Association of Accommodation and Convergence with Axial Length Elongation in Children with Basic Intermittent Exotropia: A 12-Month Observational Study

Intermittent exotropia (IXT) is the most common type of childhood-onset exotropia [1‒3]. In Asian children, the prevalence of IXT was 0.12–3.90% [3‒6], and the population has been increasing for several decades [7]. IXT not only affects ocular appearance and eye position but also affects the development of refractive error in children [8], which is another common public ocular disorder.

Several previous studies have indicated that IXT could facilitate the development of myopia in children [8‒10]. The differences in accommodation and convergence functions between IXT patients and healthy subjects may provide potential explanations. Accurate accommodation and convergence are needed for controlling eye position and facilitating the use of clear and single images of IXT, but the understanding of the underlying mechanisms of action is limited. It has been reported that IXT patients suffer from insufficient binocular accommodation [11], lower binocular accommodative facility (AMF) [12], and reduced convergence amplitudes [13]. However, increasing accommodative loads [14], more binocular accommodation [15], greater accommodative response [16], and greater convergence [17] were also observed in patients with IXT. The clinical evidence regarding the correlation between accommodation and convergence in IXT children remains controversial.

Clinical studies and studies conducted with animal models of myopia have provided ample evidence that axial elongation is the primary factor driving myopia progression [18‒20]. Axial length (AL) growth could result in a reduction in hyperopia reserves or the development of myopia. In addition, ocular dominance plays an important role in the development of refractive error in nonstrabismic individuals [21, 22]. Differences in myopia progression were also detected between dominant and nondominant eyes in IXT patients [23].

Recently, the International Myopia Institute white paper reviewed accommodation in myopia development and progression, elucidating correlations between sustained near work demanding high levels of ocular accommodation and the development of myopia [24, 25]. For IXT patients, there was a mechanism proposing that the effort of convergence required to compensate for the exodeviation activates accommodation resulting in convergence-induced myopia [14]. Although this increase in accommodation can be one of supporting factors for the suggested hypothesis that IXT patients develop myopia faster than the normal population [8‒10], no direct evidence has been showed that this leads to a permanent change in AL [26, 27].

The purpose of this study was to investigate whether accommodation and convergence may influence AL elongation in IXT children. This study investigated the accommodation, convergence, and refraction characteristics of dominant and nondominant eyes. The differences in parameters among the different AL elongation growth groups were compared to help clinicians predict AL growth in advance and to provide myopia prevention and control for IXT children.

The subjects enrolled in the current prospective study were outpatients who first visited the Department of Strabismus and Pediatric Ophthalmology of Beijing Tongren Hospital between August 2022 and November 2022. The inclusion and exclusion criteria are shown in Table 1. A total of 163 children diagnosed with the basic type of IXT [28] were recruited for this study. All patients were required to be followed for 12 months and re-examined at 6-month intervals. There were 7 patients lost to follow-up, 10 patients accepted strabismus operation, 1 patient switched to another type of IXT, and 5 patients received orthokeratology intervention during the 12-month follow-up duration. A total of 140 subjects were ultimately included in the analysis (Fig. 1).

During each visit, all patients underwent complete ophthalmic examinations and assessments, including the following tests.

Parents disclosed their symptoms, past illness, habit of using eyes, and lifestyle in detail.

Slit-lamp imaging and fundus color photography were performed to exclude anterior and posterior segmental diseases.

Refractive tests included uncorrected visual acuity (UCVA), best-corrected visual acuity (BCVA), AL (Lenstar LS-900; Haag-Streit, Bern, Switzerland), and cycloplegic refraction (Topcon RM-800; Topcon Corp, Tokyo, Japan). The AL elongation was defined as the difference between AL at 12 months and AL at baseline. Cycloplegia was measured 30 min after 2 instillations of 1% cyclopentolate hydrochloride (Cyclogyl, Alcon Health care S.A.) were administered at 20-min intervals. Refraction was defined as the spherical equivalent refraction (SE; SE = spherical power + cylinder power/2). The assessments of strabismus, accommodation, and convergence were carried out on the basis of the correction of refraction 8–10 days after the administration of cycloplegia.

The exotropia deviation angle, Newcastle control score (NCS) [29], and eye movement were evaluated by the same experienced pediatric ophthalmologist (Dr. J.F.). The angle of deviation was assessed using prism and alternate cover testing at distance (6 m) and near (33 cm) after at least 1 h of monocular occlusion.

Results of the worth 4-dot test were interpreted as monocular suppression when two or three dots were observed.

Patients were asked to point the target 6 m away with his right index finger with both eyes open and then repeated with left index finger. The eye that occluded by fingers was determined as the dominant eye. If the pointing test results were inconsistent with different fingers, the dominant eye was evaluated by the hole-in-the-card test. The subjects were told to hold a card with a hole in the middle by both hands and to search for the target 6 m away through the hole. Only the dominant eye was able to reach the target when the nondominant eye was covered, and the tests were repeated 3 times.

Tests involved positive and negative relative accommodation (PRA/NRA), accommodative amplitude (AMP), AMF, accommodative response (monocular estimation method [MEM]), near point of convergence (NPC) and accommodative convergence/accommodation ratio (AC/A). When measuring the NRA and PRA with correction, people were asked to fix on the line above the best visual acuity at 40 cm with both eyes. +/−0.25 diopter (D) lenses were added to change the accommodation gradually until the first sustained blur was reported. The total number of plus or minus lenses was recorded as the NRA or PRA, respectively. The NRA was tested first, followed by the PRA and AMP. The monocular AMP was measured with the minus lens method at a distance of 40 cm. After the PRA was measured, minus lenses were added continually until unchangeable blurring was reported. The sum of the absolute dioptric value of minus lens for blur and the dioptric equivalent of the viewing distance (+2.5D) was recorded as the AMP. The AMF concentration was tested by the ±2.0D flip method. The subjects were asked to recognize the near visual target (20/30) 40 cm away with full-correction spectacles and a flipper. The test was started with a +2.0D flipper, and patients were required to switch to −2.0D as soon as the target was identified clearly and then back to +2.0D. The number of blades clearing both the plus and minus lenses was considered one cycle. The number of cycles per minute (cpm) was recorded. The accommodation response was measured via the MEM method. A special card with a text paragraph in the Chinese language was attached to the retinoscope, which was designed to be the same as the Bernell Corporation MEM card. The patients were required to read the text at 40 cm, while the examiner estimated the retinoscopic reflex in the horizontal meridian. Trial lenses were added until a neutral solution was reached. The corresponding lag or lead of accommodation was recorded. The accommodation responses of all patients were assessed by an experienced examiner. For NPC, the subjects were told to fixate on an accommodation target 40 cm in front of the eyes. The target was allowed to move slowly toward the eyes until diplopia was reported or one eye drifting outward was found. The distance from this point to the plane of the subject’s spectacles was measured. The test was repeated twice, and the average was recorded as the NPC. The stimulus AC/A ratio was tested via the synoptophore method right after prism and alternate cover testing. The deviation was measured with complete corrected spectra and measured again with −3.0D lenses added. The AC/A ratio was calculated by dividing the difference in deviation between two conditions by −3.0D.

After receiving comprehensive ophthalmic assessments, parents were advised to provide a pair of fully corrected spectacles, and children were required to wear the glasses throughout the day. Telephone calls were made to schedule the clinical examinations after 6 months (Fig. 1). Professional advice relating to strabismus surgery was given to each patient and their parents at each visit. Written informed consent to participate was obtained from the parents or legal guardians of any participant prior to participation. The study followed the tenets of the Declaration of Helsinki and was approved by the Ethics Committee of Beijing TongRen Hospital (Approved No. TRECKY2020-142).

Subjects were divided into 4 age brackets: younger than 6 years (n = 32), 6–9 years (n = 68), 9–12 years (n = 31), and 12–15 years (n = 9). For all subjects, AL elongation of dominant and nondominant eyes showed a significant correlation (p < 0.001). AL elongation of both eyes was averaged for each subject, and the averaged parameter was used to divide the subjects into slower or faster AL elongation groups. There were no significant differences in AL growth among the age brackets (younger than 6 years: 0.36 ± 0.18 mm; 6–9 years: 0.43 ± 0.23 mm; 9–12 years: 0.43 ± 0.21 mm; 12–15 years: 0.27 ± 0.12 mm; F(3,136) = 2.219, p = 0.089). The median AL growth for different age brackets were 0.32, 0.39, 0.40 and 0.26 mm, which were chosen to be cutoff values to divide the children into the slower AL elongation group (group A) and faster AL elongation group (group B). There were 69 subjects included in group A and 71 in group B ultimately.

The statistical analysis was performed using SPSS version 26.0 (SPSS Inc., Chicago, IL, USA). The data concerning accommodation and convergence (including angle of deviation, NCS, PRA, NRA, AMP, AMF, NPC, accommodative response, and AC/A ratio) within 12 months were averaged for analysis. The normality of the measurements was determined by the Shapiro-Wilk test. Continuous characteristics were compared between two groups with independent t tests or Mann-Whitney U tests. For categorical characteristics, χ² tests were applied. Parameters were compared between dominant and nondominant eyes with paired t tests. Univariate and multivariate logistic regression analyses were used to evaluate the correlations of AL growth (defined as fast or slow) with various parameters, as was linear regression analysis. Parameters that were significant at p < 0.10 were considered for multivariate regression analysis. For each analysis, a 2-tailed model was utilized, and p < 0.05 was considered to indicate statistical significance.

A total of 163 subjects were recruited in this prospective study and 140 of them completed the 12-month follow-up (Fig. 1; Table 2). Ninety-seven (69.3%) of the participants were right-eye dominant, and 43 (30.7%) were left-eye dominant. Sixty-nine patients were assigned to the slower AL elongation group (group A), and 71 were assigned to the faster AL elongation group (group B) due to the median AL growth. The mean age of the subjects was 7.82 ± 2.26 years, and 63 patients (45.0%) were male.

As shown in Tables 2 and 3, AMFs showed significant differences between the dominant eyes and nondominant eyes for both group A (8.00 ± 2.37 cpm vs. 7.62 ± 2.46 cpm, p = 0.016) and group B (8.23 ± 2.67 cpm vs. 7.71 ± 2.66 cpm, p = 0.014). The annual AL elongation demonstrated no significant differences between the dominant and nondominant eyes in both group A (0.24 ± 0.09 mm vs. 0.24 ± 0.11 mm, p = 0.772) and group B (0.57 ± 0.20 mm vs. 0.56 ± 0.21 mm, p = 0.593). No significant differences were observed in other refractive and accommodation parameters, including baseline SE, AMP, and accommodative response, among all groups (all p > 0.05).

As illustrated in Table 2 and Figure 2, there were significant differences between group A and group B. In binocular convergence, the NPC differed significantly, with group A at 9.15 ± 4.35 cm and group B at 7.70 ± 2.81 cm (t = 2.347, p = 0.020). Furthermore, significant differences were observed in the dominant eyes for baseline SE and AMP. The spherical equivalent was found to be −0.13 ± 1.72D in group A and −1.36 ± 1.96D in group B (t = 3.956, p < 0.001). The amplitude of accommodation was found to be 8.13 ± 2.40D in group A and 8.96 ± 2.01D in group B (t = −2.238, p = 0.027). Group B subjects exhibited greater myopic baseline SEs, higher AMPs in dominant eyes, and narrower binocular NPCs. Furthermore, a significant difference was also found in the baseline spherical equivalent of the nondominant eyes between the two groups, with a mean difference of −0.19 ± 1.98D versus −1.30 ± 1.93D (t = 3.352, p = 0.001). Other parameters, including age, sex, angle of deviation, NCS, PRA, NRA, and AMF in both eyes, accommodative response of both eyes, and the AC/A ratio, demonstrated no significant differences between the groups (all p > 0.05).

Univariate and multivariate logistic regression analyses were used to evaluate the correlations of AL elongation group (defined as fast or slow) with various parameters related to accommodation and convergence. For 140 subjects with basic IXT in this study, univariate logistic regression indicated that more negative SEs (OR = 0.690; p < 0.001), greater AMPs (OR = 1.191; p = 0.030), and fewer NPCs (OR = 0.889; p = 0.027) were correlated with faster axial elongation within 12 months of the dominant eye (Table 4). For nondominant eyes, more negative SEs (OR = 0.745; p = 0.002) and fewer NPCs (OR = 0.889; p = 0.027) were correlated with severe disease.

Multivariate logistic regression was subsequently used to assess the effects of SE, AMP, and NPC for dominant eyes. When age and sex were adjusted, more negative SEs (OR = 0.603; p < 0.001), greater AMPs (OR = 1.201; p = 0.027), and fewer NPCs (OR = 0.883; p = 0.021) were correlated with faster AL elongation within 12 months in the dominant eyes. More negative SEs (OR = 0.682; p = 0.001) and fewer NPCs (OR = 0.883; p = 0.021) were correlated with those in the nondominant eyes.

The 12-month AL elongation of dominant or nondominant eyes of all patients with the basic type of IXT (n = 140) was used for the linear regression analysis, respectively. The 12-month AL elongation of dominant eyes was significantly correlated with baseline SE (R = 0.296, p < 0.001), AMP (R = 0.213, p = 0.011), and NPC (R = 0.193, p = 0.022), according to univariate linear regression. After adjusted by age and sex, multivariate linear regression revealed that these three parameters were significantly associated with 12-month AL elongation (SE: β = −0.045, p < 0.001; AMP: β = 0.023, p = 0.010; and NPC: β = −0.012, p = 0.019) (Table 5).

For nondominant eyes, univariate linear regression showed that more myopic SEs (R = 0.201, p = 0.017) and greater AMPs (R = 0.172, p = 0.042) were correlated with faster axial elongation within 12 months. After further analysis, multivariate linear regression revealed that more negative baseline SEs (β = −0.029, p = 0.005) were the only parameters correlated with faster annual AL elongation.

To our best knowledge, for the first time, we investigated the association of accommodation and convergence parameters and AL growth in both dominant and nondominant eyes of IXT patients for a 12-month follow-up period. Interestingly, we found that faster AL elongation in the dominant eyes was associated with more myopic SEs, greater AMPs, and lower NPCs. These accommodative parameters can serve as potential clinical indicators for monitoring myopia progression in addition to AL.

Moon et al. [23] reported that nondominant eyes experienced faster myopia progression than dominant eyes did in IXT patients, which was attributed to clinically severe exotropia in terms of the amount of deviation and the degree of control. The main cause of this controversy is thought to be related to differences in the subjects. Unlike when patients were selected after surgery for IXT, this research recruited children who did not undergo surgery, eliminating the likely influence of surgery on AL growth [30]. The present study also showed that the AMF density in the dominant eyes was greater than that in the nondominant eyes, which was consistent with previous studies based on the IXT population [12]. The nondominant eye, which commonly manifests itself as a squint, needs to use accommodative convergence to maintain binocular fusion vision. This will lead to asymmetric accommodation between eyes [31], resulting in bilateral eye competition, which will cause a decrease in AMF.

With more children being accustomed to near work and short-distance reading, the asymmetry of head posture leading to differences in accommodative demands between the two eyes cannot be neglected. The accommodative differences increased as the reading distance decreased or the head tilt increased [32, 33]. Eyes closer to the near target could consistently experience greater accommodative demand than could the other eye, leading to anisoaccommodation between the eyes. As accommodation is a binocular process, anisoaccommodation is likely to be rather infrequent (0.25D or less) for the normal population [34, 35]. However, for IXT children, when one eye (usually the dominant eye) focused on the near task, the other eye (usually the nondominant eye) turned outward and lost the near work in focus or made greater accommodation to align the binocular eye position. The binocular accommodation was interrupted; thus, the anisoaccommodation potential could be much greater for IXT [31]. The competition-between-eyes theory was used to explain anisoaccommodation in patients with strabismus [36]. The brain selectively accepts information from the dominant eye, and the accommodation neural impulses are transmitted through the negative feedback mechanism to both eyes. When impulses of convergence accommodation were strengthened to align with eye position, the impulses of reactive accommodation generated by blurred images weakened, leading to abnormal underaccommodation in nondominant eyes [36]. However, compared to those of dominant eyes, the underaccommodation and overaccommodation of nondominant eyes are unmeasurable in daily life; thus, the accommodative parameters are chaotic and unpredictable. Therefore, the axial elongation of nondominant eyes cannot be easily predicted by accommodative and convergent parameters.

A more negative baseline SE seemed to have an effect on more rapid AL growth in IXT patients. One might reasonably assume that myopic eyes have relatively more hyperopic peripheral refractive errors than emmetropic eyes, the same as orthophoric people [37, 38]. This difference may be related to the oblate shape of the myopic eyeball and the corresponding variational position of the peripheral retina [39]. In addition, several myopic IXT subjects recruited in this research never accepted corrected lenses on the first visit. The extra effort at accommodating and converging before wearing fully corrected spectacles may have contributed to the excess axial elongation at the beginning of this 12-month visit.

IXT patients may stimulate excess convergence accommodation due to greater demand for accommodation for controlling exodeviation [40, 41]. Horwood et al. [16] reported that increased vergence demand to control intermittent distance exotropia for near also drives significantly more accommodation. A recent study suggested that the change in accommodation of patients with IXT when binocular fusion is maintained is more significant than that of normal controls [42]. AMP represents the maximum ability of the eye to change its refractive power from the relaxed state by accommodating when fixating on a near target [43], which could be influenced by accommodation demand [44]. Additional convergence accommodation led to increased accommodation demand and wider accommodation amplitude for IXT. Patients experienced a delay in accommodation relaxation when shifting focus from a near to a far target, which is related to transient myopia.

Previous experiments [45‒47] have shown that the eye experiences a transient period of axial elongation on the axis after brief periods of sustained accommodation, with the magnitude of change increasing with increasing accommodative demand [48]. This can be explained by one hypothesis [49, 50] that the accommodative ciliary muscle applies an internal mechanical force upon the globe, thus decreasing the scleral and choroidal equatorial circumference. The only way to maintain the globe volume was axial elongation. Persistent retinal defocus is induced by this disease, after which the disease progresses to permanent myopia [51, 52], which is associated with ocular rigidity and myopia susceptibility or progression [53].

This research also revealed the relationship between faster AL growth of IXT and their fewer NPCs, which could represent the total convergence amplitude. One explanation is based on the near-response triad [54], which consists of normal synkinesis between accommodation, convergence, and miosis. When one or more of these components exceeded the demand required by the stimulus, a “spasm of near reflex” occurred. IXT has been reported as one of the certain risk factors for spasms of the near reflex [55]. There are case reports [56, 57] about IXT adults suffering from intermittent accommodative spasm related to pseudomyopia, present under binocular conditions, and absent with cycloplegia [55]. Greater convergence effort, which is required for near-target binocular fixation, might lead to chronic spasm of accommodation through feedback from the near reflex following pseudomyopia, a decrease in vision and a shift to persistent myopia. Hargrave et al. [58] supported this hypothesis suggesting that much use of convergence may be a contributing factor in the progression of myopia. They speculated that more convergence led to extraocular muscular imbalances, and AL elongation occurred by a stretching of the delicate elastic fibers behind the cornea. Nevertheless, a lower NPC meant more convergence exercises the patients undertook and a higher level of IXT engaging in near work, which was a significant parameter associated with the development of myopia in schoolchildren [59].

Recently, the PEDIG study [60] reported a significantly higher myopic shift in the overminus lens therapy group for IXT children, which was not consistent with previous studies [26, 27]. Transient AL elongation during accommodation has been reported [48, 53] but whether it could remain permanent with constant accommodation has not reached a common understanding. Sustained accommodation caused by hyperopic defocus [61] has been suggested as a precursor for eye elongation. This study revealed that accommodation and convergence may affect sustained AL elongation, which agreed with the PEDIG study [60], and provided evidence that accommodation or convergence due to binocular position alignment might have a correlation with elongation of AL in IXT children, but the underlying mechanisms were not clear.

One potential limitation of this study is that the accommodative response was tested by the MEM, which increased by at least 0.25 diopters. An open-field autorefractor could be used to analyze the accommodative response in the future. Nevertheless, normal controls could be included in future research to compare these findings with those of the IXT to reveal abnormalities in binocular visual function and myopia progression in both eyes of children with strabismus.

The present study found that faster AL elongation in IXT children is associated with more myopic spherical equivalents (SEs), greater AMPs, and lower convergence (NPCs) in dominant eyes. These parameters could potentially serve as clinical indicators for monitoring myopia progression in IXT patients. The study contributes to the understanding of myopia development in IXT by clarifying the role of accommodation and convergence, providing a nuanced view of how these visual functions affect AL elongation. Future research directions may involve further investigation of the mechanisms underlying these associations and evaluation of intervention strategies that could mitigate the progression of myopia in children with IXT.

This study followed the tenets of the Declaration of Helsinki and was approved by the Ethics Committee of Beijing Tongren Hospital (Approved No. TRECKY2020-142). Written informed consent to participate was obtained from the parents or legal guardians of any participant prior to participation.

The authors have no conflicts of interest to declare.

This work was supported by the National Natural Science Foundation of China (Grant No. 82070998); the “Yangfan” Clinical Technology Innovation Project Beijing Municipal Administration of Hospitals (XMLX202103); and the Capital Research Project of Clinical Diagnosis and Treatment Technology and Translational Application, Beijing Municipal Science and Technology Commission (Z201100005520044).

J.F: study design and protocol draft; J.H., X.X.L., and J.H.: study protocol draft; J.X.L: research design, research execution, data manipulation, and manuscript preparation; L.L: statistical consulting; H.X.L., Q.Y.Z., and Y.Y.Z: data acquisition and research execution. All the authors reviewed the study protocol and approved the final manuscript.

The data that support the findings of the current study are not publicly available due to their containing information that could compromise the privacy of research participants but are available from the corresponding author Jing Fu.