region containing the stimulus. The vertical location of the stimulus was reinforced before each stimulus pattern with the nonblanking calibration pattern. The vertical-tracking limitations were imposed in an effort to provide cleaner horizontal eye position data from the limbus system. This became important when the target blanked during the simulated scotoma condition. The ISCAN system was used to monitor vertical eye movements for postcollection analysis. 
Data Analysis
Blink Removal.
Data collected during each session were coded and stored. These data were reviewed to remove blinks or to mark “bad” segments for exclusion from further analysis. Blinks stood out in the data files as very large deviations with durations up to 250 ms. An interactive program allowed the beginning and end of each blink to be defined with two cursors. The blink was then removed and replaced with a linear fit between the two cursor locations. Most of the collected data were blink free. 
Cross Talk.
The combined 10-point vertical and horizontal calibration files provided a measure of system cross talk for the respective scotoma stimulus files that they preceded. The cross-talk calculations were performed in multiple stages. In the first stage, both vertical and horizontal gain and offset values were computed. These values were then used to compute the changes in the recorded horizontal eye position as a function of the discrete vertical positions in the calibration. A first-order regression line through these cross-talk data quantified and linearized that change, providing a cross-talk measure expressed in degrees of horizontal change per degree of vertical offset. The mean cross-talk slope for all subjects was 0.198° horizontal change per degree of vertical offset. 
A review of the vertical eye position data revealed that the subjects with normal vision maintained a constant vertical eye position throughout a perceived scotoma trial and that this position may be different from zero. The vertical data were digitally low-pass filtered, with a cutoff frequency of 10 Hz. The mean vertical eye position was then computed for each trial. Cross talk was calculated from the regression formula for the mean ± 0.32° (the resolution of the ISCAN). The largest absolute values in each pair were compared to an acceptable cross-talk value of 0.2°. If that 0.2° threshold was exceeded, the trial was considered compromised and was removed from the analysis. 
Constant Error Segments.
Data segments in which a near-constant stimulus tracking error was achieved were tabulated. These segments were termed constant error segments (CESs) and were defined as tracking segments in which a constant tracking error of ±0.2° was achieved for >300 ms. The means of the CES data were computed to quantify the subject’s preferred retinal placement of the target or PRL. Because complete calibrations were available, the horizontal offset of the PRL for each subject could be computed. 
Results
Qualitative Overview
When individuals with normal vision were confronted with the task of tracking periodic stimulus without an imposed visual impairment, their reactions were similar. Visual tracking began with a saccade or series of saccades to correct for retinal position error. Smooth pursuit of the target soon followed. Small corrective saccades were used to minimize tracking error and promote foveal tracking. A typical tracking response to a 0.2-Hz periodic stimulus is illustrated in Figure 2 . Under these no-scotoma conditions, subjects were routinely able to contain tracking error to within ±0.5° of central vision. Tracking error was computed by subtracting the eye position (response) from the target position (stimulus). Responses from the higher-frequency periodic stimuli displayed similar results. The number of corrective saccades appeared to increase with stimulus frequency, as previously reported. 23 The temporal profile of the nonperiodic response was similar to that of the periodic responses, except that the amplitude of the tracking error was greater. Corrective saccades were still present, but were larger. 
Stabilized retinal tracking with an imposed scotoma is illustrated in Figure 3 . The error signal portion of this figure depicts the subject’s attempt to stabilize the target image near the edge of the artificial scotoma. Saccades were most often used to reposition a nonvisible target in the usable peripheral field. The sawtooth-shaped error curve was present at all periodic stimulus frequencies and all artificial scotoma sizes. Similar patterns have been seen in fixation experiments with imposed scotomas. A drifting fixation point into the scotoma region caused a periodic “jerk nystagmus” to reimage the target. 2  
The error signal associated with nonperiodic stimulus tracking is illustrated in Figure 4 . It also indicates an effort by the subject to keep the target in the useable retina. The repeated sawtooth pattern evident in the periodic tracking was not present, and there was a larger percentage of target positioning within the scotoma region. This was probably the result of the unpredictable nature of the stimulus. 
All the simulated scotoma trials showed a strong tendency to track the stimulus by placing it in the left visual field. The subjects looked to the right of the target. Using this control scheme, the subject’s point of gaze would be ahead of the target in movements from left to right and would follow the target in movements from right to left. A comparison of the temporal error data for all applied scotoma sizes illustrates this trend (Fig. 5) . These results are from the 0.2-Hz periodic stimulus trials. Similar examples can be found at all stimulus frequencies. 
The left visual field preference is evident in Figure 5 . The error signal offset appears to be correlated with the size of the scotoma. Also evident in the error plots is the characteristic saccadic activity. Tracking strategies with an artificial scotoma appeared to rely heavily on peripherally directed saccades to make the stimulus target visible. The frequency and size of the peripherally directed saccades increased as a function of stimulus frequency. 
Error Histograms
Error histograms were generated for each subject from all response data (20 trials per scotoma size). These data were pooled by scotoma size and sorted into 0.5° bins. Typical results for a single subject are illustrated in Figure 6 . The peaks of the distributions center on the retinal area with the highest available acuity. This was the fovea in the no-scotoma trials and the edge of the artificial scotoma in the scotoma trials. The left visual field preference was very pronounced in these data. One subject showed a bimodal distribution when reviewing several individual trials, but this trend was suppressed when viewing pooled data results. These data also came from early trials and may have been the result of conscious experimenting by the subject to test various tracking strategies. 24 The unilateral tracking shift was the predominant trend. 
CES Histograms
Further analysis of the error data required the extraction of error segments in which a constant tracking error (±0.2° from the segment initiation) was maintained for >300 ms. The mean CES was used to determine the PRL used by each subject with each scotoma size. This was the area of the retina onto which the stimulus target was placed most frequently, conforming to the previously described accuracy requirements. This preferred location was identified based on the smooth-pursuit portion of the response signal. Saccades tended to end a constant tracking error segment, because the saccade size was generally larger than the ±0.2° constraint. A typical CES analysis histogram, representing all data from a single subject, pooled by scotoma size and sorted into 0.5° bins, is presented in Figure 7 . Note that these data are from the same responses presented in Figure 6 , but with the CES restriction imposed during histogram tabulation. 
PRL values for each subject as a function of scotoma size are presented in Table 2 . These results represent the modes of pooled CES duration data for a given subject and scotoma size. The mode was used due to the skewed nature of the histograms. Because the mode represents the peak of a histogram, it follows that the PRL associated with this point is the region of the retina most frequently used by the subject. Also indicated in Table 2is the percentage of the total stimulus presentation time in which CES segments were found. The larger the percentage, the more time the subject spent in constant error tracking, as defined above. Note that the PRL values show a consistent increase as a function of scotoma size in all but one subject (MH). Also note that the PRL locations for the ±2° and ±3° conditions for subject RC are within the scotoma boundaries, but the time spent at these locations is the least among all subjects. 
Saccadic System Analysis
Saccades were identified in the eye position data based on two criteria: eye movement velocity > 30°/s and amplitude ≥ 0.1°. These were verified via visual inspection. The mean number of saccades increased with stimulus frequency for all scotoma trials. The mean number of saccades in the nonperiodic response fell between values observed for the 0.6- and 0.8-Hz periodic stimulus responses. This is consistent with the relationship of the peak velocities in these stimulus files, and links the production of saccades to the velocity of the stimulus rather than to the stimulus frequency. 25 There was a slight decrease in the mean number of saccades for the scotoma trials at the 0.8-Hz stimulus frequency, and in the nonperiodic stimulus data when compared with the no-scotoma data. 
Saccadic endpoints were analyzed in the data from the subjects with normal vision. Two endpoint locations were of interest, the fovea and the PRL identified in the CES analysis. Each target location was given a window of ±0.5°. Saccades ending in these defined regions were tabulated, with the totals stored as a percentage of total saccades. Results are displayed in Figure 8
In the absence of a scotoma (scotoma size = 0°), the PRL corresponds to the location of the fovea. With an artificial scotoma, the total number of primary saccades decreased. This decrease was partially due to the tabulation method, since only primary saccades were counted in this analysis. Any additional saccades occurring within the area of interest were not counted. However, PRL saccades outnumbered foveating saccades by almost 2:1 in all simulated scotoma trials. 
Gain of Pursuit Analysis
The magnitudes of the stimulus and response data were computed using a Chirp z-transform method. 26 Gain was defined as the response magnitude divided by the stimulus magnitude for each stimulus frequency. Zero padding of the nonperiodic data was performed to provide magnitudes whose discrete interval fell more closely to the actual stimulus frequency of interest. 
The periodic gain results are displayed in Figure 9 . The no-scotoma data had gains of near unity at each frequency, with a slight reduction in gain as the stimulus frequency increased. The scotoma data had further reduced gains as a function of stimulus frequency, resulting in a family of curves when compared to one another. 
The nonperiodic gain data are displayed in Figure 10 . The no-scotoma data had gains below unity except at the highest-frequency components. The scotoma data again showed reduced gain and the familial trend as a function of scotoma size. However, the gain reductions noted in this family were greater than those found in the periodic results. 
Discussion
When subjects with unimpaired vision were confronted with the task of tracking stimuli with a simulated central scotoma, the normal foveating tracking strategy was replaced with an eccentric strategy. The subjects had been instructed to track the stimulus target “as accurately as possible” and to “keep the target on as much of the time as possible.” They tracked with a stabilized error signal and were often able to keep the target visible more than 90% of the time. This response is characterized by a saw-toothed stimulus-response error curve located at the simulated scotoma boundary (Figures 3 4 5) . Tracking was accomplished via the generation of peripherally directed saccades to visualize the target (generating an eccentric targeting error relative to a foveal reference), then gradual reduction of the error during smooth pursuit. When target loss occurred secondary to the target entering the scotoma region, another peripheral saccade was generated, and the process repeated. Subjects learned to eccentrically track within four 1-hour sessions with limited instruction, supporting the positive training results found with visual rehabilitation using eccentric viewing 27 28 and formal training times averaging 5 to 6 hours. 29  
The stimulus-response error curves also display the subject’s visual field preference during scotoma-based tracking. All subjects favored the left visual field when tracking with the imposed scotoma, visualizing the target by attending to the right. This is consistent with literature, 8 10 17 but may be more of a task-based preference in this case. Guez et al. 10 suggested that during reading, a PRL to the left of the scotoma border in the visual field might be beneficial, because past information may help to guide eye movements. In a dynamic tracking task, the same argument can be made. During left-to-right target movement, attending to the right of the target may provide target position and velocity information to help plan and direct eye movement to stay ahead and maintain the visual patency of the target. This is not beneficial in reading, 15 but is still an appropriate strategy for this type of visual tracking. Subject debriefing interviews indicated that this was a conscious strategy and was perceived as the easiest method of tracking. The subjects also noted that their task was more difficult during the left-to-right movement when they had to stay ahead of the target. The subjects stated that they felt the target would often catch up. During right-to-left movements, the subject’s point of gaze followed the target. Evidence of what the subjects observed is illustrated in Figure 5
In the periodic stimulus trials, peripherally directed saccades were more frequent in the left-to-right target movement, apparently triggered by the target entering the scotoma boundary. A gradual decrease in the error signal followed each peripherally directed saccade (Fig. 3) . The target appeared to be catching up to the point of gaze as both moved in the same direction. This was due, in part, to the inability of the subject to accurately match the target velocity during eccentric tracking secondary to acuity decreases. The velocity drive to the oculomotor system can come from a parafoveal stimulus, 30 but this ability progressively diminishes with increased tracking eccentricity. 31 The decrease in the error signal for right-to-left target movement is more likely associated with the predictability of the periodic stimuli, because this phenomenon did not exist in the nonperiodic stimuli. 
Pooled stimulus-response error data histograms reveal the eccentric shift in point of gaze and the visual field preference in the simulated scotoma trials (Fig. 6) . This shift was unilateral with a pronounced peak. The observed peaks were very close to the edge of the scotoma in the spared retinal region, indicating the subject’s preference for the area of useable retina with the highest visual acuity and/or for the area that produced the least amount of eccentric viewing. Eccentric viewing tends to induce in subjects a feeling of “looking past” the object they are attempting to image. 6 32 In this scotoma simulation, reducing that off-axis viewing sensation has the additional benefit of also maximizing acuity. 
Although the peak in these error distributions could be used to quantify the location of a new PRL, the PRL would be better defined if only those tracking segments were used in which constant error tracking was performed. CES tracking implies that the subject is able to track the target with a constant offset (±0.2°) for a minimum time (>300 ms). Using only CES data, a more pronounced peak in the error histograms emerges, because nonimaged, scotoma-oriented responses are removed (Fig. 7) . The deselected data include “blind tracking” segments and searching saccades that may have spanned the simulated scotoma. Blind tracking has been reported in experiments where the target was extinguished for a short time during constant-velocity tracking, and subjects were asked to continue tracking the invisible target until it reappeared. Continued smooth-pursuit tracking for a short period was found to exist, but with a compromised gain. 33 The CES analysis was used to remove any effects associated with blind tracking or gross saccadic search from the estimate of the PRL. Results of the PRL computation, presented in Table 2 , indicate a strong effort by the subjects to maintain an image of the target on the highest-acuity retina available, with the least eccentric viewing angle. 
The number of saccades observed during tracking increased as a function of stimulus frequency. 23 This increase was probably not a function of frequency, but instead a function of the associated target velocity. The velocity of the target was a function of both stimulus frequency and amplitude. This observation is supported by the results of tracking the nonperiodic stimulus. The mean number of saccades generated during nonperiodic tracking consistently fell between the mean number of saccades observed for the 0.6- and 0.8-Hz periodic stimuli, even though the nonperiodic stimulus had frequency components at 0.8 and 1.0 Hz. The peak velocity of this stimulus, however, fell between those of the 0.6- and 0.8-Hz periodic stimuli. 
With the imposed scotoma, the number of saccades did not appear to differ significantly from normal tracking except for the higher velocity stimuli, where a slight reduction in number of saccades was observed, with little difference between the imposed scotoma sizes. This may have been due to the reduction in target-on time. The average target-on time (when pooled across subjects and scotomas) fell below 70% for the three highest velocity stimuli. These data suggest that saccades are not generated as frequently when the target is not visible to the subject. 
The amplitude of the generated saccades showed an increase as a function of scotoma size. These saccades were separated into those used to refoveate the target and those used to place the target on the new PRL defined in the CES analysis (Fig. 8) . Recall that the PRL was identified based on smooth-pursuit portions of the response data. The results revealed a suppression of foveally directed saccades during the imposed scotoma trials. This was consistent with work by Whitaker et al. 5 Furthermore, saccades directing the target to the new PRL outnumbered foveally directed saccades by approximately 2:1. Evidence from fixation experiments on patients with bilateral macular disease shows a complete absence of foveating saccades and a complete re-referencing of eye movements to the PRL in some patients. 20  
The reduction in the percentage of total saccades directed toward the PRL with increasing scotoma size was a result of the PRL eccentricity itself. Previous experiments showed that fixation variability increases with retinal eccentricity. 2 The target window around the PRL was not weighted based on this eccentricity. Its boundaries were always ±0.5° of the PRL. This would result in a reduced number of saccades falling within the defined window as the PRL moved further into the periphery. 
Pursuit gain in response to no-scotoma–based tracking followed what has been reported in the literature. 34 The periodic responses had a gain of near unity, with slight gain reductions at the highest stimulus frequencies. The smooth no-scotoma response to the same periodic stimulus showed a greater reduction in gain as the stimulus frequency increased. This illustrated the effect of the saccades on the total system gain. The saccadic system appeared to add more gain as target velocities increased. Similar results have been previously reported. 23  
The scotoma-based tracking data revealed reduced gains for all periodic stimulus frequencies when compared to the no-scotoma data. The gain curves were progressively depressed as the scotoma size increased. These results are consistent with previous experiments that showed that the ability to match the velocity of the eye with a moving target degrades with increasing target eccentricity. 31  
The nonperiodic responses for the no-scotoma tracking were also similar to previous reports. 34 The composite data showed gains greater than unity at the highest-frequency components of the stimulus. This implied that the oculomotor system preferentially responded to the highest frequency present and is consistent with previous research. 23  
The results with imposed scotoma were similar to those seen in the periodic response data without scotoma. The response gain shifts downward with scotoma size, resulting in what can loosely be called a family of curves. The separation and gain reduction in the nonperiodic smooth responses was greater than that seen in the periodic smooth responses. 
Conclusions
Subjects with imposed scotoma can develop a peripherally located PRL to replace the nonfunctional fovea within 4 hours of training. The subjects in this study learned to track with an offset near the edge of the scotoma boundary and showed a left visual field preference. Foveating saccades were suppressed and replaced by saccades that placed the target in the new PRL, revealing a preference toward the identified PRL over the fovea in the simulated scotoma environment. 
 
Table 1.
 
Stimulus Position and Velocity Characteristics
Table 1.
 
Stimulus Position and Velocity Characteristics
Stimulus Frequency (Hz) Position (deg) Velocity (deg/s)
Min Max Range Min Max
0.2 −4.99 4.99 9.97 −6.79 6.79
0.4 −4.99 4.99 9.97 −13.57 13.57
0.6 −4.99 4.99 9.97 −19.92 19.92
0.8 −4.99 4.99 9.97 −26.70 26.70
Sum −4.95 4.48 9.42 −24.73 21.23
Figure 1.
 
A 15-second section of each horizontal stimulus file. All stimulus files had both a left and a right start direction.
Figure 1.
 
A 15-second section of each horizontal stimulus file. All stimulus files had both a left and a right start direction.
Figure 2.
 
Top: periodic 0.2-Hz sinusoidal stimulus (light line) and typical response (dark line) for a single subject (DH) under the normal (no-scotoma) tracking condition. Bottom: computed error signal.
Figure 2.
 
Top: periodic 0.2-Hz sinusoidal stimulus (light line) and typical response (dark line) for a single subject (DH) under the normal (no-scotoma) tracking condition. Bottom: computed error signal.
Figure 3.
 
Top: typical response (dark line) for a single subject (AK) to a 0.2-Hz periodic stimulus (light line) with ±3° artificial scotoma. Bottom: computed error signal.
Figure 3.
 
Top: typical response (dark line) for a single subject (AK) to a 0.2-Hz periodic stimulus (light line) with ±3° artificial scotoma. Bottom: computed error signal.
Figure 4.
 
Top: typical response (dark line) for a single subject (MH) to nonperiodic stimulus (light line) with ±3° artificial scotoma. Bottom: computed error signal.
Figure 4.
 
Top: typical response (dark line) for a single subject (MH) to nonperiodic stimulus (light line) with ±3° artificial scotoma. Bottom: computed error signal.
Figure 5.
 
Comparison of computed error (stimulus-response position) for a single subject (AK) with a 0.2-Hz periodic stimulus with and without an artificial scotoma.
Figure 5.
 
Comparison of computed error (stimulus-response position) for a single subject (AK) with a 0.2-Hz periodic stimulus with and without an artificial scotoma.
Figure 6.
 
Typical error histograms for no-scotoma and artificial-scotoma data from a single subject (AK), compiling single scotoma size error data from all trials into 0.5° bins. The vertical axis represents the percentage of time spent by the eye at a given foveal offset for the different scotoma conditions. Figure contains four data sets; the vertical axis for each data set starts at 0% and is incremented by 10% per division.
Figure 6.
 
Typical error histograms for no-scotoma and artificial-scotoma data from a single subject (AK), compiling single scotoma size error data from all trials into 0.5° bins. The vertical axis represents the percentage of time spent by the eye at a given foveal offset for the different scotoma conditions. Figure contains four data sets; the vertical axis for each data set starts at 0% and is incremented by 10% per division.
Figure 7.
 
Typical CES histograms for no-scotoma and artificial-scotoma data from a single subject (AK), compiling single scotoma size error data from all trials into 0.5° bins. The vertical axis represents the percentage of time spent by the eye at a given foveal offset for the different scotoma conditions. Figure contains four data sets; the vertical axis for each data set starts at 0% and is incremented by 10% per division.
Figure 7.
 
Typical CES histograms for no-scotoma and artificial-scotoma data from a single subject (AK), compiling single scotoma size error data from all trials into 0.5° bins. The vertical axis represents the percentage of time spent by the eye at a given foveal offset for the different scotoma conditions. Figure contains four data sets; the vertical axis for each data set starts at 0% and is incremented by 10% per division.
Table 2.
 
PRL as Measured via CES Analysis
Table 2.
 
PRL as Measured via CES Analysis
Subject PRL
0 ±1 ±2 ±3
L (deg) % L (deg) % L (deg) % L (deg) %
AK −0.2 41.1 −1.3 22.5 −2.4 19.1 −3.3 17.3
DH 0.6 12.9 −2.2 15.6 −2.5 17.5 −3.7 10.3
MH 0.4 29.4 −2.2 19.4 −4.1 18.1 −3.8 17.4
PP 0.1 29.2 −1.8 18.4 −3.3 15.2 −3.4 20.2
RC 0.2 20.8 −1.4 13.3 −1.7 11.3 −2.4 8.9
Figure 8.
 
Comparison of saccadic endpoints as a function of artificial scotoma size. The saccadic endpoints displayed are the fovea and the PRL estimated via the CES technique. (N = total number of saccades.)
Figure 8.
 
Comparison of saccadic endpoints as a function of artificial scotoma size. The saccadic endpoints displayed are the fovea and the PRL estimated via the CES technique. (N = total number of saccades.)
Figure 9.
 
Periodic stimulus response gains computed using the Chirp z-transform method to compare the magnitudes of the stimulus and response data.
Figure 9.
 
Periodic stimulus response gains computed using the Chirp z-transform method to compare the magnitudes of the stimulus and response data.
Figure 10.
 
Nonperiodic stimulus response gains computed using the Chirp z-transform method to compare the magnitudes of the stimulus and response data.
Figure 10.
 
Nonperiodic stimulus response gains computed using the Chirp z-transform method to compare the magnitudes of the stimulus and response data.
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Figure 1.
 
A 15-second section of each horizontal stimulus file. All stimulus files had both a left and a right start direction.
Figure 1.
 
A 15-second section of each horizontal stimulus file. All stimulus files had both a left and a right start direction.
Figure 2.
 
Top: periodic 0.2-Hz sinusoidal stimulus (light line) and typical response (dark line) for a single subject (DH) under the normal (no-scotoma) tracking condition. Bottom: computed error signal.
Figure 2.
 
Top: periodic 0.2-Hz sinusoidal stimulus (light line) and typical response (dark line) for a single subject (DH) under the normal (no-scotoma) tracking condition. Bottom: computed error signal.
Figure 3.
 
Top: typical response (dark line) for a single subject (AK) to a 0.2-Hz periodic stimulus (light line) with ±3° artificial scotoma. Bottom: computed error signal.
Figure 3.
 
Top: typical response (dark line) for a single subject (AK) to a 0.2-Hz periodic stimulus (light line) with ±3° artificial scotoma. Bottom: computed error signal.
Figure 4.
 
Top: typical response (dark line) for a single subject (MH) to nonperiodic stimulus (light line) with ±3° artificial scotoma. Bottom: computed error signal.
Figure 4.
 
Top: typical response (dark line) for a single subject (MH) to nonperiodic stimulus (light line) with ±3° artificial scotoma. Bottom: computed error signal.
Figure 5.
 
Comparison of computed error (stimulus-response position) for a single subject (AK) with a 0.2-Hz periodic stimulus with and without an artificial scotoma.
Figure 5.
 
Comparison of computed error (stimulus-response position) for a single subject (AK) with a 0.2-Hz periodic stimulus with and without an artificial scotoma.
Figure 6.
 
Typical error histograms for no-scotoma and artificial-scotoma data from a single subject (AK), compiling single scotoma size error data from all trials into 0.5° bins. The vertical axis represents the percentage of time spent by the eye at a given foveal offset for the different scotoma conditions. Figure contains four data sets; the vertical axis for each data set starts at 0% and is incremented by 10% per division.
Figure 6.
 
Typical error histograms for no-scotoma and artificial-scotoma data from a single subject (AK), compiling single scotoma size error data from all trials into 0.5° bins. The vertical axis represents the percentage of time spent by the eye at a given foveal offset for the different scotoma conditions. Figure contains four data sets; the vertical axis for each data set starts at 0% and is incremented by 10% per division.
Figure 7.
 
Typical CES histograms for no-scotoma and artificial-scotoma data from a single subject (AK), compiling single scotoma size error data from all trials into 0.5° bins. The vertical axis represents the percentage of time spent by the eye at a given foveal offset for the different scotoma conditions. Figure contains four data sets; the vertical axis for each data set starts at 0% and is incremented by 10% per division.
Figure 7.
 
Typical CES histograms for no-scotoma and artificial-scotoma data from a single subject (AK), compiling single scotoma size error data from all trials into 0.5° bins. The vertical axis represents the percentage of time spent by the eye at a given foveal offset for the different scotoma conditions. Figure contains four data sets; the vertical axis for each data set starts at 0% and is incremented by 10% per division.
Figure 8.
 
Comparison of saccadic endpoints as a function of artificial scotoma size. The saccadic endpoints displayed are the fovea and the PRL estimated via the CES technique. (N = total number of saccades.)
Figure 8.
 
Comparison of saccadic endpoints as a function of artificial scotoma size. The saccadic endpoints displayed are the fovea and the PRL estimated via the CES technique. (N = total number of saccades.)
Figure 9.
 
Periodic stimulus response gains computed using the Chirp z-transform method to compare the magnitudes of the stimulus and response data.
Figure 9.
 
Periodic stimulus response gains computed using the Chirp z-transform method to compare the magnitudes of the stimulus and response data.
Figure 10.
 
Nonperiodic stimulus response gains computed using the Chirp z-transform method to compare the magnitudes of the stimulus and response data.
Figure 10.
 
Nonperiodic stimulus response gains computed using the Chirp z-transform method to compare the magnitudes of the stimulus and response data.
Table 1.
 
Stimulus Position and Velocity Characteristics
Table 1.
 
Stimulus Position and Velocity Characteristics
Stimulus Frequency (Hz) Position (deg) Velocity (deg/s)
Min Max Range Min Max
0.2 −4.99 4.99 9.97 −6.79 6.79
0.4 −4.99 4.99 9.97 −13.57 13.57
0.6 −4.99 4.99 9.97 −19.92 19.92
0.8 −4.99 4.99 9.97 −26.70 26.70
Sum −4.95 4.48 9.42 −24.73 21.23
Table 2.
 
PRL as Measured via CES Analysis
Table 2.
 
PRL as Measured via CES Analysis
Subject PRL
0 ±1 ±2 ±3
L (deg) % L (deg) % L (deg) % L (deg) %
AK −0.2 41.1 −1.3 22.5 −2.4 19.1 −3.3 17.3
DH 0.6 12.9 −2.2 15.6 −2.5 17.5 −3.7 10.3
MH 0.4 29.4 −2.2 19.4 −4.1 18.1 −3.8 17.4
PP 0.1 29.2 −1.8 18.4 −3.3 15.2 −3.4 20.2
RC 0.2 20.8 −1.4 13.3 −1.7 11.3 −2.4 8.9
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