Axial Growth and Changes in Lenticular and Corneal Power during Emmetropization in Infants

Abstract

purpose. To evaluate the contribution made by the ocular components to the emmetropization of spherical equivalent refractive error in human infants between 3 and 9 months of age.

methods. Keratophakometry in two meridians was performed on 222 normal-birthweight infant subjects at 3 and 9 months of age. The spherical equivalent refractive error was measured by cycloplegic retinoscopy (cyclopentolate 1%). Anterior chamber depth, lens thickness, and vitreous chamber depth were measured by A-scan ultrasonography over the closed eyelid.

results. Both the mean and SD for spherical equivalent refractive error decreased between 3 and 9 months of age (+2.16 ± 1.30 D at 3 months; +1.36 ± 1.06 D at 9 months; P < 0.0001, for the change in both mean and SD). Average ocular component change was characterized by increases in axial length, thinning, and flattening of the crystalline lens, increases in lens equivalent refractive index, and decreases in lens and corneal power. Initial refractive error was associated in a nonlinear manner with the change in refractive error (R ² = 0.41; P < 0.0001) and with axial growth (R ² = 0.082; P = 0.0005). Reduction in hyperopia correlated significantly with increases in axial length (R ² = 0.16; P < 0.0001), but not with changes in corneal and lenticular power. Decreases in lenticular and corneal power were associated with axial elongation (R ² = 0.40, R ² = 0.12, respectively; both P < 0.0001).

conclusions. Modulation in the amount of axial growth in relation to initial refractive error appeared to be the most influential factor in emmetropization of spherical equivalent refractive error. The associations between initial refractive error, subsequent axial growth, and change in refractive error were consistent with a visual basis for emmetropization. The cornea and crystalline lens lost substantial amounts of dioptric power in this phase of growth, but neither appeared to play a significant role in emmetropization.

Refractive error represents a mismatch between the eye’s focal length and its axial length. Infant eyes undergo a process of emmetropization whereby both the average amount and the variance in the distribution of refractive errors are reduced. The precise mechanisms coordinating the optical and structural development of the eye are not completely understood. Results of animal experiments suggest that this process is guided by feedback from visual input. ^{1 2 3 4 5} The current model of human emmetropization from animal studies is that hyperopic defocus caused by an infant’s hyperopic refractive error modulates the growth of the eye to reduce refractive error. ^{4 6}  

Also poorly understood is the role played in emmetropization by the ocular components, such as the cornea or crystalline lens. The visual feedback model of emmetropization holds that defocus modulates the axial growth of the eye to reduce refractive error. Visual guidance of ocular growth might therefore be termed an “active” mechanism. In contrast, the cornea and lens could be important contributors to emmetropization if the eye grew at a certain random rate, but changes in the power of the cornea and crystalline lens occur in appropriate proportion to the initial refractive error. The crystalline lens loses substantial amounts of power during infancy. ⁷ If the crystalline lens and cornea lost relatively small amounts of power in comparison with the dioptric effect of axial growth, then highly hyperopic infants would lose hyperopia quickly and move rapidly toward emmetropia. Infants with little initial hyperopia could move more slowly toward emmetropia if lenticular or corneal power decreased by a large number of diopters per millimeter of axial growth. Emmetropization could therefore result from the loss of anterior segment power at different rates, depending on initial refractive error. Variation in the contribution of the equatorial gradient index profile to power changes during axial growth has been proposed as a source of graded changes in lenticular power. ⁷ Emmetropization resulting from this type of optical coordination between lenticular power change, corneal power change, and initial refractive error might therefore be termed “passive,” because visual guidance of axial growth would not be necessary. This particular type of passive emmetropization would be distinct from a previously described passive mechanism for emmetropization due to scaling—the decrease in refractive error as a proportion of the decreasing power of the eye. ⁸  

The purpose of the Berkeley Infant Biometry Study (BIBS) is to document the development of the major optical ocular components during emmetropization. The purpose of this report is to examine how the major ocular components—namely, axial length, corneal power, and crystalline lens power—change to produce emmetropia and whether that process operates more by an active or passive process. Support for an active mechanism would come from evidence of emmetropization through modulation of axial growth, analogous to that seen in animal experimentation, whereas a passive mechanism would be inferred from emmetropization occurring primarily through modulation of corneal and lenticular power. 

Methods

Subjects for the BIBS were recruited from several sources, including advertisements in diaper service newsletters, word-of-mouth, and letters sent to parents of newborns identified from birth records in Contra Costa County, California. Parents provided written informed consent according to the tenets of the Declaration of Helsinki after all procedures were explained. The BIBS protocol was reviewed and approved by the Institutional Review Boards for The Ohio State University, the University of California, Berkeley, and the State of California. Inclusion criteria were both genders, all refractive errors (including emmetropia), birthweight over 2500 g, and confirmation that the infant was under the general care of a pediatrician. Existing strabismus was allowed, although no infant entered the study with strabismus. Infants were excluded if they had a history of difficulty with pupil dilation, a history of cardiac, liver, asthma, or other respiratory disease, or a history of ocular disease or active ocular inflammation. This report analyzes 222 (53% female) of 302 subjects with examination data for both the 3-month (±1 month) and the 9-month (±1 month) visit. Subjects were excluded from analysis because of age outside the visit window (n = 60), losses to follow-up (n = 15), inability to test (n = 3), low birthweight (n = 1), and incorrect cycloplegia (tropicamide instead of cyclopentolate (n = 1). The 15 subjects lost to follow-up were not significantly different from the sample as a whole in initial refractive error, axial length, corneal or lenticular power, gender, family income, or any ocular component measure. Ethnicity was unknown in 13 of the 15. Subject participation by parent-reported ethnicity and family income is given in Table 1 . 

Refractive error was measured by two observers performing retinoscopy 25 minutes after instillation of 1 drop of proparacaine 0.5%, followed by 2 drops of cyclopentolate 1.0% in each eye with 5 minutes between cyclopentolate drops. The second examiner’s measurement was made without knowledge of the first examiner’s findings. Refractive error is reported as the average of the two examiners’ retinoscopy results for the cycloplegic spherical equivalent refractive error of the right eye. The 95% limits of agreement between the two examiners have been reported as −0.71 to +0.98 D for spherical equivalent. ⁹ Changes in refractive error and ocular components were defined as the values at 9 months of age minus the values at 3 months. 

All reported biometric measurements were performed on the right eye only. Keratometry and phakometry were performed with a custom, hand-held, video-based phakometer described in detail elsewhere. ⁷ An equivalent refractive index and radii of curvature for the crystalline lens were determined by using an iterative procedure that produced agreement between the measured refractive error and that calculated from ocular component values. ¹⁰ This hand-held method produces measurements comparable to the conventional slit lamp mounted phakometer used in a large-scale longitudinal study of school-aged children. ¹⁰ The average difference between the two techniques was 0.03 ± 0.22 D in a validation study of 35 6-year-old children. The lens and corneal dimensions analyzed were the averages of the two meridians. Ocular axial dimensions were measured with an A-scan ultrasound (model 820; Carl Zeiss Meditec, Dublin, CA). Measurements were taken through the closed eyelid in semiautomatic mode, with the “dense cataract” setting at 100% gain. This method has been shown to produce results comparable to the standard corneal contact technique. ^{11 12} One comparison found a 0.05-mm difference in axial length, ¹² whereas another found that the through-the-lid technique resulted in thicker lenses by 0.12 mm and longer vitreous chambers by 0.18 mm. ¹¹ Any small bias present in the technique would be expected to cancel out as differences between examinations were taken to calculate longitudinal change. The repeatability (95% limits of agreement) of the through-the-lid measurement technique on adults was ±0.32 mm, ¹² similar to that with the corneal contact technique. ¹³ The repeatability between two examinations of infants 3 to 7 months in age was ±6.22 D for lenticular power and ±0.84 mm for vitreous chamber depth, ¹⁴ roughly twice that in children. ¹⁵ Given these estimates for repeatability, a sample size of 210 was calculated to provide power of at least 0.90 to find differences of 0.13 mm in axial growth and 1 D in change in lenticular power between hyperopes above compared with below the upper tertile for refractive error at 3 months (+2.50 D). 

Data were transmitted to the Optometry Coordinating Center at The Ohio State University for dual data entry. The Optometry Coordinating Center verified that all forms were accounted for. A computer running commercial software (SAS ver. 8.0; SAS Institute, Cary, NC) was used for verification of ranges and missing information, as well as for data analysis. Regression analyses were used to assess the relationship between ocular components (SAS JMP, ver. 3.1.5; SAS Institute). Paired Student’s t-tests were used to compare mean refractive errors between examinations. The correlated variances for refractive error were compared using the method described by Cox and Hinkley. ¹⁶  

Results

Considerable emmetropization took place between 3 and 9 months of age (Fig. 1) . The proportion of infants with hyperopia ≥ +3.00 D decreased from 24.8% at 3 months of age to 5.4% at 9 months. The average refractive error decreased from +2.16 D at 3 months to +1.36 D at 9 months (P < 0.0001). In addition, the SD of the distribution of refractive error decreased between 3 and 9 months (1.30 D compared with 1.06 D, respectively; P < 0.0001). ¹⁶ Gender was not a factor in this process. The change in refractive error was not different between boys (−0.84 ± 0.93 D) and girls (−0.76 ± 0.87 D; P = 0.51, two-sample t-test). Axial growth was also similar for each gender between 3 and 9 months of age at 1.20 ± 0.54 mm in boys and 1.20 ± 0.49 mm in girls (P = 0.97, two-sample t-test). 

The change in refractive error between 3 and 9 months of age was closely related to initial refractive error at 3 months. The relation was linear over moderate levels of initial hyperopia, as noted in a previous longitudinal study of refractive error between the first 6 months of life and age 12 to 17 months. ¹⁷ However, infants at the extremes of the range of initial refractive errors, near emmetropia or with hyperopia in excess of +5.00 D, did not follow a linear pattern of change. Change in refractive error was minimal when initial refractive error was either highly hyperopic or near plano. The data were best fit by a third-order polynomial (Fig. 2A ; R ² = 0.41; model P < 0.0001; P < 0.0001 for the third-order term). More hyperopic initial refractive errors were also associated with larger increases in axial length between 3 and 9 months of age. The data for initial hyperopia and change in axial length were also best fit by a third-order polynomial (Fig. 2B ; R ² = 0.082, model P = 0.0005; P = 0.004 for the third-order term). Initial refractive error was not related to either change in lenticular power (R ² = 0.007, P = 0.26) or change in corneal power (R ² = 0.006, P = 0.25). 

The eye grew rapidly during the period between 3 and 9 months of age with all the ocular components undergoing significant change (paired t-tests; Table 2 ). The axial length of the eye increased on average by 1.20 ± 0.51 mm in 6 months. Most of that increase came from expansion of the vitreous chamber with a smaller amount of growth in the anterior chamber. The crystalline lens thinned during this period of rapid growth. Both the anterior and the posterior lens radii of curvature flattened between 3 and 9 months of age, contrary to an earlier report that found no change in infant lens radii of curvature with age. ⁷ Surface flattening was accompanied by an increase in the equivalent refractive index of the crystalline lens. The net effect was a large decrease in the power of the crystalline lens as the eye grew. The cornea also decreased in power, but only by approximately one third the amount of the decrease in crystalline lens power. 

The role played by the three major ocular components in determining refractive change was examined by regression analysis. Although significant decreases took place in both lens and corneal power (Table 2) , these changes did not correlate with change in refractive error (Figs. 3B 3C ; crystalline lens R ² = 0.0013, P = 0.62; cornea R ² = 0.0006, P = 0.72). Only change in axial length was significantly correlated with change in refractive error (Fig. 3A ; R ² = 0.16, P < 0.0001). Increases in axial length were associated with decreases in hyperopia, consistent with the significant associations seen in Figures 2A and 2Bbetween higher initial hyperopia and greater change in both refractive error and axial length. 

Increases in axial length correlated significantly with decreases in both crystalline lens and corneal power between 3 and 9 months of age (Figs. 4A 4B ; R ² = 0.40, P < 0.0001; R ² = 0.12, P < 0.0001, respectively). According to the passive emmetropization model, these slopes should differ, depending on how quickly hyperopia decreased. Specifically, when the loss of hyperopia is small, there should be a greater change in power per millimeter of axial growth, but when the loss of hyperopia is substantial, there should be a smaller change in power per millimeter of axial growth. An interaction analysis was performed to determine whether this variation in slope occurred. Subjects were divided into tertiles comprising large decreases in hyperopia (−3.56 to −1.19 D), smaller decreases in hyperopia (−1.12 to −0.37 D), and minimal decreases-to-increases in hyperopia (−0.31 to +1.19 D) over the 6-month period. The refractive error rate of change grouping did not significantly affect the slope for either change in crystalline lens power by change in axial length or for change in corneal power by change in axial length (for interaction, P = 0.31 and 0.43, respectively). 

The two surfaces of the crystalline lens showed different associations with axial growth. Figure 5Adepicts the relationship between axial growth and change in anterior lens radius of curvature. The clustering of points at positive values indicates surface curvature flattening and axial growth, and there is a positive relationship between the two (R ² = 0.029, P = 0.018). Faster growth of the eye was related to greater amounts of flattening. In Figure 5B , for the posterior surface, the clustering of points also indicates surface flattening, but there was no relationship between the change in posterior radius of curvature and axial growth (R ² = 0.0085, P = 0.20). As seen in Figure 5C , the equivalent refractive index of the crystalline lens increased on average and showed a negative relationship with axial growth (R ² = 0.16, P = <0.001). Either decreases or smaller increases in equivalent refractive index were associated with faster rates of axial growth. Therefore, the decrease in lenticular power occurring as a function of axial growth resulted from anterior lens surface flattening with some modifications by changes in equivalent refractive index. 

Discussion

We have documented the development of the major ocular optical components during emmetropization between 3 and 9 months of age in a large sample of infants. Eyes in the present study were longer on average compared with previous samples in the literature. The average axial length at age 3 months (Table 2)was roughly 1.2 mm longer, vitreous chamber depth 0.49 mm longer, and anterior chamber depth 0.35 mm deeper than those parameters in 16 infants studied by Isenberg et al. ¹⁸ The current results are closer to values from the 12 to 19 infants studied by Pennie et al. ¹⁹ (after we added 0.50 mm for the thickness of the cornea missing in their technique). In the present study, axial length was 0.54 and 0.27 mm longer at roughly 3 and 9 months, respectively; lens thickness was approximately 0.27 mm thicker at each age; and anterior chamber depth was nearly identical. All measured ocular components, as expected, underwent significant change between 3 and 9 months of age. The basic pattern was for the eye to lengthen, the anterior chamber to deepen, the cornea and crystalline lens to flatten and lose power, and the crystalline lens to thin. Unlike in a previous pilot study, ⁷ the crystalline lens radii flattened with age. Possible reasons for the discrepancy include the pilot study’s smaller sample size, the lack of experience in measurement during these preliminary stages of phakometer development, and possible errors in specifying or entering dates of birth without dual data entry. As a general limitation, values from any one sample may not necessarily generalize to all infants. There may be variation, depending on the refractive error of parents or sample ethnicity. 

Substantial emmetropization took place between 3 and 9 months of age, with significant reductions in both average refractive error and its variance. Emmetropization appeared to be a rapid phenomenon. Cross-sectional and longitudinal data suggest that most emmetropization takes place between 3 and 12 months of age. ^{9 19 20 21} No significant differences in spherical equivalent refractive error were found between 9 and 36 months in BIBS infants in a separate analysis of astigmatism and emmetropization. ⁹ Modulation in the amount of axial growth was the major factor associated with emmetropization. Higher initial levels of hyperopia were related to faster rates of axial growth, and this faster growth was effective in decreasing hyperopia. This net decrease in hyperopia occurred despite decreases in both corneal and lenticular power. Changes in corneal and lenticular power were not independent of axial growth, but rather showed significant negative correlations with increases in axial length (Figs. 4A 4B) . Axial growth appeared to dominate in this optical “give and take,” as the net effect of the correlated growth of length and optical power was a loss of hyperopia. 

It seems likely that the human eye, as in neonate animals, is responding to some feature related to refractive error through active visual feedback to reduce the amount of refractive error. The relationships between initial hyperopia, axial growth, and refractive change are consistent in a model of active, visually controlled emmetropization. BIBS results are comparable to emmetropization studies in neonate monkeys in which imposed defocus from spectacle lenses was used. ⁴ Similar to infant monkeys, compensation occurred in a linear fashion in response to a range of initial refractive errors from near emmetropia to moderate hyperopia. The linear range of effective emmetropization was qualitatively smaller in infants, from approximately +1 to +5 D of initial hyperopia compared with −2 to +8 D in monkeys. ⁴ A limited effective range could be responsible for the departures from linearity observed in Figure 2Afor refractive change. The most highly hyperopic infants, those in excess of +5 D, tended to not emmetropize effectively, creating an inflection in the curve at that point. This was also suggested by other recent longitudinal data. ¹⁹ A clinical trial of correction of infant hyperopia has also shown a persistence of initially high levels of hyperopia. ²² Conversely, those infants with initial refractive errors closer to emmetropia either changed little or (rarely) became myopic, creating the second inflection in this curve. 

Although the axial response in proportion to initial refractive error suggests an active emmetropization mechanism analogous to that in animal experimentation, another nonvisual hypothesis for emmetropization, proportional growth, should also be discussed. ⁸ This model states that if refractive error is maintained as a constant proportion of total eye power throughout growth, refractive error decreases as the size of the eye increases and its power decreases. The refractive error produced by proportional growth was estimated from BIBS data by multiplying the power of the eye at 9 months by the ratio of refractive error at 3 months and the power of the eye at 3 months. The estimated refractive error at 9 months calculated from emmetropization due to scaling was +2.11 ± 1.25 D, representing virtually no emmetropization compared with the initial value of +2.16 ± 1.30 D at 3 months. The observed value at 9 months of +1.36 ± 1.06 D clearly demonstrates emmetropization has occurred beyond the effects of scaling. This result is consistent with a recent longitudinal study of refraction and ocular growth in infants that also found that the older eye is not a simple scaled version of the infant eye. ¹⁹  

Axial growth correlated inversely with changes in corneal and crystalline lens power, but the question arises of which component “drives” the correlation between the two. At least two alternatives are possible: that equatorial expansion of the eye creates a flatter, less powerful cornea and lens, or that intrinsic power losses for the cornea and lens create hyperopic defocus that stimulate continued eye growth. The first alternative is based on van Alphen size and stretch factors. ²³ According to this model, the cornea becomes flatter because of increased eye size, and the lens flattens because of the equatorial stretch. The second alternative follows from animal models of active emmetropization. Some combination of the two is possible, but we propose that the first alternative is more likely. The lens thinning that was observed seems most easily explained by stretching. The lens actively grows during the period between 3 and 9 months of age. Lens wet weight is expected to increase by 10% during this time. ²⁴ The simple addition of new fibers should flatten and thicken the crystalline lens. Concurrent flattening and thinning of the crystalline lens is consistent with the van Alphen stretch operating as a coordinating factor between axial growth and lenticular power change in infancy. If lens power changes occur because of equatorial stretching and lens power changes correlate highly with axial growth, then equatorial and axial expansion may be related in normal infant eye growth. Correlated equatorial and axial change does not always occur; animal experiments suggest these two dimensions may be regulated separately. ^{25 26 27 28} They may not be regulated separately during normal development, or their separate regulators may be correlated through some common process. 

The slope of the relationship between change in lenticular power and axial growth is also not consistent with the hypothesis that changes in lenticular power add to hyperopic defocus and stimulate eye growth. The refractive change that results from hyperopic refractive error typically approaches 1:1. For example, an orthogonal regression performed on the data in Figure 2Bover a clearly linear range of emmetropization, between initial refractive errors of 0.00 to +3.00 D, gives a slope of −0.96. Smith and Hung ⁴ found that compensation over the effective emmetropization range in infant monkeys had a slope of −0.78. With the considerations of effectivity and that each millimeter of uncompensated axial growth in an infant eye is equivalent to approximately 4.8 D of refractive error, it would take 7 to 9 D of change in crystalline lens power to stimulate each millimeter of axial compensation. This prediction clearly exceeds the slope seen in Figure 4A(−4.1 D/mm by orthogonal regression). It seems unreasonable to assume that the eye has a different sensitivity to defocus caused by refractive component errors compared with axial errors. It seems more reasonable to assume that changes in lenticular power occur at a rate of approximately 4 D/mm during axial growth, as a byproduct of stretching. 

We conclude that the change in refractive error between 3 and 9 months of age shows evidence of active emmetropization analogous to that in animal experimentation. An active contribution was seen in the modulation of axial growth in response to initial refractive error and in its relationship with change in refractive error. Although the cornea and crystalline lens underwent substantial decreases in power, these changes were not of sufficient magnitude to prevent emmetropization, nor did they make passive contributions to emmetropization. 

 Supported by National Eye Institute Grants R01-EY11801 (DOM) and R21-EY12273 (KZ).

 Submitted for publication August 30, 2005; revised January 8 and 31, March 4, and April 5, 2005; accepted April 25, 2005.

 Disclosure: D.O. Mutti, None; G.L. Mitchell, None; L.A. Jones, None; N.E. Friedman, None; S.L. Frane, None; W.K. Lin, None; M.L. Moeschberger, None; K. Zadnik, None

 The publication costs of this article were defrayed in part by page charge payment. This article must therefore be marked “advertisement” in accordance with 18 U.S.C. §1734 solely to indicate this fact.

 

Table 1.

 

Subject Ethnicity and Family Income

	Number (%) (N = 221)
Ethnicity
African-American	8 (3.6)
Asian-American (Chinese, Japanese, Korean, Filipino)	26 (11.8)
White	164 (74.2)
Hispanic (Latino, Chicano)	12 (5.4)
Native American	1 (0.5)
Other	10 (4.5)
Family income ($)
<20,000	9 (4.1)
20,000 to <40,000	19 (8.6)
40,000 to <60,000	45 (20.4)
60,000 to <80,000	48 (21.7)
80,000 to <100,000	34 (15.4)
>100,000	66 (29.9)

Figure 1.

 

Histograms of the distribution of refractive error at (A) 3 and (B) 9 months of age. The mean (±SD) spherical equivalent refractive error is also given for each age.

Figure 2.

 

Change in refractive error (A) and change in axial length (B) over a 6-month period (9 months − 3 months) as a function of initial refractive error at 3 months. Note the mirror image symmetry of the pattern of third-order polynomial fits.

Table 2.

 

Ocular Component Values at 3 and 9 Months of Age

Component	3 Months	9 Months	6-Month Change (9 − 3 mo.)	P
Refractive error (D)	+2.16 ± 1.30	+1.36 ± 1.06	−0.80 ± 0.90	<0.0001
Corneal power (D)	43.90 ± 1.46	42.83 ± 1.42	−1.07 ± 1.09	<0.0001
Lenticular power (D)	41.01 ± 2.20	37.40 ± 2.09	−3.62 ± 2.13	<0.0001
Anterior lens radius (mm)	7.21 ± 0.60	8.97 ± 0.75	1.79 ± 0.61	<0.0001
Posterior lens radius (mm)	4.68 ± 0.31	5.21 ± 0.36	0.53 ± 0.33	<0.0001
Equivalent refractive index	1.4526 ± 0.0076	1.4591 ± 0.0093	0.0066 ± 0.0106	<0.0001
Anterior chamber depth (mm)	2.76 ± 0.27	3.03 ± 0.35	0.26 ± 0.32	<0.0001
Lens thickness (mm)	3.92 ± 0.17	3.86 ± 0.18	−0.05 ± 0.19	0.0003
Vitreous chamber depth (mm)	12.35 ± 0.51	13.34 ± 0.56	0.99 ± 0.40	<0.0001
Axial length (mm)	19.03 ± 0.58	20.23 ± 0.64	1.20 ± 0.51	<0.0001

 Values for lens radii, power, equivalent index, and corneal power are the average of two meridians. P indicates the significance of change between 3 and 9 months and was obtained by paired t-test.

Figure 3.

 

Change in refractive error as a function of change over a 6-month period (9 months − 3 months) in axial length (A), lenticular power (B), and corneal power (C; 9 months − 3 months). Only the significant correlation is fitted with a regression line.

Figure 4.

 

Change in crystalline lens power (A) and change in corneal power (B) over a 6-month period (9 months − 3 months) as a function of change in axial length over the same period.

Figure 5.

 

Change in crystalline lens parameters over a 6-month period (9 months − 3 months): anterior lens radius of curvature (A), posterior lens radius of curvature (B), and lens equivalent refractive index (C) as a function change in axial length over the same period. Only the significant correlations are fitted with a regression line.

The authors thank Stephanie J. Kirschbaum, OD, J. Daniel Twelker, OD, PhD, and Robert I. Sholtz, MS, for contributions to earlier phases of this project.