How Do Most Young Moderate Hyperopes Avoid Strabismus?

Abstract

Purpose: Uncorrected hyperopic children must overcome an apparent conflict between accommodation and vergence demands to focus and align their retinal images. This study tested hypotheses about simultaneous accommodation and vergence performance of young hyperopes to gain insight into ocular motor strategies used to maintain eye alignment.

Methods: Simultaneous eccentric photorefraction and Purkinje image tracking were used to assess accommodative and vergence responses of 26 adult emmetropes (AE) and 94 children (0–13 years) viewing cartoons. Children were habitually uncorrected (CU) (spherical equivalent refractive error [SE] −0.5 to +4 D), corrected and aligned (CCA), or corrected with a history of refractive esotropia (CCS). Accommodative and vergence accuracy, dissociated heterophoria, and vergence/accommodation ratios in the absence of retinal disparity cues were measured for 33- and 80-cm viewing distances.

Results: In binocular viewing, median accommodative lags for 33 cm were 1.0 D (AE), 1.33 D (CU), 1.25 D (CCA), and 1.0 D (CCS). Median exophorias at 80 and 33 cm were 1.2 and 4.5 pd (AE), 0.8 and 2.5 pd (CU), and 0 and 1.2 pd (CCA), respectively. Without disparity cues, most response vergence/accommodation ratios were between 1 and 2 meter angle/D (∼5–10 pd/D) (69% of AE, 44% of CU, 60% of CCA, and 50% of CCS).

Conclusions: Despite apparent conflict in motor coupling, uncorrected hyperopes were typically exophoric and achieved adultlike accuracy of both vergence and accommodation simultaneously, indicating ability to compensate for conflicting demands rather than bias to accurate vergence while tolerating inaccurate accommodation. Large lags and esophoria are therefore atypical. This analysis provides normative guidelines for clinicians and a deeper mechanistic understanding of how hyperopes avoid strabismus.

Uncorrected young hyperopes must accommodate more than emmetropes if they are to achieve focused retinal images.^1,2 Beyond the additional demand on their accommodation system, the neural coupling between accommodation and vergence responses^3–6 suggests they will overconverge when achieving a focused image, putting them at risk for refractive esotropia, a form of strabismic misalignment of the eyes.^7,8 

Human infants are typically born with hyperopia^9–11 but go on to lose much of it over the first months after birth.^12,13 The approximately 3% who retain >4 D hyperopia into childhood^14,15 are the children most at risk for refractive esotropia, at an age of onset of between approximately 6 months and 6 years.⁷ Interestingly, only approximately 20% of the children with moderate hyperopia develop this convergent strabismus.^8,16–19 How do the eyes of young hyperopes remain aligned given their ocular motor demands? A typical young adult generates a mean of approximately 6 pd of convergence per diopter of increased accommodation, when the accommodation and vergence responses are measured simultaneously in the absence of disparity and proximal cues^20–24 and 3 to 4 pd of convergence per diopter of increased accommodation if only the vergence response is measured and accommodation is assumed to be accurate²⁵ (accommodative convergence to accommodation [AC/A] ratios of 6 pd/D or 3.5 pd/D; 3.5 pd/D is equivalent to 2 deg/D and 0.582 MA/D, where a meter angle [MA] can be considered equivalent to a diopter, the reciprocal of distance in meters). An individual with 4 D of uncorrected hyperopia would therefore be expected to generate 24 pd (6*4) of convergence more than an emmetrope when focusing accurately at infinity. 

In considering how young hyperopes might avoid strabismus, one logical hypothesis would be that children with hyperopia could relax their accommodation and tolerate the resulting blur to stay aligned—prioritizing single vision over focused images. The evidence from studies of accommodative accuracy suggests the opposite relationship, however. While children with hyperopia do exhibit a range of accommodative accuracy,^26–32 the ones who accommodate accurately tend to remain nonstrabismic while those with the reduced accommodative responses tend to develop the strabismus.^8,17,26,33 This suggests that the hyperopes with larger lags are more challenged and that those accommodating accurately are capable of compensating for their hyperopia while maintaining eye alignment. Are nonstrabismic uncorrected hyperopes achieving typical levels of accommodation and vergence accuracy simultaneously given their extra accommodative demand, and can this behavior be facilitated in management of children at risk for strabismus or used in predicting those who will develop a deviation? 

The purpose of this study was to understand systematically the role of the different components of the ocular motor responses in maintaining typical accommodative and vergence accuracy for nonstrabismic young hyperopes. Accommodation and vergence responses are frequently described as consisting of four components³⁴: a baseline tonic “resting” state (tonic accommodation or vergence), a proximal component driven by the sense of “nearness” (proximal accommodation or vergence), a coupled component driven by the paired system (accommodative vergence or vergence accommodation), and an error-correcting component driven by blur feedback in the accommodative system or retinal disparity feedback in the vergence system (reflex accommodation or vergence).^35,36 Although accommodation and vergence responses are neurally coupled, studies of hyperopia and development of refractive esotropia have typically measured one or other motor response rather than their simultaneous performance.^{1,17,26,37–39} Clinical tests also do not assess them simultaneously (e.g., measures of accommodative lag or assessment of eye alignment using cover testing). Specifically, this study was designed to understand the simultaneous accommodation and vergence performance of young nonstrabismic hyperopes to gain insight into the ocular motor strategies being used to maintain alignment of their eyes. This analysis provides normative guidelines for clinicians evaluating these patients and a mechanistic understanding of how hyperopes can avoid strabismus. 

The following questions were addressed (as illustrated in Fig. 1): (1) Do nonstrabismic hyperopes accommodate less accurately than emmetropes and those with strabismus (Fig. 1A)? (2) When retinal disparity cues are removed, preventing error-correcting fusional vergence, is the latent vergence error an overconvergence for those without strabismus (esophoria resulting from the sum of tonic vergence, proximal vergence, and accommodative vergence) (Fig. 1B)? (3) Does this latent error for nonstrabismic participants increase during extended absence of retinal disparity cues, indicating a relaxation of protective tonic vergence adaptation^40–43 (Fig. 1C)? (4) How much vergence error is the nonstrabismic fusional vergence response capable of overcoming and correcting (Fig. 1D)? (5) Is the combination of proximal and accommodative vergence responses reduced in nonstrabismic hyperopes relative to those with strabismus, reducing their tendency to overconverge (Fig. 1E)? 

Figure 1.

 

An illustration of the questions addressed in this study. An uncorrected child with nonstrabismic hyperopia could be predicted to have inaccurate accommodation (A), a large esophoria (B), a robust vergence adaptation system (C), a large fusional vergence range (D), and/or reduced proximal vergence and a low AC/A ratio (E) when they view a target.

Methods

Participants

Ninety-four children (0–13 years of age, 56 female) and 26 functionally emmetropic adults (17–31 years of age, 12 female) completed the study. The children were recruited from the Atwater Eye Care Center at Indiana University School of Optometry and were required to be hyperopic or functionally emmetropic (with no more than 0.5 D of myopia, no more than 2.5 D of anisometropia, and no more than 2 D of astigmatism) with a history of no additional visual or neurologic disorders beyond amblyopia or refractive esotropia. The children with no history of refractive correction (0–10 years) were assigned to the children uncorrected group (CU). The children with a history of refractive correction and no history of strabismus (0–10 years) were assigned to the children corrected aligned group (CCA), and those with a history of esotropia (0–18 years) were assigned to the children corrected strabismic group (CCS). The emmetropic adults (AE), with no history of visual or neurologic disorders, were recruited from the population of students and staff at the school, and 23 were naive observers. Informed consent was obtained from adult participants and the guardians of the children. Assent was gathered from the 19 children aged more than 8 years. The study was approved by the Indiana University Institutional Review Board and followed the guidelines of the Declaration of Helsinki. 

Equipment

Simultaneous binocular Purkinje image tracking and eccentric photorefraction were used to record vergence alignment, refractive state, and pupil size at 50 Hz (PowerRef3; PlusOptix, Nuremberg, Germany). Each refractive state estimate was derived from the slope of the light intensity distribution across the image of the pupil in recorded video images^44,45 while eye position was computed by comparing the position of the first Purkinje image and the center of the pupil in the video. The instrument's video camera was mounted at a viewing distance of 1 m from the participant at one end of a motorized track (Fig. 2A). The participants viewed spatially and temporally broadband video images (naturalistic commercial cartoon movies) on the 6.8-cm × 6.8-cm screen through the aperture at the other end of the track. The screen was capable of being moved between viewing distances of 33 and 80 cm from the participant. 

Figure 2.

 

(A) A participant watching a movie through an aperture, while the horizontally mounted screen was moved back and forth along a motorized track in front of the PowerRef3 camera. The movie was presented using a beamsplitter mounted below the screen. The inset processed image collected by the camera demonstrates the principles of eccentric photorefraction and Purkinje image tracking. The equipment was covered with the lid during data collection and the room lights were dim to reduce distraction. (B) An illustration of the addition of a mirror for MEM retinoscopy.

Procedure

Clinical Assessment of Accommodative Accuracy

Before collecting the simultaneous accommodation and vergence motor responses, the participants’ accommodative accuracy was measured using clinical monocular estimation method (MEM) dynamic retinoscopy.^46,47 It was performed from a distance of 1 m by mounting a second beamsplitter over the movie viewing aperture while the participant was looking at the screen at a viewing distance of 33 cm (Fig. 2B). The clinician performing the retinoscopy was masked as to the power of the lens being held before the eye. They merely reported the reflex as “with” or “against” while another examiner changed the lenses. This retinoscopy was performed to permit comparison between the PowerRef 3 eccentric photorefraction data and the typical clinical approach to assess accommodative accuracy. The linear operating range of the PowerRef 3 is from approximately 7.00 D of myopic defocus to 5.00 D of hyperopic defocus relative to infinity for a 5-mm pupil,⁴⁵ and therefore, a wide range of accommodative errors could be recorded with both techniques. 

Accommodative Accuracy, Phoria, and Vergence to Accommodation Ratio Measurement

Simultaneous PowerRef3 accommodation and vergence data were recorded for 80-cm and 33-cm viewing distances, under binocular and monocular viewing conditions. During monocular viewing, the right or left eye was covered for a short (5 seconds) or long (30 seconds) duration. Objective dissociated heterophoria (the latent misalignment of the eyes when one eye is covered) was estimated by measuring the difference in eye alignment between monocular and binocular viewing conditions. Covering one eye with an infrared passing filter (Kodak Wratten filter 87b; Kodak, Rochester, NY, USA) to generate monocular viewing permitted the measurement of eye position and accommodation from both eyes while blocking vision of the occluded eye.^48–50 The right eye was occluded with the filter for 5 seconds (short cover), followed by binocular viewing for 5 seconds and then cover of the left eye for 5 seconds. This cycle was repeated two additional times. The duration of monocular viewing was then increased with the eyes covered for 30 seconds (long cover) during a final fourth cycle to determine whether prolonged dissociation resulted in larger phoria. Figure 3 shows example data from a single trial at one viewing distance for a hyperopic child. 

Figure 3.

 

An example phoria measurement trial collected from a 5.5-year-old child with +4.00 D uncorrected hyperopia at a 33-cm viewing distance. Data were smoothed for illustration purposes. The top panel shows the refractive state for the right eye (RE) and left eye (LE), and the bottom panel shows the vergence alignment data. The white background indicates periods of binocular viewing (B), light shading indicates RE covered (R), and darker shading indicates LE covered (L). The covering of either eye elicits a latent convergent misalignment (esophoria) for this participant, with minimal change in accommodation. The accommodation data are separated vertically for clarity and merely represent change in response over time.

Fusional Divergence and Convergence Measurements (at 33 cm)

The ability of fusional vergence responses to overcome these latent heterophoria misalignments during binocular viewing was assessed using a lightweight prism bar apparatus introduced before both eyes.⁴⁹ This apparatus was adjusted to the subject's interpupillary distance. A baseline estimate of habitual vergence position in binocular viewing at a 33-cm viewing distance was recorded and then retinal disparity was introduced with prisms during simultaneous PowerRef3 recording of accommodation and vergence responses for approximately 2 to 4 seconds at each increasing disparity step (the combined powers from the two commercial prism bars proceeded through values of 2, 4, 8, 12, 16, 20, 24, 28, 32, 36, and 40 pd). A video recording was used to code prism amount over time for synchronization with the recorded responses. An example data set is provided in Figure 4. 

Figure 4.

 

Data from an example fusional divergence trial. A hyperopic child's responses to increasing and then decreasing steps of Base-In prism during a 140-second trial. Top panel: Refractive state of the right (RE) and left (LE) eyes, with upward indicating relaxation of accommodation. Bottom panel: Measured vergence position and magnitude of introduced prism (black step function), with upward indicating increased Base-In prism or apparent convergent alignment of the eyes. If the eyes realigned to overcome the prismatic demand, there was no change in the measured vergence position from the baseline value. When the participant was unable to overcome the prism driving divergence, the optical effect of the prism is visible in the apparently convergent vergence position data (gray shaded region). The accommodation data are vertically separated for clarity. The white background indicates periods when the eyes were aligned, and the participant was able to overcome the demand.

Calibration

Calibration of the simultaneously collected Purkinje image tracking and photorefraction data was also attempted for each participant, using prisms and anisometropia induced with lenses.⁵¹ Although the default calibration function used in the PowerRef3 software provides a reasonable estimate of the average calibration across a group of participants, there is significant variation in individual calibration.^45,52,53 The analyses in the current study were therefore performed for both individually calibrated and uncalibrated versions of the data to confirm that the results were robust to calibration effects. 

Data Analysis

Data analyses were performed using Datavyu (Creative Commons Attribution 4.0 International License, Mountain View, CA, USA) and MATLAB (MathWorks, Natick, MA, USA). The video from each PowerRef3 recording was stored for coding offline. Coding timestamps were generated to indicate the placement and removal of the filter, lens, or prism for later analyses of the data. 

Nonphysiologic outliers were removed from the PowerRef3 pupil, refractive state, and eye position data using the Tukey outlier method.⁵⁴ A sliding algorithm was then used to find the final 2-second period of stable data in each condition when the standard error⁵⁵ of vergence position was less than 0.5 pd and of refractive state was less than 0.05 D based on an analysis of the sensitivity of the equipment. The median accommodation and vergence responses for each of these 2-second periods for each viewing condition were determined. 

Accommodative lag derived from the photorefraction data was defined as the difference between the dioptric position of the stimulus screen and the photorefraction refractive state estimate, both in diopters. The heterophoria was computed as the difference between eye alignment in monocular and binocular viewing⁴⁸ and was compared with any associated difference in the simultaneously recorded accommodation data. For short cover calculations, the median difference between the monocular and binocular sections in the three short cover intervals was used. Fusional divergence and convergence limits were defined as the last prism for which the subject could maintain alignment. The median difference in accommodation response between the no prism and that last prism time period was also calculated for each participant. The ratio of change in accommodative and proximal vergence per diopter of measured accommodation was calculated as the ratio of monocular viewing vergence position difference to refractive state difference between 80- and 33-cm viewing distances in the short cover phoria condition. 

Results

Participant Details

Sixty-nine children (0–10 years of age) and 26 adults (17–31 years of age) who had not worn refractive correction previously, plus 25 children who were already wearing optical correction (1–13 years of age), were included in the analyses. Eleven additional participants (2 adults, 9 children) were excluded due to instrument limitations or poor data quality, and another 11 participants (4 adults, 7 children) were excluded as they did not have an eye examination. The children who wore correction habitually were recruited for comparison with the uncorrected hyperopes. They were tested in their correction and divided into two groups depending on their history (CCA and CCS were defined as children without and with a history of esotropia, respectively). The participant details are provided in the Table. The participants had a conventional clinical eye examination within 6 months before or after their study participation, and their clinical cycloplegic spherical equivalent refractive error is plotted as a function of age in Figure 5. 

Table.

 

Clinical Details of Participants

 

Figure 5.

 

The distribution of participants’ spherical equivalent refractive error as a function of age. CU (A), AE (B), CCA (C), and CCS (D). Open triangles represent the eye with less hyperopia (LHE), and filled dots represent the eye with more hyperopia (MHE).

Do Nonstrabismic Hyperopes Accommodate Less Accurately Than Emmetropes and Those With Strabismus?

Twenty-five adults and 89 children (65 CU, 14 CCA, and 10 CCS) underwent MEM retinoscopy to determine their accommodative accuracy for binocular viewing of the cartoon movie target at a 33-cm viewing distance. Figure 6 presents MEM accommodative lag as a function of spherical equivalent refractive error. The data were divided into less and more hyperopic eye panels because the less hyperopic eye typically guides accommodative responses.^56,57 For equal spherical equivalents in the two eyes, the right eye was plotted in the less hyperopic eye panel. The median (interquartile range [IQR]) MEM accommodative lags for the AE, CU, CCA, and CCS groups were 1.00 (1.06) D, 1.33 (0.75) D, 1.25 (1.25) D, and 1.0 (1.25) D for the less hyperopic eye, respectively. These four groups were not statistically significantly different (Kruskal–Wallis ANOVA, p = 0.056). The only participants with less hyperopic eye accommodative lags greater than 3 D were three CU, one CCA, and one CCS, all with more than 2 D of hyperopia in that eye. 

Figure 6.

 

MEM accommodative lag of the less hyperopic (A) and more hyperopic (B) eye as a function of its spherical equivalent refractive error (cycloplegic refraction for children), for a 33-cm viewing distance. Positive values indicate accommodative lag and negative indicate accommodative lead.

Comparison of Accommodative Lag Estimates From MEM and Photorefraction

To permit the eccentric photorefraction accommodative lag data to be considered in the context of routine clinical measures, the lag data collected at the 33-cm viewing distance were compared with the MEM retinoscopy data in mean-difference plots (Fig. 7). This figure demonstrates that, on average, the raw PowerRef data tended to indicate less than a diopter more lag than the MEM technique for all groups. Although individual participants’ accommodation could have changed between the two measurements, these mean values are consistent with the presence of the correction offset factor built into the PowerRef 3.⁴⁵ 

Figure 7.

 

Mean-difference plots for the MEM retinoscopy and PowerRef 3 accommodative lag data for the less hyperopic eye, which was assumed to be used to view the target. (A) AE and CU. (B) CCA and CCS. The solid and dashed colored lines represent the mean and 95% limits of agreement for the group represented by each color.

What Is the Vergence Error in the Absence of Fusional Vergence (Dissociated Heterophoria)?

If children with uncorrected hyperopia accommodate to focus their retinal images, one might predict that their accommodative convergence would result in overconvergence and esophoria in dissociated conditions. To test this hypothesis, the heterophoria at the two viewing distances was computed for each participant, in each case from the difference in PowerRef 3 vergence alignment data between monocular and binocular viewing conditions.⁴⁸ These data are shown in Figures 8A and 8B, as a function of the spherical equivalent refractive error of the less hyperopic eye. The median (IQR) adult emmetrope values were small exophorias of 1.2 (3.3) pd at 80 cm and 4.5 (3.8) pd at 33 cm, while the median values for the uncorrected children were 0.8 (2.5) pd of exophoria at 80 cm and 2.5 (3.7) pd of exophoria at 33 cm. 

Figure 8.

 

Dissociated heterophoria (A, B) and simultaneous accommodation changes between binocular and monocular viewing (C, D) during the 5-second measurements as a function of spherical equivalent refractive error of the less hyperopic eye for AE, CU, and CCA at 80-cm and 33-cm viewing distances. Positive values indicate exophoria and relaxation of accommodation. The lines in panels A and B represent the predicted amount of phoria, based on the median emmetropic adult phoria for each distance with a stable accommodative lag and a stimulus AC/A ratio of 3.5 pd/D (solid lines) or a response AC/A ratio of 8.6 pd/D (dashed lines).

The lines in Figures 8A and 8B represent the predicted amount of heterophoria based on the median emmetropic adult phoria and a stable accommodative lag, with a stimulus AC/A ratio of 3.5 pd/D or a response AC/A ratio of 8.6 pd/D.²² In general, the uncorrected children have less esophoria than the prediction based on the neural coupling between accommodation and vergence. In fact, 75% of uncorrected children with up to 4D of hyperopia were exophoric with 5 seconds of dissociation for 33 cm and only 13% of children were esophoric while accommodating to the target with typical accuracy. The data shown in Figures 8C and 8D confirm that the participants typically held their accommodation stable with changes of less than 1 D between binocular and monocular viewing. This confirms that, on average, the change in alignment described here as dissociated heterophoria is indeed likely to be associated with stable accommodative behavior. The heterophorias of the corrected aligned children are also shown and indicate similar behavior to the uncorrected children and adults. Their median (IQR) heterophoria at 80 cm was 0 (1.7) pd of exophoria and at 33 cm was 1.2 (2.9) pd exophoria. Overall, the phoria values were significantly different between 80 cm and 33 cm (p < 0.0001, Wilcoxon signed-rank test) and only marginally significantly different between the three groups (p = 0.037, Kruskal–Wallis test). 

Interestingly, the impact of optical correction does not create the anticipated difference in phoria between uncorrected nonstrabismic hyperopes and corrected nonstrabismic hyperopes, despite comparable accommodative accuracy to the target. The two groups of children with 2 to 4 D hyperopia, uncorrected or with correction, did not differ in accommodative lag (p = 0.29, Wilcoxon rank sum test), 33 cm phoria (p = 0.74, Wilcoxon rank sum test), or 80 cm phoria (p = 0.69, Wilcoxon rank sum test), with 5 seconds of dissociation. 

Does the Vergence Error Increase During Prolonged Occlusion, Suggesting a Relaxation of Protective Tonic Vergence Adaptation?

Figure 8 suggests that the uncorrected hyperopic children have levels of dissociated heterophoria that are clinically similar to adult emmetropes after 5 seconds of occlusion and that they do not reveal the esophoria predicted from their hyperopia and accommodative lags. Does their heterophoria become more esophoric after 30 seconds of occlusion, suggesting a relaxation of protective tonic vergence compensation?^42,43 Figure 9 shows dissociated heterophoria after the 30 seconds of occlusion for all three groups. The range of phorias increases after the longer duration of occlusion, but there was no increase in the number of participants with esophoria. In fact, 30% and 13% of CUs were esophoric at 80 and 33 cm after 5 seconds of dissociation, respectively, and 22% and 10% were esophoric at 80 and 33 cm after 30 seconds of dissociation. Similarly, the proportion of adults with esophoria decreased from 24% to 13% at 80 cm with no change at 33 cm (17%) between 5 and 30 seconds of dissociation. 

Figure 9.

 

Dissociated heterophoria after 30 seconds of occlusion as a function of spherical equivalent refractive error of the less hyperopic eye for AE, CU, and CCA. The (A) 80-cm and (B) 33-cm viewing distances. Positive values indicate exophoria and hyperopia. The lines in panels A and B represent the predicted amount of phoria, based on the median emmetropic adult phoria for each distance with a stable accommodative lag and a stimulus AC/A ratio of 3.5 pd/D (solid lines) or a response AC/A ratio of 8.6 pd/D (dashed lines).

Overall, the adults tended to have an increase in the exophoric direction with 30 seconds of dissociation, with a median (IQR) increase of 2.5 (9.1) pd at 80 cm and 0.2 (4.2) pd at 33 cm. Similarly, uncorrected children tended to an increase in the exophoric direction, with a median (IQR) increase of 1.2 (3.9) pd at 80 cm and 0.8 (3.3) pd at 33 cm. The aligned children with correction had a median (IQR) increase in the esophoric direction of 1.0 (2.5) pd at 80 cm and 1.0 (5.4) pd at 33 cm. 

Relationship Between Accommodative Lag and Heterophoria

While the median accommodative lags and dissociated heterophorias were not clinically different across the groups, individual hyperopes may exhibit strategies to protect themselves from overconvergence and risk for strabismus. Figure 10 presents the relationship between accommodative lag and phoria after 5 seconds of dissociation at the 33-cm viewing distance, as a function of spherical equivalent refractive error of the less hyperopic eye. Predictions might include individuals who either underaccommodate to maintain a typical phoria or accommodate accurately and produce esophoria. The data collected from the uncorrected hyperopes presented in Figure 10B indicate that, while most exhibit exophoria, the participants with the larger amounts of hyperopia tend to have smaller exophorias and larger accommodative lags. The corrected and aligned CCA participants in Figure 10C exhibited a similar range of phorias to those in Figure 10B, but with higher hyperopes more distributed over the range. 

Figure 10.

 

The relationship between accommodative lag, phoria, and spherical equivalent refractive error in the adult emmetropes (A), uncorrected hyperopes of up to 4 D (B), and aligned hyperopes with correction (C) for the 33-cm viewing distance. The marker colors in each panel represent spherical equivalent refractive error as shown in the color bar. Positive values indicate hyperopia, accommodative lag, and exophoria.

A principal components analysis was performed to determine the axis through the data from the uncorrected children (Fig. 10B) that captured the most variance and therefore the relationship between the three variables. The phoria data were converted to units of meter angles to make the units equivalent for all three variables and to compensate for differences in interpupillary distance, and therefore vergence demand, with age. For the 80-cm viewing distance, the first principal component explained 72% of the variance with a slope of 0.94 D for refractive error, 0.33 D for accommodative lag, and –0.08 MA for phoria, indicating that the accommodative lag and phoria were changing less than each diopter change in refractive error (only 0.33-D increase in lag and 0.5-pd increase in esophoria per diopter of increase in hyperopia). The second (21% of the variance; slopes: Lag = −0.94 D, refractive error (Rx) = 0.33 D, Phoria = −0.02 MA) and third (7% of the variance; slopes: Phoria = 1.00 MA, Rx = 0.09 D, Lag = <0.01D) orthogonal components aligned near the lag and phoria axes, respectively. The components were qualitatively similar for the 33-cm viewing distance (first component explained 63% of the variance [slopes: Rx = 0.93 D, Lag = 0.35 D, Phoria = −0.14 MA], second component explained 28% of the variance [slopes: Lag = 0.93 D, Rx = −0.33 D, Phoria = 0.15 MA], and third component explained 9% of the variance [slopes: Phoria = −0.98 MA, Rx = −0.18 D, Lag = 0.10 D]). 

Figure 11 presents the phoria and accommodative lag of the uncorrected hyperopes. The children who have ≥3.0 D of hyperopia are shown as filled black circles, those who have anisometropia ≥1.0 D are shown with an additional small circle around their data, and those with amblyopia are shown with a larger additional circle around them. Anyone with <3.0 D of hyperopia is represented by a small open circle. This figure illustrates that the distributions are largely overlapping, with the exception of one significant outlier with the combination of anisometropia and amblyopia. This outlier is the only participant with significant esophoria. 

Figure 11.

 

The relationship between accommodative lag and phoria in uncorrected hyperopes of up to 4 D for the 33-cm viewing distance. The children who have ≥3.0 D of hyperopia are shown as filled black circles, those who have anisometropia ≥1.0 D are shown with an additional circle around their data, and those with amblyopia are shown with a larger additional circle around them. Anyone with <3.0 D of hyperopia is represented by a small open circle. Positive values indicate accommodative lag and exophoria.

How Much Vergence Error Is the Fusional Vergence Response Capable of Overcoming?

A young hyperope's ability to align their eyes from their latent dissociated heterophoria position will depend on the range of misalignment their fusional, disparity-driven, vergence response can overcome. Figure 12 shows the participants’ fusional vergence ranges relative to alignment at the target (33-cm viewing distance) and their dissociated heterophoria. Each line represents an individual participant. The crosses indicate the dissociated heterophoria position for cases where it could be measured. For example, a participant with an exophoria would have a cross at a positive value, and the line would extend from the prism value at which they were no longer able to sustain alignment in the divergent direction (positive: Base In prism) to their value in the convergent direction (negative: Base Out prism). The absence of a line means either inability to estimate the fusional range or no fusional capability. Figure 12A presents the data from the AE. Both convergence and divergence median fusional ranges were 20 pd from 0-pd alignment for 33 cm. Figure 12B presents the data from the uncorrected children (CU: median convergence, 20 pd, and divergence, 16 pd). Similarly, Figure 12C shows the data from the optically corrected aligned children (CCA: median convergence, 32 pd, and divergence, 16 pd). The heterophorias for the currently strabismic participants cannot be measured, and hence, their clinical near deviation is plotted with diamond symbols. Some of the participants in the CCS group did not show evidence of fusion and, hence, have no line. The median fusional ranges of the participants with a history of strabismus who completed the task were 20 pd and 8 pd for convergence and divergence, respectively. To overcome latent vergence error (heterophoria) and achieve comfortable binocular vision, it is recommended that a patient has a typical fusional range and a compensating range of double their heterophoria in the opposite direction.⁵⁸ For example, to overcome an exophoria, fusional convergence beyond alignment of at least double the amount of heterophoria is recommended. Ninety-seven percent of uncorrected hyperopic children who completed this condition demonstrated that amount of compensating range or more. Sreenivasan et al.⁴⁹ found mean ± SD fusional ranges in preschoolers of 8.8 ± 2.8 pd for base-in (BI) and 15.3 ± 8.3 pd for base-out (BO). Only 15% of the uncorrected children here had fusional ranges (for both BI and BO) below that range. 

Figure 12.

 

Fusional vergence ranges around the dissociated heterophoria position and alignment of the eyes at the target (0 pd). (A) Adult emmetropes, (B) uncorrected children, (C) corrected and aligned children, and (D) corrected children with a history of esotropia. Each line represents the range of prismatic values over which an individual participant could realign their eyes (1 pd = 0.57 deg). Positive x-axis values represent divergent demand and exophoria. In each case, the asterisk represents the prism where the eyes have been stimulated to reach the position of their dissociated heterophoria. Currently strabismic participants have a diamond at their strabismic angle. The color scale represents the cycloplegic spherical equivalent refractive error of the less hyperopic eye in diopters.

Figure 13 presents change in accommodation during these fusional range measurements for the four groups. It was calculated as the difference between the refractive state measurement during the last prism for which the participant maintained alignment and the baseline refractive state measurement with no prism. These data demonstrate that some of the participants were able to manipulate up to 6 D of accommodation in either direction—increase or relaxation—when using accommodation vergence coupling in achieving vergence alignment. The corrected children with a history of strabismus (CCS) did not manipulate accommodation as significantly after they had exhausted their fusional vergence. 

Figure 13.

 

Change in accommodation during fusional range measurements for the AE, CU, CCA, and CCS groups. The change in accommodation is plotted as a function of the limit of the fusional range. Positive fusional range limits indicate divergence and positive accommodation changes indicate relaxation of accommodation toward hyperopic defocus.

Is the Combination of Proximal and Accommodative Vergence Responses Reduced in Nonstrabismic Hyperopes Relative to Emmetropes?

In theory, the uncorrected hyperopes may not have developed strabismus as a result of a lower vergence-to-accommodation coupling gain. Figure 14 shows individual relationships between changes in accommodation and vergence in monocular viewing while the viewing distance changed from 80 cm to 33 cm. The black diagonal line represents a ratio of 1 MA/D (blue 2 MA/D and red 0.5 MA/D). The metric presented in this figure is similar to a calculated response AC/A method that might be used in clinical care. In clinics, however, the accommodation response is typically assumed to equal the stimulus, rather than measured, resulting in an estimate of a smaller stimulus AC/A ratio. The participants were viewing monocularly, and all cues other than interocular retinal disparity were available (accommodative and proximal vergence). Figure 14A shows the data from the AE, with the majority of values (69%) lying between 1 and 2 MA/D, for the demand of 1.75 D or MA of change. Figure 14B shows the data from the CU, for whom a greater proportion of values fall between ratios of 0.5 and 1 MA/D (41%), largely as a result of additional accommodation for the same amount of proximal and accommodative vergence as the adults, indicating potential protection against overconvergence relative to an emmetropic adult. There are some participants with very small or negative accommodative changes of less than 0.5 D and some participants with no vergence change or a divergent change to the near position. These ambiguous responses were not included in the proportion calculations in the figure (gray box). It is possible that these children were not attending to the task. Figures 14C and 14D show the data from the CCA and the CCS. These two groups almost exclusively (other than two participants) have ratios equal to or higher than 1 MA/D. Interestingly, there is more variance in the accommodation change in the uncorrected groups and a tendency to greater vergence change in the corrected groups. The uncorrected groups, AE and CU, had 0.5 D and 0.8 D standard deviation in accommodation and 0.4 MA and 0.6 MA in vergence, respectively. The corrected groups, CCA and CCS, on the other hand, had 0.5 D and 0.9 D standard deviation in accommodation and 0.7 MA and 1.8 MA in vergence, respectively. The ratios of standard deviation in convergence to accommodation were 0.8, 0.6, 1.4, and 2.1 for AE, CU, CCA, and CCS, respectively. This difference in responses may be an effect of the glasses wear, or, as these hyperopic children were prescribed glasses for a clinical reason, it may also be that the clinicians perceived them to be at increased risk (e.g., based on family history or complaints of headache or asthenopia). 

Figure 14.

 

The relationship between change in vergence and accommodation responses when changing fixation from a target at an 80-cm to a 33-cm viewing distance in monocular viewing. The color scale represents the spherical equivalent refractive error of the less hyperopic eye in diopters. The diagonal black line represents a ratio of changes of 1 MA/D, the blue line represents 2 MA/D, and the red line indicates 0.5 MA/D. Positive values indicate increasing accommodation and convergence. The black dotted line indicates the demand of 1.75 MA of vergence. In the absence of a measurement of accommodation, all data on this line would be interpreted as a stimulus AC/A ratio of 1 MA/D (6 pd/D for an adult with a 6-cm interpupillary distance [IPD] and 4.5 pd/D for a child with a 4.5-cm IPD). The gray shaded area represents accommodation changes of <0.5 D that were excluded from summary analyses.

The Impact of Calibration

Ninety-seven participants (26 AE, 49 CU, 13 CCA, 9 CCS) provided a calibration function for eccentric photorefraction and 86 (25 AE, 48 CU, 7 CCA, 6 CCS) for the Purkinje image tracking. The overall median (IQR) slope for the relative calibration of refractive state was 0.81 (0.17) and for eye position was 0.92 (0.34). Median slopes for refractive state and vergence for each group were as follows: AE, 0.92 (0.23) and 0.92 (0.34); CU, 0.95 (0.43) and 0.89 (0.33); CCA, 0.85 (0.20) and 1.07 (0.52); and CCS, 0.80 (0.55) and 1.30 (0.52), respectively. The higher variability in the slopes of the corrected participants (CCA and CCS) was likely due to the addition of another optical surface (spectacles), and the magnification effect of the plus lenses was likely to have resulted in the apparently higher values noted for the eye positions of the CCA and CCS groups. These median calibration factors suggest that errors in estimation resulting from using the group average calibration are likely to have had a small effect on the estimated ratios in Figure 14 and they cannot have impacted the direction of a phoria estimate, for example. 

Discussion

In theory, there are different paths a young hyperopic child could take in the presence of the apparent conflict between their neurally coupled accommodation and vergence responses. They could underaccommodate to a target to maintain alignment if they have a bias toward single vision, have accurate accommodation and vergence if they are able, or accommodate more accurately but overconverge if they have a bias toward focused images.¹ 

The simultaneous measures of accommodation and vergence of young uncorrected hyperopes in this study confirmed that many of the nonstrabismic participants (CU: ∼0–4 D) were, in fact, performing similarly to emmetropic adults when viewing the cartoon movie at a 33-cm viewing distance (Figs. 6, 7, 8, and 10). A number of previous studies have considered accommodation alone. They have found children with low amounts of uncorrected hyperopia to have typical accommodative lags, with the range of lags only tending to increase at hyperopia of more than approximately 4 D.^{26–30,33,59} Consistent with this, only four uncorrected participants in the current study had a lag of greater than 2.5 D when viewing a target at 33 cm (Fig. 6). Previous studies have suggested that it is, in fact, the children with the larger lags who are at most risk for strabismus and amblyopia,^26,28,29,33 and when considered with the insights provided by this study, these results suggest that the large lag is a consequence of strained binocular function rather than a beneficial primary protective strategy. The strategy proposed in Figure 1A, of protective underaccommodation, is therefore not supported. Behaviors of patients with larger amounts of hyperopia are less well understood, and the observation that many of them develop reduced acuity in both eyes with no strabismus suggests that they are experiencing significant periods of inaccurate accommodation. 

How could the uncorrected hyperopes of the range included here accommodate and align their eyes in binocular conditions almost as accurately as an emmetropic adult? One hypothesis suggests they might overconverge into esophoria in monocular viewing, based on the neural coupling between their accommodation and vergence responses, and use robust fusional divergence to bring the eyes to binocular alignment. The data in Figures 8 and 10 provide no evidence that the nonstrabismic uncorrected hyperopic children are more esophoric than the emmetropes or those with the same refractive errors wearing optical correction, at either 80-cm or 33-cm viewing distances. There is, therefore, little support for that hypothesis in the group of participants studied here (Figs. 1B, 1D). In addition, extended occlusion for 30 seconds (Fig. 9) tended to result in an increase in these phorias rather than a systematic shift to esophoric posture with relaxation of any adaptation on that time scale (Fig. 1C),^43,60 suggesting that vergence adaptation on this time scale had only acted to bring the eyes into better alignment from a larger phoria position rather than consistently compensating for excessive convergence. 

The combination of small accommodative lags and exophorias suggests that most uncorrected hyperopes can generate additional accommodation without generating excessive coupled vergence responses when disparity cues for fusional vergence are removed. The data in Figure 14B confirm that the vergence response was relatively constant across participants compared with the range of accommodation responses in the CU group, when targets changed viewing distances with proximal cues (Fig. 1E). This comparison of vergence responses with the actual accommodation responses differs from the typical clinical approach of comparing the vergence response with the accommodative stimulus demand and reveals that the approximately constant vergence response leads to an increased response AC/A ratio for smaller actual accommodative responses on the left side of the graph (51% having response AC/A ratios of more than 5 pd/D). The relationship in Figure 14, in the presence of all cues except disparity, suggests that some of the uncorrected children on the right side of Figure 14B did indeed generate more accommodation relative to their vergence response when compared with emmetropic adults, which is logically protective against overconvergence and esotropia. In the language of the Maddox terminology, this may have been achieved either through a lower accommodative vergence to accommodation coupling gain or reduction of proximal vergence responses in the viewing conditions tested here. Measuring the gradient response AC/A ratio, without proximal cues, would have been a useful addition to this analysis given this interesting result that accommodative and proximal vergence appear to be combined effectively by these young children for near viewing. Of note, the participants in this study did not exhibit aniso-accommodation of greater than 1 D for our recording in the operating range of the instrument and so they do not appear able to use that as a strategy when viewing near targets. 

A number of groups have developed control theory models of the combination of accommodation and vergence motor responses.^35,36 In thinking about the combination of response components assessed here, the data confirm that the hyperopic patients in the clinic to be most concerned about are those with a large accommodative lag, esophoria, and/or reduced visual function at near^{26–32,37,61} and that the lag and/or esophoria are not protective strategies typically adopted by these children for the movie-watching task used here. Other components of the models appear to be compensating for the motor demands. In particular, it is interesting to note the similarity in accommodative lag and heterophorias in Figures 6, 8, and 9 between the corrected and uncorrected participants with the same 2 to 4 D of hyperopia. Is this an indication of an underlying form of vergence adaptation and does this suggest that this amount of exophoria is optimal in some sense and the goal of adaptation for these young hyperopes? An important question will be how the function of these patients may deteriorate during longer-duration visual tasks such as extended periods of reading, which was not examined here. Of note, the uncorrected hyperopes examined here were relatively consistent with each other in their median response over 2 seconds (e.g., Fig. 8). If the individuals were varying in their accommodation and vergence performance over time in a meaningful way, we would have predicted more variance between participants in the analyses conducted here. Other limitations of the current study might include the specific viewing distance used and the type of stimulus presented, plus the absence of information about the motivation of the children during the data collection. 

Current clinical surveys^62–64 and consensus prescribing guidelines^65,66 for younger ages often suggest prescribing for nonstrabismic hyperopia at higher amounts than found in the current uncorrected participants. While this study did not include many uncorrected participants with high hyperopia, it does provide evidence in support of these guidelines for patients with accurate accommodation and typical exophorias. It confirms that those who are aligned before or after correction can exhibit typical function (when adapted to their spectacles if corrected). Interestingly, the similarity in the data from the children with refractive error between 2 and 4 D with and without correction also suggests that optical correction did not result in less esophoric posture or reduced accommodative lags for the tasks tested here. While some of these patients were prescribed glasses as result of anisometropia or amblyopia, the fact that their accommodation and phoria values largely overlap indicates the capacity to achieve equivalent performance despite a difference of 2 to 4 D in motor demand. Given this apparent ability to adapt behavior, the question of why children with hyperopia commonly develop refractive esotropia between 1 and 3 years of age becomes even more interesting. 

Considering visual experience over extended periods of time raises the question of emmetropization and how motor binocular function defines retinal image quality and the potential for experience-driven growth of the eye.^26,67–69 While most of the participants in this study were beyond the period of typical emmetropisation,^10,12,27,70 up to approximately 18 months of age, the consistent evidence of typical accommodative lags for lower amounts of hyperopia once again suggests that the integrated foveal defocus signal over extended time may be uninformative for emmetropization during typical infant development^68,71,72—if the retinal image is consistently well focused, the literal magnitude of the foveal blur signal over time would approximate emmetropia and be a poor signal for control of eye growth. 

In addressing the core question of how young hyperopes are remaining aligned, the current study would suggest that most are not resolving their apparent motor conflict by significantly reducing their accommodative accuracy to achieve motor alignment. Rather, the relative weighting of the components of their ocular motor responses appears to adjust to the point of routine exophoria and typically focused and aligned retinal images. The principal component analysis for the data in Figure 10 reiterates that the first component shows small changes in both accommodative lag and phoria per diopter of hyperopia. This analysis provides clinicians with a clearer understanding of the behaviors that indicate a patient is at risk for atypical development and leads to further mechanistic questions about the factors placing a young child at risk for refractive esotropia. 

Acknowledgments

The authors thank Stephanie Biehn for subject recruitment and help with data collection. 

Supported by National Institutes of Health (NIH; Bethesda, MD, USA) Grant EY014460 (TRC), P30 EY019008 (Indiana University), and A Fight for Sight PostDoctoral Fellowship (VS). 

Disclosure: S. Neupane, None; V. Sreenivasan, None; Y. Wu, None; C. Mestre, None; K. Connolly, None; D.W. Lyon, None; T.R. Candy, None