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Keywords:

  • aberrations;
  • accommodation;
  • children;
  • natural pupils;
  • refractive error;
  • wavefront aberrations

Abstract

  1. Top of page
  2. Abstract
  3. METHODS
  4. RESULTS
  5. DISCUSSION
  6. REFERENCES

Background:  The relationship between ocular wavefront aberrations and refractive error in children's eyes remains controversial. The purpose of this study is to re-examine this relationship in Chinese school children under natural distance accommodation.

Methods:  Ocular wavefront aberrations were measured in 86 Chinese children with spherical equivalent refraction (SER) between +0.5 D and -6.0 D and astigmatism less than -1.00 D. Wavefront aberrations were calculated using an objective method based on the Hartmann-Shack principle. Refractive error was obtained using a phoropter after cycloplegia. Subjects were categorised into three groups based on the mean SER: emmetropia (SER from -0.50 D to +0.50 D), mild myopia (SER greater than -0.50 D to -3.00 D) and moderate myopia (SER greater than -3.00 D to -6.00 D). Of the 86 participants, 22 were emmetropic, 43 were mildly myopic and 21 were moderately myopic. The root mean square (RMS) values of higher-order aberrations, Zernike coefficients (third-, fourth- and fifth-order aberrations) and Rj (the ratio of third-, fourth- or fifth-order aberrations to total higher-order aberrations) were compared across the three refractive groups.

Results:  No significant correlations were found between the RMS values of total higher-order aberrations, third-order aberrations, fourth-order aberrations, fifth-order aberrations, spherical aberration or coma and SER. No significant differences in the RMS values of total higher-order aberrations or Rj were observed among the groups. The difference in fifth-order aberrations was statistically significant among the groups (p = 0.022); no other differences in higher-order aberration were found. Aside from C (3,1), no other differences were observed for Zernike coefficients.

Conclusion:  Ocular wavefront aberrations are similar among Chinese school children with different refractive errors under natural accommodation for a distance target. There is no evidence that myopes have a different amount of ocular higher-order aberrations than emmetropes.

The human eye has a series of deficiencies in the optical path from the tear film to the retina that result in ocular wavefront aberrations. Measurement of these aberrations was first accomplished in 1894 by Tscherning1 and objective measurement using a Hartmann-Shack wavefront sensor was later accomplished in1994.2 Measurement of wavefront aberrations has now been widely used to evaluate the eye.

Optimal retinal image quality might induce the process of emmetropisation.3 As one of the contributing factors, wavefront aberrations might have an impact on visual development. Accordingly, there have been numerous studies investigating the potential relationship between wavefront aberrations and refractive error, although no consistent conclusions have been drawn. Some previous studies found a greater amount of higher-order aberrations4,5 or smaller spherical aberration6 (SA) in myopic eyes compared with emmetropic eyes. Similarly, animal experiments showed a higher amount of wavefront aberrations in form-deprived eyes with myopia.7–9 In contrast, other studies reported no significant differences in higher-order aberration across different refractive error groups.10–12

A wide age range of subjects might have been a confounding factor in previous experiments, as ocular wavefront aberrations vary with age.13–17 Furthermore, wavefront aberrations also vary with accommodation, with a typical trend towards negative spherical aberration during accommodation.18–20 Optical quality of the eye is largely dependent on the balance and interaction between the cornea and crystalline lens. Cycloplegic agents can reverse the spherical aberration from negative to positive,21 which could be attributed to the anatomical changes in crystalline lens shape;22 however, wavefront aberrations in some of the previous studies were obtained after cycloplegia, not under normal physiological conditions like in the real world. The purpose of the present study is to re-examine the relationship between ocular wavefront aberrations and refractive error in Chinese school children under natural distance accommodation.

METHODS

  1. Top of page
  2. Abstract
  3. METHODS
  4. RESULTS
  5. DISCUSSION
  6. REFERENCES

Subjects

All subjects were recruited from the Department of Ophthalmology and Vision Science of Fudan University Eye and the ENT Hospital in Shanghai, China. Eighty-six Chinese children (41 boys, 45 girls) aged 10.0 ± 1.9 years were enrolled. Mean age was 10.2 ± 1.8 years (range: seven to 13) for boys and 9.8 ± 1.9 years (range: seven to 13) for girls. There was no significant difference in age between genders (p = 0.27). Spherical equivalent refractions (SER) were between +0.50 D and -6.00 D and astigmatism was less than -1.00 D. Subjects were further categorised into three groups based on the mean SER of cycloplegic subjective refraction: emmetropia (SER from -0.50 D to +0.50 D); mild myopia (SER greater than -0.50 D to -3.00 D); and moderate myopia (SER greater than -3.00 D to -6.00 D). Of the 86 participants, 22 were emmetropic with a mean SER of -0.28 ± 0.39 D, 43 were mildly myopic with a mean SER of -1.92 ± 0.68 D and 21 were moderately myopic with a mean SER of -4.47 ± 0.70 D. The mean SER was -2.19 ± 1.67 D and -1.94 ± 1.74 D for boys and girls, respectively (p = 0.51). Subjects were in good ocular health, had no personal history of ocular pathology or cycloplegic agent use within the past month and had no family history of pathological myopia. All procedures conformed to the tenets of the Declaration of Helsinki and written informed consent was obtained from the children's parents or guardians. This research was approved by the Human Subjects Ethics Sub-Committee of Fudan University Eye and ENT Hospital.

Apparatus

Ocular wavefront aberrations were calculated from images recorded with an aberrometer (Schwind ORK Wavefront Analyzer, Kleinostheim, Germany) based on the Hartmann-Shack principle. The principle of this experimental system has been demonstrated in detail in previous studies.5,23,24 Wavefront aberrations were reconstructed using computer software (COAS Software Version 1.41.37, Bavaria, Germany). All data were analysed according to the Optical Society of America standards.25 A phoropter (Topcon CV3000, Tokyo, Japan) was used for cycloplegic subjective refraction.

Procedures

Before examination, the patient was positioned on a chin rest with the right eye fixated on the centre of a grid, which was optically fogged by approximately 1.50 D to avoid patient accommodation during the measurement.26 Wavefront aberrations were measured with natural pupils after adaptation to ambient dim lighting in the examination room. Three consecutive Hartmann-Shack measurements were collected for the right eye and averaged for analysis. Pupil sizes measured by the aberrometer were all larger than 5.0 mm. Children then underwent cycloplegic subjective refraction, the results of which were used to categorise the different refractive groups. Cycloplegia was reached by topical application of five drops of 0.5% tropicamide at five-minute intervals. Refractive results were obtained 30 minutes after the last eye drop.

Statistical analysis

Analysis of wavefront aberration coefficients was based on a common pupil size of 5.0 mm. To determine the effects of each higher-order aberration on total higher-order aberrations in different refractive error groups, we used an equation to calculate the ratio, Rj:

Rj= RMSj/RMSt,

where RMS represents the root mean square, j represents the third-, fourth- or fifth-order aberrations and t represents the total higher-order aberrations.

Independent-samples t-tests were used to compare mean age and SER between genders. Linear regression was performed to assess the associations between the RMS values of total higher-order aberrations, third-, fourth- and fifth-order aberrations, spherical aberration and coma with SER. One-way analysis of variance (ANOVA) was used to compare the total higher-order aberrations, wavefront error from third- to eighth-order aberrations, Zernike coefficients from third- to fifth-order aberrations and Rj among the groups. If ANOVA showed a significant difference, a Bonferroni post-hoc test was applied to determine if there were significant differences between pairs of groups. Moreover, a paired-samples t-test was performed to compare SER measured by the wavefront sensor and the phoropter. A significance level of α= 0.05 was used for all tests.

RESULTS

  1. Top of page
  2. Abstract
  3. METHODS
  4. RESULTS
  5. DISCUSSION
  6. REFERENCES

Figure 1 shows no significant association between the RMS values of total higher-order aberrations and SER (r = 0.062, p = 0.57). No significant correlations were found between the RMS values of third-order aberrations (r = 0.098, p = 0.37), fourth-order aberrations (r = 0.024, p = 0.83), fifth-order aberrations (r = 0.106, p = 0.33), spherical aberration (r = 0.093, p = 0.40) or coma (r = 0.013, p = 0.91) and SER.

image

Figure 1. No significant correlation was found between the RMS values of total higher-order aberrations and spherical equivalent refraction (r = 0.062, p = 0.57). RMS: root mean square, SER: spherical equivalent refraction.

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As illustrated in Figure 2, one-way ANOVA shows that the difference in mean RMS values of total higher-order aberrations among the three groups was not statistically significant (F = 0.154, p = 0.86). The difference in RMS values of fifth-order aberrations among the groups was statistically significant (F = 4.019, p = 0.022). A Bonferroni post-hoc test further revealed the mean RMS value of fifth-order aberrations was larger in the emmetropic group compared with the mild myopic group (p = 0.017). No significant difference was found between the emmetropic and moderate myopic groups (p = 0.32) or between the mild and moderate myopic groups (p = 1.00). No differences in the RMS values of the other higher-order aberrations were found among the different refractive error groups.

image

Figure 2. Mean RMS value ± standard deviation (SD) of each higher-order and total higher-order aberrations in different refractive groups. Error bars indicate the standard error of the mean. *: significant at the 0.05 level, HO: higher-order, RMS: root mean square.

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Zernike coefficients of higher-order (third-, fourth- and fifth-order) aberrations are presented in Figure 3. There was a significant difference in horizontal coma C (3,1) among the three refractive error groups (F = 3.137, p = 0.049), with no significant differences for paired comparisons. No other Zernike coefficients differed significantly among the three refractive error groups. As shown in Table 1, no significant differences in R3 and R5 were found among the three groups. R4 could not be compared due to not having a normal distribution.

image

Figure 3. Comparisons of Zernike coefficients in the third-, fourth- and fifth-order aberrations and coma among the three refractive groups. Error bars indicate the standard error of the mean. *: significant at the 0.05 level.

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Table 1. Rj± SD in the three groups; Rj= RMSj/RMSt, where j represents the third-, fourth- or fifth-order aberrations and t represents the total higher-order aberrations
 R3R4R5
  1. —: cannot be compared, ANOVA: analysis of variance, RMS: root mean square, SD: standard deviation

Emmetropia0.70 ± 0.170.50 ± 0.160.27 ± 0.13
Mild myopia0.71 ± 0.170.52 ± 0.200.22 ± 0.09
Moderate myopia0.79 ± 0.120.47 ± 0.150.23 ± 0.10
ANOVAp = 0.14p = 0.15

Mean SER measured by the wavefront sensor and phoropter were -2.62 ± 1.69 D and -2.06 ± 1.70 D, respectively. This difference was statistically significant (-0.56 ± 0.31 D; p < 0.001).

DISCUSSION

  1. Top of page
  2. Abstract
  3. METHODS
  4. RESULTS
  5. DISCUSSION
  6. REFERENCES

In the present study, no significant correlations were found between the RMS values of total higher-order aberrations, third-, fourth- and fifth-order aberrations, spherical aberration or coma and SER. No significant differences in the RMS values of most of the higher-order aberrations were observed among the three refractive groups. The third- to fifth-order aberrations contributed most to the total higher-order aberrations, yet no significant differences in Rj were found among the different refractive groups.

Direct comparison between the present results and those from previous investigations is complicated by several confounding factors. First, most previous experiments obtained wavefront aberrations measurements after cycloplegia, rather than under conditions of natural pupils and accommodation. In a large population study of 200 young adult eyes, Cheng and colleagues11 found that the RMS values of third- and fourth-order aberrations and spherical aberration in myopic eyes were not significantly different from those of emmetropic eyes after cycloplegia. A similar study by Carkeet and colleagues10 revealed no significant differences in higher-order aberrations across different refractive error groups in school children. Paralysis of the ciliary muscles could significantly reshape the crystalline lens, rendering differences in aberration levels between the cycloplegic and physiological conditions. In the current study, patients were undilated and optically fogged by approximately 1.50 D to avoid accommodation during the measurement using the fogging technique by the aberrometer.26 The wavefront sensor used only C (2,0) (defocus) to compute the spherical equivalent power. Consequently, the difference between SER measured using the wavefront sensor and phoropter was merely -0.56 ± 0.31 D, indicating that accommodation was well controlled during measurements and accommodation-related changes in aberrations were relatively moderate. Furthermore, Holzer, Sassenroth and Auffarth26 have shown good reliability and repeatability using the Hartmann-Shack wavefront sensor with natural pupils in young subjects.

Additionally, most previous studies on wavefront aberrations were done in older subjects. Some previous studies found that higher-order aberrations and spherical aberration increased with age from childhood to advanced age due to changes in the lens;14,15,17 however, Brunette and colleagues24 found that higher-order aberrations and spherical aberration initially decreased with age, reached a minimum level during the fourth decade of life and then increased. In this present study, a narrow age band was used to minimise the confounding effect of age on wavefront aberrations. The average RMS value of 0.180 µm for total higher-order aberrations acquired in the present study was similar to that reported by Carkeet and colleagues.10 Both of these studies were conducted on school children. Moreover, the RMS values of higher-order aberrations were significantly larger than those reported by Kwan, Yip and Yap6 and Collins, Wildsoet and Atchison,27 who evaluated adult populations. These comparisons are in good agreement with the trend of wavefront aberration as a function of age reported by Brunette and colleagues.24

In the present study, the difference in fifth-order aberration was statistically significant but clinically negligible among the three groups (mean RMS value: 0.012 µm). The result was in agreement with the findings of He and colleagues4 and investigations are needed to confirm this finding. It is interesting to note that there was a statistical difference in C (3,1) among the three refractive error groups (p = 0.049), although Bonferroni post-hoc tests showed no significant differences between pairs of groups (Figure 3). According to the results of Carkeet and colleagues10 and Atchison, Schmid and Pritchard,12 the average value of C (3,1) in all subjects was significantly different from zero but no comparisons were performed among different refractive error groups in their studies. In the present study, it was difficult to elucidate the positive finding in C (3,1) among the groups. It could simply be due to a small sample in the study population, because coma as a whole was not different. Further studies with a larger sample are warranted.

The current study was of a cross-sectional design, which might not clarify the impact of wavefront aberrations on refractive development. Numerous studies have focussed on the possible relationship between wavefront aberrations and myopia with similar designs, yet no definitive conclusions have been drawn. Longitudinal, prospective studies are required to provide further insight into the notion of causality in the question of eye growth and development.

In conclusion, we found that ocular higher-order aberrations are similar among Chinese school children with different refractive errors under natural distance accommodation. There is no evidence that myopes have a different amount of ocular higher-order aberrations than emmetropes.

REFERENCES

  1. Top of page
  2. Abstract
  3. METHODS
  4. RESULTS
  5. DISCUSSION
  6. REFERENCES