Abstract
Purpose:
This study aims to compare the effectiveness of pencil push-up training and binocular vision training in treating post-operative mild under-correction in patients with intermittent exotropia.
Methods:
A prospective cohort study was conducted, including patients who underwent surgery for intermittent exotropia at Children’s Hospital of Nanjing Medical University between June 2022 and January 2023 and experienced post-operative mild under-correction (-8∆ to -15∆). Patients were divided into two groups: pencil push-up training group and binocular vision training group. All patients underwent measurements of exodeviation and stereoacuity at distance and near, sensory fusion, and fusion convergence amplitude. The data were analyzed using independent sample t-tests, repeated measures analysis of variance, and Chi-square tests.
Results:
There were no statistically significant differences in exodeviation at distance and near between the two training groups before the training. After 6 months of training, the exodeviation at distance and near achieved a significant decrease in both groups (P < 0.05), and the pencil push-up training group showed a similar distance and near exodeviation compared to the binocular vision training group (t = 1.58, P > 0.05; t = 0.43, P > 0.05). After 6 months of training, the binocular vision training group exhibited significantly superior stereoacuity and fusion convergence amplitude compared to the pencil push-up training group (P < 0.001).
Conclusion:
Both pencil push-up training and binocular vision training are effective in reducing exodeviation in patients with post-operative mild under-correction of intermittent exotropia. However, binocular vision training demonstrates superior efficacy in restoring stereopsis and fusion convergence amplitude compared to pencil push-up training.
Keywords: Intermittent exotropia, pencil push-up, vision therapy
Intermittent exotropia is the most prevalent form of strabismus in clinical practice, representing 50% to 90% of all exotropia cases.[1] Surgical intervention constitutes the primary approach for managing this disease. The occurrence rate of residual and recurrent exotropia after surgery ranges from approximately 25.8% to 35.5%,[2,3,4,5] significantly impacting the long-term effectiveness of surgical treatment. Post-operative deviations in the range of -8∆ to +5∆ (+ indicating esotropia, - indicating exotropia) are indicative of successful IXT surgery.[6] Surgical intervention is recommended when the angle of exotropia is equal to or greater than 15∆. Exodeviations between -8∆ and -15∆ following surgery represent a transitional phase between successful surgery and the potential need for reoperation, often requiring a secondary procedure. Clinical observations indicate that a second surgery not only imposes physical and psychological burdens on the affected child and their family but also places a psychological burden on the operator. Additionally, research suggests that binocular visual function plays a critical role in preserving post-operative eye alignment, and the recurrence of IXT surgery is mainly caused by a decrease in binocular vision function. If the post-operative exodeviation is less than 15∆, appropriate binocular visual training can be provided to enhance the child’s control over exotropia and potentially obviate the need for further surgery.
Common methods of visual function training in clinical practice include pencil push-up training and hospital-and-home-based binocular vision training. Pencil push-up training is straightforward to perform, but the efficacy lacks empirical support. Conversely, hospital-and-home-based binocular vision training has demonstrated clinical effectiveness.[7,8] However, this training method is time-consuming and challenging to perform. The present study aimed to comparably analyze the outcomes of pencil push-up training and binocular vision training in 162 cases of mild under-correction exotropia following IXT surgery at the Ophthalmology Department of Children’s Hospital of Nanjing Medical University from June 2022 to January 2023. Our investigation observed the therapeutic effects of these two training methods on patients with post-operative exodeviation ranging from -8∆ to -15∆, aiming to assess the potential of promoting pencil push-up training as a standard training approach.
Methods
Objectives
The study aimed to include individuals who met the following criteria: 1. Age between 5 and 18 years. 2. Best corrected visual acuity (BCVA) ≥0.8 and anisometropia ≤1.50D. 3. Stereopsis ≤3000 seconds of arc. 4. Basic or convergence insufficiency-type IXT with residual exodeviation of 8∆ to 15∆ at distance or near. 5. Willingness to strictly adhere to training requirements and cooperate with all examinations. 6. Absence of functional or organic ocular diseases affecting binocular vision.
Exclusion criteria involved: 1. Constant exotropia. 2. Concurrent dissociated vertical deviation (DVD), A or V patterns, paralytic or restrictive factors, and nystagmus. 3. Moderate to severe amblyopia.
A total of 162 patients who had previously undergone IXT surgery at our hospital and experienced under-correction were included in the study. Informed consent was obtained from a parent and/or legal guardian of all subjects. This study was approved by the Nanjing Children’s Hospital Review Board and complied with the principles outlined in the Declaration of Helsinki.
Pre-operative examinations
Prior to training, all patients underwent a series of examinations, including BCVA, cycloplegic autorefraction, slit-lamp biomicroscopy, indirect ophthalmoscopy, ocular motility, presence of amblyopia, lateral incomitance, prism and alternative cover test (monocular occlusion for 1 hour), and evaluation of distance and near stereopsis、sensory fusion and fusion convergence amplitude. Deviation measurements were conducted using the prism and alternate cover test. Near deviation measurements were performed with the target placed 33 cm in front of the eyes, while distance deviation measurements were conducted with the target positioned at 6 m. These measurements were carried out by the same examiner. Amblyopia was defined as a difference of two or more lines in terms of the BCVA between each eye. Patients were considered to have a lateral incomitance if exotropia shows a difference of at least 5 PD between central and lateral fixation. Distance stereopsis was measured using a random dot stereogram. Stereopsis ≤80 seconds of arc was considered normal foveal stereopsis, while values >80 seconds of arc were classified as abnormal. Participants who did not pass the 800 seconds of arc stereogram but passed the stereoblind screening test were recorded as having 3000 seconds of arc. Near stereoacuity was evaluated using a Titmus stereo test. Sensory fusion was tested using four Worth dots at 40 cm and 5 m fixation. The amplitude of fusional convergence was assessed using a 1 to 40 PD fixed horizontal prism bar both at distance (3 m) and then near (1/3 m).[9]
Training methods
The training methods used were as follows:
Pencil push-up training group: Patients held a pencil between their eyes, with the tip positioned at one arm’s length from the root of the nose at the same height as the root. They performed repetitive movements from far to near until diplopia occurred and then returned to the original position. This exercise was performed for 20 cycles, constituting one set. Three sets were completed consecutively, taking approximately 15 minutes. The exercise was conducted twice daily, 5 days a week, for a duration of 6 months.
Binocular vision training group: Patients received a 60-minute session of in-hospital training once a week administered by an optometrist. Additionally, they performed 15 minutes of home-based training five times a week. The training duration was also 6 months. The specific details of in-hospital and home-based training were based on references,[10] and individualized training guidelines were provided to each patient. During in-hospital treatment, patients practiced under supervision for 4–5 periods following the standard protocol provided by the therapist.
Follow-up
Follow-up examinations were conducted at 1, 3, and 6 months to measure deviation and stereopsis at near and distance, sensory fusion, and fusional convergence amplitude. Post-operative ocular alignment was classified as follows: post-operative horizontal strabismus angle ranging from -8∆ to +5∆ (including -8∆ and +5∆) is considered satisfactory, exodeviation >8∆ indicated under-correction, and esodeviation >5∆ indicated over-correction.
Adherence to the treatment plan
Parents were responsible for recording the daily time of home-based training on a provided calendar and evaluating the patient’s compliance with the treatment plan. Weekly reviews were conducted to confirm completion of the exercises. For patients showing poor compliance, interventions such as alternative rewards were employed.
Statistical methods
A prospective cohort study was conducted to analyze the data using SPSS 20.0. The observed data primarily consisted of measurement data, expressed as mean ± standard deviation, following a normal distribution. For the multi-timepoint observation data, two factor repeated measures ANOVA was utilized, along with the Chi-square test to compare the differences in the rates of attaining distant stereopsis and sensory fusion between the two groups. When comparing within groups, the adjusted significance level is P1 < 0.05/3 ≈ 0.017, and the significance level for other comparisons is P < 0.05.
Results
Basic information
A total of 162 patients who completed their follow-up were enrolled in this study, with 78 assigned in the pencil push-up training group (48 males and 30 females) and 84 in the binocular vision training group (36 males and 48 females). Three patients from each group were lost to follow-up. Prior to the training, there were no statistically significant differences observed in terms of age, BCVA, equivalent spherical diopter, deviation and stereopsis at distance and near, sensory fusion, and fusional convergence amplitude between the pencil push-up training group and the binocular vision training group (P > 0.05) [Table 1].
Table 1.
Baseline data of the patients
| Characteristic | Pencil Push-up training (78) | Binocular vision training (84) | P | |||
|---|---|---|---|---|---|---|
| Age (years) | 7.00±2.50 | 7.00±2.30 | 0.94a | |||
| Sex (Male:Female) | 35:43 | 40:44 | 0.42b | |||
| Stereoacuity (arcsecond) | 1149.24±789.42 | 1245.56±800.37 | 0.66a | |||
| SER (D) | ||||||
| OD | -1.1±1.3 | -1.4±1.5 | 0.44a | |||
| OS | -1.1±1.4 | -1.2±1.3 | 0.75a | |||
| Deviation (PD) | ||||||
| At distance | -11.58±1.60 | -11.71±1.74 | 0.76a | |||
| At near | -11.78±1.88 | -12.11±1.67 | 0.50a | |||
| Fusional convergence amplitude | ||||||
| At distance | 18.2±9.46 | 17.9±9.86 | 0.78a | |||
| At near | 13.21±8.96 | 13.3±9.32 | 0.86a | |||
| Sensory fusion (suppression) | ||||||
| At distance | 11 | 12 | 0.97b | |||
| At near | 3 | 4 | 0.78b | |||
| Amblyopia (n, %) | 3/78 (3.85%) | 5/84 (5.95%) | 0.32b | |||
| Lateral incomitance (n, %) | 8 (10.26%) | 6 (7.14%) | 0.22b | 
PD, Prism diopters; D, Diopters; OD, Right eye; OS, Left eye. aAnalysis of variance. bChi-squared test
Comparing the effects of two training methods on post-operative exodeviation at distance
The interaction between training methods and duration has a statistically significant impact on the exodeviation at distance (F interaction = 5.59, P = 0.002). Consequently, separate assessments were conducted to evaluate the individual effects of the training methods and duration on the two groups. There was no significant overall difference observed between the groups (Fgrouping = 0.01, P = 0.86). At baseline, 1 month, and 6 months, no statistically significant differences were found in the angle of distant exotropia between binocular vision training group and Pencil push-up training group (t = -1.15, -1.63, 1.58, all P > 0.05). However, binocular vision training group exhibited significantly lower exodeviation at distance compared to the pencil push-up training group at 3 months (t = 3.44, P < 0.001). A significant overall variation was noted in terms of duration (Ftime = 5.60, P < 0.001), indicating a decrease in exodeviation at distance over time in both pencil push-up training group (F = 172.20, P < 0.001) and binocular vision training group (F = 235.37, P < 0.001), as displayed in Table 2 and Fig. 1. The difference in exodeviation at distance between 3 months and 1 month was significantly higher in binocular vision training group when compared to pencil push-up training group (t = -3.17, P = 0.003). No significant differences were found between 1 month and baseline as well as 6 months and 3 months, in comparison to pencil push-up training group (t = 0.27, P = 0.79; t = -1.94, P = 0.06), as shown in Fig. 2.
Table 2.
Comparison of distance and near deviation in the pencil push-up and binocular vision training groups
| At distance | At near | |||||||
|---|---|---|---|---|---|---|---|---|
| 
 | 
 | 
|||||||
| PPT | BVT | PPT | BVT | |||||
| Before training | -11.75±1.75 | -12.32±1.90 | -12.15±1.90 | -12.32±1.95 | ||||
| After training | ||||||||
| 1 month | -10.76±1.52a | -11.53±1.90 | -11.46±1.83 | -10.92±1.53a | ||||
| 3 months | -7.60±1.32b | -6.49±1.04b | -10.04±2.03b | -8.52±2.33b | ||||
| 6 months | -3.70±0.92c | -3.39±0.47c | -4.12±0.89c | -4.01±0.93 | ||||
PPT: Pencil push-up therapy. BVT: Binocular vision training. Compare with distance deviation before training, aP<0.05; Compare with distance deviation after 1 month training, bP<0.05; Compare with distance deviation after 3 months training, cP<0.05
Figure 1.

The mean angle of deviations at distance and near at pre-training (pre) and each post-training (po) time with the pencil push-up therapy group and the binocular vision training group. The negative values on the vertical axis represent exodeviation
Figure 2.

Comparison of differences in distance deviation at each follow-up time point
Comparison of the effects of two training methods on post-operative exodeviation at near
The comparison between binocular vision training group and pencil push-up training group in terms of exodeviation at near before and after training at different time points revealed statistically significant differences in both grouping and duration (F grouping = 4.36, P = 0.04; F duration = 234.70, P < 0.001; F interaction = 2.44, P = 0.08). Both groups exhibited a decrease in exodeviation at near as the training duration increased (F = 117.06, P < 0.001; F = 119.43, P < 0.001). No statistically significant differences in exodeviation at near were observed between binocular vision training group and pencil push-up training group at baseline, 1 month, and 6 months (t = -0.32, 1.18, 0.43, all P > 0.05). However, binocular vision training group demonstrated significantly lower exodeviation at near compared to the pencil push-up training group at 3 months (t = 2.55, P = 0.01), as depicted in Table 2 and Fig. 1. The difference in exodeviation at near between 1 month and 3 months was significantly greater in binocular vision training group than in pencil push-up training group (t = 2.32, P = 0.02). There were no significant differences between 1 month and baseline or between 3 months and 6 months (t = -1.03, P = 0.31; t = -1.26, P = 0.21) when compared to pencil push-up training group (as presented in Table 2, Fig. 3).
Figure 3.

Comparison of differences in near deviation at each follow-up time point
Under-correction and over-correction after training
Nine patients in the pencil push-up training group still exhibited distant and near exotropia greater than -8∆ after 6 months of training, whereas all patients in the binocular vision training group achieved the success criteria. No cases of over-correction were observed in either group following the training.
Comparison of the effects of two training methods on post-operative stereopsis at distance
The interaction between training methods and training time showed statistically significant differences in the effects on stereopsis at distance (F interaction = 5.30, P = 0.003). Consequently, separate analyses were conducted to examine the individual effects of training methods and time within each group. There were no significant overall differences between the groups (F grouping = 0.03, P = 0.89). At baseline, 1 month, and 3 months, no statistically significant differences in stereopsis at distance were found between binocular vision training group and pencil push-up training group (t = -1.04, -0.59, 0.36, all P > 0.05). However, binocular vision training group demonstrated superior distant stereopsis compared to the pencil push-up training group, with a statistically significant difference at 6 months (t = 9.33, P < 0.001). A significant overall difference was observed in terms of time (F time = 74.71, P < 0.001), indicating that both pencil push-up training group and binocular vision training group experienced an improvement in distant stereopsis over time (F = 136.21, P < 0.001; F = 200.35, P < 0.001), as presented in Table 3. Neither pencil push-up training group nor binocular vision training group exhibited cases of normal stereopsis at baseline. However, after 6 months of training, 2 cases in pencil push-up training group and 9 cases in binocular vision training group achieved normal stereopsis, with a statistically significant difference (χ2 = 5.02, P = 0.03).
Table 3.
Comparison of distance and near stereoacuity in the pencil push-up group and binocular vision training groups
| At distance | At near | |||||||
|---|---|---|---|---|---|---|---|---|
| 
 | 
 | 
|||||||
| PPT | BVT | PPT | BVT | |||||
| Before training | 1103.33±651.05 | 1295.38±704.48 | 135.89±78.65 | 148.49±84.33 | ||||
| After training | ||||||||
| 1 month | 976.75±363.16 | 1056.86±600.23 | 132.46±75.52 | 140.65±72.34 | ||||
| 3 months | 707.41±390.06b | 672.80±300.39b | 127.44±69.84 | 102.13±69.58b | ||||
| 6 months | 440.79±150.13c | 160.44±51.78c | 125.89±52.56 | 79.43±32.46c | ||||
PPT: Pencil push-up therapy. BVT: Binocular vision training. Compare with distance deviation after 1 month trainin; bP<0.05; Compare with distance deviation after 3 months training; cP<0.05
Comparison of the effects of two training methods on post-operative stereopsis at near
After 6 months of training, the pencil push-up group did not show any change in stereopsis at near (F = 0.93, P = 0.35), while the binocular vision training group demonstrated a significant improvement (F = 7.00, P < 0.001). Results from 1-month training indicated no notable difference between the binocular vision training and pencil push-up training groups (t = -0.70, P = 0.48). In the case of the data from the 3-month and 6-month visit, the binocular vision training group exhibited a significantly better near stereopsis compared to the pencil push-up training group (t = 2.31, P = 0.02; t = 6.82, P < 0.001) [Table 3].
Sensory fusion
Before the training, there were 11 children in the pencil push-up training group and 12 children in the binocular vision training group who experienced monocular suppression at distance. After 6 months of training, all children in the binocular vision training group achieved normal sensory fusion, whereas 4 children in the pencil push-up training group still exhibited monocular suppression (χ2 = 5.28, P = 0.02). In terms of near sensory fusion, prior to the training, 3 children in the pencil push-up training group and 4 children in the binocular vision training group had monocular suppression. Following 6 months of training, all children in the binocular vision training group regained normal sensory fusion, while 2 children in the pen push-up training group continued to experience monocular suppression (χ2 = 3.73, P = 0.05).
Comparison of the effects of two training methods on fusion convergence amplitude
The fusion convergence amplitude was significantly improved from the pretraining to 6-month follow-up visits in the pencil push-up training group and binocular vision training group at both near and distance (at near: F =16.77, 31.19, both P < 0.001; at distance: F =24.44, 33.40, both P < 0.001). According to 1-month training results, there was no significant difference between the binocular vision training and pencil push-up training groups at distance (t = 0.19, P = 0.84). In the case of the data from the 3-month and 6-month visit, binocular vision training group showed a significantly higher fusion convergence amplitude than pencil push-up training group (t = -2.98, P < 0.001; t = -2.42, P = 0.016). Similar results were observed for the fusion convergence amplitude at near [Table 4].
Table 4.
Comparison of fusional convergence amplitude at distance and near in the PPT group and BVT groups
| At distance | At near | |||||||
|---|---|---|---|---|---|---|---|---|
| 
 | 
 | 
|||||||
| PPT | BVT | PPT | BVT | |||||
| Before training | 13.21±8.96 | 13.3±9.32 | 18.2±9.46 | 17.9±9.86 | ||||
| After training | ||||||||
| 1 month | 15.4±9.37 | 15.86±9.96 | 19.4±10.36 | 19.6±10.12 | ||||
| 3 months | 17.65±10.66 | 21.77±10.05b | 21.45±11.40 | 26.64±10.65b | ||||
| 6 months | 21.34±11.22c | 25.4±11.84 | 24.2±11.56c | 28.8±12.42 | ||||
PPT: Pencil push-up therapy. BVT: Binocular vision training. Compare with distance deviation after 1 month training; bP<0.05; Compare with distance deviation after 3 months training; cP<0.05
Discussion
IXT is a common eye disease, but there is still a lack of unified standard for surgical treatment. Different researchers have proposed various criteria for defining the success of surgery. Chia et al.[11] and Figueira et al.[12] defined success as maintaining postoperative horizontal strabismus angle in the primary position within ±10∆. Lee et al.[13] suggested that a range of ±8∆ would be more appropriate. On the other hand, Maruo et al.[14] even considered a range of ±20∆ as successful in their studies. Wang et al.[2] and PEDIG[15] stated that a postoperative esotropia degree ≤5∆ and exotropia degree ≤10∆ would be considered satisfactory. Wang et al.[6] found that an exotropia degree ≤8∆ can lead to extramacular binocular vision. In this study, we adopt the definition of surgical success proposed by Wang et al.[6] Another aspect of defining surgical success is that the angle of exotropia ≤8∆ does not require external intervention.
Horizontal exotropia ≥15∆ after IXT is the threshold for considering surgery. It is not recommended to undergo training at this stage as the purpose of training is to enhance the patient’s autonomous vergence, enabling them to overcome exotropia through voluntary vergence when experiencing fatigue or neurological instability. However, in cases where the degree of exotropia is significant, foveal suppression is persistent, and fusion ability is poor, relying solely on training to strengthen convergence may lead to excessive convergence after surgery without the ability to control it, resulting in esotropia and subjective diplopia. Managing the resulting diplopia is more challenging than dealing with the original exotropia symptoms. Patients with mild undercorrection (between -8∆ and -15∆) after IXT surgery, who do not meet the surgical criteria, may experience recurrence of IXT due to exodrift if timely intervention is not provided. Studies have revealed a wide range of long-term recurrence rates after exotropia surgery.[2,3,6] Implementing functional training or timely interventions can potentially help prevent the need for secondary surgeries.
Pencil push-up training method has gained popularity in clinical practice due to its simplicity, ease of learning, lack of cost, and absence of follow-up requirements. Internal training within the hospital should be conducted once a week. If clinical trials demonstrate that pencil push-up training is as effective as in-hospital training, it could substantially reduce healthcare expenses and alleviate the burden on patients.
In clinical settings, patients diagnosed with convergence insufficiency frequently necessitate binocular vision training. Moreover, the training process and evaluation system have achieved a commendable level of comprehensiveness. Despite the differences in patient sources between this study and those with convergence insufficiency, both groups share a common training objective of enhancing binocular visual function, and the training methods employed are identical. The training in this study strictly adheres to the established process for patients with convergence insufficiency and has been proven to be effective.
Prior to training, there were no statistical differences in the angle of exotropia between the two groups at distance and near; however, binocular vision training group exhibited a higher angle of exotropia than the pencil push-up training group. At 3 months, the angle of exotropia in binocular vision training group was smaller than that in pencil push-up training group, and this difference was statistically significant. Furthermore, the difference in the angle of exotropia between 1 month and 3 months in binocular vision training group was greater than that in pencil push-up training group, with statistical significance. This disparity may be attributed to the simplicity and ease of understanding of the pencil push-up training method, which lacks a learning curve, whereas binocular vision training method is more intricate and influenced by the learning curve, resulting in lesser early effectiveness when compared to the pencil push-up training group. After 6 months of training, there were no statistical differences in the angle of exotropia between the two groups, suggesting that both training methods reached a stable level. Extending the training duration might further diminish the angle of exotropia. However, considering that the majority of individuals have exophoria, the impact might not be readily apparent. No statistically significant difference between the stereopsis before training and 1 month after training was observed; however, after 3 months of training, a difference became apparent, albeit without significant variation between the two groups. After 6 months of training, binocular vision training group showcased superior stereopsis compared to the pencil push-up training group, with statistical significance. The improvement in deviation decrease may be temporary if there is still suppression and poor convergence amplitudes. In this study, both training methods showed improvement in sensory fusion and fusion vergence amplitude, but binocular vision training resulted in greater improvements.
The comparison may not be fairly balanced as the binocular vision training group is having repeated reinforcement and supervision by the optometrists. Nonetheless, pencil push-up training showed a similar effect to binocular vision training in reducing exodeviation at both distance and near. We believe that pencil push-up training is worth popularizing.
In summary, both pencil push-up training and binocular vision training methods can decrease the postoperative degree of exotropia and maintain it at a stable level. However, if binocular vision training method is mastered early, it can lead to a faster reduction in exotropia angle. While both methods are effective at reducing exodeviation, binocular vision training surpasses the effectiveness of pencil push-up training in terms of functional recovery. It has been observed that if the role of physiological diplopia is explained to the patients, the pencil push-ups do very well.[16] So, ophthalmologists should consider explaining physiological diplopia as an integral part of convergence exercises. When selecting training methods, it is crucial for clinical physicians or vision trainers to consider various factors, including cost, efficiency, and effectiveness. They should opt for the most beneficial method for individualized training of the target population.
Financial support and sponsorship:
Nil.
Conflicts of interest:
There are no conflicts of interest.
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