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Accommodation, Accommodative Convergence, and Response AC/A Ratios Before and at the Onset of Myopia in Children


Optometry and Vision Science: April 2005 - Volume 82 - Issue 4 - p 273-278
doi: 10.1097/01.OPX.0000159363.07082.7D
Original Article

Purpose. The purpose of this study was to investigate accommodation, accommodative convergence, and AC/A ratios before and at the onset of myopia in children.

Methods. Refractive error, accommodation, and phorias were measured annually over a period of 3 years in 80 6- to 18-year-old children (mean age at first visit = 11.1 years), including 26 who acquired myopia of at least -0.50 D and 54 who remained emmetropic (-0.25 to + 0.75 D). Refraction was measured by noncycloplegic distance retinoscopy. Concomitant measures of accommodation and phorias were taken for letter targets at 4.0 m and 0.33 m using the Canon R-1 open field-of-view autorefractor with an attached motorized Risley prism and Maddox rod. The accommodation and phoria measurements were used to calculate response AC/A ratios.

Results. Compared with children who remained emmetropic, those who became myopic had elevated response AC/A ratios at 1 and 2 years before the onset of myopia, in addition to at onset and 1 year later (t’s = -2.97 to -4.04, p < 0.01 at all times). The significantly higher AC/A ratios in the children who became myopic are a result of significantly reduced accommodation. Accommodative convergence was significantly greater in myopes only at onset.

Conclusions. These findings suggest that the abnormal oculomotor factors found before the onset of myopia may contribute to myopigenesis by producing hyperopic retinal defocus when a child is engaged in near-viewing tasks.

Myopia Research Center, The New England College of Optometry, Boston, Massachusetts

Received September 1, 2004; accepted December 15, 2004.

Myopic children and adults are known to have reduced accommodative responses, nearpoint esophoria, and high AC/A ratios compared with emmetropes (for a review, see reference1). One possible outcome of these abnormal oculomotor factors may be that when these individuals are engaged in near activities, they may experience prolonged periods of hyperopic retinal defocus, which then may produce axial elongation, as has been demonstrated in animal models.2, 3 Although the association of these factors with progressing myopia is well established, less is known about their link, if any, to the onset of myopia. Most of the relevant human data have been obtained at or after myopia onset, with limited premyopic findings, especially from prospective studies. If defocus, or the inability to use defocus cues appropriately, combined with extensive near work, initiates eye growth and myopia in susceptible children, then the abnormal factors should be evident not only during myopia progression, but also some time before its onset. A longitudinal study that tracks both refraction and oculomotor factors such as the one ongoing in our laboratory can address this issue. Results of such a study also may show whether one abnormal factor triggers the cascade of related oculomotor findings or whether they present simultaneously, suggesting an inherent synkinesis.

Myopic children have been found to have reduced accommodation (large accommodative lags), whether measured in the laboratory4, 5 or clinically.6, 7 The magnitude of the effect varies with the method used to stimulate accommodation, with larger lags found with accommodation induced with negative lenses than when the target was moved closer.4, 8 The magnitude of the difference in accommodation between myopes and emmetropes also depends on how the data from myopes are grouped. For example, Abbott et al.8 reported that when myopic adults were separated into progressing vs. stable, the progressing myopes had reduced accommodative responses to negative lenses, whereas the stable myopes accommodated as well as emmetropes. However, there were no differences in accommodation when the myopes were grouped by age of onset of myopia (early vs. late).

Clinically, reduced accommodation frequently is associated with exophoria at near, and excessive accommodation with near-point esophoria, such as in uncorrected hyperopes. However, two studies of myopic and emmetropic children found that reduced accommodation was associated with near-point esophoria.6, 9 This finding suggests that an esophoric child must relax accommodation to reduce accommodative convergence and thus maintain single binocular vision.6, 9 The reduction in accommodation may produce hyperopic defocus during near work, which could lead to the onset of myopia or progression of extant myopia.

The rationale for a recent clinical trial, the Correction of Myopia Evaluation Trial (COMET), was based in part on the hypothesis that hyperopic retinal defocus resulting from inaccurate accommodation when children are engaged in near work is a stimulus to myopia progression, and that progressive addition lenses may slow progression by providing clear retinal images at distance and near.10 Results showed an overall slowing of 3-year progression of myopia of 0.20 D in 469 children randomized to progressive addition vs. single-vision lenses.10 A follow-up analysis of the COMET data by magnitude of accommodative lag showed that the largest 3-year treatment effect (0.64 D) was found for myopic children with larger accommodative lags in combination with near esophoria.11

In part because near esophoria has been identified as a risk factor for progression of myopia, Fulk and colleagues conducted a clinical trial of 84 myopic children with near esophoria randomized to either bifocals or single-vision lenses.12 Overall, a 0.25-D treatment effect was found, similar in magnitude to other studies that did not limit enrollment by phoria status. The results of these clinical trials suggest that myopic children with both reduced accommodation and near esophoria may benefit more than children with either factor alone from a spectacle lens intervention.

Reduced accommodation is associated with elevated AC/A ratios. Children with progressing myopia have been found to have reduced accommodation and slightly enhanced synkinetic convergence responses, the combination of which is manifested in significantly elevated response AC/A ratios compared with emmetropes.9 Elevated response AC/A ratios have been found to be a significant risk factor for the onset of myopia in both adults and children. In a study with a limited number of subjects, AC/A ratios were found to be high in emmetropic young adults before the onset of myopia and during the period when myopia was progressing.13 An elevated response AC/A ratio was reported to be a significant risk factor for the onset of myopia in children,14 although large accommodative lags have not been found to occur before myopia onset in a similar group of children.15

To explain the abnormal oculomotor factors in myopic children, an alternative to the blur hypothesis described here is a model proposed by Mutti et al.14 As the vitreous chamber grows, its equatorial expansion pulls the ciliary body away from the lens, tightening the zonules and flattening the lens. The tension on the lens as it reaches its stretching limit then induces a “pseudocycloplegia” in the myopic eye that results in the underaccommodation and high AC/A ratios of young myopes. In this model, the changes in refraction and accommodation/convergence either occur concomitantly or the abnormal oculomotor factors precede the myopia by only a short time.

The purpose of the present study was to investigate accommodation, accommodative convergence, and AC/A ratios before, at, and after the onset of myopia in children to determine whether abnormal oculomotor factors are associated with the development of myopia.

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A total of 80 subjects ranging in age from 6 to 18 years (mean age at first test session = 11.1 years) participated in the experiment. They were tested at approximately annual intervals over a period of at least 3 years and were part of a longitudinal study of refraction and visual function ongoing in our laboratory for 30 years.

All of the subjects were refracted with noncycloplegic distance retinoscopy before each test session. No subject had astigmatism or anisometropia >1.0 D. Mean spherical equivalent refractions for two groups of subjects, one that became myopic by at least -0.50 D in both eyes and one that remained emmetropic (-0.25 to +0.75 D), are shown in Figure 1. All were emmetropic (-0.25 D to +0.75 D) on the first visit, and the mean for each group of subjects was +0.30 D. Over the next 3 years, 26 acquired myopia and 54 remained emmetropic. Refractions were significantly lower in the group that became myopic at all test sessions after the first (p < 0.01).



The research followed the tenets of the Declaration of Helsinki and was approved by the Institutional Review Board of the New England College of Optometry. Informed consent was obtained from the parents and assent from the children after the study was explained to them.

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The apparatus consisted of a Canon R-1 infrared open field-of-view autorefractor (Canon Europa NV, Amstelveen, The Netherlands) with a motorized Risley prism clamped on the R-1 headrest. The prism was moved laterally to line up with the subject’s eye. Vertical alignment of the subject’s eye with the center of the prism aperture was achieved by adjusting the chinrest on the R-1. The prism was controlled by the child with a bidirectional joystick. Trial frames and lenses were used to correct for the distance refraction taken from the Canon R-1 autorefractor. A Maddox rod was placed in the trial frame before the child’s left eye.

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An isolated line of five rear-illuminated 20/100 letters was positioned 4.0 m from the subject’s eye as a distant accommodative stimulus. The near accommodative stimulus consisted of another line of five rear-illuminated 20/100 letters mounted on the Canon R-1 at a distance of 0.33 m from the subject’s eye. For phorias measured with the Maddox rod, a point source of light from a penlight was illuminated directly above the letters.

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The child was positioned in the Canon R-1 wearing a trial frame containing a lens at a forward tilt of 15° (for the autorefractor to take a reading) to correct the refractive error of the right eye. The power of the correcting lens was taken from Canon R-1 autorefractor readings on the right eye viewing the distant target just before accommodation was measured. Because at every visit the best correction was determined before testing, this means that the lens power used for these measurements changed as the refractive error developed. A Maddox rod was placed in the trial frame in front of the left eye.

The distant letter target was illuminated first. The child was instructed to keep the letters clear, and when clear, to move the joystick to align the center letter with the vertical red line created by the penlight. When the child indicated that this had occurred, concomitant measurements of phoria and accommodation were taken. The distant target was then extinguished, and the near target, a rear-illuminated array of 20/100 letters, was presented at 0.33 m. Again, the child was instructed to keep the letters clear and to move the joystick to align the vertical red line created by the penlight with the center letter. When this occurred, concomitant measurements of phoria and accommodation were taken. At least three phoria readings and nine accommodation measures were taken for each condition.

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Data Analysis

For accommodation, the spherical equivalent values were summarized using means and standard errors. For phorias, measurements in volts were converted to prism diopters by fitting the data to a third-order polynomial function relating volts to prism diopters. The equation was obtained by calibrating the motorized Risley prism with a laser. Phorias in prism diopters (PD) then were summarized using means and standard errors. For all children, the mean standard deviation of the three phoria measurements was 0.62 PD at far and 0.95 PD at near.

Response AC/A ratios were calculated from the accommodation and phoria measurements for each child at every visit using the following formula:

Response AC/A ratio = \[(IPD \x NAS) \- (FP \- NP) / NAR \- FAR)

where: IPD = interpupillary distance in centimeters = 6.0

NAS = near accommodative stimulus in diopters = 3.0

FP = far phoria in prism diopters

NP = near phoria in prism diopters

NAR = near accommodative response in diopters

FAR = far accommodative response in diopters

To calculate stimulus AC/A ratios, the near accommodative stimulus (3.0 D) was used as the denominator in place of measured accommodation. Negative AC/A ratios and extremely large values are most likely produced by a combination of small accommodative responses and noise in the measurements.16 Therefore, negative AC/A ratios and those >20 were eliminated from the statistical analysis, as reported previously.9 T-tests were used to test for differences between refractive groups.

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Figure 2 shows that accommodation (defined as the difference between far and near like in the denominator of the response AC/A ratio) is less in the group that became myopic at all four times. It is significantly less for this group 2 years before myopia onset (t = 2.69, p = 0.01), when both groups had the same mean refractive error. Accommodation is slightly less in the group that became myopic 1 year before onset (t = 1.87, p = 0.07) and is significantly less in that group at onset (t = 3.68, p < 0.01) and 1 year later (t = 2.22, p < 0.05).



Figure 3 shows that accommodative convergence (the numerator of the response AC/A ratio) is slightly greater for children who became myopic at all times, but the difference between refractive groups is statistically significant only at onset (t = -3.14, p < 0.01). Accommodative convergence increased over time in children who became myopic and remained constant in the emmetropic children. Mean near phorias were -0.4 PD (range = -11.8 to 15.3 PD) for myopes and -2.9 PD (range = -14.6 to 8.5 PD) for emmetropes. Mean distance phorias were 3.2 PD (range = -5.5 to 15.0 PD) for myopes and 1.8 (range = -6.0 to 11.5 PD) for emmetropes.



The data in Figure 2 (denominator) and Figure 3 (numerator) were used to calculate the distance-induced response AC/A ratios shown in Figure 4. The response AC/A ratios are significantly higher in the group that became myopic at all times: at each of the 2 years before myopia onset, at onset, and 1 year after onset (t’s = -2.97 to -4.04, p < 0.01 at all times). The significantly higher AC/A ratios in the children who became myopic are a result of their reduced accommodation, because accommodative convergence was only significantly greater in myopes at onset. Additional analyses of the data separately from younger and older subjects showed that the results did not differ by age.



The distance-induced stimulus AC/A ratios in Figure 5 show the same pattern as accommodative convergence in Figure 3. This is not surprising, because in calculating the stimulus AC/A ratio, the convergence values are divided by a constant (3.0), the stimulus to accommodation. In contrast to the response AC/A ratios in Figure 4, which are significantly higher in the group that became myopic at all points in time, the stimulus AC/A ratios are significantly higher in this group only at onset (t = -3.14, p < 0.01).



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Although there have been many reports of abnormal oculomotor factors at or after myopia onset, including some from this laboratory,4, 5, 9 the current data are new in showing that higher AC/A ratios and reduced accommodation precede myopia onset by at least 2 years. The significantly decreased accommodation is manifested in significantly elevated response AC/A ratios in myopes 2 years before, at, and after the onset of myopia.

Two previously proposed hypotheses, summarized as the blur hypothesis and the ocular growth hypothesis, may account for the observed findings. These two are not mutually exclusive; it is possible that either or both mechanisms could operate in the same eye. In the first hypothesis, blur or the inability to use blur cues appropriately, combined with extensive near work, can initiate myopia in susceptible children.4, 17 In the second, poor accommodation and high AC/A ratios are simply an offshoot of the hypothesized structural growth of the eye slightly before and during myopia progression.

The first hypothesis has emerged from consideration of animal experiments (for reviews, see references 2, 3). Emmetropization in early childhood appears to depend on a feedback control mechanism that primarily controls vitreous chamber elongation so as to match axial length with the optical power of the anterior segment to place a relatively clear image on the retina. If this process is disrupted through retinal image degradation, it may lead by default to excessive axial elongation (analogous to mild form-deprivation in animal experiments). If the process is biased by extended periods of hyperopic defocus, like when children underaccommodate for near distances, excessive axial elongation may be guided by the feedback control mechanism.

Mutti et al.14 suggested that elevated AC/A ratios found in premyopic children are a transient occurrence reflecting mechanical abnormalities in the lens and choroid that induce a state of “pseudocycloplegia.” Support for this was provided by data showing elevated AC/A ratios in 13 children who became myopic within 1 year.14 However, data were only collected on two occasions 1 year apart, so it is not possible to know when the high AC/A ratios first occurred. The 2-year premyopic period in the present study cannot be considered transient, and it may be that these children had elevated AC/A ratios even earlier. We know from previous work that it is unlikely for the AC/A ratio to be maintained at a high level once a child’s myopia has stabilized,9 consistent with our finding of improved accommodation with stability of myopia.5 If the AC/A ratio is not maintained at a fixed level in school-aged children as their myopia progresses and then stabilizes, it is also unlikely to be static in preschool (and premyopic) children. More research is needed to determine the association of abnormal oculomotor factors and emmetropization in very young children.

Two years before the onset of myopia, the subjects in the current study, both those who later became myopic and those who remained emmetropic, had the same mean spherical equivalent refraction (+0.30 D). This is an important control because emmetropia in a young child is a risk factor for myopia.18, 19 The fact that the mean spherical equivalent refractions were the same in the two groups of children 2 years before myopia onset is also important because it means that the same range of low-power lenses was used for testing all subjects at their initial visit. One year before the onset of myopia, the two groups had refractions that were significantly different, which is not surprising. At that time, the myopization process most likely had begun in those children whose refractions later crossed the commonly used but arbitrary cutoff for myopia of -0.50 D.20

In the current study, accommodative convergence increased with time in the children who became myopic. This finding is similar to earlier reports showing that the onset and progression of myopia in children was accompanied by a shift toward more esophoria at near.6, 21 In the present study, the vergence change from far to near most likely includes both accommodative and proximal convergence. The contribution of proximal vergence to the overall vergence output has been shown to be large under open-loop conditions when disparity and defocus are not effective and much smaller under closed loop conditions, which are closer to normal viewing and to the experimental setup of the present study.22

The current data differ slightly (within 0.25 D) from what was published previously by this laboratory with respect to the magnitude of accommodative responses in myopes. Previously, we reported that accommodation for a target at 3.0 D was 1.75 D for myopes and 1.89 D for emmetropes.9 In the current report, mean accommodation in emmetropes is very close to 2.0 D for the 3.0-D demand, similar to the earlier value, whereas for myopes, it is slightly more than 1.5 D, but not quite at 1.75 D. A possible reason for finding less accommodation in myopes in the current analyses is the fact that our previous report likely included some myopes further along in progression and nearing stabilization, whereas the current report only includes progressing myopes around onset. Because it is known that accommodation is poorer in progressing compared with stable myopes, mean accommodation in a group of purely progressing myopes like in the current study would be less than in a group of children at various stages of progression. With respect to premyopic children, an earlier report from this laboratory5 found that of six subjects with refractive errors that changed from emmetropic to myopic, one had a large accommodative lag and five of six showed normal accommodation. As stated in the discussion of that paper, “further tracking studies are needed to clarify this issue.” The current report with a larger number of subjects helps to clarify this issue.

It is not surprising that the stimulus AC/A ratio shows the same pattern as accommodative convergence because the stimulus to accommodation, which is the same for all subjects, and not the measured accommodative response, which differs by refractive group, was used in the denominator. Because the stimulus AC/A ratio, which is common in clinical practice, uses only the accommodative convergence response, it will not reveal future myopes.

In summary, the current results show that before the onset of myopia, before the need for optical correction, emmetropic children who later became myopic had elevated AC/A ratios and poorer accommodation compared with those who remained emmetropic. The finding of some abnormal oculomotor factors before the development of myopia suggests that they may contribute to myopigenesis by producing hyperopic retinal defocus when a child is engaged in near-viewing tasks. Continued testing of premyopic children is needed to more precisely determine the chronologic coupling of these abnormal oculomotor factors and the development of myopia.

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This work was supported by NEI/NIH EY01191. The authors thank Alexandra Beale and Jeremy Gwiazda for their help.

Jane Gwiazda

The New England College of Optometry

424 Beacon Street

Boston, Massachusetts 02115


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1.Gwiazda J, Marran L. The many facets of the myopic eye: a review of genetic and environmental factors. In: Trends in Optics and Photonics, vol 35. Washington, DC: Optical Society of America, 2000:393–406.
2.Norton TT. Animal models of myopia: learning how vision controls the size of the eye. ILAR J 1999;40:59–77.
3.Wildsoet CF. Active emmetropization—evidence for its existence and ramifications for clinical practice. Ophthal Physiol Opt 1997;17:279–90.
4.Gwiazda J, Thorn F, Bauer J, Held R. Myopic children show insufficient accommodative response to blur. Invest Ophthalmol Vis Sci 1993;34:690–4.
5.Gwiazda J, Bauer J, Thorn F, Held R. A dynamic relationship between myopia and blur-driven accommodation in school-aged children. Vision Res 1995;35:1299–304.
6.Goss DA. Clinical accommodation and heterophoria findings preceding juvenile onset of myopia. Optom Vis Sci 1991;68:110–6.
7.Drobe B, de Saint-Andre R. The pre-myopic syndrome. Ophthal Physiol Opt 1995;15:375–8.
8.Abbott ML, Schmid KL, Strang NC. Differences in the accommodation stimulus response curves of adult myopes and emmetropes. Ophthal Physiol Opt 1998;18:13–20.
9.Gwiazda J, Grice K, Thorn F. Response AC/A ratios are elevated in myopic children. Ophthal Physiol Opt 1999;19:173–9.
10.Gwiazda J, Hyman L, Hussein M, Everett D, Norton TT, Kurtz D, Leske MC, Manny R, Marsh-Tootle W, Scheiman M. A randomized clinical trial of progressive addition lenses versus single vision lenses on the progression of myopia in children. Invest Ophthalmol Vis Sci 2003;44:1492–500.
11.Gwiazda JE, Hyman L, Norton TT, Hussein ME, Marsh-Tootle W, Manny R, Wang Y, Everett D. Accommodation and related risk factors associated with myopia progression and their interaction with treatment in COMET children. Invest Ophthalmol Vis Sci 2004;45:2143–51.
12.Fulk GW, Cyert LA, Parker DE. A randomized trial of the effect of single-vision vs. bifocal lenses on myopia progression in children with esophoria. Optom Vis Sci 2000;77:395–401.
13.Jiang BC. Parameters of accommodative and vergence systems and the development of late-onset myopia. Invest Ophthalmol Vis Sci 1995;36:1737–42.
14.Mutti DO, Jones LA, Moeschberger ML, Zadnik K. AC/A ratio, age, and refractive error in children. Invest Ophthalmol Vis Sci 2000;41:2469–78.
15.Mutti DO, Mitchell GL, Jones LA, Hayes JR, Moeschberger ML, Zadnik K. Accommodative lag at the onset of myopia in children. Invest Ophthalmol Vis Sci 2004;45:ARVO E-abstract 3514.
16.Ciuffreda KJ, Rosenfield M, Chen HW. The AC/A ratio, age and presbyopia. Ophthal Physiol Opt 1997;17:307–15.
17.Flitcroft DI. A model of the contribution of oculomotor and optical factors to emmetropization and myopia. Vision Res 1998;38:2869–79.
18.Hirsch MJ. Predictability of refraction at age 14 on the basis of testing at age 6—interim report from the Ojai Longitudinal Study of Refraction. Am J Optom Arch Am Acad Optom 1964;41:567–73.
19.Zadnik K, Mutti DO, Friedman NE, Qualley PA, Jones LA, Qui P, Kim HS, Hsu JC, Moeschberger ML. Ocular predictors of the onset of juvenile myopia. Invest Ophthalmol Vis Sci 1999;40:1936–43.
20.Thorn F, Gwiazda J, Held R. Myopia progression is specified by a double exponential growth function. Optom Vis Sci 2005;81:286–97.
21.Goss DA, Jackson TW. Clinical findings before the onset of myopia in youth: 3. Heterophoria. Optom Vis Sci 1996;73:269–78.
22.Hung GK, Ciuffreda KJ, Rosenfield M. Proximal contribution to a linear static model of accommodation and vergence. Ophthal Physiol Opt 1996;16:31–41.

myopia; accommodation; refractive error; children; visual development

© 2005 American Academy of Optometry