Binocular Visual Deficits at Low to High Spatial Frequency in Intermittent Exotropia After Surgery

Abstract

Purpose: To investigate binocular visual deficits at low to high spatial frequencies in patients with intermittent exotropia (IXT) after surgical correction, using the binocular orientation combination task.

Methods: Thirteen patients whose IXT has been aligned surgically (17 ± 4.8 years old; 7 females) and 13 normal individuals (21.8 ± 2.5 years old; 6 females) were recruited. All participants had normal or corrected-to-normal visual acuity. The IXT patients had undergone surgery at least one month prior to the study and achieved successful eye alignment post-surgery. We measured participants’ balance points (BPs), defined as the interocular contrast ratio (nondominant eye/dominant eye) when both eyes contributed equally to binocular combination, using the binocular orientation combination task at three spatial frequencies (0.5, 4.0, and 8.0 cycles/degree). The absolute values of log10(BP) (i.e., |logBP|) and the area under of the |logBP| versus spatial frequency curve were used to quantify the extent of binocular imbalance.

Results: Surgery aligned the eye position of patients with IXT, with a postoperative exodeviation of −4.92 ± 4.29 prism diopters at distance. Participants’ |logBP| values showed significant differences between groups, F_(1,24) = 9.175, P = 0.006, and across spatial frequencies, F_(2,48) = 7.127, P = 0.002. However, the interaction between group and spatial frequency was not significant, F_(2,48) = 0.379, P = 0.687.

Conclusions: Patients whose IXT has been alighted surgically experience binocular imbalance across a wide range of spatial frequencies, with greater binocular imbalance occurring at high spatial frequencies than low spatial frequencies.

Intermittent exotropia (IXT), also known as distance exotropia, divergence excess exotropia and exotropia of inattention, is the prevailing form of exotropia encountered during early childhood.^1–3 It accounts for approximately 50% to 90% of all exotropia and impacts approximately 1% of the general population.^2,4,5 Research indicates that 1 out of every 30 preschool children in eastern China experiences IXT.⁶ Individuals with IXT typically manifest with one eye unconsciously turning outward, while the other eye fixates forward, especially during moments of inattention, fatigue, or when gazing into the distance. Symptoms may include photophobia, with patients usually closing one eye in bright sunlight, and some may encounter diplopia in the absence of suppression.¹ These manifestations significantly impact the quality of life for both patients and their families.⁷ 

Eye muscle surgery remains the primary treatment for IXT, aiming to align the eye deviation to no more than 10 prism diopters.^1,5 Previous studies have shown that patients with IXT, even after surgical correction, still exhibit deficits in binocular function, such as abnormal sensory fusion status, decreased fusional convergence amplitude, and poor stereoacuity.^8–12 Visual psychophysical methods have provided new insights into understanding binocular visual processes.^13–17 Recently, two studies that used psychophysical methods found that patients with IXT still exhibited pronounced sensory eye imbalance immediately after IXT had been aligned surgically and had no improvement at 12 months after surgery,^18,19 indicating an absence of surgical adaptation for balanced binocular function after correction. However, these observations focused only on a low spatial frequency, namely 1 cycles/degree. Considering the broad spectrum of spatial frequencies present in our natural scenes,²⁰ sensory eye imbalance at a low spatial frequency may not adequately represent binocular visual deficits. This finding has been actually demonstrated in cases of amblyopia, where previous studies have shown that amblyopes, whether treated for normal visual acuity²¹ or left untreated,²² manifested stronger sensory eye imbalance at high spatial frequencies compared with low spatial frequencies. Therefore, a critical question that remains unanswered in patients with IXT after surgical correction is whether their sensory eye imbalance is consistent across spatial frequencies or if they exhibit more severe sensory eye imbalance at high spatial frequencies. 

To address this question, we adopted a binocular orientation combination paradigm, which has been demonstrated could precisely estimate sensory eye imbalance of up to 8 cycles/degree in previous reports,²³ to investigate the binocular vision function in patients with IXT after surgery at 0.5, 4.0, and 8.0 cycles/degree. Our findings indicated that patients with IXT after surgical correction exhibited significant sensory eye imbalance across these frequencies, with more pronounced imbalance occurring at high spatial frequencies. 

Methods

Participants

Thirteen patients whose IXT has been aligned surgically (17 ± 4.8 years old; 7 females) and 13 normal controls (21.8 ± 2.5 years old; 6 females) with normal or corrected-to-normal visual acuity (≤0.00 logMAR) participated in this study. All subjects in the experimental group were recruited from the Eye Hospital of Wenzhou Medical University. Detailed inclusion and exclusion criteria for all subjects are provided in Table 1, and their clinical particulars, including age, gender, and refraction, are shown in Table 2. During the experiment, subjects wore their corrective lenses if necessary. Written informed consent was obtained from all participants or their accompanying parents or guardians. The study followed the tenets of the Declaration of Helsinki and was approved by the Ethics Committee of the Eye hospital of Wenzhou Medical University. 

Table 1.

 

Inclusion and Exclusion Criteria of Subjects

 

Table 2.

 

Demographics and Clinical Details of Patients With IXT

 

Clinical Examinations

All patients with IXT underwent comprehensive ophthalmic examinations after surgery, encompassing refraction, best-corrected visual acuity (Table 2), squint angle, stereoacuity, sensory fusion function, control of exodeviation, slit-lamp biomicroscopy, and fundus examination (Table 3). 

Table 3.

 

Clinical Characteristics of IXTs Before and After Surgery

 

Squint angle was measured by the prism and alternate cover test at a distance of 5 m. Stereoacuity at both far (3 m) and near (40 cm) distance was evaluated using the distant Random Dots Stereograph (P/N 1006, Vision assessment Corporation, IL, USA) and the TNO stereotest (Laméris Ootech B.V., Nieuwegein, the Netherlands), respectively, with a range of 60 to 400 and 60 to 480 arcsec. If patients did not exhibit stereo perception under the largest disparity, their stereoacuity was recorded as “nil”. Sensory fusion was evaluated with Worth's four-dot test at near (33 cm) and far distance (6 m). If four dots were reported by patients, we assessed that they had normal sensory fusion function.^24,25 Control of exodeviation was quantified using a 0- to 5-point (best to worst control) scale at distance (3 m) and near (1/3 m). Levels 3 to 5 on the scale grade the proportion of time any spontaneous exotropia is present during a 30-second period of observation (5 represent constant tropia) and levels 0 to 2 grade the speed of recovery after a 10-second dissociation (worst of three 10-second dissociations; 0 represents <1 second recovery).²⁶ After surgery, all patients had a score of 0 (pure phoria) or 1 (recovery 1–5 seconds after dissociation) points. 

Apparatus

The binocular orientation combination task was conducted using MATLAB R2016b (v9.1.0 MathWorks, Inc., Natick, MA, USA) with Psychtoolbox extension 3.0.14^27–29 run on a MacBook Pro (13-in., 2017; Apple, Inc., Cupertino, CA, USA). Stimuli were presented dichoptically to observers through gamma-corrected goggles (GOOVIS, AMOLED display, NED Optics, Shenzhen, China), which had a resolution of 2560 × 1600, a refresh rate of 60 Hz, and a maximal luminance of 150 cd/m². 

Stimuli and Design

We used a binocular orientation combination paradigm to assess the sensory eye imbalance of observers at three different spatial frequencies (0.5, 4.0, and 8.0 cycles/degree). Two horizontal sinusoidal gratings (size: 2 cycles) with equal and opposite tilts (±7.1°) were dichoptically presented to the two eyes. The tilt of the fused grating would be 0° relative to horizontal position if the two eyes were balanced (Fig. 1A). The contrast of the grating presented to the nondominant eye (nonDE) was fixed at 50% (Fig. 1B), and the contrast of the grating presented to the DE was varied from 0% to 100% (7 interocular contrast ratios) in different trials. To eliminate positional bias, we designed two distinct orientation configurations for the gratings. In the first configuration, relative to horizontal position, the orientation was +7.1° in the nonDE and −7.1° in the DE. The situation was reversed in the second configuration—the orientation was +7.1° in the DE and −7.1° in the nonDE. Each orientation configuration at one interocular contrast ratio was tested with 20 repetitions, resulting in a total of 280 trials (7 interocular contrast ratios × 2 orientation configurations × 20 repetitions) to evaluate sensory eye imbalance at one spatial frequency. 

Figure 1.

 

The binocular orientation combination task. (A) Illustration of the binocular orientation task. Two horizontal sinusoidal gratings with equal and opposite tilts (±7.1°) were dichoptically presented to the two eyes. The tilt of the fused grating would be 0° relative to the horizontal position if the two eyes were balanced. Seven different interocular contrast ratios (ranging from 0 to 2) were set for each subject, and the contrast of the grating presented to nonDE was fixed at 50%. (B) In both the experimental and control group, the contrast of the grating with different spatial frequencies (0.5, 4.0, and 8.0 cycles/degree) presented to the nonDE was fixed at 50%. The size of gratings in the figure does not represent their actual sizes. (C) An illustration of the psychometric function. The cumulative Gaussian distribution function was used to fit the psychometric function. The x-axis represents the interocular contrast ratio (DE/nonDE), and the y-axis represents the probability that the binocular perceived orientation of the fused grating is biased toward the DE. The orange point, namely the BP, is the interocular contrast ratio when the two eyes are balanced in binocular orientation combination.

Procedure

Referencing previous studies,^18,30,31 we used a hole-in-the-hand test³² to ascertain the DE of each subject. The experimental protocol comprised two phases: the alignment phase and the test phase.^22,23 During the alignment phase, subjects perceived a cross featuring four white dots positioned diagonally through the dichoptic display. They were asked to align the stimuli from the two eyes, ensuring the formation of a square with the four dots. Once aligned, subjects initiated the test phase by pressing the space key. During the test phase, sinusoidal gratings with different tilts relative to the horizontal were dichoptically presented to subjects. They were required to report the orientations of the gratings (clockwise or anticlockwise) using a keyboard. The gratings remained visible until subjects responded, and the next trial started automatically after responses. Observers underwent sufficient practice to ensure a clear understanding of the task before the formal test. 

Data Analysis

A cumulative Gaussian distribution function was used to estimate the balance point (BP), representing equal contribution from both eyes in the binocular combination task (Fig. 1C). A BP of 1 indicates optimal binocular balance, and a deviation from 1 indicates a gradual imbalance between the eyes. For comparative purposes, we transformed the BP into the absolute value of log10 units (|logBP|). Therefore, a |logBP| of 0 indicates optimal binocular balance, and a greater |logBP| indicates increased imbalance between the two eyes in binocular combination. 

Statistical Analyses

Data analysis was conducted using IBM-SPSS 26.0 (IBM Corporation, Armonk, NY, USA), and visualization was performed using MATLAB R2016b (v9.1.0 MathWorks, Inc.). Normal distribution of data and homogeneity of variance were assessed through the Shapiro–Wilk test and Levene test. For normally distributed data, a repeated measures ANOVA^29,33 was used, with group as a between-subject factor and spatial frequency as a within-subject factor, to analyze the effect of subject group and spatial frequency on |logBP|. Moreover, the area under the curve (AUC) of |logBP| dependent on spatial frequency was calculated, and an independent samples t test was used to identify differences between the experimental and control groups. 

Results

Psychometric Functions

We plotted the psychometric functions for patients with IXT after surgical correction and normal controls in Figures 2 and 3, respectively. At spatial frequencies of 0.5, 4.0, and 8.0 cycles/degree, the mean BPs in the normal controls were 0.90 ± 0.11, 0.77 ± 0.15, and 0.78 ± 0.15 (mean ± SD) and in patients were 0.8 ± 0.16, 0.63 ± 0.20, and 0.66 ± 0.20 (mean ± SD). Comparison with the normal controls revealed that the BPs of the patients with IXT after surgical correction deviated more from 1, indicating they had relatively imbalanced binocular vision. Additionally, both groups exhibited a decrease in BPs with increasing spatial frequency of stimuli, suggesting greater binocular imbalance in intermediate and high spatial frequencies. But notably, there was only a marginal difference between the spatial frequencies of 4.0 and 8.0 cycles/degree. 

Figure 2.

 

Binocular orientation combination task. Patients with IXT after surgical correction. The relationship between the probability that the binocular perceived orientation of the fused grating is biased toward the DE and the interocular contrast ratio (DE/nonDE) in patients with IXT after surgical correction.

Figure 3.

 

Binocular orientation combination task, normal controls. The relationship between the probability that the binocular perceived orientation of the fused grating is biased toward the DE and the interocular contrast ratio (DE/nonDE) in normal participations.

Binocular Imbalance Analysis

In Figure 4A, the average |logBP| (the absolute values of log10(BP)) is plotted as a function of the spatial frequency for both normal controls and individuals with IXT after surgical correction. The visual representation demonstrates vividly the escalating binocular imbalance with the increasing spatial frequency of the stimulus. Owing to the data conformity with a normal distribution and homogeneity of variance, we used repeated measures analysis of variance (between-subject factor: group; within-subject factor: spatial frequency). Significant main effects were observed for both group, F_(1,24) = 9.175, P = 0.006, and spatial frequency, F_(2,48) = 7.127, P = 0.002, whereas the interaction effect was not significant, F_(2,48) = 0.379, P = 0.687. 

Figure 4.

 

Average |logBP| and area under curve (AUC) analysis. (A) Average |logBP| as a function of spatial frequency. The results of patients with IXT after surgical correction are represented by orange lines, whereas those of normal subjects are represented by blue lines. The thick orange and blue lines indicate the average |logBP|. The black dashed line, where the |logBP| equal zero, denotes optimal binocular balance, and the distance from the dashed line indicates the degree of binocular imbalance. (B) The AUC of the experimental and normal group. The bars are calculated by averaging the area under curve of each group, with the experimental and normal groups respectively shown in orange and blue. Error bars represent SE. *P < 0.05 in the independent samples t test of the two groups.

Figure 4B illustrates the comparison of the average AUC between normal controls and patients with IXT after surgical correction. The average AUC of the experimental group (0.380 ± 0.18) was notably higher than that of the normal group (0.213 ± 0.11), as evidenced by a statistically significant difference (t = 2.814; P = 0.01). 

Clinical Parameters Analysis

To explore the potential association between control and sensory eye imbalance, we investigated the correlation between control of exodeviation, squint angle and binocular imbalance. No significant correlation was observed between the near and distant control score of exodeviation, preoperative squint angle, remaining squint and AUC of |logBP| (all P > 0.05). 

Discussion

In this investigation, a binocular orientation combination paradigm was used to evaluate sensory eye imbalance in individuals with IXT after surgical correction across diverse spatial frequencies. We observed significantly higher |logBP| values in patients when compared with the control group, indicating pronounced binocular combination imbalance, particularly at higher spatial frequencies. 

The binocular deficits in IXTs after surgery manifest differently across various binocular visual processes. Specifically, surgical intervention enhances binocular summation at the contrast threshold level.³⁴ The postoperative binocular summation is similar to that of normal adults across spatial frequencies ranging from 1.5 to 24.0 cycles/degree.³⁵ However, at the supracontrast threshold level, IXTs may retain residual binocular imbalance in binocular phase combination at 1 cycles/degree, even among those with normal stereopsis after surgery.¹⁸ In addition, high spatial frequency information is crucial in our daily life.³⁶ This study aims to evaluate the ability of patients whose IXT has been aligned surgically to process binocular visual information across different spatial frequencies, particularly at high spatial frequencies. Therefore, we used a binocular orientation combination task that was more precise than the binocular phase combination task in measuring binocular imbalance at both low and high spatial frequencies in our study.²³ The findings revealed similar binocular deficits at low spatial frequencies: the average BP of patients with IXT after surgical correction (0.80 ± 0.157) was smaller than that observed in normal individuals (0.9 ± 0.108) at 0.5 cycle/degree. Notably, individuals whose IXT had been aligned exhibited more severe binocular deficits at intermediate and high spatial frequencies (e.g., 4.0 and 8.0 cycles/degree). 

Our results propose that the AUC, representing the accumulation of sensory eye imbalance across spatial frequencies, may serve as a more effective descriptor of binocular imbalance compared with the BP or |logBP| measured at low spatial frequency in patients with IXT after surgical correction. It was crucial to note a greater variability in patients compared with normal controls with respect to the AUC: the AUC ranged from 0.137 to 0.718 in individuals with postoperative IXT and from 0.034 to 0.393 in normal participations. Despite this variability, no significant correlation was found between AUC and the squint angle, implying that binocular imbalance in patients with IXT after surgical correction likely originates in the brain rather than the eyes. Binocular imbalance in patients with IXT is a complex phenomenon influenced by various factors. This imbalance is not merely a consequence of discrepancies in visual acuity and contrast sensitivity between two eyes. In fact, IXT does not induce monocular visual deficits,¹ suggesting that the underlying causes of binocular imbalance extend beyond simple visual clarity. The binocular orientation combination paradigm is a method that can reveal problems not captured by traditional measurements. Currently, several model theories, such as contrast gain control model,¹⁵ two-stage contrast gain control model,¹⁶ and a multichannel contrast gain control model,¹⁷ have been widely applied to explain binocular vision information processing in binocular combination. According to these models, suppression (a mechanism by which the brain ignores the input from one eye to prevent double vision) is central to sensory eye imbalance. Therefore, we speculate that the binocular imbalance observed in postoperative IXTs may be attributed to uneven mutual inhibition between the two eyes, rather than differences between the monocular channels.^37–39 

There are two limitations in our study. First, although the pattern is relatively consistent among participants, the sample size is relatively small. Additionally, the age range of included patients is quite narrow. This factor leads to a question about the generalizability of our results to all patients with IXT. To address it, further research involving a larger and more diverse population is necessary. Second, this study uses a cross-sectional design, which only allows us to observe abnormalities in the integration of visual information between the two eyes at a single point in time for patients whose IXT has been aligned surgically. To gain a more comprehensive understanding, future studies should incorporate long-term follow-up to monitor sensory imbalance, especially at higher spatial frequencies, to determine whether these imbalances improve over time. 

In conclusion, our study indicates that, even with aligned eyes and normal visual acuity, patients with IXT encounter binocular imbalance at low to high spatial frequencies. The imbalance is particularly pronounced at high spatial frequencies in comparison with low spatial frequencies. 

Acknowledgments

Supported by the National Key Research and Development Program of China Grant (2023YFC3604104), the Natural Science Foundation for Distinguished Young Scholars of Zhejiang Province, China (LR22H120001), the Non-profit Central Research Institute Fund of Chinese Academy of Medical Sciences (2023-PT320-04), and the Project of State Key Laboratory of Ophthalmology, Optometry and Vision Science, Wenzhou Medical University (No. J02-20210203) to JZ, and the Zhejiang Medical and Health Science and Technology Program (2024KY1293) to MX. 

Disclosure: X. Yu, None; L. Wei, None; Y. Chen, None; H. Zhang, None; H. Yu, None; J. Zhou, None; M. Xu, None