Refractive errors are common in developmentally normal children, with the spherical refraction of newborns showing a normal distribution with a mean of about 2 D (± 2) of hyperopia. 1–3 Large astigmatic errors are also found more frequently in infants. 4, 5 The active process of emmetropization 6 reduces the magnitude and variance of both hyperopia 5, 7, 8 and astigmatism. 5, 8–15 The prevalence of astigmatism (>1 D; noncycloplegic) among infants (0 to 12 mo) has been reported to be about 45% to 53% 5, 16 and only about 2% to 4% by the age of 5 to 6 years. 13
The type of astigmatism that predominates at birth appears to vary geographically. Atkinson and Braddick 9 found a predominance of with-the-rule (WTR) astigmatism in infants (aged 6 to 9 mo) tested in Cambridge, similar to a population in Kettering, whereas there was a predominance of against-the-rule (ATR) astigmatism in infants tested at Bristol. Studies 4, 5, 12, 13, 15, 17 reporting the steady decline in astigmatism with age typically reveal a greater frequency of ATR astigmatism during the first 3 to 4 years. Longitudinal studies show that this higher prevalence of ATR astigmatism reduces sharply with age, 10, 17–19 with mild WTR astigmatism becoming the norm by school age. Children with WTR astigmatism do not show axis shifts, although their astigmatism may progress. 20
Corneal astigmatism arises from the anterior corneal surface and contributes to total astigmatism. The ocular astigmatism that cannot be attributed to the anterior corneal surface is referred to as residual, or lenticular, astigmatism (see Lyle 21 for a review). The contribution of the posterior cornea is small, given the slight difference between the indices of refraction of the cornea and aqueous compared to that of the cornea and air. Thus, total astigmatism is the sum of corneal and residual astigmatism. Studies with infants and young children indicate that astigmatism is predominantly of corneal origin. 18, 19 It has been shown that all astigmatism that is not corneal and presumably attributable to the lens is normally distributed with a mean of 0.5 D 22 and is ATR for most eyes. 23, 24 The constancy of lenticular astigmatism has been represented mathematically by Javal's rule for WTR and ATR astigmatisms (see Bannon and Walsh 25). Studies with adults and children18, 26, 27 have found that total astigmatism varies in proportion to corneal astigmatism, with the lenticular component held constant at approximately 0.50 D. It should be noted, however, that clinical studies 28, 29 point out that this relation does not hold for individuals but represents averaged data. Recent studies on ocular aberrations including astigmatism 30, 31 find that in individuals < 45 years of age, the lenticular aberrations are opposite in sign and thereby balance corneal aberrations. The data show evidence of low overall astigmatism despite high corneal astigmatism measures.
When the corneal and ocular astigmatic power axes coincide, residual astigmatism is simply calculated by subtracting corneal astigmatism from total astigmatism. 32 However, this parallel alignment is not typical, so that lenticular astigmatism cannot simply be calculated by subtracting corneal astigmatism from total astigmatism in the spherocylinder format. A recently developed method 33 allows the decomposition of spherocylinder notation, using a Fourier transformation, into the equivalent sphere (M) and two cross-cylinder components, J 0 and J 45. This decomposition provides three independent components that can be readily summed to determine corneal and lenticular contributions. The components M, J 0, and J 45 are defined as follows:EQUATION
where S is the sphere, C is the magnitude of cylinder power present, and α is the axis in radians. The J 0 component denotes a Jackson cross-cylinder with axes at 180° and 90°, and the J 45 component denotes a Jackson cross-cylinder with axes at 45° and 135°. This isolation of the astigmatic components from the equivalent sphere allows summation and analysis of all forms of astigmatism.
Previous studies 4, 5, 9, 10, 12, 13, 15, 17 have considered total astigmatism present in preschool children. However, very few studies have looked at the corneal and lenticular contributions. This has been investigated in the Native American population, 18, 34, 35 but so far as we are aware, these data are lacking in a mainly white population. Cowen and Bobier 36 looked at the total astigmatism that existed in a population of predominantly white preschool children in a single county in Canada and found that WTR astigmatism was most prevalent, followed by ATR and oblique astigmatism, respectively.
The present study was conducted to compare the relative amounts of corneal and lenticular astigmatism in children with high and moderate amounts of astigmatism and to determine whether, in the developing eye, the lenticular astigmatism increases beyond normal levels in eyes that have a high amount of corneal astigmatism.
The Nikon Retinomax K-Plus (Nikon Inc., Melville, NY) provided refractive and keratometric measures. The Retinomax has had good success in a number of studies with children in the 3- to 5-year range. 37–39 With the Retinomax, measurements can be obtained quickly, thus reducing possible errors from factors like fatigue, loss of attention, and changes in subject position. 40 However, cycloplegic testing is required to obtain accurate measures of hyperopia or myopia due to varying amounts of proximal accommodation induced by the close working distance of the instrument. 41–43 The Retinomax has been successful in assessing astigmatism 36, 39, 44 without cycloplegia because the cylinder values are not significantly affected by accommodation. 45
Subjects for this study were 129 preschool children (mean age, 51.1 ± 8.4 mo; 46.5% male and 53.5% female) randomly recruited for a follow-up study (May to July 2001) from the annual Oxford County preschool vision screening program (see Robinson et al. 46 for details).
Informed consent for participation was obtained through an information letter reviewed and returned from parents of all children enrolled in the study, and verbal assent was obtained from the participants themselves. Ethics clearance was also obtained from the Office of Research Ethics, University of Waterloo.
Noncycloplegic and cycloplegic (1 to 2 gtt. 0.5% cyclopentolate hydrochloride) autorefractive measures using two autorefractors (DAV, a prototype of Welch Allyn's SureSight, and Retinomax K-Plus), as well as cycloplegic retinoscopy measures, were obtained for all children. This study reports on the cycloplegic measurements obtained with the Retinomax K-Plus.
The Retinomax was used according to the manufacturer's specifications in the refractive and keratometry modes. All readings were taken using the automatic fogging mode, during which fogging lenses are added automatically to encourage accommodation relaxation once the eye is correctly aligned. During testing, the subject was seated with the instrument aligned to the right eye, and was asked to focus on a high-contrast target (an evergreen tree). After the instrument automatically took 8 readings, the procedure was repeated on the left eye. The Retinomax supplied a “representative” value from the 8 measurements, which was taken to be the refractive error of the subject. The representative value has a confidence value that indicates the degree of variance of the measured 8 readings. We obtained manufacturer-recommended confidence values of 8 or higher for all analyzed readings. Keratometric measurements were simultaneously obtained. The Retinomax takes 8 keratometric measurements per eye, and the supplied “representative” value was used for analyses. Normally, there is a high potential for variability in axis measurements when total astigmatism and corneal measurements are taken separately, especially when using a hand-held instrument on young children. Because in the present study the refractive and corneal measurements were obtained simultaneously, the possibility of any variability in axis measures due to variations in head orientation and/or instrument orientation between corneal and total astigmatism measures was minimized.
Wet refractive Retinomax and keratometry readings were taken for all subjects to obtain total and corneal astigmatism measures, respectively. Subjects showing ≥1 D of cylinder in one eye as measured by the Retinomax were classified as “high astigmats.” The 1.0-D cutoff for high astigmatism was selected in light of the population-based work in Oxford County. 36 A cumulative distribution of all cylinder magnitudes showed that the 95th percentile for this population was at 1.25 D, indicating that most of the children had astigmatism <1.25 D. The eye with the larger astigmatism, or the right eye, if both had equal cylinders, was taken for analyses. Subjects with ≤0.75 D of cylinder in both eyes were classified as being “normal astigmats,” and readings from the eye with the lower astigmatism, or the right eye, if both had equal cylinders, were taken for analyses. The spherocylinder values were transformed 33 into M, J 0, and J 45 and the keratometry readings into J 0 and J 45.
Classification of Subjects
Of the 129 subjects, 29 were classified as high astigmats (≥1 D of cylinder; mean, 1.38 ± 0.43 D) in one or both eyes, and the other 100 subjects were classified as normal astigmats (≤0.75 D of cylinder; mean, 0.22 ± 0.20 D). Thirteen children in the normal astigmatism group had 0 cylinder. Although no child in the normal astigmatic group had anisometropia (based on spherical equivalent difference) or strabismus, of the 29 children in the high astigmat group, 3 had anisometropia (≥1 D), 3 had strabismus, and 2 had both anisometropia and strabismus.
Prevalence of Different Forms of Astigmatism
The negative cylinder axes of the total refractive astigmatism produced by the Retinomax were classified as WTR (0° to 30° and 151° to 180°), ATR (61° to 120°), or oblique (31° to 60° and 121° to 150°). 47 The distribution of the three forms of astigmatism in the high and normal astigmats is given in Fig. 1. There was a predominance of WTR astigmatism in both the high astigmats (69%) and the normal astigmats (78%).
Components of Astigmatism: Total, Corneal, and Lenticular
Cycloplegic refractive readings obtained by the Retinomax defined the total astigmatism of subjects, and those obtained by keratometry provided the corneal astigmatism of subjects. Because lenticular astigmatism is not easily measured directly, it was obtained from the difference between total and corneal astigmatism.
The relation between corneal and lenticular astigmatism as a function of total astigmatism was determined with regression plots for high and normal astigmats. In high astigmats, corneal J 0 and J 45 were highly correlated with total J 0 and J 45 (J 0, r = 0.90, p 30.01; J 45, r = 0.73, p < 0.01). Correlations between total and lenticular J 0 and J 45 were not significant (J 0, r = −0.06, p = 0.77; J 45, r = 0.18, p = 0.36) (Fig. 2). For normal astigmats, total J 0 was significantly correlated with corneal J 0 (r = 0.38, p < 0.01). There was also a significant correlation between total and lenticular J 45 (r = 0.46, p < 0.01). No other correlation was found to be significant for the normal astigmats (Fig. 3).
Cylinder Measures Versus Fourier Transformation
The magnitudes of total and corneal cylinders were significantly greater in high astigmats, whereas overall lenticular cylinder was similar in both groups. However, when the orientation of the astigmatism was considered between high and normal astigmats, J 0 and J 45 magnitudes differed in both the lens and cornea. High astigmats had significantly higher total J 0 and J 45 and higher corneal J 0; however, lenticular J 0 remained ATR but was lower, whereas lenticular J 45 was higher than in normal astigmats (see Table 1 and Fig. 4).
Total, Corneal, and Lenticular Astigmatism for Different Forms of Astigmatism
To determine whether total, corneal, and lenticular components of astigmatism varied for the different forms of astigmatism, we reanalyzed the data separately for WTR (normal, n = 91; high, n = 20), ATR (normal, n = 5; high, n = 1), and oblique (normal. n = 4; high, n = 8) astigmats. For the WTR subjects, total J 0 (M D = 0.54, t109 = 9.93, p < 0.01), total J 45 (M D = 0.16, t109 = 4.78, p < 0.01), corneal J 0 (M D = 0.48, t109 = 5.27, p < 0.01), and lenticular J 45 (M D = 0.11, t109 = 2.52, p< 0.01) differences between high and normal astigmats were maintained, but lenticular J 0 did not differ between high and normal astigmats (Fig. 5).
For the ATR subjects, only lenticular J 45 values were higher in high astigmats than in normal astigmats (M D = 0.30, t4 = 3.04, p = 0.038), whereas no astigmatic components were different between high and normal oblique astigmats.
Classification of Subjects
In this study, 22.48% of children had clinically significant astigmatism, and 77.52% had less than a diopter, or no astigmatism, in the eye that was taken for analyses. We found a predominance of WTR astigmatism in this sample of 3- to 5-year-old children. This is consistent with findings from the population study 36 conducted in the same geographical area. Our sample had 63 children under the age of 4 years and 66 children over the age of 4 years, and the prevalence may be reflecting the reported trend of ATR astigmatism declining to mild WTR astigmatism later in childhood. 10, 17
Components of Astigmatism
Corneal astigmatism exceeded total astigmatism for both groups of subjects in our study, indicating that total astigmatism was mainly driven by corneal astigmatism, as found by others. 18, 19 There was also a significant high correlation between total astigmatism and corneal astigmatism for both groups of subjects. Native North American preschool populations show high levels of WTR astigmatism, 35 which is primarily corneal in origin, 18 and our results with mainly white children showed a similar pattern of predominantly corneal WTR astigmatism.
If the lens attenuated corneal astigmatism, a negative J 0 (ATR) would be found in the lenticular astigmatism to compensate for the high positive corneal J 0. This was not the case. Although J 0 was found to be negative, a larger negative J 0 was found in the normal astigmats compared with the high astigmats. Furthermore, lenticular J 45 added to corneal J 45 in both normal and high astigmats. Thus, no evidence was found that the lens compensated for corneal astigmatism. For this predominately WTR sample, a constant lenticular astigmatism as shown by others18, 26, 27 is supported. Thus, the finding that lenticular aberrations compensate for corneal aberrations 30, 31 was not supported in our study for astigmatism, but the subjects used for the aberration studies were adults aged 25 to 45 years with normal refractions.
Components of Astigmatism for the Different Forms
Because the population of high astigmats was predominantly WTR, the conclusions of this research may represent only WTR astigmatism. When the analysis was restricted to the highly predominant WTR astigmats, similar patterns were found. However, there was no reduction in lenticular J 0 observed in the whole group because the level of J 0 for high astigmats was similar to that of normal astigmats, suggesting no compensation for corneal astigmatism. The absence of a significant effect in this subsample may be due to reduced power due to reduced sample size. Lenticular patterns were different for ATR and oblique astigmats and may indicate that lenticular, as well as corneal, astigmatism varies, depending on the form of astigmatism, but this may be an effect of the reduced sample size and needs to be examined further.
In summary, this study found that there was a predominance of WTR astigmatism in this sample of subjects that was mainly driven by the cornea. In high astigmats, there does not seem to be any lenticular compensation for the high corneal component, and there is a slight increase in oblique astigmatism.
Astigmatism in preschool 3- to 5-year-old children is primarily corneal and predominantly WTR. However, lenticular and corneal astigmatism varies, depending on the form of astigmatism. There is no lenticular compensation for high levels of corneal astigmatism in the preschool eye, and in fact, the lens seems to act to increase the oblique astigmatic component.
Supported by grants from Welch Allyn Inc., U.S., and NSERC, Canada, to WRB. Neither author has any financial interest in the Nikon Retinomax K-Plus. Many thanks to team members Dr. C. Machan, Dr. K. Ball, R. Suryakumar, D. Wintermeyer, S. Andreason, S. Park, A. Moradian, L. Ting, B. Moyle, and I. Markeljevic for their help. Presented at the Annual Meeting of the Association for Research in Vision and Ophthalmology, in Ft. Lauder-dale, FL, 2002.
1. Banks MS. Infant refraction and accommodation. Int Ophthalmol Clin 1980;20:205–32.
2. Cook RC, Glasscock RE. Refractive and ocular findings in the newborn. Am J Ophthalmol 1951;34:1407–13.
3. Goldschmidt E. Refraction in the newborn. Acta Ophthalmol (Copenh) 1969;47:570–8.
4. Howland HC, Atkinson J, Braddick O, French J. Infant astigmatism
measured by photorefraction. Science 1978;202:331–3.
5. Mohindra I, Held R, Gwiazda J, Brill J. Astigmatism
in infants. Science 1978;202:329–31.
6. Troilo D. Neonatal eye growth and emmetropisation—a literature review. Eye 1992;6:154–60.
7. Atkinson J, Anker S, Bobier W, Braddick O, Durden K, Nardini M, Watson P. Normal emmetropization in infants with spectacle correction for hyperopia. Invest Ophthalmol Vis Sci 2000;41:3726–31.
8. Mayer DL, Hansen RM, Moore BD, Kim S, Fulton AB. Cycloplegic refractions in healthy children aged 1 through 48 months. Arch Ophthalmol 2001;119:1625–8.
9. Atkinson J, Braddick O. Vision screening and photorefraction—the relation of refractive errors to strabismus and amblyopia. Behav Brain Res 1983;10:71–80.
10. Atkinson J, Braddick O, French J. Infant astigmatism
: its disappearance with age. Vision Res 1980;20:891–3.
11. Cordonnier M, Kallay O, Kever C. Why and how to correct hypermetropia?. Bull Soc Belge Ophthalmol 1997;264:47–51.
12. Fulton AB, Dobson V, Salem D, Mar C, Petersen RA, Hansen RM. Cycloplegic refractions in infants and young children. Am J Ophthalmol 1980;90:239–47.
13. Gwiazda J, Scheiman M, Mohindra I, Held R. Astigmatism
in children: changes in axis and amount from birth to six years. Invest Ophthalmol Vis Sci 1984;25:88–92.
14. Howland HC. Infant eyes: optics and accommodation. Curr Eye Res 1982;2:217–24.
15. Howland HC, Sayles N. Photorefractive measurements of astigmatism
in infants and young children. Invest Ophthalmol Vis Sci 1984;25:93–102.
16. Gwiazda J, Mohindra I, Brill S, Held R. Infant astigmatism
and meridional amblyopia. Vision Res 1985;25:1269–76.
17. Dobson V, Fulton AB, Sebris SL. Cycloplegic refractions of infants and young children: the axis of astigmatism
. Invest Ophthalmol Vis Sci 1984;25:83–7.
18. Dobson V, Miller JM, Harvey EM. Corneal
and refractive astigmatism
in a sample of 3- to 5-year-old children with a high prevalence of astigmatism
. Optom Vis Sci 1999;76:855–60.
19. Howland HC, Sayles N. Photokeratometric and photorefractive measurements of astigmatism
in infants and young children. Vision Res 1985;25:73–81.
20. Goss DA. Childhood myopia. In: Grosvenor T, Flom MC, eds. Refractive Anomalies: Research and Clinical Applications. Boston: Butterworth-Heinemann, 1991:81–100.
21. Lyle WM. Changes in corneal astigmatism
with age. Am J Optom Arch Am Acad Optom 1971;48:467–78.
22. Hofstetter HW, Baldwin WR. Bilateral correlation of residual astigmatism
. Am J Optom 1957;34:388–91.
23. Carter JH. Residual astigmatism
of the human eye. Optom Weekly 1972;54:1271–2.
24. Neumueller J. Optical, physiological and perceptual factors influencing the ophthalmometric findings. Am J Optom Arch Am Acad Optom 1953;30:281–91.
25. Bannon RE, Walsh R. On astigmatism
, part 11: limitations of objective tests. Am J Optom Arch Am Acad Optom 1945;22:162–81.
26. Grosvenor T, Quintero S, Perrigin DM. Predicting refractive astigmatism
: a suggested simplification of Javal's rule. Am J Optom Physiol Opt 1988;65:292–7.
27. Grosvenor T, Ratnakaram R. Is the relation between keratometric astigmatism
and refractive astigmatism
linear? Optom Vis Sci 1990;67:606–9.
28. Mote HG, Fry GA. The significance of Javal's rule. Am J Optom 1939;16:362–5.
29. Elliott M, Callender MG, Elliott DB. Accuracy of Javal's rule in the determination of spectacle astigmatism
. Optom Vis Sci 1994;71:23–6.
30. Artal P, Guirao A, Berrio E, Williams DR. Compensation of corneal
aberrations by the internal optics in the human eye. J Vis 2001;1:1–8.
31. Artal P, Berrio E, Guirao A, Piers P. Contribution of the cornea and internal surfaces to the change of ocular aberrations with age. J Opt Soc Am A 2002;19:137–43.
32. Dunne MC, Elawad ME, Barnes DA. A study of the axis of orientation of residual astigmatism
. Acta Ophthalmol (Copenh) 1994;72:483–9.
33. Thibos LN, Wheeler W, Horner D. Power vectors: an application of Fourier analysis to the description and statistical analysis of refractive error. Optom Vis Sci 1997;74:367–75.
34. Heard T, Reber N, Levi D, Allen D. The refractive status of Zuni Indian children. Am J Optom Physiol Opt 1976;53:120–3.
35. Maples WC, Herrmann M, Hughes J. Corneal astigmatism
in pre-school Native Americans. J Am Optom Assoc 1997;68:87–94.
36. Cowen L, Bobier WR. The pattern of astigmatism
in a Canadian preschool population. Invest Ophthalmol Vis Sci 2003;44:4593–600.
37. Cordonnier M, Dramaix M, Kallay O, de Bideran M. How accurate is the hand-held refractor Retinomax(R) in measuring cycloplegic refraction: a further evaluation. Strabismus 1998;6:133–42.
38. Cordonnier M, Dramaix M. Screening for refractive errors in children: accuracy of the hand held refractor Retinomax to screen for astigmatism
. Br J Ophthalmol 1999;83:157–61.
39. Miller JM, Dobson V, Harvey EM, Sherrill DL. Comparison of preschool vision screening methods in a population with a high prevalence of astigmatism
. Invest Ophthalmol Vis Sci 2001;42:917–24.
40. McKendrick AM, Brennan NA. Distribution of astigmatism
in the adult population. J Opt Soc Am A 1996;13:206–14.
41. el-Defrawy S, Clarke WN, Belec F, Pham B. Evaluation of a hand-held autorefractor in children younger than 6. J Pediatr Ophthalmol Strabismus 1998;35:107–9.
42. Harvey EM, Miller JM, Dobson V, Tyszko R, Davis AL. Measurement of refractive error in Native American preschoolers: validity and reproducibility of autorefraction. Optom Vis Sci 2000;77:140–9.
43. Wesemann W, Dick B. Accuracy and accommodation capability of a handheld autorefractor. J Cataract Refract Surg 2000;26:62–70.
44. Cordonnier M, Kallay O. Non-cycloplegic screening for refractive errors in children with the hand-held autorefractor Retinomax: final results and comparison with non-cycloplegic photoscreening. Strabismus 2001;9:59–70.
45. Millodot M, Thibault C. Variation of astigmatism
with accommodation and its relationship with dark focus. Ophthalmol Physiol Opt 1985;5:297–301.
46. Robinson B, Bobier WR, Martin E, Bryant L. Measurement of the validity of a preschool vision screening program. Am J Public Health 1999;89:193–8.
47. Borish IM. Clinical Refraction, 3rd ed. Chicago: Professional Press, 1975.
Keywords:© 2004 American Academy of Optometry
astigmatism; Retinomax K-Plus; corneal; lenticular; preschool children