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. Author manuscript; available in PMC: 2014 Aug 30.
Published in final edited form as: Vision Res. 2013 Jul 24;89:54–64. doi: 10.1016/j.visres.2013.07.012

Revisiting corrective saccades: role of visual feedback

Jing Tian a,*, Howard S Ying b, David S Zee a,b,c,d
PMCID: PMC3784029  NIHMSID: NIHMS509218  PMID: 23891705

Abstract

To clarify the role of visual feedback in the generation of corrective movements after inaccurate primary saccades, we used a visually-triggered saccade task in which we varied how long the target was visible. The target was on for only 100 ms (OFF100ms), on until the start of the primary saccade (OFFonset) or on for 2 s (ON). We found that the tolerance for the post-saccadic error was small (− 2%) with a visual signal (ON) but greater (−6%) without visual feedback (OFF100ms). Saccades with an error of −10%, however, were likely to be followed by corrective saccades regardless of whether or not visual feedback was present. Corrective saccades were generally generated earlier when visual error information was available; their latency was related to the size of the error. The LATER (Linear Approach to Threshold with Ergodic Rate) model analysis also showed a comparable small population of short latency corrective saccades irrespective of the target visibility. Finally, we found, in the absence of visual feedback, the accuracy of corrective saccades across subjects was related to the latency of the primary saccade. Our findings provide new insights into the mechanisms underlying the programming of corrective saccades: 1) the preparation of corrective saccades begins along with the preparation of the primary saccades, 2) the accuracy of corrective saccades depends on the reaction time of the primary saccades and 3) if visual feedback is available after the initiation of the primary saccade, the prepared correction can be updated.

Keywords: Primary saccade, Corrective saccade, Visual feedback, LATER model, Forward control

1. Introduction

Saccades rapidly redirect the fovea to a new location in the environment, typically to where a target of interest is or is soon expected to be. In this way the image of an object of interest is placed on the fovea where visual acuity is sharpest. Saccades, though, are not perfectly accurate and usually do not land exactly on target. Due to the inherent noise that characterizes biological control systems, some inaccuracy of saccades becomes inevitable. Consequently a second, corrective saccade is often necessary to reduce a discrepancy between the position of the eye at the end of the primary saccade and the position of the target. Weber and Daroff (1971) showed that the major influence upon the accuracy of saccades is the amplitude of the required initial saccade. They found that nearly 70% of 10° saccades were accurate, and did not require a correction. Of the remaining 30% undershooting was more common than overshooting. But as the amplitude of the target displacement increased, requiring a larger initial saccade, undershooting became more prevalent. The reason why larger saccades commonly undershoot is still unknown. It has been proposed that the brain undershoots purposefully to minimize the time to trigger any subsequent corrections by keeping the processing for generating the corrective saccade within the same cerebral hemisphere (Cohen & Ross, 1978, Robinson, 1973). Using a similar rationale, Harris (1995) proposed that saccadic undershoot would be consistent with a control mechanism that attempts to minimize total saccadic flight time (duration of the primary plus any corrective saccades). Since larger saccades last longer than smaller saccades the total time to make the primary and corrective saccade is less if the first saccade is hypometric. Indeed, it has been shown that undershooting is a deliberate mechanism of the saccade system because it reestablishes itself even when visual feedback after the primary saccade eliminates a need for any corrections (Havermann & Lappe, 2010, Henson, 1978). Further evidence for this idea comes from Wong and Shelhamer who took advantage of this inherent hypometria to show that the saccade adaptation error signal is derived from a realistic prediction of movement outcome (Wong & Shelhamer, 2011). Finally, Bahill et al (1975) have shown that most naturally-occurring saccades are less than 15° because larger gaze changes combine saccades with head movements. Thus the infrequent occurrence of larger saccades with the head still may remove evolutionary pressure to use adaptive mechanisms to correct for the relatively small degrees of inaccuracy of larger saccades.

In the early 1970s, the role of visual feedback in generating corrective saccades was debated (Becker, 1972, Becker, 1976, Becker & Fuchs, 1969, Prablanc & Jeannerod, 1975, Prablanc, Masse & Echallier, 1978, Weber & Daroff, 1972). One group of studies showed that corrective saccades occurred at latencies too low to be generated by visual feedback and that they occurred even if the target was no longer visible (Barnes & Gresty, 1973, Becker, 1972, Becker, 1976, Becker & Fuchs, 1969, Shebilske, 1976, Weber & Daroff, 1972). Therefore, it was conceivable that primary and corrective saccades were preprogrammed as a “package” (Becker & Fuchs, 1969). Extraretinal feedback has also been suggested to account for short latency corrections (Weber & Daroff, 1972). These explanations, however, are not mutually exclusive since extraretinal feedback could help determine the amplitude of corrective saccades and/or the initiation of the preprogrammed correction (Becker, 1972, Shebilske, 1976). On the contrary, Prablanc and Jeannerod (1975) found that corrective saccades were generally absent if the target disappeared before the onset of the primary saccade. Corrective saccades were elicited only if the target was restored briefly at the end of the primary saccade (Prablanc & Jeannerod, 1975). These results seem to contradict the previous findings that corrective saccades occurred in the absence of visual feedback (Barnes & Gresty, 1973, Becker, 1972, Shebilske, 1976). Although these discrepancies may relate to different experimental procedures (Becker, 1976, Prablanc & Jeannerod, 1975), further experiments showed that the probability of corrective saccades without visual feedback increased with the size of the error of the primary saccade (Prablanc et al., 1978). The mechanism underlying corrective saccades has been explored further by manipulating the time and location of the reappearance of the initial target using the double-step paradigm (Becker & Jurgens, 1979, Deubel, Wolf & Hauske, 1982, Eggert, Ditterich & Straube, 1999, Gerardin, Gaveau, Pelisson & Prablanc, 2011). In this case, however, the secondary saccades elicited by the second target step may not be the typical corrective saccades following a primary saccade since the error could originate not only endogenously (inaccuracy of the primary saccade) but also artificially (second target step).

In the present study, we used a conventional visually-triggered saccade task to investigate the corrective saccades induced by endogenous errors. In this paradigm, the subject is neither aware of any error at the end of the primary saccade nor of making any corrective saccades. By varying how long the target was visible, we attempted to separate the contributions of the error signals used by the saccade system to bring the eyes on target based upon extraretinal feedback (efference copy or proprioceptive feedback) from the contribution of visual feedback of the target itself. To achieve this goal, we analyzed corrective saccades using traditional variables of timing and accuracy as well as using the LATER model (Linear Approach to Threshold with Ergodic Rate) of decision-making to provide insight into the decisional mechanisms underlying the generation of corrective saccades (Carpenter & Williams, 1995, Carpenter, 1981).

2. Material and methods

Nine healthy human subjects (6 females, 3 males; 19–40 years of age) participated in this study.All subjects had normal or corrected-to-normal vision and no condition that impaired their ability to make normal saccades. After being informed about the experimental procedures, all subjects gave written consent. The protocol was approved by the Johns Hopkins Medicine Institutional Review Board and was in accordance with the Declaration of Helsinki.

Subjects sat in a dark room with their heads restrained by a dental bite-bar. We used a scleral search coil system to record horizontal and vertical eye movements of either the right or the left eye (Robinson, 1963). Eye position signals from the coils were filtered in hardware with a bandwidth of 0–90 Hz, sampled at 1000 Hz, and then saved on a computer for later analysis. A 0.2° red laser beam was rear-projected onto a translucent screen located 1 m in front of the subject. Target position was varied by computer-controlled mirror galvanometers, which produces a 25° step-response within 6 ms. In order to avoid the streak across the screen we blanked the laser right before it started to move for 18 ms. For each subject, the center between the eyes was aligned with the center of the screen.

The experimental task consisted of the subject making a series of horizontal saccades to a target presented on the screen. During each trial, subjects were asked to fix on a centrally located target. After a randomized time delay of 1500–2300 ms at intervals of 200 ms (with equal probability in blocks of 54 trials), the target stepped 10°, 20° or 25° to either the left or the right of fixation. This target was switched off after 100 ms (OFF100ms) on one-third of trials or at the onset of the primary saccade (OFFonset) on another third of trials. In both cases there was a 1-s blank after the target was switched off and then the target reappeared at the same location for 1 s. The 1-s blank period ensured that any secondary saccades were not visually guided. On the remaining one-third of trials, the target remained on for 2 s (ON). After an inter-trial interval of 500 ms the next trial started. Subjects were given instructions with some practice trials before data were collected. Subjects were required to follow the target as accurately as possible and keep their eye on the target until the end of a trial. In the case of blanked target, subjects were asked to look at the remembered location of the target after it disappeared. No time-pressure was imposed to avoid any possible trade-off between reaction time and accuracy. Participants completed six blocks of 18 trials for each type of target with the different directions and amplitudes pseudo randomly interleaved. Because of this interleaving procedure, there was no predictable sequence of target presentation. Each experimental block lasted 3 min and 45 s. Between blocks subjects could move their head and relax for about 30 s. A calibration block was performed before the test blocks.

Data were analyzed using custom software developed in MATLAB™ (The Mathworks, Natick, MA). Saccades were detected and marked using velocity criteria. A third-order Savitzky-Golay filter was applied to the position signal to derive the velocity and acceleration signals. The onset and the end of the primary and secondary saccades were determined by a 16°/s speed threshold. Each trial was visualized to ensure the accuracy of the automatic procedure. Abnormal trials were excluded from analysis (9%) using global criteria that were applied to all subjects, as follows: (1) primary saccade amplitude differed >3 SDs from the mean of all saccades the subject made to that target; (2) primary saccade reaction time <100 ms or >500 ms; and (3) abnormal saccade trajectories due to large blinks. No inter-subjects differences were found between leftward and rightward saccades latencies and amplitudes (p > 0.1). Data were combined for both leftward and rightward saccades. Saccade amplitude was calculated as the difference between the saccade end and initial eye positions, and saccade duration as the difference between the end and onset times. The final eye position was selected during steady fixation after the target reappeared for conditions OFF100ms and OFFonset and during the last 1-s of fixation for condition ON. The saccade error after the primary saccade was calculated as the difference between the final eye position and the saccade end position. The percentage error after the primary saccade was calculated as the ratio between the saccade error and the final eye displacement (difference between the final eye position and the initial fixation). If a primary saccade was followed by one or more secondary saccades, we only considered the first corrective saccade directed to the target. We also calculated the latency of the corrective saccade, i.e., the time interval between the end of the primary saccade and the onset of the first corrective saccade. The latencies of corrective saccades were analyzed using SPIC software (Carpenter, 1994). A cumulative frequency histogram of corrective saccade latency was plotted on a probit scale as a function of reciprocal latency (Carpenter & Williams, 1995, Carpenter, 1981) and two straight lines were fit to the distribution by minimizing the Kolmogorov-Smirnov statistic. The first passed through any population of early saccades of short latency and the second through the majority of the distribution. The distribution was characterized by three variables: the slope of the early component, the slope of the main component, and the median latency. Each subjects contributed between 247 – 318 trials, resulting in a total of 2655 saccades among which 1471 were followed by corrective saccades.

3. Results

3.1. Primary saccades

The overall characteristics (amplitude, peak velocity, duration and latency) of the primary saccades depended on the pattern of the presentation of the target and the eccentricity as shown in Table 1. For both the mean and the dispersion (standard deviation, SD) of these variables, no significant difference was found among the three target conditions. Therefore, whether or not the target remained visible after it jumped to a new location did not affect the primary saccade.

Table 1.

Primary saccade variables

Mean
 Variance
Amplitude
(°)		 Peak velocity
(°/s)		 Duration
(ms)		 Latency
(ms)		 Amplitude
(°)		 Peak velocity
(°/s)		 Duration
(ms)		 Latency
(ms)
OFF100ms
10° 9.4 (0.5) 298.8 (26.3) 54 (3) 206 (31) 0.5 (0.3) 24.8(10.9) 4 (1) 28 (22)
20° 17.9 (1.0) 373.4 (42.0) 80 (6) 260 (48) 1.1 (0.5) 21.6 (20.0) 7 (4) 39 (30)
25° 22.1 (1.9) 377.9 (43.4) 96 (13) 296 (65) 1.5 (0.8) 26.6 (16.7) 10 (5) 58 (27)
OFFonset
10° 9.6 (0.5) 305.1 (28.0) 53 (3) 203 (29) 0.5 (0.2) 15.1 (9.3) 4 (1) 28 (12)
20° 18.2 (1.2) 375.9 (44.5) 80 (6) 258 (46) 1.0 (0.5) 23.8 (10.2) 6 (2) 43 (14)
25° 22.7 (1.7) 389.2 (49.0) 96 (12) 297 (59) 0.9 (0.9) 21.8 (13.0) 6 (11) 52 (23)
ON
10° 9.4 (0.6) 300.3 (27.9) 53 (3) 206 (30) 0.6 (0.3) 20.9 (7.7) 4 (3) 30 (15)
20° 17.9 (1.4) 370.9 (45.6) 81 (9) 259 (39) 0.8 (0.7) 22.5 (13.2) 7 (6) 39 (23)
25° 22.5 (1.6) 390.6 (46.2) 95 (12) 293 (56) 1.1 (0.8) 21.1 (5.6) 7 (5) 55 (22)
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Mean (mean and SD) and variance (median and interquartile range of SD) of saccade variables estimated for all subjects. Amplitude, peak velocity, duration and latency of 10°, 20° and 25° saccades for target condition OFF100ms, OFFonset and ON

In general, saccade responses to target steps of all the sizes used in our study undershot. To determine further the accuracy of the saccade, we measured the eye position error at the end of the primary saccade. Figure 1 shows the normalized (percentage) position error for the three different target conditions. No significant difference was found (p = 0.87), hence neither the time the target was on before the saccade nor the presence of any possible visual feedback during the saccade affected the accuracy of primary saccades.

Figure 1.

Figure 1

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The box plots of mean percentage position error after the primary saccade for all subjects in the three different target conditions OFF100ms, OFFonset and ON. The boxes indicate the median and include the two middle quartiles for each condition. The whiskers encompass the full range of data values, except for a single outlier (+) in the OFF100ms condition. Negative errors indicate undershooting.

3.2. Occurrence of corrective saccades

Among all the trials (pooled from all nine subjects), 55% of primary saccades were followed by a corrective saccade. We compared the normalized errors after primary saccades with and without a corrective saccade for each subject. Seven subjects showed significant differences in condition ON and five subjects in conditions OFF100ms and OFFonset (ps < 0.05). To fit a Gaussian function to the error distributions, data were then pooled across all subjects. In Fig. 2, the distributions of normalized saccade errors in the trials with (gray bars) or without a corrective saccade (black bars) are shown for the three different target conditions OFF100ms (left panel), OFFonset (middle panel) and ON (right panel). Many important features about the occurrence of corrective saccades in the different test conditions emerged. For all three target conditions, the distributions of the positions errors after the primary saccades with and without a corrective saccade were significantly different (p < 10−8). For primary saccades that were not followed by a corrective saccade, the mean value of the position errors was smallest when the target remained on (ON, −2%). The mean position errors were shifted toward the side of undershooting when the target disappeared immediately after saccade onset (OFFonset, −4%) and even further when the target disappeared after 100ms and well before saccade onset (OFF100ms, −6%). The dispersion (standard deviation) of the position errors was smallest in the condition ON. The distributions of the position errors in the three target conditions were significantly different from each other (p < 10−8). These results indicate that the tolerance range of the position error is small (−2% ± 2%) when there is a visual error signal at the end of the primary saccade. If the target disappears before the primary saccade, however, the tolerance range of the error increases to −6% ± 6%. For primary saccades followed by a corrective saccade, the position errors in the three target conditions had similar distributions (∼−10% ± 8%). A slight but significant difference was found only in the distributions between target conditions OFF100ms and ON (p = 0.048). This suggests that when the primary saccades undershoot the target by an amount that reaches a certain threshold (on average, 10% here), a corrective saccade is likely to occur regardless of whether or not visual feedback is present.

Figure 2.

Figure 2

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The superimposed histograms (normalized) show percentage position errors sorted according to whether there is (gray) or is not (black) a corrective saccade after the primary saccade in the three target conditions OFF100ms, OFFonset and ON. The corresponding σ and µ values represent the standard deviation and mean of the fitted Gaussian (blue and red). Data of all nine subjects are pooled. Negative errors indicate undershooting.

3.3. Latency of corrective saccades

There was a significant effect of target condition on the latency of corrective saccades in eight of nine subjects (p < 0.05). The mean latencies of the first corrective saccades across all subjects in the three different target conditions are shown in Fig. 3, for the three target eccentricities. There was a highly significant difference among the means of the three stimulus conditions (p < 10−5, two-way ANOVA), but no effect of target eccentricities over the range we tested (p = 0.33). The mean latencies of the corrective saccades in the three target conditions were significantly different from each other (Bonferroni method of multiple comparisons). The corrective saccades in the condition ON had the shortest latencies, whereas the corrective saccades in the condition OFFonset had the longest latencies. This indicates that the corrective saccades are generated later when visual error information is absent, especially in the condition when the target disappeared after the primary saccade has already begun.

Figure 3.

Figure 3

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Mean latencies of corrective saccades for all three target eccentricities in the three different target conditions OFF100ms, OFFonset and ON. Error bars represent the standard deviation.

To find out whether the latency of the corrective saccade depends on the size of the position error at the end of the primary saccade, we plotted all saccades in the three different stimulus conditions separately in Fig. 4. For condition ON, the dense cluster in the scatter plot (right panel) suggests a negative correlation between the latency of the corrective saccade and the size of the position error when larger than 2 deg and smaller than 5 deg. For larger errors, the latencies of the corrective saccades were less than the regular saccade reaction time (200 ms). For smaller errors, however, the latencies spread considerably and usually were much longer than 200 ms. The latencies of the corrective saccades for positive errors were not different from those for negative errors of the same size. In contrast, for both conditions OFF100ms and OFFonset (left and middle panels), the wide scatter indicates a slight, but weak negative correlation between the latency of the corrective saccades and the size of the position errors.

Figure 4.

Figure 4

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Scatter plots of latencies of first corrective saccades as a function of position error at the end of the primary saccades in the three target conditions OFF100ms, OFFonset and ON, separately. Data pooled over all subjects and target eccentricities. Negative errors indicate undershooting and positive errors overshooting. Red line indicates the average latency as a function of the size of the position errors.

Note that in both conditions OFF100ms and OFFonset there were also a small group of corrective saccades occurring earlier than the regular saccadic reaction time. Due to these early corrective saccades, it became necessary to characterize the entire distribution of latencies. We chose the LATER model for this analysis. Fig. 5A shows reciprobit plots of the corrective saccade latencies for the three different stimulus conditions for one subject (Kolmogorov-Smirnov, p > 0.8); Fig. 5B for the pooled data from all nine subjects (p > 0.7). Table 2 shows the three variables that were measured from the pooled data. The LATER model assumes that a decision signal, starting at an initial baseline, rises linearly until it reaches a threshold at which a saccade is triggered. According to this model, saccade reaction times can be lengthened or shortened by changing the rate of signal rise and/or the distance between the baseline and threshold (Carpenter & Williams, 1995, Carpenter, 1981). The two changes can be judged quantitatively from reciprobit plots of the latency distributions. If the target visibility changed the rate of rise, the distribution should shift along the time axis. In contrast, if the target visibility changed the distance between the baseline and threshold for saccade initiation, the distribution should swivel at a common intercept on the infinite time axis (Carpenter & Williams, 1995). Using this approach, a number of important features about the latency of the corrective saccade are demonstrated in both the single subject shown and the pooled data. (1) Median latency was shortest for condition ON and longest for condition OFFonset, which is consistent with the results measured as means across the subjects (Fig. 3). (2) In all three conditions, there were short latency corrective saccades with a similar slope. This indicates that the time of occurrence of the early corrective saccade was similar whether or not visual feedback was present. (3) The slopes of the main component were similar in conditions OFFonset and OFF100ms, but steeper than in condition ON (swivel is favored over shift, p < 0.001). In terms of the LATER model this implies a larger uncertainty about the target position and/or the saccade error (higher threshold level) in both conditions OFF100ms and OFFonset than in condition ON. (4) This analysis was unable to tell whether the difference in the distributions of condition OFFonset and condition OFF100ms (∼40 ms) was a parallel shift or swivel from either the single subject or the pooled data. However, we speculated that the shorter median latency in condition OFF100ms means that the transient signal generated by the target going off in advance of the initiation of the primary saccade strengthens the decision signal (increases the rate of rise to saccade initiation) for triggering corrective saccades.

Figure 5.

Figure 5

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Distributions of corrective saccade latencies shown using reciprobit plots for the three different target conditions OFF100ms, OFFonset and ON. A: one representative subject. B: data pooled over all subjects and target eccentricities. Three variables (the slope of the early component, the main slope, and the median latency) were calculated to characterize the distribution.

Table 2.

Variables of the LATER model of corrective saccade latency

Earlyslope Main slope Medianlatency
OFF100ms 0.20 1.06 326
OFFonset 0.21 1.19 366
ON 0.17 0.71 251
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3.4. Accuracy of corrective saccades

Figure 6 illustrates the correlation between the position error after the primary saccade and the amplitude of the first corrective saccade in the three target conditions OFF100ms, OFFonset and ON, separately. The slope of the linear regression is an index of how much the corrective saccade compensates for the primary saccade. If compensation were perfect the slope would be 1. Fig. 6A shows the results for a representative subject. Note the slope in condition ON (0.75) is much greater than that in conditions OFF100ms and OFFonset (0.51 and 0.40). This difference was true for the groups as a whole (Fig. 6B). All nine subjects showed a significant correlation between primary saccade error and corrective saccade amplitude (range of correlation coefficients: 0.43 to 0.95 for OFF100ms, 0.56 to 0.92 for OFFonset and 0.85 to 0.97 for ON; all ps < 0.05). Over all subjects, the average of the individual correlation coefficients was 0.77 ± 0.16 in condition OFF100ms, 0.70 ± 0.15 in condition OFFonset, and 0.93 ± 0.04 in condition ON. The average of the individual slopes of the linear regression was 0.54 ± 0.23 in condition OFF100ms, 0.49 ± 0.27 in condition OFFonset, and 0.71 ± 0.08 in condition ON. The correlation coefficients and the slopes in conditions OFF100ms and OFFonset were each significantly lower than those in condition ON (ps < 0.05, paired t test) but not different from each other (ps > 0.1). These results indicate that, on average, the corrective saccade compensate for 70% of primary saccade error if a retinal error signal is available at the end of the primary saccade, but only 50% if not. Fig. 6B also shows the correction slopes are more variable among subjects in conditions OFF100ms and OFFonset than in condition ON. The slopes in conditions OFF100ms and OFFonset were significantly correlated with each other across the nine subjects (r = 0.73, p < 0.05) but not with those in condition ON (ps > 0.5). This is not surprising, because visual (retinal) signals are presumably more reliable than nonvisual (extraretinal) signals.

Figure 6.

Figure 6

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Correlation between the position error after the primary saccade and the amplitude of the first corrective saccade in the three target conditions OFF100ms, OFFonset and ON. A: representative linear regressions are shown for one subject. Negative errors indicate undershooting and positive errors overshooting. Dotted lines denote perfect compensation of the error. B: regression lines for all subjects.

One interesting question is, however, what determines the goodness of correction in the absence of visual feedback. First, we asked whether the correction slope is affected by the latency of initial saccade (Fig. 7). Over all subjects, there was a positive correlation between correction slope and latency of primary saccades with correction in conditions OFF100ms (r = 0.71, p < 0.05) and OFFonset (r = 0.86, p < 0.01), but not in condition ON (r = 0.21, p = 0.59). This suggests that corrective saccades without visual feedback are more accurate for subjects with longer-latency primary saccades than subjects with shorter-latency primary saccades. We further tested to see if the correction slope were correlated with the latency of corrective saccades (also calculated from the moment at which the target presented) and the primary saccade error (data not shown). None of these correlations in all three target conditions were statistically significant (p > 0.1). Therefore, the accuracy of the correction in the dark was neither related to the latency of corrective saccades nor to the error size of the primary saccades. Taken together, these results suggest that corrective saccades are preprogrammed with primary saccades that have relatively longer reaction times. Note two subjects made corrections with slopes close to 1 in the condition OFFonset, which was even higher than their correction slopes in the condition ON. We will propose an explanation of this observation in the Discussion.

Figure 7.

Figure 7

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Correlation between correction slope and mean latency of primary saccades with correction in the three target conditions OFF100ms, OFFonset and ON. Each subject is represented by a different color. Over all subjects, the mean latency of primary saccades with correction correlates well to the correction slope in both conditions OFF100ms and OFFonset, but not in condition ON.

4. Discussion

This study was designed to understand better the visual and nonvisual mechanisms for generating corrective saccades by varying the duration of the target presentation. Several conclusions stand out from our experiments. Firstly, we found no sign of an online correction of the primary saccade due to the presence of the target during the saccade. Secondly, the tolerance for a post-saccadic error was small in the presence of a visual signal but was greater in the absence of visual feedback. However, saccades with an error of −10% were likely to be followed by corrective saccades regardless of whether or not visual feedback was present. Thirdly, corrective saccades were generated earlier when visual error information was available and their latency was related to the size of the error. Fourthly, in the absence of visual feedback, the accuracy of corrective saccades was related to the latency of the primary saccade. We will discuss and interpret these findings in the following text.

4.1. Effects of target duration on primary saccades

The duration of the target presentation was varied randomly in our experiments. In one-third of trials, the target was on for only 100 ms (OFF100ms, short duration) so that by the time the primary saccade occurred no visual target was available and the primary saccade could only be made from the memory of the target location. In the remaining two-thirds of trials, the target stayed on either until the start of the primary saccade (OFFonset, medium duration) or for 2 s (ON, long duration) so that visual information was either absent or present during and after the primary saccade. It is important to know the effect of target visibility on primary saccades, as it provides a basis for evaluating the corrective saccades. Firstly, no differences were found between the latencies of the primary saccades for the different times the target was visible. For this reason we assume that our subjects did not use different strategies for programming saccades in the different target conditions. Although it has been reported that saccadic latency is inversely related to the time the target is visible (van Loon & Adam, 2006), the discrepancy with our results may be largely attributed to the smaller target eccentricities (0.7 – 8.4°) in their study and to their instructions which stressed the promptness of initiation and not the accuracy of the saccade. While the same inverse relationship was also reported by Barnes and Gresty (1973), who used targets eccentricities and instruction similar to ours, their figure 2 showed almost no differences in latencies within the range of target durations of 5 – 400 ms, which was comparable to our range of stimuli.

Secondly, neither the amplitude nor the dynamics (peak velocity and duration) of the primary saccades showed significant difference among the three different target conditions. On the one hand, this shows that the visual information acquired during that short period of 100 ms is sufficient to generate a saccade similar to that made to the sustained target. On the other hand, it suggests that intrasaccadic visual information is not used to modify the ongoing saccade. This agrees well with the findings by Eggert et al. (1999) and Munuera et al. (2009) that intrasaccadic target steps had no effect on the metrics and dynamics of the primary saccade. In addition, the analysis of eye position error further determined that the overall error after the primary saccade was not different among the three target conditions. This shows that neither the time the target was on before the saccade nor the presence of the target during the saccade made a difference in the accuracy of the primary saccade. Our results confirm the finding by Becker (1972) that saccade accuracy is independent of the amount of time that the target is presented (within a range of 50–200 ms), whereas Prablanc and Jeannerod (1975) reported that saccade accuracy decreased as the target duration became shorter (within a range of 20–200 ms). This discrepancy may be due to different methodologies between these studies. In summary, in our experiments, the general characteristics of the primary saccades were unaffected by the time the target was visible. Thus, the corrective mechanism with and without visual feedback was provided with comparable sized errors.

4.2. Error tolerance with and without visual feedback

As previously discussed saccades tend to undershoot the target necessitating corrective saccades. In our experiments, we found no corrective saccades occurred following saccades with a position error of −2% ± 2% in the condition ON, −4% ± 5% in the condition OFFonset, and −6% ± 6% in the condition OFF100ms. In contrast, for saccades that were followed by corrective saccades, the error distributions were similar (∼−10% ± 8%) in all three target conditions. Two important points emerged from these findings. Firstly, when the primary saccades undershoot the target by ∼10%, a corrective saccade is likely to occur regardless of whether or not visual feedback is present. Secondly, the tolerance for smaller postsaccadic error is different in the conditions with and without visual feedback. When there is a retinal error signal at the end of the primary saccade (condition ON), the tolerance of the position error was around 0.5° for the largest target eccentricity (25°) tested. The image of the target still falls within the high acuity fovea (∼0.5°), thus a correction is not necessary. When no visual information is available during and after the execution of the primary saccade (conditions OFF100ms and OFFonset), the tolerance for position errors increased, especially in the condition with shorter target duration. This suggests that the extraretinal signals required for error detection are not very sensitive and/or the nervous system is willing to tolerate larger saccadic error in the absence of visual feedback. There are few reports about the tolerance range of retinal and non-retinal errors. Shebilske (1976) compared the errors with and without visual feedback after primary saccades that were not followed by corrective saccades, but a generalizable conclusion cannot be made from his study because only two subjects were tested. Prablanc et al. (1978) reported that almost no corrective saccades occurred when the non-retinal error was within 10% of the stimulus eccentricity in all but one subject. This discrepancy between our results and theirs might relate to the much larger target eccentricity (24 – 52°) used in their experiment, but without comparable experimental paradigms a full explanation cannot be given.

4.3. Latency of corrective saccades and LATER model

We found that, on average, the corrective saccades had the smallest latencies in the condition ON and the largest latencies in the condition OFFonset. In the condition ON, the latency of corrective saccades was related to the size of the primary saccade error. For errors smaller than 2 deg, the distribution of the latencies widened considerably and the values were much higher than the normal reactive saccade latency (200 ms). For errors between 2 and 5 deg, the latencies decreased with increasing error size. For errors larger than 5 deg (fewer data), the average latency remained relatively constant (about 130 ms). In contrast, in both conditions OFF100ms and OFFonset, there was no close relationship between the latency of corrective saccades and the position error of primary saccades. The latencies associated with both small and large errors scattered widely. Findings largely comparable to ours were reported by Becker (1972), who ran the experiments in conditions similar to ours (sustained and brief target durations of 50 – 200 ms) and studied the latency of corrective saccades with respect to their amplitude. Ohl et al. (2011) also showed that the latency of secondary saccades to sustained targets was influenced by the magnitude of the saccade error, but their analysis was limited to the early secondary (micro-)saccades with latencies within 350 ms and saccade errors below 2°. Taking these findings together, it can be concluded that corrective saccades are generated earlier when visual error information is available and their latency is associated with the error size. To explain the relatively long latency of corrective saccades for small retinal errors (less than 2°), Becker (1972) suggested that the image of a target falls on the retina within an area in which visual acuity is still high, thus a correction is not very urgent. Another explanation could be that very small saccades in general need more time to be executed (Ohl et al., 2011). As the retinal error increases, the latency of the corrective saccades decreases until it reaches a stable value which is much less than the saccade reaction time to a visual stimulus. This suggests that the corrective saccade can be prepared before the end of the ongoing initial saccade but its need for execution has to be verified by subsequent visual information (Becker, 1976).

When is visual information available for corrective saccades? Prablanc et al. (1978) compared the corrective saccades in the conditions where the target was turned off at the onset or during the deceleration phase of the primary saccade and found the average latency of corrective saccades was decreased in the latter condition and most of the latencies were centered around 100 ms. Therefore, they suggested that retinal signals acquired during the deceleration phase of a saccade can lead to a corrective saccade with a short latency. No correlation between the corrective saccade latency and the error size, however, was found in their experiments. Unfortunately, there were no comparable conditions in our and Becker (1972)’s experiments. Thus, we cannot make any conclusion about the effect of visual information during a saccade on the latency of corrective saccades. Nevertheless, in a double-step paradigm, it has been demonstrated that the latency of secondary saccades increased after a target step during the deceleration phase, but not during the acceleration phase of the preceding primary saccade (Eggert et al., 1999). These findings provide evidence that intrasaccadic visual input during the deceleration phase has a direct effect on the timing of the subsequent corrective saccade. More recently, Gerardin et al. (2011) showed that when the target was stepped at saccade onset and then maintained at least until the start of the secondary saccade, the latency of secondary saccades was significantly less than when the stepped target was maintained only until the end of the primary saccade. These results suggested a major role of postsaccadic visual feedback in the production of the secondary saccade. In contrast to the findings by Eggert et al. (1999), however, their results showed that when the stepped target was maintained until the end of the trial, the latency of secondary saccades increased comparing with the single-step trials. The discrepancy may be due to that the direction and location of the initial displacement of the target were predictable in the experiments of Gerardin et al (2011).

When no visual feedback is available during and after the primary saccade, the long latencies of corrective saccades may be caused by waiting for the expected visual information and/or by accessing stored information about target position. Nevertheless, in both conditions OFF100ms and OFFonset, we also observed a small sub-population of corrective saccades with very short latencies irrespective of the error size. A similar observation was made in the experiments of Prablanc et al. (1978) in the condition in which the target was turned off at the onset of the primary saccade. Such early corrective saccades without visual feedback have been largely ignored for years, as only the mean values of the latency of corrective saccades were reported. To quantify and compare the entire distribution of corrective saccade latencies in the three different target conditions, we used the LATER model. The LATER model was originally developed to explain the reaction time distribution of visually-triggered saccades, and hence to infer an underlying neural mechanisms of the decision process. Comparing with visually-triggered saccades, most corrective saccades are involuntary and their latencies can provide information about the underlying decision process in a more natural situation. Firstly, the fits of the LATER model to the latency distributions revealed that median latency was shortest for condition ON and longest for condition OFFonset. This is consistent with the results measured as means across subjects. Secondly, the main distributions in both conditions OFFonset and OFF100ms were steeper than that in the condition ON (swivel), implying a higher threshold level to initiate the corrective saccade when no visual target is available. Thirdly, the difference in the main distributions of condition OFFonset and condition OFF100ms is compatible with the idea of a faster rise of the decision signal if the target is extinguished before the initiation of the primary saccade than after. We speculate that the target offset before the primary saccade provides a warning that shortens the latency of the corrective saccade if no subsequent target is visible. Last but most importantly, there was a similar population of short latency corrective saccades in all three conditions. Such short latencies (small intersaccadic intervals) indicate that programming of the corrective saccade had been initiated prior to the end of the primary saccade irrespective of the target visibility. We speculate that normally these preprogrammed corrective saccades are inhibited until they are verified by the retinal afference, whereas they might occasionally escape the normal inhibition under conditions of great urgency (large retinal error) or lack of visual feedback. Accordingly, the main distribution of latencies represents the decision time of higher cortical levels and the early distribution represents the actions at lower, perhaps more reflexive levels.

If corrective saccades are programmed before the end of the primary saccade, one might ask whether the way we determined the latency (from the end of the primary saccade) can truly represent the reaction time of the corrective saccade. We also tried measuring the latency from the moment when the target was presented. However, due to the large differences in the primary saccade latency and duration among the three target eccentricities we tested, we could not reliably identify the early corrective saccades of short latency. Although our data did not allow us to determine when the programming of corrective saccades actually begins, we can still use the intersaccadic interval to compare the decision time of corrective saccades in the three different stimulus conditions assuming the programming begins at the same time. In addition, it has been demonstrated that the intersaccadic intervals of spontaneous saccades, such as in reading or optokinetic nystagmus (OKN), can be well described by the LATER model (Carpenter, 1993, Carpenter & McDonald, 2007). Interestingly, the latencies of corrective saccades in our experiments showed similar patterns of distribution to the intersaccadic intervals for those more “spontaneous”, reflexive saccades, with longer median latencies and more of the early latency saccades than those of visually-triggered saccade. Of course, we pooled data from all nine subjects and all target eccentricities for fitting because of the limited number of the data set in our experiments. Therefore, further experiments must confirm our results on the level of individual subjects.

4.4. Accuracy of corrective saccades

Our results showed that, on average, the corrective saccade compensates for 70% of the primary saccade error if a retinal error signal is available at the end of the primary saccade. This indicates that corrective saccades driven by a visual error signal still under correct for the error, although it is usually assumed that they are performed to take the target to the fovea. A similar finding has been reported by Munuera et al (2009); they found that the corrective saccade with visual feedback only compensate for 70% of intrasaccadic target jump (20% of 18° target eccentricity) in a modified double-step paradigm. Their following experiment (Morel, Deneve & Baraduc, 2011) also showed incomplete corrections (with gain lower than the main saccade gain). The reason for this incomplete correction is still unknown, though it may again be a time optimal strategy to avoid overshooting because of inherent noise. On the other hand the calculation might also be based not only on the perceived visual error, but also on the predicted visual error (Morel et al., 2011, Vaziri, Diedrichsen & Shadmehr, 2006, Wong & Shelhamer, 2011).

When no visual error is available at the end of the primary saccade, we found that the corrective saccade only compensates for about 50% of the error. This is similar to the ratio 0.46 reported by Prablanc et al. (1978) in the condition in which the target was extinguished at the onset of the primary saccade. However, Becker reported that corrective saccades without retinal signals (their target duration 50 – 200 ms) can eliminate 90% of the error (Becker, 1972) or 80% if the postsaccadic drift were also taken into account in the calculation of the size of the correction (Becker, 1976). Such high correction ratios without the assistant of visual feedback might be explained by the fact that he counted all the corrective saccades (at least two) and that the large target eccentricity (20 – 60°) in his experiments favored the generation of multiple corrective saccades.

We also found considerably more intersubject variability in the ratio of the size of the corrective saccade to the eye position error when no visual feedback was available in which case the correction ratios were mostly lower. In the absence of the visual feedback, what determines the accuracy of the corrective saccades in each individual subject? Our results showed that the accuracy of the correction in the dark was correlated with the latency of the primary saccades but neither with the latency of corrective saccades nor with the error size of the primary saccades. The longer a subject takes to make the initial saccade, the more accurate the corrective saccade. This implies that the preparation of corrective saccades begins relatively early, along with the preparation of the primary saccades and that their accuracy depends on the reaction time of the primary saccades. If visual feedback is available after the initiation of the primary saccade, the prepared correction can be modified according to the perceived visual error and also possibly to the predicted visual error. The two subjects who had the longest primary saccade latency in our experiments made almost perfect corrections in the condition in which the target was extinguished at the onset of the primary saccade. Instead, the action of their corrections deteriorated in the condition in which the target remained on, although the primary saccade latency was similar in these two conditions. Comparing these two target conditions, the subject would not know the difference until after the initiation of the primary saccade. Therefore, the difference in the corrective saccade accuracy further confirms our conclusion that corrective saccades are preprogrammed with the primary saccades and that their magnitude can be updated by the visual error (if available) to become more accurate or paradoxically, in a few subjects, even worse. The preprogramming of corrective saccades was first suggested by Becker and Fuchs (1969), based on their finding that the latency of corrective saccades with visible targets and in the dark was both very short (130 ms). In their experiments, however, the two targets were stationary, separated by as much as 40°. Thus the subjects made voluntary saccades at their own pace which may have influenced the pattern of corrective saccades. In contrast, the saccades we tested were reactive saccade in response to the sudden appearance of a visual target at an unpredictable location. The generation of these two types of saccades involves separate neural substrates (Johnston & Everling, 2008, McDowell, Dyckman, Austin & Clementz, 2008, Muri & Nyffeler, 2008). In addition, recent evidence in an adaptation study indicates that visual error signals processing leading to the generation of corrective saccades differs between reactive and voluntary saccades (Panouilleres, Urquizar, Salemme & Pelisson, 2011). Ditterich et al. (1998) also suggested that sequences of memory-guided saccades can be performed in a preprogramming mode. Similarly, Sharika et al. (2008) demonstrated that motor preparation for the second corrective saccade may proceed in parallel with the preparation of the first erroneous saccade using a modified double-step redirect task. Thus, whether or not the preprogramming of corrective saccades for different types of primary saccades relies on the same processing mechanism is a key unanswered question. Recently, a study measuring secondary saccades in the absence of postsaccadic visual feedback provided evidence that an extraretinal error signal contributes to the programming of secondary saccades, but did not favor a strict preprogramming hypothesis (Ohl, Brandt & Kliegl, 2013). However, we suggest that these explanations are not mutually exclusive. In addition, Ohl et al.’s study limited their analysis to very small saccades with many less than 1° and there were differences in the experimental instructions (stressing accuracy versus promptness of initiation) and in the patterns of data collection.

4.5.Extraretinal signals and saccade error correction

When visual feedback is absent, corrective saccades can only be driven by an internally generated error signal, and can only be accurate if the position of the eye after the primary saccade is known. A few sources of extraretinal signals have been suggested to monitor eye position. One is proprioception of eye muscles (Wang, Zhang, Cohen & Goldberg, 2007), which arises peripherally and reaches the cortex after a saccade. Therefore, its role in the production of corrective saccade can be excluded since proprioceptive signals seem to arrive too late to be used. Another candidate is corollary discharge (Guthrie, Porter & Sparks, 1983), which is of central origin and occurs just before the saccade (Sommer & Wurtz, 2008). Our earlier work suggested that the brain maintained a real-time estimate of the eye positions via corollary discharge by demonstrating that the perturbed saccade can be corrected via internal feedback with compensatory motor commands that brought the eyes near the target (Xu-Wilson, Tian, Shadmehr & Zee, 2011). Consequently, the internal feedback control allows programming of the corrective saccade to begin only after the primary saccade has occurred. Of course, the existence of such a real-time estimate of the position of the eye remains to be proven since in a multiple-saccade sequence study the variability of endpoints to a target increased with the number of saccades suggesting a prefect estimate of eye position over time is not available (Collins, 2010).

To allow programming of the corrective saccade to begin before the occurrence of the inaccurate primary saccade, the brain might use feed forward control to predict the end position of the primary saccade. A forward predictor of motor outcomes could explain 1) concurrent programming of corrective saccades with an initially erroneous saccade during a double-step task (Sharika et al., 2008), 2) saccade adaptation (Wong & Shelhamer, 2011), and 3) combining visual feedback to adjust the next saccade during sequences of saccades (Morel et al., 2011, Munuera et al., 2009). The results of our study using a simple visually-triggered saccade task conform to this forward model hypothesis of error correction.

4.6. A conceptual scheme for saccade error correction

Figure 8 is a conceptual scheme of saccade generation. It includes a pathway for error prediction using forward motor control (top gray path) (Fig. 8A). In this scheme, visual information from the retina is processed to create a high-level internal representation of target position ( , or desired eye position) and then a decision to generate a saccade to the target is made. The desired eye position is combined with a prediction of eye position provided by an efference copy of the motor command for the initial saccade. The result is a predicted error ( ) that feeds into the central decision and computing circuit (Fig. 8A, grey hexagon, expanded in Fig. 8B), which is used both to guide the primary saccade and for generating a corrective saccade. If the predicted error is below the error threshold, a saccade without any correction is triggered. If the predicted error exceeds the error threshold, the programming of a corrective saccade is started even before the primary saccade is generated. The primary saccade is then triggered. The final decision about generating the corrective saccade can be altered, depending upon the target visibility (Fig. 8B, grey oval and rectangle) and upon internal feedback of the position of the eye during and after the primary saccade. If visual feedback is available (ON), the magnitude of the preprogrammed corrective saccade is updated. If not (OFFonset and OFF100ms), the triggering of the corrective saccade is based on internal feedback of eye position or remapping of target position (Collins, Rolfs, Deubel & Cavanagh, 2009). If the target goes off before the primary saccade (OFF100ms) the process for triggering the corrective saccade is accelerated. The presence of very short latency, “express” corrective saccades suggests a separate pathway for an early correction as discussed earlier. Finally, we emphasize that this conceptual scheme is speculative including the idea of forward motor control.

Figure 8.

Figure 8

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Conceptual scheme of saccade generation with and without corrective saccade. A: represents high-level internal representation of target position, top gray path represents a pathway for error prediction using forward motor control, is predicted error. B: the expanded structure of the central decision and computing circuit. Threshold = ∼2%; condition OFF100ms might shorten the waiting time by 40 ms on average comparing with condition OFFonset.

4.7. The neural substrates of error correction

It has been suggested that forward models, possibly located in the cerebellum, generate a prediction of the expected motor outcomes at very short latency (Shadmehr, Smith & Krakauer, 2010). The cerebellum receives input from the superior colliculus and exerts its influence on saccades via two pathways leaving the caudal fastigial nucleus. The short pathway projects directly to the brainstem burst generator. The LATER model analysis of corrective saccade latencies unveiled a small population of early corrective saccades regardless of whether or not visual feedback was present. We infer that these early corrective saccades may be generated by subcortical structures, possibly via this short pathway. The long pathway ascends via the thalamus to various cortical eye fields, which then influence the superior colliculus and the saccade pulse generator. The generation of regular corrective saccade (main distribution) may depend on the long pathway involving the cortex. Recent neurophysiological experiments in monkey have found that the movement-related activity leading to corrective saccades in the frontal eye filed (FEF) usually began before errors could be detected through visual or monitoring feedback (Murthy, Ray, Shorter, Priddy, Schall & Thompson, 2007). Although in this study the corrective saccade was generated to correct the errant initial saccade during a double-step task, we speculate that a similar neural substrate contributes to the generation of the involuntary corrective saccade seen in our experiments. Further experiments will look for the neural basis of this hypothetical model by examining corrective saccades of patients with focal lesions of cerebellum and frontal eye field.

  • New insights into the mechanisms of corrective saccades programming.

  • The preparation of corrective saccades begins along with the primary saccades.

  • Corrective saccade can occur without a subsequent visual error signal.

  • The prepared correction can be updated by visual feedback.

Acknowledgements

This study was supported by the National Institutes of Health Grants: R01-EY001849 (DSZ) and R01-EY019347 (HSY), Research to Prevent Blindness Disney Award (HSY) and Cross Foundation (HSY). Dr. Tian is a Paul and Betty Cinquegrana Scholar.

Footnotes

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