August 2000
Volume 41, Issue 9
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Clinical and Epidemiologic Research  |   August 2000
AC/A Ratio, Age, and Refractive Error in Children
Author Affiliations
  • Donald O. Mutti
    From the College of Optometry; the
  • Lisa A. Jones
    Biostatistics Program; the
  • Melvin L. Moeschberger
    Division of Epidemiology and Biometrics, College of Medicine and Public Health, and the
  • Karla Zadnik
    From the College of Optometry; the
    College of Medicine and Public Health, The Ohio State University, Columbus.
Investigative Ophthalmology & Visual Science August 2000, Vol.41, 2469-2478. doi:https://doi.org/
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      Donald O. Mutti, Lisa A. Jones, Melvin L. Moeschberger, Karla Zadnik; AC/A Ratio, Age, and Refractive Error in Children. Invest. Ophthalmol. Vis. Sci. 2000;41(9):2469-2478. doi: https://doi.org/.

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      © ARVO (1962-2015); The Authors (2016-present)

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Abstract

purpose. To examine how the response AC/A ratio (the amount of accommodative convergence per unit of accommodative response) varies as a function of refractive error and age, to determine whether it is a risk factor for the onset of myopia, and to examine the relation between ocular structural features and the AC/A ratio.

methods. Accommodation was stimulated by a letter target presented in a Badal system at 0.00, 2.25, and 4.37 D to 828 children aged 6 through 14 years in 1996. Of these, 726 had no myopia in 1996 and were available for examination the following year. Accommodative response and cycloplegic refractive error were measured by autorefraction and convergence by monitoring the relative movement of Purkinje images I and IV. Lens radii of curvature were measured by video phakometry, corneal radius of curvature by topography, and ocular axial dimensions by A-scan ultrasonography.

results. Adjusted for age, the response AC/A ratio was highest in myopes (6.39 Δ/D), intermediate in emmetropes (3.94 Δ/D), and lowest in hyperopes (3.40 Δ/D; P < 0.0001; two-way analysis of variance [ANOVA]). The stimulus AC/A ratio did not vary with refractive error. Adjusted for refractive error, the response AC/A ratio did not change as a function of age. In non-myopic children, having a response AC/A ratio of 5.84 Δ/D or more elevated the risk of development of myopia within 1 year by 22.5 times (95% CI = 7.12–71.1). In a subsample of children without myopia who had refractive errors less than +0.75 D, having a response AC/A ratio of 5.84 Δ/D or more elevated the risk of development of myopia within 1 year by 3.21 times (95% CI = 1.14–9.07). The AC/A ratio was associated with all measured ocular features except lens spherical volume. Only the negative correlations with refractive error and the shape of the crystalline lens (Gullstrand lens power) were significant in a multiple regression model (adjusted R 2 = 0.16).

conclusions. An elevated response AC/A ratio was associated with myopia and was an important risk factor for its rapid onset. The association between higher AC/A ratios and flatter crystalline lens shapes, as well as other reported features of accommodation in myopia, may be explained by“ pseudocycloplegia,” which the authors define as tension on the crystalline lens that increases the level of effort needed to accommodate. Accommodative deficits in myopia may be the functional consequences of the underlying anatomy of the enlarged eye.

Myopia is one of the more prevalent human visual disorders, affecting approximately 25% of American adults, 1 with associated costs of correction and management of nearly $5 billion per year. 2 One of the major theories for the cause of myopia has been termed use–abuse. 3 This theory states that the use of the eyes during prolonged close work promotes excessive ocular growth and leads to myopia. Because the cornerstone of this theory is near visual activity, there is great interest in understanding the role accommodation and convergence may play in the risk of development of myopia. 
Recent insights into the accommodative system and refractive error have come from data showing that children with myopia have a deficient accommodative response compared with emmetropes—namely, a lower amplitude and an accommodative response function with a lower slope. 4 5 Children with progressing myopia show a deterioration in accommodative response compared with myopes whose refractive error is stable. 5 Myopes’ accommodative lag has been likened to the defocus induced by spectacle lenses in experimental myopia and has therefore become a putative risk factor for the onset and progression of myopia. 6 7 8 To date, however, lag has not been shown to be a valuable predictive factor. Children do not have a poorer accommodative response function or greater accommodative lag before the onset of myopia than do those who remain emmetropic. 5 9  
Open-loop, or tonic, accommodation is associated with refractive error, with adults who have late-onset myopia and children with myopia typically having the lowest levels, emmetropes and adults with early-onset myopia having intermediate levels, and hyperopes the highest levels of tonic accommodation. 10 11 12 13 14 An elevated level of tonic accommodation is associated with the onset of myopia in adults, 11 but larger longitudinal evaluations do not support this finding. Studies have found that, despite an association with prevalent refractive errors, the level of tonic accommodation in non-myopic adults 15 and children 14 is not a risk factor for the onset of myopia. 
The amount of accommodative convergence (AC) per unit of accommodative (A) response, the AC/A ratio, is an important parameter of the convergence system. It increases with age with the approach of presbyopia, but few subjects less than 20 years of age have been studied. 16 17 18 A convergent shift in near phoria with age has been reported in childhood. 19 The source of this change is unclear, but it may be explained by an increase in the AC/A ratio with age or an improvement in the accuracy of accommodation in older children. 
The few studies investigating refractive error and the AC/A ratio agree that myopes have higher AC/A ratios than other refractive groups. 20 21 Among adults, it is uncertain whether different forms of myopia have different AC/A ratios. In one study, those with early-onset myopia had higher AC/A ratios than did emmetropes and those with late onset of myopia, 22 whereas in another those with late-onset myopia had higher AC/A ratios than emmetropes. 11 In addition to being higher in late-onset myopia than in emmetropia, the AC/A ratio is elevated in emmetropes in whom myopia develops later, suggesting that an increased AC/A ratio may also predict the onset of myopia in adults. 11 An increase in the AC/A ratio may be inferred from a convergent shift in phoria toward more esophoria or less exophoria, but evidence regarding its relation with the onset of myopia is mixed. Retrospective data from children with myopia show that the near phoria is more convergent approximately 1 year before the last examination when the child was emmetropic and becomes more convergent for approximately 1 year after the onset of myopia. 23 Prospective data from the same report do not support this finding. A convergent shift in the near phoria occurs after, but not before, the onset of myopia. 23 Additional uncertainty about the value of the AC/A ratio as a risk factor for myopia in children arises because both esophoria and exophoria at near, and presumably therefore a wide spectrum of AC/A ratios, are found in emmetropes who later become myopes. 6 23  
Because children may accommodate inaccurately, 4 it is preferable to calculate the AC/A ratio on the basis of the measured accommodative response rather than the accommodative stimulus and assumed response. To our knowledge, the response AC/A ratio has not been evaluated as a risk factor for the onset of myopia in children. The purpose of the present study was to assess the response AC/A ratio in a large sample of children as a function of refractive error and age, to determine whether it is a risk factor for the onset of myopia and to examine whether there are structural correlates to the AC/A ratio among the ocular components. 
Methods
The Orinda Longitudinal Study of Myopia (OLSM) is a community-based cohort study of risk factors for predicting the onset of juvenile myopia. There were 847 children (47.1% female) in grades one through eight examined in the OLSM in 1996, with sufficient data (i.e., AC/A ratio and age) available for 828. Parents gave consent for their children’s participation after all study procedures were explained in accordance with the Declaration of Helsinki. Spherical refractive errors ranged from −9.18 to +5.48 D with a leptokurtic distribution skewed toward myopia typical for children of this age. 24 Age at last birthday ranged from 6 to 15 years. Children tested in 1996 enrolled in the study as cohorts of first graders in each year from 1989 through 1996 and were tested annually in the fall for from 1 to 7 years of follow-up. The number of subjects tested by age at last birthday is shown in Table 1
The accommodative stimulus was a 4 × 4 grid of letters, with each letter and space between letters subtending 38.75 minutes of arc at the eye (20/155 equivalent). The print was chosen to be similar in size to that found in children’s books. Although print size tends to decrease in books for older children, we thought it was important to choose an adequate size for younger children and to maintain a consistent stimulus across the years of testing. The target was illuminated by ambient room lighting, which was variable due to changing weather and time of day, but was supplemented by accessory lights to produce a target luminance of between 30 and 50 candelas (cd)/m2. Accommodative stimulus levels of 0.00, 2.25, and 4.37 D relative to optical infinity were produced by moving the letter target on a track behind a +6.50-D Badal lens positioned in front of the right eye. 
Accommodative response was measured at each of the three stimulus levels using an autorefractor (Canon R-1; Canon Europa, Amstelveen, The Netherlands). At least five autorefractor readings were taken with the right eye in primary gaze. In grades one and two, a minimum of three readings was acceptable because of younger children’s shorter attention spans. Fixation was monitored by viewing eye movements on the autorefractor’s television screen. Any unsteady fixation resulted in invalid measurements that could be identified by cylinders that differed from the mode value for cylinder by more than 1.00 D. Rejecting these readings also eliminated most erroneous sphere values, but remaining readings with spurious spheres, those differing by at least ±5.00 D from the mode value for sphere readings, were also rejected. If more than five acceptable readings were available, the number was reduced by eliminating readings from the beginning alternating with the end of the set of measurements until only five remained. 
The amount of convergence of the left eye was monitored on a second channel. A focused infrared LED light source (SFH 484-2; Siemens, Munich, Germany) was mounted on top of a CCD camera (XC-77RR; SONY, Tokyo, Japan) and aimed at the left eye of the subject by way of a infrared-reflecting “hot” mirror (Fig. 1) . The CCD camera was fitted with a 50-mm focal length F1.4 C-mount lens on a 20-mm extension tube with the camera’s stock infrared filter removed. The infrared LED produces Purkinje images I and IV. Eye rotation may be monitored by measuring the relative lateral movement of these two images, similar to eye trackers and recent clinical applications of eye tracking. 25 26 The two data channels, accommodative response from the right eye and convergence eye movement from the left eye, were recorded simultaneously by a video multiplexer (Duet; Dedicated Micros, Reston, VA). This unit displays a divided image of both channels on a monitor, but maintains resolution by recording full frames of video alternating at 25 Hz on a standard VHS recorder for later analysis. 
The protocol for measurement was as follows. A subject was placed behind the autorefractor, and the right eye was occluded. Calibration was achieved by making a 10° eye movement with the left eye, alternating fixation two times between a green dot and two red circles printed on a card and placed at the 1.00-D stimulus level on the Badal track in front of the left eye. After calibration, the right eye was uncovered and the subject given a pair of modified glasses frames. The left side of the frame held a gel filter (Wratten 89B; Kodak, Rochester, NY). This filter passes only wavelengths longer than 680 nm, disrupting fusion by appearing opaque to the observer, but remaining transparent to the CCD camera. The right side of the frame remained empty if the subject wore no spectacle prescription or held a trial clip with the subject’s prescription in trial lenses if the subject had ametropia and had worn spectacle correction to the testing session. If the subject wore contact lenses, the right contact lens was left in place, and the left lens was removed to prevent extra reflections during calibration and testing. The Badal track was then moved in front of the right eye, and the 10° calibration target was exchanged for the letter target. Accommodative response was then measured as described at each stimulus level while eye position was recorded on the second channel. 
Ametropia was corrected only if the subject wore a spectacle or contact lens correction to the testing session. Ideally, it would have been desirable to have both corrected and uncorrected data collected from the children with ametropia. Subjects were tested during school hours, however, which placed limitations on the amount of time allotted for completion of the protocol. We decided that the more important information was measurement of the child in the habitual accommodative state, determined by the child’s own compliance with wearing a correction. Therefore, children were tested without correction if they arrived for testing without glasses or contact lenses, regardless of ametropia. The right eyes of children wearing glasses were refracted using the autorefractor with the left eye occluded. Subjective refraction techniques were simulated by moving the letter target along the Badal track away from the subject’s right eye to relax accommodation as though plus lenses had been added. Readings were recorded when the target was clear and any movement to further relax accommodation resulted in the subject’s reporting blur. The sphere and, if necessary, the cylindrical trial lens correction were placed in a trial clip over the right eye of the glasses frames. The trial lens correction was modified as needed to keep the overrefraction at the 0.00-D stimulus level within ±0.50 D for sphere and −1.00 D or less for cylinder. 
Eye position data were extracted from the multiplexer videotapes. Measurements were of the lateral separation of Purkinje images I and IV using image analysis software (Image Analyst ver. 8.1; Acuity Imaging, Nashua, NH). This computer program finds the center of the brightness distribution of the individual Purkinje images and measures the distance separating their centers. The two 10° eye movements used for calibration agreed to within 7 pixels (approximately 2°) for all subjects. The tape was advanced until an acceptable accommodative reading appeared. The simultaneous recording of accommodative response and eye position maintained correspondence between the measured level of each variable. A measurement of eye position was then made on the next frame of video on the tape. Averages for accommodative response (AR) and accommodative convergence (AC) were then calculated for each stimulus level. The response AC/A ratio (in prism diopters per diopter) was calculated at the 4.37-D stimulus level from the following formula  
\[\frac{100\ \mathrm{tan}\ \left\{\frac{0.1745(\mathrm{AC4D-AC0D})}{Calibration}\right\}}{(\mathrm{AR4D-AR0D})}\]
where 0.1745 is radians/10°, calibration is pixels/10°, AC4D and AC0D are the average eye positions in pixels at the 4.37-D and 0.0-D stimulus levels, respectively, and AR4D and AR0D are the average accommodative responses in diopters at the 4.37-D and 0.0-D stimulus levels, respectively. All raw autorefractor accommodative responses (Raw AR) among spectacle wearers were adjusted for lens effectivity into corrected AR values according to the following formula, assuming a vertex distance of 15 mm: Image not available  
The inverse of the raw autorefractor reading plus the vertex distance gives the distance from the spectacle lens of a point conjugate with the retina of the subject. The vergence of that point is then found at the plane of the spectacle lens and then at the plane of the cornea after refraction through that lens. The corrected accommodative response is the difference between the vergence of that point at the corneal plane and the cycloplegic refractive error of the subject. 
Phoria was measured by cover test to calculate a stimulus AC/A ratio. Distance phoria was measured while the child fixated a letter two lines above threshold on the distance visual acuity chart. If the child wore spectacles or contact lenses, those remained in place during the cover test. Vision in children who did not wear a correction remained uncorrected if any meridian on retinoscopy had ±1.00 D or less ametropia. If ametropia in any meridian exceeded ±1.00 D or the difference between the two meridians in either eye was at least 1.50 D, the lens cross from retinoscopy was converted to a spectacle prescription, placed in a trial frame, and worn during the cover test. Near phoria was measured at 40 cm while the child wore the same correction and fixated a 20/100 equivalent single letter E. Movement during either the distance or near cover test was neutralized to the nearest prism diopter with a prism bar. 
Ocular axial dimensions were measured by A-scan ultrasonography (model 820, Humphrey Systems, Dublin, CA), consisting of five readings using a hand-held probe set on semiautomatic mode. Lens radii of curvature were measured using a video-based phakometer. 27 Lens power was calculated by two methods. In one method the anterior and posterior radii of curvature obtained from phakometry, Gullstrand–Emsley schematic indices of refraction, and the thickness of the crystalline lens (LT) from ultrasonography are used to calculate the Gullstrand Lens power (GLP). This variable may be considered a composite of the two-lens radii of curvature, thereby representing lens shape. In the second method, an iterative procedure was used to find the posterior lens radius of curvature (PLC) and the equivalent refractive index (IND) and from that the equivalent power of the crystalline lens (CLP), which produce agreement between the measured refractive error and that calculated from ocular component values. Lens spherical volume (LSV) was calculated from the lens thickness and the spherical lens radii obtained from phakometry. These variables are described in detail elsewhere. 24 Corneal power (K) represents the average component from the Fourier analysis of four TMS-1 corneal topography images. 28 Refractive error (REF) was the average of 10 readings on the autorefractor obtained 25 minutes after instilling 2 drops of 1% tropicamide. 
Cross-sectional analyses were conducted on the participants for 1996 to investigate associations between the AC/A ratio, age, and ocular components. Descriptive statistics, Pearson’s correlation coefficients, and general linear models were used. Least-squares means were presented for models in which adjustments for confounding variables were made. To determine which combination of ocular components were associated with the AC/A ratio, a stepwise multiple regression model was used. 
Subjects identified as having no myopia in 1996 were observed again in 1997 to evaluate the relation between the AC/A ratio in 1996 and conversion to myopia. Myopia was defined as −0.75 D or more myopia in each principal meridian, hyperopia as +1.00 D or more hyperopia in each meridian, and emmetropia as having neither myopia nor hyperopia. To identify a potential predictive cutoff point for the AC/A ratio, 2 × 2 tables were constructed and relative risks and 95% confidence intervals (CIs) were calculated. A logistic regression was completed, to evaluate the risk of onset of myopia within 1 year based on the AC/A ratio, while controlling for refractive error using the cycloplegic sphere measurement. A receiver operating characteristic (ROC) curve was also fitted, graphically representing the trade-off between sensitivity and specificity as a function of predictive cutoff point. All analyses were completed using SAS software (SAS, Cary, NC). 
Results
The 10° calibration measurement was significantly correlated with several ocular parameters that may influence the position of Purkinje images I and IV—namely, corneal power, crystalline lens thickness, and posterior radius of the crystalline lens (Table 2) . Anterior chamber depth did not appear to affect the position of the Purkinje images. Taken together in the following multiple regression model, each term retained significance (P < 0.0001), with an adjusted model R 2 = 0.47:  
\[Calibration{=}\mathrm{-}1.09(\mathrm{K})-5.16(\mathrm{LT}){+}2.12(\mathrm{PLC})\]
Each of these parameters shows both intersubject variation and age-related changes. 24 29 30 Applying an individual calibration factor should reduce variability from these sources. 
Only subjects with an accommodative response of more than 1.00 D between the 0.00-D and either the 2.25-D or the 4.37-D stimulus level were included in these analyses. This avoided the problem of inflating the AC/A ratio by including very small denominators. A substantial proportion of children did not accommodate by more than 1.00 D at the 2.25-D stimulus level (311/847, 36.7%), as might be expected from the amounts of accommodative lag reported for children tested with a similar protocol. 21 This 1.00-D criterion excluded only 13 subjects at the 4.37-D stimulus level. Screening for poor accommodative responses did not appear to exclude a higher proportion of myopes than other refractive groups, despite evidence that myopes have greater amounts of accommodative lag than emmetropes in previous studies 4 5 and in our sample (1.44 D and 1.03 D, respectively, at the 4.37-D stimulus level; least-squares means comparison; P = 0.0044). Of the 13 excluded subjects, 2 were myopes, 7 hyperopes, and 4 emmetropes. These few excluded subjects may have been slightly older; nine were in the upper grades 5 to 7, whereas one each was in grades 1 to 4. 
The response AC/A ratio adjusted for age differed as a function of refractive error category (two-way ANOVA; P < 0.0001). Myopes had the highest AC/A ratios (6.39 Δ/D), emmetropes the intermediate ratios (3.94 Δ/D), and hyperopes the lowest ratios (3.40Δ /D; Fig. 2 ). AC/A ratios at the 2.25-D stimulus level were also higher in myopes (5.61 Δ/D) than in emmetropes (4.12 Δ/D) and hyperopes (3.56 Δ/D; two-way ANOVA; P < 0.0001). As in a previous study 31 the AC/A ratio appeared to be linear over the stimulus interval with an average value of 3.98 ± 2.10 Δ/D at the 2.25-D stimulus level and 3.90 ± 1.78 Δ/D at the 4.37-D level. There was a slightly higher average AC/A ratio at the 2.25-D level for the subjects with valid measurements at both levels, 0.34 ± 1.44 Δ/D, with statistical significance at this large sample size, (paired t-test, P = 0.0001). As a function of refractive group for the 533 children with valid measurements at both stimulus levels, the AC/A ratio was slightly higher at 2.25 D for hyperopes (0.23 ± 1.42 Δ/D; P = 0.038) and emmetropes (0.42 ± 1.43 Δ/D; P < 0.0001), but not for myopes (−0.04 ± 1.96Δ /D; P = 0.92; all paired t-tests). 
Response AC/A ratios unadjusted for refractive error increased significantly with age (one-way ANOVA; P = 0.0002; Table 3 ). Because the prevalence of myopia also increases with age, we looked at whether an increase in the AC/A ratio with age might be due to a change in refractive error. This appeared to be the case. Age was no longer a significant factor after adjustment for refractive error (least-squares means comparison; P = 0.098). Unless otherwise indicated, subsequent analyses were conducted on the data from the 4.37-D stimulus level. 
The association between refractive error and AC/A ratio can be examined in more detail in the scatterplot shown in Figure 3 . The pattern suggested by the age-adjusted least-squares means shown in Figure 2 is apparent in Figure 3 —that is, myopes have the highest AC/A ratios and hyperopes the lowest. Additionally, there was a group of subjects with elevated AC/A ratios located between refractive errors of− 2.00 D to +1.00 D, suggesting that these children were either at higher risk of development of myopia or had had recent onset of myopia. We therefore tested whether an elevated AC/A ratio was associated with an increased risk of the onset of myopia. Of the 828 children examined in 1996, 726 did not have myopia and were available for re-examination in 1997. Of the 102 children not seen in 1997, 67 were in eighth grade in 1996, 23 already had myopia, and 12 were lost to follow-up. An ROC curve displaying the sensitivity (probability AC/A ≥ x Image not available myopia onset) and 1 − specificity (1 − probability AC/A < x Image not available no myopia onset) of the AC/A ratio as a test for the onset of myopia is shown in Figure 4 . The point of maximum discrimination was an AC/A ratio of 5.84 Δ/D. 
Using this value as a cutoff point, the relative risk for the onset of myopia within 1 year associated with having an AC/A ratio of 5.84 Δ/D or more was significantly elevated at 22.5 (95% CI = 7.12–71.1; Table 4 ). As Gwiazda et al. 9 point out, this increased risk may be severely confounded by having an emmetropic refractive error, another risk factor for myopia. Table 5 presents the data of Table 4 but excludes children with refractive errors of +0.75 D or more hyperopia. We have previously identified this level of hyperopia as a useful cutoff point when using refractive error as a predictor of future myopia. 32 The relative risk for the onset of myopia within 1 year among children without myopia with refractive errors of less than +0.75 D and an AC/A ratio of 5.84 Δ/D or more was 3.21 (95% CI = 1.14–9.07). Although refractive error had a confounding effect, an elevated AC/A ratio remained a significant risk factor for the onset of myopia even after stratifying by refractive error. 
This estimate of the relative risk may be elevated when calculated from the same data used to determine the cutoff point. Ideally, it should be evaluated in the future using an independent sample. We also modeled the risk of the onset of myopia within 1 year without using cutoff points, with the AC/A ratio and refractive error as continuous variables. As shown in Table 6 , a Δ/D unit elevation in the AC/A ratio was associated with a 50% to 60% increase in risk of the onset of myopia within 1 year, whether the entire sample of 726 children was used or restricted to children with refractive errors less hyperopic than +0.75 D. A diopter difference toward greater hyperopia was highly protective against the onset of myopia in both samples. 
The preceding analysis indicates that the response AC/A ratio was an important risk factor for the onset of myopia. Yet the more common clinical measure of the AC/A ratio is the stimulus AC/A ratio, obtained from the patient’s distance and near cover test results and interpupillary distance. This measurement does not require an assessment of accommodative response at a given stimulus level. The stimulus AC/A ratio was not associated with refractive error group (Fig. 5 ; least-squares means comparison; P < 0.60), indicating that the difference between the distance and near phoria was not associated with refractive error group. Consistent with our previous result, 19 increased esophoria at near was not significantly more common among myopes, possibly because there were higher amounts of accommodative lag in myopes than in other refractive groups in previous studies 4 5 and in our current sample. 
To determine whether there were structural correlates to the AC/A ratio, we performed univariate and multivariate analyses of AC/A ratio values and ocular components measured in the OLSM test battery. As seen in Table 7 , every ocular component measured, except for the spherical volume of the crystalline lens, was associated with the AC/A ratio at P < 0.05. Because there are numerous correlations between the structures of the eye, multivariate regression was used to identify ocular components with independent effects on the AC/A ratio.  
\[\mathrm{AC/A{=}}-0.52(\mathrm{REF})-0.21(\mathrm{GLP})\]
with adjusted R 2 = 0.16. Higher AC/A ratios were associated with myopic refractive errors as well as flatter crystalline lenses. Refractive error was the most significant term (P < 0.0001) accounting for 15.1% of the variance. Gullstrand lens power was the only remaining significant term (P < 0.0001), accounting for 2.4% of the variance. One reason for the independent influence of these two factors on the AC/A ratio is that they are not associated. Age-adjusted Gullstrand lens powers were not different for myopes, emmetropes, and hyperopes (20.58, 20.35, and 20.46 D, respectively; least-squares means comparison; P = 0.41). This result is somewhat unexpected, because elongated vitreous chambers were associated with lower Gullstrand lens powers—that is, flatter lens shapes (Pearson r = −0.53; P < 0.0001) and with less hyperopic, or more myopic, refractive errors (Pearson r = −0.53; P < 0.0001). Lens shape appears to contribute to the AC/A ratio outside its association with the size of the eye. 
Discussion
The response AC/A ratio was clearly associated with a child’s current refractive error, consistent with previous results. 11 20 21 22 Myopes had the highest AC/A ratios, emmetropes had substantially lower ratios, and hyperopes had the lowest average ratio. Additionally, having an AC/A ratio of 5.84 Δ/D or more or a unit increase in the AC/A ratio elevated the risk of development of myopia within 1 year. Behavior of the AC/A ratio after the onset of myopia is less clear. The pattern in Figure 3 suggests that an increase in AC/A ratio may affect those who are crossing or who have just crossed the border from emmetropia into myopia and then decrease to levels still higher on average than for emmetropia. This would be consistent with the assumption by Gwiazda et al. 21 that a reduction in the AC/A ratio after stabilization of myopia explains the negative correlation with age seen in myopes in their study. We did not see a difference in the average AC/A ratio as a function of degree of myopia. The average ratio in children with myopia between −0.75 D and− 2.50 D was 6.85 ± 2.64 Δ/D, similar to that in children with more myopia than −2.50 D, 5.89 ± 1.78 Δ/D (unpaired t-test; P < 0.21). Additional longitudinal data are needed to determine the relations between myopia progression, stabilization, and the AC/A ratio. 
After adjustment for refractive error, the average AC/A ratio did not change significantly as a function of age. Therefore, the increase in the prevalence of esophoria at near 19 was not explained by an intrinsic, age-related increase in the AC/A ratio. AC/A ratios unadjusted for refractive error tended to increase with age, suggesting that the prevalence of esophoria could increase with age along with the prevalence of myopia. Evidence for an association between myopia and esophoria is mixed, however. There is no association when phoria is evaluated while children wear their current, habitual corrections. 19 Yet many studies report a high prevalence of esophoria (22%–54%) 33 34 35 36 among children with myopia wearing a new, rather than a habitual correction, compared with the 14.8% reported by Walline et al. 19 This difference may be explained by adaptation. When children with myopia receive a new correction, their near phoria becomes more convergent, but only temporarily. 37 Testing children while they are either undercorrected or unadapted makes determining the true association between phoria and refractive error problematic. An alternate explanation for an increase in esophoria with age in children is an improvement in the accuracy of the accommodative response with age. This possibility will be examined in future longitudinal analyses of accommodative lag. 
Schor and Horner 38 have provided evidence that an elevated AC/A ratio represents an imbalance in the relative strengths of accommodative and vergence adaptation. If accommodative adaptation is limited, phasic accommodative inputs to vergence through their cross-link remain high and increase the AC/A ratio. This model does not explain the AC/A ratios of myopes, however, because adults with late-onset myopia 39 40 41 42 43 and children with myopia 13 show more prolonged accommodative adaptation after near work than do emmetropes, not less. It could be argued that the relative strength of accommodative and vergence adaptation is more important than their absolute levels. This model could apply if myopes had more robust vergence adaptation than accommodative adaptation. However, evidence suggests that myopes’ vergence adaptation is either deficient or no different from that of other refractive groups. 40 44 Therefore, it appears unlikely that poor accommodative adaptation or excess vergence adaptation are the cause of elevated AC/A ratios in myopes. Jiang hypothesizes that myopes are hampered by a sensory deficit—that is, they have a higher threshold for blur. 45 A poorer sensitivity to blur has recently been reported in adult myopes than in adult emmetropes. 46 This would explain the greater amount of accommodative lag in myopia 4 47 but does not explain myopes’ higher AC/A ratio. 
Accommodation in myopes has certain characteristics besides an elevated AC/A ratio. Tonic accommodation values are closer to the far point, 10 13 14 and accommodative lag is greater, both in previous work 4 47 and in the current sample. All three of these characteristics are produced by cycloplegia: low tonic accommodation 48 ; obviously, a greater accommodative lag; and a high AC/A ratio. 49 Some have speculated whether a common factor could tie a poor accommodative response and myopia together. 5 We propose that this common factor is a state of pseudocycloplegia present in the eye at risk for myopia and recently myopic, and further that the deficit is in the accommodative“ plant,” the crystalline lens and choroid, rather than in the neurologic controllers of accommodation and convergence. The hypothesized primary deficit is tension on the crystalline lens in the large, myopic eye providing resistance to accommodation, increasing the level of effort needed to accommodate. In the cycloplegia analogy, this tension would result in low levels of tonic accommodation, high levels of lag, and a high AC/A ratio. 
Two lines of evidence support this view. The first is based on anatomy. Our ocular component results indicated that the AC/A ratio was elevated when the crystalline lens was flat, which was the lens geometry found in larger eyes in this study and in previous work. 50 51 The crystalline lens may attain this flat shape by being stretched by the equatorial growth of the eye. 24 30 This stretching process may help to maintain emmetropia by decreasing lens power during ocular growth, both equatorially and axially. 51 52 53 54 55 56 Longitudinal data show that patterns of lens development potentially driven by equatorial stretch in early childhood, such as lens thinning and decreases in equivalent power and refractive index, all cease in later childhood—also the time when myopia becomes more prevalent, perhaps because lens stretch has been interrupted. 24 Failure of continued equatorial growth has both potential optical and structural consequences that may promote myopia. If lens power changes compensating for axial growth are driven by equatorial stretch, a failure to stretch means that the equivalent power of the lens will not decrease despite continued axial growth. 24 Additionally, absence of equatorial stretch would distort the shape of the eye into the prolate shape found in the eyes of children with myopia, 57 potentially promoting axial elongation. 24 The lens was not substantially flatter in myopic eyes despite the eyes’ large size. This is consistent with previous work 51 and indicates that the crystalline lens may not follow the size of the eye in a simple linear manner during the development of myopia. 
Failure of continued equatorial expansion may have a functional consequence for accommodation as well. The crystalline lens is connected to the uvea by the epichoroidal attachments of the ciliary muscle. The choroid is therefore a potential transducer of the expansive forces of ocular growth to the crystalline lens. Van Alphen and Graebel 52 have demonstrated that the crystalline lens thins and flattens in response to stretching forces placed on the eye in vitro. If excessive ocular expansion and resistance of the crystalline lens to that expansion increase tension within the choroid, choroidal resistance can impede accommodation, consistent with our proposed model of pseudocycloplegia. 58 An increase in the AC/A ratio in presbyopia has been attributed in part to the greater effort needed to accommodate as the lens becomes sclerotic. 16 17 18 An increase in the AC/A ratio in childhood may indicate a greater effort needed to accommodate in the stretched lens of the myope. Although presbyopia does not regress, the lens continues to grow throughout life and stops thinning after the age of 10 years. 24 Growth of the axial length of the eye, however, slows in later childhood. 24 If pseudocycloplegia represents an imbalance between eye size and lens dimensions, the continuation of lens growth during the slowing of eye growth could alter these dynamics in a direction favorable to accurate accommodation. Again, longitudinal data are needed to determine the eventual state of the AC/A ratio in myopia and the role played by the ocular components. 
It might be argued that this greater effort is due to geometry rather than tension. Erickson 59 has calculated the impact of variation in ocular anatomy on accommodative efficiency. Deeper anterior chambers reduce efficiency, whereas variations in lens radii of curvature have little effect. We found that higher response AC/A ratios were associated with deeper anterior chambers, but this association lost statistical significance in a multivariate model with GLP, the shape of the crystalline lens. It therefore seems unlikely that the effect of GLP on the AC/A can be explained by geometric optics. 
The second line of evidence for a mechanical rather than a neurologically based explanation for accommodation and convergence behavior in children with myopia is based on the rapid onset of myopia in the presence of an elevated AC/A ratio. Our data suggest that the onset of myopia follows rather quickly, within 1 year, if the AC/A ratio is high. It therefore seems less likely that the increased AC/A ratio is a long-standing feature of a child’s accommodation-vergence system. This assumption should be tested with longitudinal data. Recent evidence suggests that low levels of tonic accommodation and high accommodative lag behave in this manner. They are associated with myopia and the onset of myopia but do not precede it by a number of years. 5 9 14 15 It seems more likely that transient events such as these are based on structural development, rather than on neurologic change. 
Despite the increase in the risk of development of myopia associated with an elevated AC/A ratio, its value as a predictive factor may be limited because the conversion happens so quickly. However, it may be a more useful and sensitive predictor than tonic accommodation or accommodative lag. Accommodative lag is constrained by the depth of field, making for only small differences in accommodative lag between refractive groups while viewing real target stimuli (e.g., 0.22 D at a 3.00-D accommodative demand). 4 Tonic accommodation is an open-loop measure that is lower in myopes. This creates a possible floor effect that could hide differences. Tonic accommodation may only decrease as far as zero. The AC/A ratio is less constrained on both counts. It is the open-loop measure that becomes higher, rather than lower with myopia. 
Pseudocycloplegia is a simple, parsimonious explanation of accommodative and vergence behavior in myopia. Considering the current state of knowledge regarding accommodation and hyperopic defocus in myopia, one possible view is that the incipient myope has an accommodative system that deteriorates rapidly. The premyopic child would have a high level of sensitivity to the ocular growth-promoting effects of hyperopic defocus. In contrast to this position, the findings of this report indicate that changes in accommodation and vergence occur near the onset of myopia because they are symptoms, or functional consequences, of underlying anatomic changes driving an eye toward myopia. It is hoped that ongoing clinical trials of bifocal spectacle therapy in children with myopia will shed light on these two views, providing information on the impact on myopia of relieving deficient accommodation and overactive vergence. 60 61  
 
Table 1.
 
Number of Children Tested per Age Group in 1996
Table 1.
 
Number of Children Tested per Age Group in 1996
Age (y)
6 7 8 9 10 11 12 13 ≥14
n (%) 46 (5.4) 133 (15.7) 109 (12.9) 113 (13.3) 113 (13.3) 127 (15.0) 88 (10.4) 66 (7.8) 52 (6.1)
Figure 1.
 
View from above the apparatus. Eye movements were recorded by an accessory CCD camera (A). Purkinje images were generated by an infrared light source (B) directed at the semisilvered mirror (C). Calibration was achieved by the subject’s alternately fixating the dot and circle target in front of the left eye. The track with the Badal lens (D) was then moved in front of the right eye and the letter target put in place. Subjects wore frames containing a gel filter (E) over the left eye and either an empty aperture or a trial lens prescription (F) over the right eye. Data were recorded by the autorefractor (G) and a VCR coupled with a video multiplexer using two channels, one for accommodative response (H) and one for Purkinje images I and IV (I).
Figure 1.
 
View from above the apparatus. Eye movements were recorded by an accessory CCD camera (A). Purkinje images were generated by an infrared light source (B) directed at the semisilvered mirror (C). Calibration was achieved by the subject’s alternately fixating the dot and circle target in front of the left eye. The track with the Badal lens (D) was then moved in front of the right eye and the letter target put in place. Subjects wore frames containing a gel filter (E) over the left eye and either an empty aperture or a trial lens prescription (F) over the right eye. Data were recorded by the autorefractor (G) and a VCR coupled with a video multiplexer using two channels, one for accommodative response (H) and one for Purkinje images I and IV (I).
Table 2.
 
Correlation of Calibration Measurement with Ocular Parameters
Table 2.
 
Correlation of Calibration Measurement with Ocular Parameters
Variable Pearson r P
Corneal power (D) −0.49 <0.0001
Anterior chamber depth (mm) −0.032 0.35
Lens thickness (mm) −0.40 <0.0001
Posterior lens radius (mm) 0.49 <0.0001
Figure 2.
 
Least-squares means for the response AC/A ratio, adjusted for age, as a function of refractive error category. Each group was significantly different from the other (two-way ANOVA; P < 0.0001). Myopia was defined as −0.75 D or more myopia in each principal meridian, hyperopia as +1.00 D or more hyperopia in each meridian, and emmetropia the absence of either myopia or hyperopia.
Figure 2.
 
Least-squares means for the response AC/A ratio, adjusted for age, as a function of refractive error category. Each group was significantly different from the other (two-way ANOVA; P < 0.0001). Myopia was defined as −0.75 D or more myopia in each principal meridian, hyperopia as +1.00 D or more hyperopia in each meridian, and emmetropia the absence of either myopia or hyperopia.
Table 3.
 
The Response AC/A Ratio Unadjusted for Refractive Error as a Function of Age Group
Table 3.
 
The Response AC/A Ratio Unadjusted for Refractive Error as a Function of Age Group
Age (y) Ratio (Δ/D)
6 3.61 ± 1.70
7 3.59 ± 1.74
8 3.52 ± 1.80
9 4.07 ± 1.68
10 4.07 ± 1.78
11 3.91 ± 1.66
12 4.07 ± 1.88
13 4.11 ± 1.60
≥14 4.46 ± 2.19
Figure 3.
 
Scatterplot of AC/A ratio as a function of refractive error.
Figure 3.
 
Scatterplot of AC/A ratio as a function of refractive error.
Figure 4.
 
ROC curve displaying the sensitivity (probability AC/A ≥ x Image not available myopia onset) and 1-specificity (1 − probability AC/A < x Image not available no myopia onset) of the AC/A ratio as a test for the onset of myopia. The arrow marks the point of maximum discrimination, an AC/A ratio of 5.84 Δ/D.
Figure 4.
 
ROC curve displaying the sensitivity (probability AC/A ≥ x Image not available myopia onset) and 1-specificity (1 − probability AC/A < x Image not available no myopia onset) of the AC/A ratio as a test for the onset of myopia. The arrow marks the point of maximum discrimination, an AC/A ratio of 5.84 Δ/D.
Table 4.
 
Elevation in Risk of Onset of Myopia with an AC/A Ratio of 5.84 Δ/D or More
Table 4.
 
Elevation in Risk of Onset of Myopia with an AC/A Ratio of 5.84 Δ/D or More
Onset of Myopia in 1997 No Myopia in 1997 Total
AC/A ratio ≥ 5.84 Δ/D in 1996 9 57 66
AC/A ratio < 5.84 Δ/D in 1996 4 656 660
Total 13 713 726
Relative risk = 22.5 (95% CI = 7.12–71.1)
Table 5.
 
Elevation in Risk of Onset of Myopia within 1 Year in the Absence of Myopia with a Refractive Error of Less Than +0.75 D and an AC/A Ratio of 5.84 Δ/D or More
Table 5.
 
Elevation in Risk of Onset of Myopia within 1 Year in the Absence of Myopia with a Refractive Error of Less Than +0.75 D and an AC/A Ratio of 5.84 Δ/D or More
Onset of Myopia in 1997 No Myopia in 1997 Total
AC/A ratio ≥ 5.84 Δ/D in 1996 9 12 21
AC/A ratio < 5.84 Δ/D in 1996 4 26 30
Total 13 38 51
Relative risk = 3.21 (95% CI = 1.14–9.07)
Table 6.
 
Relative Risk for the Onset of Myopia within 1 Year in Children with No Myopia in 1996 Re-Examined in 1997
Table 6.
 
Relative Risk for the Onset of Myopia within 1 Year in Children with No Myopia in 1996 Re-Examined in 1997
Variable Entire Sample (n = 710) Errors Less Than +0.75 D in 1996 (n = 51)
AC/A ratio (Δ/D) 1.57 (1.15–2.14) 1.52 (1.09–2.11)
Refractive error (D) 0.006 (0.0006–0.057) 0.016 (0.001–0.264)
Figure 5.
 
Least-squares means of the stimulus AC/A ratio after adjustment for age. There were no significant differences between refractive error groups.
Figure 5.
 
Least-squares means of the stimulus AC/A ratio after adjustment for age. There were no significant differences between refractive error groups.
Table 7.
 
Univariate Correlations between the Response AC/A Ratio and Ocular Component Values
Table 7.
 
Univariate Correlations between the Response AC/A Ratio and Ocular Component Values
Component Pearson r P
Spherical refractive error (D) −0.39 <0.0001
Anterior chamber depth (mm) 0.20 <0.0001
Lens thickness (mm) −0.10 0.0026
Vitreous chamber depth (mm) 0.26 <0.0001
Corneal power (D) 0.070 0.032
Lens equivalent index −0.080 0.030
Lens spherical volume (mm3) 0.055 0.12
Gullstrand lens power (D) −0.18 <0.0001
Equivalent lens power (D) −0.19 <0.0001
Anterior lens radius (mm) 0.17 <0.0001
Posterior lens radius (mm) 0.14 <0.0001
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Figure 1.
 
View from above the apparatus. Eye movements were recorded by an accessory CCD camera (A). Purkinje images were generated by an infrared light source (B) directed at the semisilvered mirror (C). Calibration was achieved by the subject’s alternately fixating the dot and circle target in front of the left eye. The track with the Badal lens (D) was then moved in front of the right eye and the letter target put in place. Subjects wore frames containing a gel filter (E) over the left eye and either an empty aperture or a trial lens prescription (F) over the right eye. Data were recorded by the autorefractor (G) and a VCR coupled with a video multiplexer using two channels, one for accommodative response (H) and one for Purkinje images I and IV (I).
Figure 1.
 
View from above the apparatus. Eye movements were recorded by an accessory CCD camera (A). Purkinje images were generated by an infrared light source (B) directed at the semisilvered mirror (C). Calibration was achieved by the subject’s alternately fixating the dot and circle target in front of the left eye. The track with the Badal lens (D) was then moved in front of the right eye and the letter target put in place. Subjects wore frames containing a gel filter (E) over the left eye and either an empty aperture or a trial lens prescription (F) over the right eye. Data were recorded by the autorefractor (G) and a VCR coupled with a video multiplexer using two channels, one for accommodative response (H) and one for Purkinje images I and IV (I).
Figure 2.
 
Least-squares means for the response AC/A ratio, adjusted for age, as a function of refractive error category. Each group was significantly different from the other (two-way ANOVA; P < 0.0001). Myopia was defined as −0.75 D or more myopia in each principal meridian, hyperopia as +1.00 D or more hyperopia in each meridian, and emmetropia the absence of either myopia or hyperopia.
Figure 2.
 
Least-squares means for the response AC/A ratio, adjusted for age, as a function of refractive error category. Each group was significantly different from the other (two-way ANOVA; P < 0.0001). Myopia was defined as −0.75 D or more myopia in each principal meridian, hyperopia as +1.00 D or more hyperopia in each meridian, and emmetropia the absence of either myopia or hyperopia.
Figure 3.
 
Scatterplot of AC/A ratio as a function of refractive error.
Figure 3.
 
Scatterplot of AC/A ratio as a function of refractive error.
Figure 4.
 
ROC curve displaying the sensitivity (probability AC/A ≥ x Image not available myopia onset) and 1-specificity (1 − probability AC/A < x Image not available no myopia onset) of the AC/A ratio as a test for the onset of myopia. The arrow marks the point of maximum discrimination, an AC/A ratio of 5.84 Δ/D.
Figure 4.
 
ROC curve displaying the sensitivity (probability AC/A ≥ x Image not available myopia onset) and 1-specificity (1 − probability AC/A < x Image not available no myopia onset) of the AC/A ratio as a test for the onset of myopia. The arrow marks the point of maximum discrimination, an AC/A ratio of 5.84 Δ/D.
Figure 5.
 
Least-squares means of the stimulus AC/A ratio after adjustment for age. There were no significant differences between refractive error groups.
Figure 5.
 
Least-squares means of the stimulus AC/A ratio after adjustment for age. There were no significant differences between refractive error groups.
Table 1.
 
Number of Children Tested per Age Group in 1996
Table 1.
 
Number of Children Tested per Age Group in 1996
Age (y)
6 7 8 9 10 11 12 13 ≥14
n (%) 46 (5.4) 133 (15.7) 109 (12.9) 113 (13.3) 113 (13.3) 127 (15.0) 88 (10.4) 66 (7.8) 52 (6.1)
Table 2.
 
Correlation of Calibration Measurement with Ocular Parameters
Table 2.
 
Correlation of Calibration Measurement with Ocular Parameters
Variable Pearson r P
Corneal power (D) −0.49 <0.0001
Anterior chamber depth (mm) −0.032 0.35
Lens thickness (mm) −0.40 <0.0001
Posterior lens radius (mm) 0.49 <0.0001
Table 3.
 
The Response AC/A Ratio Unadjusted for Refractive Error as a Function of Age Group
Table 3.
 
The Response AC/A Ratio Unadjusted for Refractive Error as a Function of Age Group
Age (y) Ratio (Δ/D)
6 3.61 ± 1.70
7 3.59 ± 1.74
8 3.52 ± 1.80
9 4.07 ± 1.68
10 4.07 ± 1.78
11 3.91 ± 1.66
12 4.07 ± 1.88
13 4.11 ± 1.60
≥14 4.46 ± 2.19
Table 4.
 
Elevation in Risk of Onset of Myopia with an AC/A Ratio of 5.84 Δ/D or More
Table 4.
 
Elevation in Risk of Onset of Myopia with an AC/A Ratio of 5.84 Δ/D or More
Onset of Myopia in 1997 No Myopia in 1997 Total
AC/A ratio ≥ 5.84 Δ/D in 1996 9 57 66
AC/A ratio < 5.84 Δ/D in 1996 4 656 660
Total 13 713 726
Relative risk = 22.5 (95% CI = 7.12–71.1)
Table 5.
 
Elevation in Risk of Onset of Myopia within 1 Year in the Absence of Myopia with a Refractive Error of Less Than +0.75 D and an AC/A Ratio of 5.84 Δ/D or More
Table 5.
 
Elevation in Risk of Onset of Myopia within 1 Year in the Absence of Myopia with a Refractive Error of Less Than +0.75 D and an AC/A Ratio of 5.84 Δ/D or More
Onset of Myopia in 1997 No Myopia in 1997 Total
AC/A ratio ≥ 5.84 Δ/D in 1996 9 12 21
AC/A ratio < 5.84 Δ/D in 1996 4 26 30
Total 13 38 51
Relative risk = 3.21 (95% CI = 1.14–9.07)
Table 6.
 
Relative Risk for the Onset of Myopia within 1 Year in Children with No Myopia in 1996 Re-Examined in 1997
Table 6.
 
Relative Risk for the Onset of Myopia within 1 Year in Children with No Myopia in 1996 Re-Examined in 1997
Variable Entire Sample (n = 710) Errors Less Than +0.75 D in 1996 (n = 51)
AC/A ratio (Δ/D) 1.57 (1.15–2.14) 1.52 (1.09–2.11)
Refractive error (D) 0.006 (0.0006–0.057) 0.016 (0.001–0.264)
Table 7.
 
Univariate Correlations between the Response AC/A Ratio and Ocular Component Values
Table 7.
 
Univariate Correlations between the Response AC/A Ratio and Ocular Component Values
Component Pearson r P
Spherical refractive error (D) −0.39 <0.0001
Anterior chamber depth (mm) 0.20 <0.0001
Lens thickness (mm) −0.10 0.0026
Vitreous chamber depth (mm) 0.26 <0.0001
Corneal power (D) 0.070 0.032
Lens equivalent index −0.080 0.030
Lens spherical volume (mm3) 0.055 0.12
Gullstrand lens power (D) −0.18 <0.0001
Equivalent lens power (D) −0.19 <0.0001
Anterior lens radius (mm) 0.17 <0.0001
Posterior lens radius (mm) 0.14 <0.0001
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