January 2024
Volume 65, Issue 1
Open Access
Eye Movements, Strabismus, Amblyopia and Neuro-ophthalmology  |   January 2024
Measuring the Interocular Delay and its Link to Visual Acuity in Amblyopia
Author Affiliations & Notes
  • Daniel Gurman
    McGill Vision Research Unit, Department of Ophthalmology & Visual Sciences, McGill University, Montreal, Quebec, Canada
  • Alexandre Reynaud
    McGill Vision Research Unit, Department of Ophthalmology & Visual Sciences, McGill University, Montreal, Quebec, Canada
  • Correspondence: Alexandre Reynaud, McGill University Health Centre (MUHC), Department of Ophthalmology and Visual Sciences, McGill Vision Research Unit (Alexandre Reynaud's Lab), 1650 Cedar Avenue, Montréal QC H3G 1A4, Canada; alexandre.reynaud@mail.mcgill.ca
Investigative Ophthalmology & Visual Science January 2024, Vol.65, 2. doi:https://doi.org/10.1167/iovs.65.1.2
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      Daniel Gurman, Alexandre Reynaud; Measuring the Interocular Delay and its Link to Visual Acuity in Amblyopia. Invest. Ophthalmol. Vis. Sci. 2024;65(1):2. https://doi.org/10.1167/iovs.65.1.2.

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Abstract

Purpose: Research on interocular synchronicity in amblyopia has demonstrated a deficit in synchronization (i.e., a neural processing delay) between the two eyes. Current methods for assessing interocular delay are either costly or ineffective for assessments in severe amblyopia. In this study, we adapted a novel protocol developed by Burge and Cormack based on continuous target tracking to measure the interocular delay on a wide range of amblyopes. Our main aims were to assess the accessibility of this protocol and to investigate the relationship between interocular delay and visual acuity.

Methods: This protocol, which consists of tracking a target undergoing random lateral motion with the mouse cursor, is performed both binocularly and monocularly. The processing speed of a given eye is computed by comparing the changes in velocity of the target and mouse via cross-correlation. The difference in processing speed between the eyes defines the interocular delay.

Results: Cross-correlations revealed that the amblyopic eye tends to be delayed in time compared with the fellow eye. Interocular delays fell in the range of 0.6 to 114.0 ms. The magnitude of the delay was positively correlated with differences in interocular visual acuity (R2 = 0.484; P = 0.0002).

Conclusions: These results demonstrate the accessibility of this new protocol and further support the link between interocular synchronicity and amblyopia. Furthermore, we determine that the interocular delay in amblyopia is best explained by a deficit in the temporal integration of the amblyopic eye.

Amblyopia is a developmental visual disorder affecting an estimated 1% to 5% of people1 and is known to be the leading cause of unilateral blindness in children in North America.2 It is caused by a disruption to normal visual experience, most commonly strabismus or anisometropia, occurring during the critical period of development of the visual system in early childhood. Although decreased visual acuity in one of the eyes is the most apparent deficit exhibited by amblyopes, it is understood that the main deficit is to binocular vision and that monocular deficits are merely a secondary consequence.3 
Research on amblyopia has most commonly focused on the deficits to spatial vision associated with the condition such as reduced visual acuity,1,4 decreased contrast sensitivity,57 and spatial distortions and aberrations.4,8 However, in recent years, the interest and understanding of the temporal deficits associated with amblyopia has increased. These deficits have concrete consequences on motion perception and discrimination,911 motion extrapolation,12,13 optic flow,14,15 motion aftereffect,16 and visuospatial attention.17,18 These could be the consequences of temporal irregularities including decreased flicker sensitivity,19 and a deficit to interocular synchronization (ie, a neural processing delay) between the eyes,2024 characterized by an interocular delay which can in fact affect either the amblyopic eye (AE) or the fellow eye (FE).25 This delay is known to be sufficient to induce a spontaneous Pulfrich phenomenon in amblyopes with rudimentary stereopsis26 and tends to be in the range of approximately 20 ms.27 Currently, the causes and consequences of this delay remain elusive, particularly given the conflicting nature of previous findings. Reynaud and Hess26 showed that the magnitude of interocular delay is moderately correlated with the difference in acuity between the eyes by combining psychophysical and electrophysiological approaches. However, Wu et al.25 failed to find such a correlation. As such, it is as yet unclear what role the interocular delay may play in amblyopia as a whole. One potential source of this discrepancy lies in the limited accessibility of the methods used for measuring processing speeds, which resulted in the inability to test participants with strong amblyopia. It is expected that this discrepancy may be elucidated by using a paradigm that is accessible to a broader range of amblyopes, including stereo blind individuals and those with poor visual acuity. 
Various methods, both psychophysical and electrophysiological, can be used to measure interocular delay. Psychophysical methods are typically very accessible in terms of required equipment. The classic reaction time test21,22 can be performed using common devices like computers, smartphones, or tablets. Stereo-based techniques such as the Pulfrich paradigm25 and dynamic random-dot stereograms (DRDS)28 estimate interocular delay by assessing perceived depth of dynamic stimuli and require specialized displays or devices. This is the same for interocular temporal asynchrony,29 which involves adjusting the temporal phase of dichoptic flickering lights until they are perceived to be synchronous. Electrophysiological methods like magnetoencephalography,27 electroencephalography,30 and eye tracking31 measure brain activity or oculomotor response time, but require specialized equipment and training. In terms of testing duration, DRDS and the Pulfrich paradigm take a few minutes, whereas eye tracking, electroencephalography, and magnetoencephalography need additional preparation and calibration time. Interocular temporal asynchrony takes approximately 30 minutes, and the classic reaction time test may take hours. Regarding accessibility for amblyopic participants, all methods are suitable, except for the Pulfrich paradigm and DRDS, which have a limited capacity to test stereoblinds. In terms of precision, all methods offer millisecond-scale precision, except DRDS, which can narrow down interocular delay to a few milliseconds at best. 
A recent tracking task invented by Burge and Cormack32 based on continuous psychophysics has the potential to offer improvements over previous methods. This method is more accessible than previous interocular delay assessments because it can be performed both binocularly and monocularly and does not require stereopsis to be performed. This method also provides improvements to the efficiency with which data is collected.33 Given the nature of continuous tracking, more than a thousand data points are collected during a single trial of this task, meaning that very few trials are needed to produce accurate assessments. Finally, this method is more accessible in terms of the equipment required. At most, a computer and mouse are needed to perform this task, so it could easily be applied in a clinical setting. 
There were three main aims of the current study. The first aim was to assess the accessibility of Burge and Cormack's tracking task in the context of amblyopia research. It was expected that this method would be more accessible than those used in previous studies owing to the lack of a reliance on stereopsis or high-acuity vision. The second aim was to investigate the relationship between interocular delay and visual acuity on a pool of participants with mild to strong amblyopia. The third aim was to evaluate the quantity of data necessary to provide clinicians with useful diagnostic information. This was done by determining the effect of decreasing the number or duration of trials on the reliability of reaction time assessments. 
Methods
Participants
Thirteen normal or corrected-to-normal sighted controls (aged 20–37 years, 8 females) and 24 participants with a history of amblyopia participated in the study. The classification of the severity of amblyopia, which was defined by the difference in visual acuity between the eyes, was adapted from Williams34: mild was classified as a difference of 0.2 to 0.3 logMAR, moderate was classified as a difference of more than 0.3 logMAR to 0.8 logMAR, and severe was classified as a difference of more than 0.8 logMAR. Five amblyopic participants presented an interocular acuity difference of less than two lines (0.2 logMAR) and were classified as recovered amblyopes (A4, A14, A17, A21, and A23) (see Table 1). Deviation was assessed either with the Maddox wing test or with an amblyoscope, depending on the time that a given participant was tested. Some participants were unable to read the numbers on the Maddox wing owing to poor vision in their AE; deviation was not reported for these participants. Participant A24 was unable to perform the task with their AE; this participant was excluded from the analysis. All participants wore their prescribed optical corrections during testing. For the controls, ocular dominance was determined using the Porta test. Tests took place at the Montreal General Hospital. Participants were provided monetary compensation for their time spent participating. All participants gave written informed consent to participate. Testing was performed in accordance with the declaration of Helsinki and was approved by the Research Ethics Board of the Research Institute of the McGill University Health Center under protocol number 2022–7835. 
Table 1.
 
Demographic Information From Our 24 Amblyopic Subjects
Table 1.
 
Demographic Information From Our 24 Amblyopic Subjects
Apparatus
The experimental code was written in MATLAB (R2018a) using Psychtoolbox and was run on an Apple MacPro computer (OSX 10.10.5). Stimuli were displayed on a gamma-corrected 45.1-cm IIyama VisionMaster Pro 513 CRT Monitor. This monitor has a resolution of 1280 × 1024 pixels, a refresh rate of 100 Hz, and a mean luminance of 82 cd.m−2. Participants sat 57 cm away from the screen. Testing was performed in a well-lit room. A wireless mouse was used to track the stimulus. 
Stimulus and Procedure
The procedure used was adapted from Burge and Cormack.32 A bar (4.0° tall × 0.5° wide) presented on a grey background moved horizontally following a random walk for 11 seconds (Fig. 1). On every frame, which lasted 10 ms each, the bar moved horizontally from a random step according to a normal distribution with a standard deviation of 0.4°. Participants were instructed to track the stimulus as accurately as possible with the mouse cursor for the duration of the trial. Participants used their preferred hand for tracking (see Table 1). Participants initiated each trial by clicking on the stimulus after which it commenced moving. Five practice trials were performed before testing commenced. During testing, participants performed 9 blocks of 40 trials; each block had a unique combination of viewing condition and contrast condition (3 viewing conditions × 3 contrast conditions). The three viewing conditions were binocular, FE only, and AE only. The binocular condition was modified slightly from that used by Burge and Cormack32 in that participants were only asked to track the lateral position of the target rather than additionally reporting the perceived depth. This strategy ensured that the tracking task was consistent across all viewing conditions, allowing for a more direct comparison. Three contrast conditions, added for exploratory purpose, were tested: −1.0, 0.2, and 1.0 as defined by the following formula: (target luminance – background luminance)/background luminance (see Fig. 1a). The choice to test both the −1.0 and 1.0 contrast conditions stemmed from the finding that amblyopia affects ON visual pathways more than OFF pathways.35 We were interested in investigating whether this observation extends into processing time. The decision to additionally test the 0.2 contrast condition was based on the fact that the AE is less impaired at suprathreshold contrasts.36 As such, we were interested in investigating whether the interocular delay would be more pronounced near threshold. During monocular viewing, a black eye patch was used to occlude the untested eye. The order of the different conditions was randomized for each participant. Participants had the freedom to take breaks when wanted and were able to spread testing out over multiple days. However, most participants completed testing in a single day. It typically took 2 hours to complete all nine blocks of trials. An example of the raw data produced in one trial of this task is displayed in Figure 1b. 
Figure 1.
 
(a) Illustration of the stimulus used in the mouse tracking task. In each trial, the stimulus underwent random lateral motion following a random walk for 11 seconds. The participant was asked to track the stimulus with the mouse cursor as accurately as possible for the duration of the trial. The three panels on the right illustrate the three contrast conditions: the top, middle, and bottom panels correspond with the −1.0, 0.2, and 1.0 contrast conditions, respectively. (b) Example of the raw data from one trial of the mouse tracking task. The horizontal position of the stimulus (black) and the horizontal position of the mouse (red) are displayed as a function of time. Here, the lag between the mouse and the stimulus is apparent. (c) Example of a gamma distribution function (grey) fit to the average cross-correlation (black) of the stimulus velocity and mouse velocity. Average cross-correlations were computed for each condition individually and for each participant individually. The product of the scale and shape parameters of the gamma fit were taken as a measure of reaction time (dotted grey vertical line).
Figure 1.
 
(a) Illustration of the stimulus used in the mouse tracking task. In each trial, the stimulus underwent random lateral motion following a random walk for 11 seconds. The participant was asked to track the stimulus with the mouse cursor as accurately as possible for the duration of the trial. The three panels on the right illustrate the three contrast conditions: the top, middle, and bottom panels correspond with the −1.0, 0.2, and 1.0 contrast conditions, respectively. (b) Example of the raw data from one trial of the mouse tracking task. The horizontal position of the stimulus (black) and the horizontal position of the mouse (red) are displayed as a function of time. Here, the lag between the mouse and the stimulus is apparent. (c) Example of a gamma distribution function (grey) fit to the average cross-correlation (black) of the stimulus velocity and mouse velocity. Average cross-correlations were computed for each condition individually and for each participant individually. The product of the scale and shape parameters of the gamma fit were taken as a measure of reaction time (dotted grey vertical line).
Data Analysis
For future reference, the term “reaction time” is used to describe the lag between the movement of the stimulus and the movement of the mouse, and “latency” is used to describe the difference in reaction time between a monocular condition and the binocular condition. Given that the main contribution to overall reaction time is the motor response, it was necessary to distinguish reaction time from latency to isolate the specific contribution of visual processing from overall reaction time. Finally, “interocular delay” is used to describe the difference in reaction time between the two monocular conditions (which is equivalent to the difference in latency). All analyses were performed in MATLAB (R2022b) on a MacBook Pro (13-inch, M1, 2020) computer. The first and last second of each trial were discarded to ensure data reflected participants’ steady-state tracking performance and to remove any influence of the anticipation of the end of the trial. Reaction time was calculated using a method adapted from Chin and Burge.37 In this method, the changes in position of the mouse and stimulus were first converted into changes in velocity. Next, the cross-correlation between the mouse and stimulus velocity sequences was computed for 200 different lags between the mouse sequence and stimulus sequence. Cross-correlograms were then averaged across trials for a given participant and condition. A gamma distribution function was then fit to the averaged cross-correlograms using an iterative least squares estimation (Matlab's nlinfit function). The gamma distribution function was defined by  
\begin{equation*}\rho \left( \tau \right) = A\left[ {1/\left( {\Gamma \left( s \right){m^s}} \right)} \right]{\tau ^s}^{ - 1}{\rm{exp}}\left[ { - \tau /m} \right],\end{equation*}
where A is the amplitude, s is the shape, and m is the scale. The mode (m × s) of the fit was used as a measure of reaction time. An example of a gamma distribution function fit to an averaged velocity cross-correlogram is presented in Figure 1c. There are several benefits of converting changes in position to changes in velocity. First, velocity data are more forgiving of positional errors, an important factor given that we were more concerned about when the mouse moved relative to when the stimulus moved rather than where the mouse was relative to where the stimulus was. Second, using velocity data results in a reduction of the ceiling effect with regard to the correlation coefficients compared with using positional data, which were an important factor in our assessment of tracking performance. Third, velocity cross-correlations provide a complete characterization of the linear component of the visual system's impulse response function.32 Once the reaction time had been extracted from each trial, some data were excluded based on either the quality of the correlations or the quality of the fits. Cross-correlograms for which the peak correlation coefficient and fits for which the reaction time was calculated to be 0 or less were excluded, because these trials reflect extremely poor tracking performance or do not reflect actual reaction time, respectively. Additionally, trials with a peak correlation coefficient below the fifth percentile were excluded owing to the low quality of the stimulus tracking in these trials. Latency was then computed for each eye by subtracting the average binocular reaction time in a given contrast condition from the average monocular reaction time of a given eye in the same contrast condition. The peak correlation coefficient of the cross-correlogram in a given condition was used as a measure of tracking accuracy, with a larger coefficient indicating better accuracy. 
Individual participants' interocular delay significance was determined by applying a Wilcoxon signed-rank test on bootstrapped data. Bootstrapping was necessary given that our protocol to extract reaction time from our tracking data involved averaging across all trials within a given condition. 
Before performing any statistical tests, a single sample Kolmogorov-Smirnov goodness-of-fit hypothesis test was used to determine whether data were likely to have originated from a normal distribution. Parametric tests were used for data deemed not normally distributed, otherwise, t tests were used. 
Results
Figure 2 provides an example of how interocular delay is captured in the cross-correlogram of the AE and FE conditions. The peak of the AE cross-correlogram is both later in time and lower in amplitude than that of the FE. Average reaction time in each condition for both controls and amblyopes are shown in Figure 3. Across conditions and participants, controls exhibited an average dominant eye reaction time of 307.8 ± 35.6 ms, an average nondominant eye reaction time of 309.0 ± 40.2 ms, and an average binocular reaction time of 298.7 ± 36.1 ms. The average absolute difference in reaction time between the two eyes in controls was 9.1 ± 7.5 ms and ranged from 0.03 to 28.9 ms. 
Figure 2.
 
Gamma distribution function (dashed line) fit to averaged cross-correlogram (solid line) for both the amblyopic (blue) and fellow (red) eyes for one representative subject in the c = 1 contrast condition. Here, the longer reaction time and lessened tracking performance attributed to the amblyopic eye can be appreciated.
Figure 2.
 
Gamma distribution function (dashed line) fit to averaged cross-correlogram (solid line) for both the amblyopic (blue) and fellow (red) eyes for one representative subject in the c = 1 contrast condition. Here, the longer reaction time and lessened tracking performance attributed to the amblyopic eye can be appreciated.
Figure 3.
 
Boxplots of the reaction times across participants in each of the 9 conditions for 13 controls (a) and 23 amblyopes (b). The horizontal line and plus symbol in each box represent the median and mean respectively. The top and bottom of each box indicate the 75th and 25th percentiles, respectively. The whiskers indicate the range of the data with datapoints identified as outliers marked with a red “plus” symbol. Wilcoxon signed-rank tests were performed between each viewing condition within each contrast condition; P values for these tests are plotted.
Figure 3.
 
Boxplots of the reaction times across participants in each of the 9 conditions for 13 controls (a) and 23 amblyopes (b). The horizontal line and plus symbol in each box represent the median and mean respectively. The top and bottom of each box indicate the 75th and 25th percentiles, respectively. The whiskers indicate the range of the data with datapoints identified as outliers marked with a red “plus” symbol. Wilcoxon signed-rank tests were performed between each viewing condition within each contrast condition; P values for these tests are plotted.
This difference in reaction time characterizes the interocular delay. It falls in the same range as what was observed by Hamasaki and Flynn20: 12.5 ± 9.3 ms using a classic reaction time test with a broadband stimulus comparable with ours. However, it is markedly longer than what Wu et al.25 reported: 3 ± 2.611 ms using a very different paradigm based on the Pulfrich phenomenon and with narrowband stimuli at 2.85 c/d. To account for differences in stimulus properties across studies, which should influence the magnitude of delay,25 we compared the coefficient of variation38 (SD/mean) of control delays and found that our coefficient (0.83) was comparable to that produced by Wu et al.25 (0.87) and Hamasaki and Flynn20 (0.74). Thus, the variability we observed is expected. 
Across conditions and participants, amblyopes exhibited an average FE reaction time of 295.8 ± 38.9 ms, an average AE reaction time of 310.6 ± 50.6 ms, and an average binocular reaction time of 290.5 ± 35.4 ms. The average absolute difference in reaction time between the eyes was 18.4 ± 24 ms and ranged from 0.64 to 113.9 ms. The main distinctions between the controls and the amblyopes lies in the consistency of the pattern of reaction time across conditions and the magnitude of the difference in reaction time between the eyes. For controls, ocular dominance did not predict the relative reaction time between the eyes and any differences in reaction time between the eyes tended to be small (Fig. 3a). This finding is supported by the ANOVAs presented in Table 2, which demonstrates an effect of viewing condition on reaction time for the amblyopes, but not for the controls. Then, in the amblyopic group, Wilcoxon signed-rank tests revealed that the AE was slower by a sizable margin across contrast conditions (Fig. 3b; see Supplementary S1). 
Table 2.
 
Two-Way ANOVAs for Both Controls and Amblyopes Using Reaction Time as the Criterion
Table 2.
 
Two-Way ANOVAs for Both Controls and Amblyopes Using Reaction Time as the Criterion
We also performed an investigation into the difference in reaction time between the contrast conditions. We were particularly interested in comparing the reaction time in the 0.2 contrast condition to the reaction time in the −1.0 and 1.05 contrast conditions because this strategy offered a comparison between near-threshold and suprathreshold stimuli. We expected to see a greater difference between the 0.2 contrast condition and the −1.0 and 1.0 contrast conditions for the AE compared with the FE. We found that the AE reaction time was marginally slower in the 0.2 contrast condition compared with the other two conditions. This difference was not meaningfully different from that seen in the FE (P = 0.121, Wilcoxon signed-rank test). Two-way ANOVAs (Table 2) corroborated the lack of a contrast effect and revealed only an effect of viewing condition on reaction time for the amblyopic subjects, F(2) = 4.21; P = 0.016, and no effects for the control subjects (Table 2). 
We were interested in comparing binocular enhancement between our control and amblyopic groups. The magnitude of binocular enhancement was equated to the difference between the binocular reaction time and the fastest eye reaction time, which in fact corresponds with the latency of the fastest eye. This finding is presented for both groups in each contrast condition (Fig. 4). t Tests revealed that the magnitude of binocular enhancement was not meaningfully different from zero for any group or condition (all P > 0.3, Supplementary S7). Additionally, no differences between groups were found in the −1.0, 0.2, or 1.0 contrast conditions (all P > 0.2, two-sample t test) offering further support for a lack of a contrast effect. Owing to the widespread absence of a contrast effect for both amblyopes and controls, reaction time was averaged across contrast condition in the analyses presented in Figures 5 and 7. Because there is some variability across participants as to which eye displays a longer latency, an investigation was performed to describe the pattern of latency for each participant. In Figure 5, the latency of one eye, averaged across the three contrast conditions, is displayed as a function of the average latency of the other eye for all individual subjects. Differences in latencies producing a P value of <0.05, as determined by bootstrapping and Wilcoxon signed-rank tests, are represented with a star symbol. For the controls, 3 participants displayed a higher latency for their nondominant eye and 10 did not show any difference (Fig. 5a). A moderate correlation between the latency of the dominant eye and the latency of the nondominant eye was found (R2 = 0.259; P = 0.076), meaning that the latency of one eye was somewhat predictive of the latency of the other eye. For the amblyopes, 17 participants displayed a higher latency for the AE and 6 participants showed a higher latency for their FE (Fig. 5b). Wilcoxon signed rank tests indicated that differences in latency were particularly large (P < 0.05) for 14 subjects, 13 of which displayed a higher latency in their AE. As such, the latency in the AE was higher in the majority of cases. A two-tailed binomial test was computed for both groups with the null expectation being that exactly 50% of participants will fall above the identity line. This resulted in a P value of 0.867 (N = 13, K = 5) for controls and a P value of 0.005 (N = 23, K = 18) for amblyopes, indicating a greater temporal imbalance between the eyes in amblyopes compared with controls. Additionally, we observed good correlation between the latencies of the two eyes in controls (R2 = 0.259; P = 0.076), but not in amblyopes (R2 = 0.052; P = 0.298). Results of binomial tests and linear regressions performed on each individual clinical group are displayed in Supplements S9 and S10, respectively. 
Figure 4.
 
Comparison of binocular enhancement between amblyopes and controls in each contrast condition. Latency (monocular reaction time minus binocular reaction time) of the fastest eye was used as a measure of binocular enhancement. The horizontal line and plus symbol in each box represent the median and mean respectively. The top and bottom of each box indicate the 75th and 25th percentiles, respectively. The whiskers indicate the range of the data with datapoints identified as outliers marked with a small black “plus” symbol. Two-sample t tests revealed no meaningful difference between groups in any of the three contrast conditions.
Figure 4.
 
Comparison of binocular enhancement between amblyopes and controls in each contrast condition. Latency (monocular reaction time minus binocular reaction time) of the fastest eye was used as a measure of binocular enhancement. The horizontal line and plus symbol in each box represent the median and mean respectively. The top and bottom of each box indicate the 75th and 25th percentiles, respectively. The whiskers indicate the range of the data with datapoints identified as outliers marked with a small black “plus” symbol. Two-sample t tests revealed no meaningful difference between groups in any of the three contrast conditions.
Figure 5.
 
The latency of the nondominant eye/AE plotted against the latency of the dominant eye/FE for both controls (a) and amblyopes (b). Each point represents an individual participant. Points plotted above the dashed reference line indicate a larger latency attributed to the nondominant eye/AE. (b) The point sizes correspond with the difference in visual acuity between the eyes (larger points indicate greater differences). Amblyopic participants are color coded based on their clinical group and recovered amblyopes are plotted with faded symbols. A Wilcoxon signed-rank test was performed to compare the eyes of each subject; differences of P < 0.05 are indicated with a star symbol. The numbers within the points correspond to participant numbers in Table 1. Results of two-tailed binomial tests are plotted in the bottom right of each panel.
Figure 5.
 
The latency of the nondominant eye/AE plotted against the latency of the dominant eye/FE for both controls (a) and amblyopes (b). Each point represents an individual participant. Points plotted above the dashed reference line indicate a larger latency attributed to the nondominant eye/AE. (b) The point sizes correspond with the difference in visual acuity between the eyes (larger points indicate greater differences). Amblyopic participants are color coded based on their clinical group and recovered amblyopes are plotted with faded symbols. A Wilcoxon signed-rank test was performed to compare the eyes of each subject; differences of P < 0.05 are indicated with a star symbol. The numbers within the points correspond to participant numbers in Table 1. Results of two-tailed binomial tests are plotted in the bottom right of each panel.
Considering the differences found in reaction time between the AE and FE, we were interested in whether these differences held true for tracking accuracy as well. As such, we assessed the effect of viewing condition and contrast condition on tracking accuracy. As mentioned in the Methods, peak correlation coefficients from the velocity cross-correlograms were used as a measure of tracking accuracy; this analysis is displayed in Figure 6. For the controls, neither eye consistently produced inferior tracking performance across contrast conditions and differences in tracking performance tended to be small (results of Wilcoxon signed-rank tests are presented in Supplementary S2a). For the amblyopes, tracking performance tended to be worse when the AE was relied on regardless of the contrast condition, and for the −1.0 and 0.2 contrast conditions, the difference in tracking performance between the eyes was meaningful, as indicated by a Wilcoxon signed-rank test (Supplementary S2b). Overall, the AE produced much worse tracking performance compared with the nondominant eye of controls. 
Figure 6.
 
Average tracking performance in each condition for controls (a) and amblyopes (b). Average correlation coefficients from the mouse and stimulus velocity cross-correlations were used as a measure of tracking performance with higher coefficients equated to better performance. The horizontal line and plus symbol in each box represent the median and mean respectively. The top and bottom of each box indicate the 75th and 25th percentiles, respectively. The whiskers indicate the range of the data with datapoints identified as outliers marked with a red “plus” symbol. Wilcoxon signed-rank tests were performed between each viewing condition within each contrast condition; P values for these tests are plotted.
Figure 6.
 
Average tracking performance in each condition for controls (a) and amblyopes (b). Average correlation coefficients from the mouse and stimulus velocity cross-correlations were used as a measure of tracking performance with higher coefficients equated to better performance. The horizontal line and plus symbol in each box represent the median and mean respectively. The top and bottom of each box indicate the 75th and 25th percentiles, respectively. The whiskers indicate the range of the data with datapoints identified as outliers marked with a red “plus” symbol. Wilcoxon signed-rank tests were performed between each viewing condition within each contrast condition; P values for these tests are plotted.
Given the differences between the AE and FE revealed in our reaction time and tracking performance analyses, we were interested in whether these differences were correlated with differences in visual acuity between the eyes. Therefore, we performed an investigation into the relationship between interocular delay and the difference in visual acuity between the eyes of the amblyopic participants (Fig. 7). Interocular delay was found to be positively correlated with visual acuity difference as revealed by a linear regression (R2 = 0.484; P = 0.0002), meaning that, as the difference in reaction time between the eyes increases, the difference in visual acuity between the eyes tends to be greater. In other words, greater severity of amblyopia is associated with larger temporal differences in processing between the eyes. Table 3 displays the results of regressions performed on each individual clinical group. Performing this regression excluding participant 12, who has an unusually high interocular delay, reduces the coefficient to R2 = 0.274, but does not change our interpretation of the correlation (P = 0.01). 
Figure 7.
 
The average interocular delay across contrast conditions for each amblyopic participant plotted against their difference in interocular visual acuity. Each point represents an individual participant and numbers within each point correspond to the participant numbers in Table 1. Participants are color coded based on their clinical group. A Wilcoxon signed-rank test was performed to compare the eyes of each subject; differences of P < 0.05 are indicated with a star symbol. Recovered amblyopes are plotted with faded symbols. Interocular delay and visual acuity difference were positively correlated (R2 = 0.484; P = 0.0002).
Figure 7.
 
The average interocular delay across contrast conditions for each amblyopic participant plotted against their difference in interocular visual acuity. Each point represents an individual participant and numbers within each point correspond to the participant numbers in Table 1. Participants are color coded based on their clinical group. A Wilcoxon signed-rank test was performed to compare the eyes of each subject; differences of P < 0.05 are indicated with a star symbol. Recovered amblyopes are plotted with faded symbols. Interocular delay and visual acuity difference were positively correlated (R2 = 0.484; P = 0.0002).
Table 3.
 
Results of Linear Regression Between Interocular Delay and Visual Acuity Difference for Each Clinical Group
Table 3.
 
Results of Linear Regression Between Interocular Delay and Visual Acuity Difference for Each Clinical Group
A two-way ANOVA was performed to investigate whether biological sex, previous interventions, or the type of amblyopia were predictive of interocular delay (Supplementary S3a). The correlation of interocular delay with age and stereoacuity was also investigated (Supplements S4a and S5a, respectively). Only a meaningful effect of prior intervention was found, F(3) = 4.31; P = 0.0237. Comparing the individual intervention groups with a Wilcoxon rank-sum test revealed a meaningful difference between the no intervention group and the patching group (p = 0.0012) (Supplementary S8). Additional linear regressions were performed to investigate the relationships between the previously mentioned clinical characteristics and interocular delay on tracking accuracy (Supplements S4b, S5b, and S6). A moderate positive correlation with age (R2 = 0.27; P = 0.011) and a weak correlation with interocular delay (R2 = 0.188; P = 0.039) were found. 
Considering that the procedure used in the present study, and continuous tracking tasks in general, are fairly new, we were interested to know how much tracking data is necessary to collect to produce reliable assessments of reaction time. With this metric in mind, we performed two additional analyses investigating the effect of reducing the number of trials or reducing the length of trials on the residual error of gamma distribution functions fit to averaged cross-correlograms (Fig. 8). Lower levels of residual error indicate a better approximation of the data and thus supply more reliable assessments. We specifically assessed the mean squared error (MSE) of the gamma fits as a function of either the number of trials or the length of trials used when performing cross-correlations between the mouse cursor and stimulus velocity data. The test of trial length revealed that MSE tends to fall below 0.0002 for trials of only 2 seconds in length, and that MSE plateaus after trials exceed 5 seconds in length. This finding means that there are minimal improvements to the reliability of reaction time estimates by extending trials beyond 5 seconds. The test of the number of trials revealed that only 10 trials were necessary to reduce the MSE below 0.0002, and that MSE plateaus after the number of trials exceed approximately 26. Therefore, using any more than 26 trials is unlikely to improve the reliability of reaction time assessments. These two analyses demonstrate that the current method would continue to produce reliable assessments of reaction time, even if fewer or shorter trials were used. 
Figure 8.
 
Effect of reducing number of trials (a) or length of trials (b) on the residual error of gamma distribution function fits. The black lines indicate average MSE, and the grey section outlines one standard deviation above and below the average. (a) A single MSE was calculated for each participant before being averaged across participants. (b) Fifty MSE calculations were averaged for each participant before being averaged across participants.
Figure 8.
 
Effect of reducing number of trials (a) or length of trials (b) on the residual error of gamma distribution function fits. The black lines indicate average MSE, and the grey section outlines one standard deviation above and below the average. (a) A single MSE was calculated for each participant before being averaged across participants. (b) Fifty MSE calculations were averaged for each participant before being averaged across participants.
Discussion
The continuous tracking task32 produces millisecond-scale estimates of interocular delay and is accessible to all but the most severe amblyopes (see Table 1). 
The absolute magnitude of interocular delay observed in our amblyopic subjects (mean 18.4 ± 24 ms; range, 0.64–113.9 ms) was comparable to a number of behavioral studies that tested a pool of amblyopes with an AE visual acuity of ≤1.0 logMAR (25 ms in Hamasaki and Flynn, 198120; 0–110 ms in Wu et al., 2020,25 who also reported a faster AE in some instances; 5–100 ms in Reynaud and Hess, 201926). This finding holds true for a study that shared a similar pool to ours, where subjects exhibited an AE acuity of ≤1.5 logMAR (5–240 ms; Ciuffreda et al., 197824). Most electrophysiological studies that tested a pool of amblyopes with AE acuity of 1.0 logMAR also reported interocular delays of approximately 20 ms27,39,40). Overall, our results are remarkably comparable with those produced with drastically different methods. 
No meaningful delay was observed in the control group, which, again, is consistent with previous findings.25 Regardless of contrast condition, the amblyopic subjects tended to show both a larger latency in their AE compared with the nondominant eye of controls and a much greater interocular delay than that seen in the controls. The lack of difference between the contrast conditions means that any visual processing differences caused by ON/OFF pathways or near-threshold versus suprathreshold stimuli are minimal or are not measurable within the range of parameters we tested. In any case, these results offer a clear demonstration of the interocular delay in amblyopia particularly in comparison with controls. 
Confirming the presence of a delay prompted our investigation into the relationship between interocular delay and visual acuity difference (Fig. 7), which revealed a strong positive correlation. This finding indicates that greater differences in visual acuity tend to be associated with more temporal asynchrony between the eyes. This result offers compelling evidence that the temporal asynchrony observed here and in previous studies has important implications for the condition as a whole. It also offers some alleviation of the conflicting results produced by Reynaud and Hess26 and Wu et al.25 and indicates that, by testing a broader range of amblyopia, the relationship between acuity and interocular delay is clearer. This finding is especially interesting considering that Chadnova et al.27 found that contrast sensitivity did not predict the magnitude of the delay. As of yet, the causal relationship between acuity and interocular delay is unknown. 
Our investigation into the pattern of the delay (ie, which eye was slower) revealed further differences between amblyopes and controls. As can be seen in Figure 5, the AE was found to be the slower of the two eyes for the majority of amblyopes. For 6 amblyopic participants out of 23, the FE was found to be slower. These were moderate or recovered amblyopes (with an interocular difference of <0.5 logMAR) (Fig. 7); this finding is consistent with previous studies.25 Furthermore, unlike the controls, the latency of one eye was not predictive of the latency of the other. Altogether, this result exemplifies that, rather than a simple delay, amblyopes may suffer a desynchronization of their eyes, indicative of the lack of cooperation between the eyes. 
Indeed, this finding is confirmed by our observation that there is no binocular enhancement in the time domain (Fig. 4). We also did not observe any binocular enhancement in the control group. For contrast summation, it has been shown that binocular summation is dependent on the speed of a stimulus, with high speeds resulting in the weakest summation.41 Moreso, it is known that binocular summation is lower in magnitude for suprathreshold stimuli.42 It is, therefore, possible that there is simply no binocular enhancement in the time domain within the range of parameters we tested. 
Is this delay caused by the poor acuity and accuracy in the AE? We observed correlations between both delay and visual acuity, and delay and tracking accuracy. First, given that we analyzed velocity data rather than positional data, acuity is not expected to have affected our estimates of reaction time to a meaningful extent.37 Second, as observed by Chin and Burge37 and Burge et al.43 with a similar task, lower spatial resolution can in fact reduce latency and improve tracking accuracy in the speed domain. Therefore, we are confident that the delay we observed is not the consequence of poor tracking performance. 
The delay can instead be explained by interocular differences in temporal integration periods37 and lower temporal resolution of the AE.19,44,45 Indeed, the difference in amplitude of the two peaks displayed in Figure 2 is consistent with the effect expected from differences in temporal integration and likely characterize differing impulse response functions between the eyes. Such changes in the temporal integration window can be induced by placing a neutral density filter over one eye, as was observed behaviorally46,47 and electrophysiologically.48 This manipulation is presumed to be a partial model of amblyopia, simulating the difference in processing speed and contrast sensitivity between the eyes in absence of differences in visual acuity.47 Furthermore, Burge et al.43,49 demonstrated that the processing speed and the temporal integration window of a given eye can be modulated as a function of the spatial frequency, with lower frequencies inducing shorter integration periods. They additionally demonstrated a counterintuitive effect: temporal processing can be accelerated using blurring filters. This result implies that poor optics of the eye do not directly induce a delay by themselves; rather, certain aspects of poor vision have specific consequences for the temporal integration window of the AE, resulting in either speeding up or slowing down of visual processing. 
The present findings, as well as those from previous studies,50,51 demonstrate the potential for the development of novel treatments for amblyopia based on interocular synchronicity. We found that previously patched amblyopes exhibit smaller interocular delays than those without prior intervention, suggesting that the delay may be linked to the progression and severity of amblyopia. Our study additionally demonstrates that interocular delay is correlated to visual acuity, further supporting the link to severity and suggesting that, by manipulating the temporal properties of the ocular inputs, visual acuity may be influenced. This finding is further supported by the results of Huang et al.,50 who found that combining standard patching with an experimental dichoptic movie treatment consisting of delaying the image shown to the FE by 1 frame (8.3 ms) produced larger shifts in ocular dominance than patching alone. Because only one temporal offset was tested in this study, it remains to be seen whether the offset that produces the greatest therapeutic effect is individualized and whether this offset correlates with the interocular delay. Eisen-Enosh et al.51 performed various assessments of binocular summation while adjusting the interocular phase difference of their stimuli and found that certain phase shifts produced much greater improvements to binocular summation than others. However, the researchers did not investigate the relationship between this optimal phase and the interocular delay of their participants. It is, therefore, conceivable that an offset perfectly synchronized to the interocular delay may produce the greatest improvements in performance, given that this should resynchronize the two eyes. 
The present study was successful in demonstrating the accessibility of continuous tracking as a method for measuring the interocular delay for all but the most severe amblyopes. This method revealed a much more prominent temporal imbalance between the eyes in amblyopes compared with controls, and importantly, the magnitude of this imbalance was found to be closely related to the difference in visual acuity between the eyes. 
Acknowledgments
Supported by a Projet-Pilote grant from the Réseau de Recherche en Santé de la Vision to AR. 
Disclosure: D. Gurman, None; A. Reynaud, None 
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Figure 1.
 
(a) Illustration of the stimulus used in the mouse tracking task. In each trial, the stimulus underwent random lateral motion following a random walk for 11 seconds. The participant was asked to track the stimulus with the mouse cursor as accurately as possible for the duration of the trial. The three panels on the right illustrate the three contrast conditions: the top, middle, and bottom panels correspond with the −1.0, 0.2, and 1.0 contrast conditions, respectively. (b) Example of the raw data from one trial of the mouse tracking task. The horizontal position of the stimulus (black) and the horizontal position of the mouse (red) are displayed as a function of time. Here, the lag between the mouse and the stimulus is apparent. (c) Example of a gamma distribution function (grey) fit to the average cross-correlation (black) of the stimulus velocity and mouse velocity. Average cross-correlations were computed for each condition individually and for each participant individually. The product of the scale and shape parameters of the gamma fit were taken as a measure of reaction time (dotted grey vertical line).
Figure 1.
 
(a) Illustration of the stimulus used in the mouse tracking task. In each trial, the stimulus underwent random lateral motion following a random walk for 11 seconds. The participant was asked to track the stimulus with the mouse cursor as accurately as possible for the duration of the trial. The three panels on the right illustrate the three contrast conditions: the top, middle, and bottom panels correspond with the −1.0, 0.2, and 1.0 contrast conditions, respectively. (b) Example of the raw data from one trial of the mouse tracking task. The horizontal position of the stimulus (black) and the horizontal position of the mouse (red) are displayed as a function of time. Here, the lag between the mouse and the stimulus is apparent. (c) Example of a gamma distribution function (grey) fit to the average cross-correlation (black) of the stimulus velocity and mouse velocity. Average cross-correlations were computed for each condition individually and for each participant individually. The product of the scale and shape parameters of the gamma fit were taken as a measure of reaction time (dotted grey vertical line).
Figure 2.
 
Gamma distribution function (dashed line) fit to averaged cross-correlogram (solid line) for both the amblyopic (blue) and fellow (red) eyes for one representative subject in the c = 1 contrast condition. Here, the longer reaction time and lessened tracking performance attributed to the amblyopic eye can be appreciated.
Figure 2.
 
Gamma distribution function (dashed line) fit to averaged cross-correlogram (solid line) for both the amblyopic (blue) and fellow (red) eyes for one representative subject in the c = 1 contrast condition. Here, the longer reaction time and lessened tracking performance attributed to the amblyopic eye can be appreciated.
Figure 3.
 
Boxplots of the reaction times across participants in each of the 9 conditions for 13 controls (a) and 23 amblyopes (b). The horizontal line and plus symbol in each box represent the median and mean respectively. The top and bottom of each box indicate the 75th and 25th percentiles, respectively. The whiskers indicate the range of the data with datapoints identified as outliers marked with a red “plus” symbol. Wilcoxon signed-rank tests were performed between each viewing condition within each contrast condition; P values for these tests are plotted.
Figure 3.
 
Boxplots of the reaction times across participants in each of the 9 conditions for 13 controls (a) and 23 amblyopes (b). The horizontal line and plus symbol in each box represent the median and mean respectively. The top and bottom of each box indicate the 75th and 25th percentiles, respectively. The whiskers indicate the range of the data with datapoints identified as outliers marked with a red “plus” symbol. Wilcoxon signed-rank tests were performed between each viewing condition within each contrast condition; P values for these tests are plotted.
Figure 4.
 
Comparison of binocular enhancement between amblyopes and controls in each contrast condition. Latency (monocular reaction time minus binocular reaction time) of the fastest eye was used as a measure of binocular enhancement. The horizontal line and plus symbol in each box represent the median and mean respectively. The top and bottom of each box indicate the 75th and 25th percentiles, respectively. The whiskers indicate the range of the data with datapoints identified as outliers marked with a small black “plus” symbol. Two-sample t tests revealed no meaningful difference between groups in any of the three contrast conditions.
Figure 4.
 
Comparison of binocular enhancement between amblyopes and controls in each contrast condition. Latency (monocular reaction time minus binocular reaction time) of the fastest eye was used as a measure of binocular enhancement. The horizontal line and plus symbol in each box represent the median and mean respectively. The top and bottom of each box indicate the 75th and 25th percentiles, respectively. The whiskers indicate the range of the data with datapoints identified as outliers marked with a small black “plus” symbol. Two-sample t tests revealed no meaningful difference between groups in any of the three contrast conditions.
Figure 5.
 
The latency of the nondominant eye/AE plotted against the latency of the dominant eye/FE for both controls (a) and amblyopes (b). Each point represents an individual participant. Points plotted above the dashed reference line indicate a larger latency attributed to the nondominant eye/AE. (b) The point sizes correspond with the difference in visual acuity between the eyes (larger points indicate greater differences). Amblyopic participants are color coded based on their clinical group and recovered amblyopes are plotted with faded symbols. A Wilcoxon signed-rank test was performed to compare the eyes of each subject; differences of P < 0.05 are indicated with a star symbol. The numbers within the points correspond to participant numbers in Table 1. Results of two-tailed binomial tests are plotted in the bottom right of each panel.
Figure 5.
 
The latency of the nondominant eye/AE plotted against the latency of the dominant eye/FE for both controls (a) and amblyopes (b). Each point represents an individual participant. Points plotted above the dashed reference line indicate a larger latency attributed to the nondominant eye/AE. (b) The point sizes correspond with the difference in visual acuity between the eyes (larger points indicate greater differences). Amblyopic participants are color coded based on their clinical group and recovered amblyopes are plotted with faded symbols. A Wilcoxon signed-rank test was performed to compare the eyes of each subject; differences of P < 0.05 are indicated with a star symbol. The numbers within the points correspond to participant numbers in Table 1. Results of two-tailed binomial tests are plotted in the bottom right of each panel.
Figure 6.
 
Average tracking performance in each condition for controls (a) and amblyopes (b). Average correlation coefficients from the mouse and stimulus velocity cross-correlations were used as a measure of tracking performance with higher coefficients equated to better performance. The horizontal line and plus symbol in each box represent the median and mean respectively. The top and bottom of each box indicate the 75th and 25th percentiles, respectively. The whiskers indicate the range of the data with datapoints identified as outliers marked with a red “plus” symbol. Wilcoxon signed-rank tests were performed between each viewing condition within each contrast condition; P values for these tests are plotted.
Figure 6.
 
Average tracking performance in each condition for controls (a) and amblyopes (b). Average correlation coefficients from the mouse and stimulus velocity cross-correlations were used as a measure of tracking performance with higher coefficients equated to better performance. The horizontal line and plus symbol in each box represent the median and mean respectively. The top and bottom of each box indicate the 75th and 25th percentiles, respectively. The whiskers indicate the range of the data with datapoints identified as outliers marked with a red “plus” symbol. Wilcoxon signed-rank tests were performed between each viewing condition within each contrast condition; P values for these tests are plotted.
Figure 7.
 
The average interocular delay across contrast conditions for each amblyopic participant plotted against their difference in interocular visual acuity. Each point represents an individual participant and numbers within each point correspond to the participant numbers in Table 1. Participants are color coded based on their clinical group. A Wilcoxon signed-rank test was performed to compare the eyes of each subject; differences of P < 0.05 are indicated with a star symbol. Recovered amblyopes are plotted with faded symbols. Interocular delay and visual acuity difference were positively correlated (R2 = 0.484; P = 0.0002).
Figure 7.
 
The average interocular delay across contrast conditions for each amblyopic participant plotted against their difference in interocular visual acuity. Each point represents an individual participant and numbers within each point correspond to the participant numbers in Table 1. Participants are color coded based on their clinical group. A Wilcoxon signed-rank test was performed to compare the eyes of each subject; differences of P < 0.05 are indicated with a star symbol. Recovered amblyopes are plotted with faded symbols. Interocular delay and visual acuity difference were positively correlated (R2 = 0.484; P = 0.0002).
Figure 8.
 
Effect of reducing number of trials (a) or length of trials (b) on the residual error of gamma distribution function fits. The black lines indicate average MSE, and the grey section outlines one standard deviation above and below the average. (a) A single MSE was calculated for each participant before being averaged across participants. (b) Fifty MSE calculations were averaged for each participant before being averaged across participants.
Figure 8.
 
Effect of reducing number of trials (a) or length of trials (b) on the residual error of gamma distribution function fits. The black lines indicate average MSE, and the grey section outlines one standard deviation above and below the average. (a) A single MSE was calculated for each participant before being averaged across participants. (b) Fifty MSE calculations were averaged for each participant before being averaged across participants.
Table 1.
 
Demographic Information From Our 24 Amblyopic Subjects
Table 1.
 
Demographic Information From Our 24 Amblyopic Subjects
Table 2.
 
Two-Way ANOVAs for Both Controls and Amblyopes Using Reaction Time as the Criterion
Table 2.
 
Two-Way ANOVAs for Both Controls and Amblyopes Using Reaction Time as the Criterion
Table 3.
 
Results of Linear Regression Between Interocular Delay and Visual Acuity Difference for Each Clinical Group
Table 3.
 
Results of Linear Regression Between Interocular Delay and Visual Acuity Difference for Each Clinical Group
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