Seventeen strabismic patients (mean age: 17.06 ± 5.16 years old) participated in our experiment. They were recruited from the department of Ophthalmology of the First Affiliated Hospital of Anhui Medical University (Anhui, China). All participants had normal or corrected to normal visual acuity (LogMAR < 0.10) in the two eyes. Some of the patients had anisometropia or myopia; their refractive errors had been corrected with eyeglasses at least 16 weeks before they participated in this study. None of the patients had amblyopia, a previous history of ocular surgery or strabismus surgery, sensory or paralytic exotropia, had nystagmus or other conditions limiting ocular movements, neurologic disorders or any other medical problems, or had undergone any kinds of vision training or patching treatment. Patients were excluded from the study if they were not successfully surgically corrected (a successful surgical alignment was defined as an exotropia of no more than 10 prism diopters at both far and near distance using the prism cover test) or any vertical misalignment. The left eyes of patients S3, S8, S9, and S17 and the right eyes of the other patients were strabismic. Clinical details of patients before and after surgery are provided in Table 1. Individuals' sensory eye balance was assessed before and after the surgery at different time points. Observers wore their prescribed optical correction, if needed, in the data collection.

All subjects were naive as to the purpose of the experiment. A written informed consent was obtained from each of them or from the parents or legal guardian of participants aged less than 18 years old, after explanation of the nature and possible consequences of the study. This study complied with the Declaration of Helsinki and was approved by the Institutional Review Boards of Wenzhou Medical University, Anhui Medical University and McGill University.

All measurements were conducted on a PC computer running Matlab (MathWorks, Inc., Natick, MA) with PsychToolBox 3.0.9 extensions (Brainard, 1997; Pelli, 1997). The stimuli were presented on a gamma-corrected LG D2342PY 3D LED screen (LG Life Science, Korea) with a 1,920 × 1,080 resolution and a 60 Hz refresh rate. Subjects viewed the display dichoptically with polarized glasses in a dimly lit room at a viewing distance of 136 cm. The background luminance was 46.2 cd/m² on the screen and 18.8 cd/m² through the polarized glasses. A chin-forehead rest was used to minimize head movements during the experiment. Prisms (no more than 50 prism diopters) were added for some observers in the pre-surgery measurement to enable patients to align the two eyes. This was conducted, base-in for exotropia and base-out for esotropia, by fixing the prism on a trial frame using tape.

We quantitatively accessed patients' sensory eye balance before the surgery, 0.5–1 months after the surgery and 5–12 months after the surgery. Limited by the ability to align the two eyes, we were only able to measure the pre-surgery sensory eye balance in seven of the 17 patients. All patients were able to fuse the two eyes and thus were able to measure their sensory eye balance after the surgery.

A binocular phase combination paradigm (Ding and Sperling, 2006; Huang et al., 2009), which quantified the contributions of each eye to the fused binocular percept, was used for quantifying sensory eye balance. The design was the same as the one we have used in previous studies (Zhou et al., 2013a,b; Feng et al., 2015), in which observers were asked to dichoptically view two horizontal sine-wave gratings having equal and opposite phase-shifts of 22.5° (relative to the center of the screen) through polarized glasses; the perceived phase of the grating in the cyclopean percept was measured as a function of the interocular contrast ratio. By this method, we were able to find a specific interocular contrast ratio where the perceived phase of the cyclopean grating was 0° indicating equal weight to each eye's image. This specific interocular contrast ratio is the “balance point” for binocular phase combination since the two eyes under these stimulus conditions contribute equally to binocular vision (Figure 1). For each interocular contrast ratio, two configurations were used in the measurement so that any potential starting positional bias will be cancelled out: in one configuration, the phase-shift was +22.5° in the non-dominant eye and –22.5° in the dominant eye and in the other, the reverse. The perceived phase of the cyclopean grating at each interocular contrast ratio (δ) was quantified by half of the difference between the measured perceived phases in these two configurations. Different conditions (2 configurations × 6 interocular contrast ratios × 8 repetitions) were randomized in different trials, thus adaptation or expectation of the perceived phase would not have affected our results. The perceived phase and its standard error were calculated based on eight measurement repetitions.

Before the start of data collection, proper demonstration of the task was provided by practice trials to ensure observers understood the task. During the test, observers were allowed to take short-term breaks whenever they felt tired.

The gratings in the two eyes, as shown in Figure 1, were defined as:

Where L₀ is the background luminance; C₀ is the base contrast in the non-dominant eye; f is the spatial frequency of the gratings, δ is the interocular contrast ratio, and θ is the interocular phase difference.

In our test, L₀ = 46.2 cd/m² (on the screen); C₀ = 100%; f = 1 cycle/°; δ = [0, 0.1, 0.2, 0.4, 0.8, 1.0] and θ = 45°.

The gratings had a size of 2° × 2°. Surrounding the gratings, a high-contrast frame (width, 0.11°; length, 6°) with four white diagonal lines (width, 0.11°; length, 2.83°) was always presented during the test to help observers maintain fusion.

We used the same phase adjustment procedure as used by Huang et al. (2009) for measuring the perceived phase of the binocularly combined grating. In each trial, subjects first completed an alignment task. During which, a fixation display was presented in the center of the binocular presented high-contrast frame with four white diagonal lines to the each eye. The fixation display also contained two monocular presented dots in the first and third quadrants for the left eye and two in the second and fourth quadrants for the right eye. They adjusted the coordinates of images in their nondominant eye to make sure the images seen by the two eyes were perfectly fused. This was followed by the binocular phase combination task. Observers were asked to adjust the position of a binocular horizontal reference line to indicate the perceived phase of the fused sine-wave grating. They did so by aligning the line with the location of the center of the dark stripe of the grating. The reference line was presented on both sides of the gratings, with its initial vertical position randomly (–9 to 10 pixels) assigned relative to the center of the frame in each trial. The reference line was moved with a fixed step size of 1 pixel. Since the gratings had a period of 2 cycles corresponding to 180 pixels, the phase adjustment had a step size of 4° of phase/pixel (2 cycles × 360 phase-degree/cycle / 180 pixels). During one trial, the stimuli were presented continually until subjects finished the phase adjustment task. The next trial started immediately after observers reported their results using a key press.

The functions of perceived phase (φ) vs. interocular contrast ratios (δ) i.e., the PvR functions, were fitted with a modified contrast-gain control model from Huang et al. (2009):

In which, bp and γ are two free parameters. “bp” represents the interocular contrast ratio when the two eyes make equally contributions to binocular combination (i.e., the balance point) and “γ” represents a non-linear factor.

Curve fitting was conducted in Matlab (MathWorks, Natick, MA) using the nonlinear least squares method to minimized Σ(φ_theory–φ_observed)². The goodness-of-fit was statistically tested by computing the r-square value:

Figure 2 shows the perceived phase vs. interocular contrast ratio (PvR) curves for seven patients, whose sensory eye balance could be measured before the surgery (other patients were not measureable because they couldn't align the two eyes during the test). For observer S3, her nondominant eye (determined by the hole-in-the-card test) was more dominant in the pre-surgery PvR test, to simplify the statistical analysis, S3's balance points were calculated as the reciprocal of the fitted balance point in the comparison. Accordingly, all the seven patients had imbalanced eyes before the surgery, as evidenced by the significant distance between the balance points (the zero-crossing point of the PVR curves) and 1.0 (i.e., the ideal observers' balance point): t₍₆₎ = –4.03, p = 0.007. At 0.5–1 months after the surgery, patients' eyes were more imbalanced (balance point decreased by 0.2 or more: S4 and S7), less imbalanced (balance point increased by 0.2 or more: S3, S5, and S6) or remained imbalanced to the same extent (balance point changed by less than 0.2: S1 and S2).

In Figure 3 we plot the balance points derived from the results shown in Figure 2 for the seven observers whose balance was measured before and immediately after strabismic surgery. The means and standard error are illustrated. A 2-tailed paired samples t-test showed that there was no significant change in the balance point as a consequence of surgery: t₍₆₎ = –0.92, p = 0.39.

The results in Figure 3 suggest that strabismic surgery doesn't produce any immediate benefit in terms of patients' sensory eye balance. One possibility is that a period of post-surgical “adaptation,” somewhat akin to refractive adaptation after an interocular refractive imbalance is first corrected (Zhou et al., 2016). To test this possibility, we evaluated the long-term effect of strabismic surgery on patients' sensory eye balance by measuring patients' PvR functions at 5–12 months after surgery. These results are plotted in Figure 4. Except for observers S12 and S16, whose balance point increased by more than 0.2 (two eyes became more balanced) at 5–12 months after the surgery, all other observers' balance points generally remained unaltered (balance point changed by less than 0.2) by surgery.

Figure 5 summarizes the range of balance points we measured in our strabismic patients immediately after surgery and how they changed 5–12 months after surgical straighting of the eyes. A 2-tailed paired samples t-test also showed that there was no significantly change of balance point after 5–12 months: t₍₁₅₎ = −0.89, p = 0.39. There was also no significant correlation between the interval between the two post-operation measure days and the change of balance point (p = 0.24, 2-tailed Pearson Correlation).

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.