Contribution of Ocular Residual Astigmatism to Anterior Corneal Astigmatism in Children with Low and Moderate Myopia


 To assess the contribution of ocular residual astigmatism (ORA) to anterior corneal astigmatism (ACA) in children with low and moderate myopia. Refractive astigmatism (RA) were received by subjective manifest refraction. ACA were obtained by IOL Master. Using Thibos vector analysis to calculate ORA. Correlation analysis was used to assess the relationship between the magnitude of ORA and ACA. The contribution of ORA to ACA was evaluated by Physical method. The study analyzed 241 right eyes of 241 children aged 8 to 18 years old. In this study, the median magnitude of ORA was 1.02 D, with interquartile range was 0.58 D. Against-the-rule ORA was seen in 232 eyes (96.3%). There was a significant and moderate correlation between ORA and ACA (r = 0.50, P < 0.001). The ORA in 240 eyes (99.6%) had a compensatory effects on ACA. The mean compensation value was 1.00 ± 0.41 D. Based on this effect, 37 eyes had different axial classification of ACA and RA. By contrast, one eye (0.4%) had oblique ORA and superimposed with-the-rule ACA. The magnitude of ORA was relatively huge in myopia children and predominantly compensated ACA. The ORA should be assessed first before fitting orthokeratology.


Introduction
Astigmatism is a common optical defect and prevails in human eyes. [1][2][3] It is defined as the difference in power between the steep and flat ocular meridians, which causes each point from an object is refracted into two line foci with specific orientations. 2 Significant astigmatism ( ≥1.0 D) reduces visual acuity, interferes with visual development and causes various symptoms like glare, monocular diplopia, asthenopia, and distortion. 2,4 The effect of against-the-rule (ATR) astigmatism on vision is greater than with-the-rule (WTR) astigmatism. Children with ATR astigmatism had higher risk of myopia than those with WTR astigmatism. 5 It is more difficult to treat astigmatism compared to other refractive errors.
Refractive astigmatism (RA), anterior corneal (ACA) and ocular residual astigmatism (ORA) are different types of astigmatism. RA is the result of the combination of ACA and ORA. It should be accentuated that ORA is mainly crystalline lens in origin, but not exclusively ascribed to it. 1 The ORA is composed of posterior corneal surface, crystalline lens, a lesser extent vitreous, retina with the perceptual physiology. 1,3,6 ORA were frequently calculated by the vectorial difference between RA and ACA. Previously studies had shown that ACA were mainly WTR astigmatism, whereas most of ORA showed ATR astigmatism. 3,7 So it is generally believed that the ORA provided a compensatory effects for ACA. [8][9][10] But so far, there is few detailed information on these effects.
Myopia is the most common ametropia, especially in school-aged children. Modern overnight orthokeratology can diminish refractive error rapidly, reliably, and reversibly. 11 It had been widely accepted due to safe, effective, reversible. The essence of orthokeratology is to shape the corneal epithelium. To be specific, orthokeratology causes central corneal epithelium thinning and mid-peripheral cornea epithelium thickening, [12][13][14] while without changing posterior corneal radius. [15][16] Multiple studies have demonstrated that orthokeratology can reduce the ACA significantly. [17][18][19] As a result, the ORA were exposed after orthokeratology treatment. As mentioned previously, ORA is mainly ATR astigmatism, which has greater interference effects on visual quality than RA (mainly WTR astigmatism). On the other hand, it's important for understanding the course of the eye's refraction to make clear distribution of the astigmatism components. 2,3 The purpose of this study was investigate the distributional characteristics of various types of astigmatism and assess the specific contribution of ORA to ACA in children with orthokeratology indications. To provide data for improving the effectiveness of orthokeratology treatment.

Materials and Methods
This study followed the tenets of the Declaration of Helsinki and was approved by Lianyungang Maternal and Child Health Hospital review board. Informed consent was obtained from at least one parent of all participating children after explanation of the nature of the study.

Participants Selection
This cross-sectional study was conducted on 241 eyes of 241 subjects aged 8-18 years. Patients were included in this study if they had myopic from -5.00 to -1.00 D and regular astigmatism between -3.00D to -0.25 D (ATR and oblique astigmatism are no less than -2.00 D), and best corrected monocular visual acuity 20/20 or better. The exclusion criteria included any organic diseases of eyes such as cataract, glaucoma, keratoconus, irregular astigmatism, nystagmus and children with strabismus. When RA was 0, it is unable to determine the properties of RA's axis. Therefore, they were also excluded. Finally, a total of 241 children met the inclusion criteria: 102 females and 139 males. The mean age was 11.8 ± 2.2 years. Only right eyes data are taken for analysis.

Examination protocol and collect parameters
Standard subjective refraction tests were performed, and the RA was received by subjective manifest refraction. The ACA was the power difference between the steep and flat meridians on the anterior corneal surface. The IOL-Master 500 (Carl Zeiss, Meditec AG Jena, Germany) was used to measure anterior corneal curvature. Multiplying the curvature by 0.3375 to calculate corneal power. Three consistent measurements were collected and the averages were analysed. 3

Data analysis and calculations
As described in our previous article, 20 the positive cylinder notation is more consistent with the laws of physics and mathematics. So both RA and ACA are converted into the positive-cylinder notation before calculation. In addition, RA was transformed into corneal plane before calculating ORA.
RA and ACA were transformed into power vector components using Thibos method: 21 where J0 and J45 were the horizontal/vertical and oblique components of astigmatism, respectively, and β was the positive-cylinder axis.
The components of ORA were determined as: According to the vector relationship of ORA, ACA and RA at the double angle vector diagram, the only corresponding positive cylinder axis of ORA (βORA) was defined. 20 For describing the distribution of astigmatic axes, with-the-rule astigmatism was determined as positive-cylinder axes from 60°to 120°, and against-the-rule astigmatism as positive-cylinder axes from 1° to 30°or 150° to 180°. Oblique astigmatism was defined as positive-cylinder axes from 31° to 59°or 121° to 149°. Analysis process of the contribution of ORA to ACA When the difference of vector angle between ORA and ACA was greater than 90°on the double angle vector diagram, ORA will compensate ACA. 20 The compensation values (CV) were calculated by multiplying ORA by cosine (180°-α), where α (rang 90°to 180°) was the included angle between vector of ORA and ACA on the double angle vector diagram ( Figure 1).

Statistical methods
SPSS statistics software package version 17.0 for Windows (IBM, Armonk, NY, USA) was used for the statistical analysis and calculations. Normality of all data samples was checked by means of the Kolmogorov-Smirnov test. The magnitude of RA, ORA, spherical refraction and spherical equivalent refraction (SER) were non-normally distributed. The non-normality measurement data were expressed as median value and interquartile range (IQR). The magnitude of ACA was normally distributed and was expressed as mean ± standard deviation (SD). Correlation coefficients (Pearson or Spearman depending if normality condition could be assumed) were used to assess the correlation of ORA and ACA. Correlations were considered to be statistically significant when the associated p-value was＜0.05.

Characteristics of the study population
Of 241 patients (241 right eyes), 139 (57.7%) were male. Mean age of patients was11.8 years old (SD: 2.2; range: 8-18 years). The sphere refraction ranged -5.00 D to -1.00 D (median value was -3.00 D, IQR was 2.0 D). The myopia was -3.00 or less in 54.8% (132 eyes). The SE ranged -6.25 D to -1.13 D (median value was -3.38 D, IQR was 2.0 D). At the corneal plane, the ACA was 1.00 or more in 85.5% (206 eyes) with mean ACA was 1.63 ± 0.62 (range 0.25 D to 3.54 D) . The RA ranged 0.22 D to 2.63 D (median value was 0.49 D, IQR was 0.46 D), 48 eyes (19.9%) were 1.00 D or more RA. The ORA ranged 0.28 D to 2.48 D (median value was 1.02 D, IQR was 0.58 D) and it was 1.00 or more in 51.5% (124 eyes). Table 1 indicates the patient's characteristics.     (Table  3). In the other hand, one eye with oblique ORA shown superimposed effect on WTR ACA. The contribution of ORA to ATR and oblique ACA One eye with oblique ORA and one eye with WTR ORA played a compensatory effects on ATR ACA. Three eyes with ATR ORA and one eye with WTR ORA exhibited compensatory effects on oblique ACA (Table 2).   3 and Singapore (19.2%) 22 or lower than Hong Kong (28.4%) 23 and Taiwan (32.6%). 24 Whereas, the prevalence of ACA (85.5%) and ORA (51.5%) were significantly higher than those studies. 3,25 Meanwhile, the magnitude of ORA was larger than other studies. Li et al. 3 analysed 1783 12-year-old students and reported the mean ORA was 0.72 D. Huynh et al. 8 found the mean ORA was 0.76 D in 6-year-old children. One possibility to reconcile these results is that the ACA and ORA of myope was significantly larger than that of emmetropia and hyperopia. Another possibility is the compensation effects of ORA to ACA in myope were more significantly than other refractive states.

Distribution of astigmatism
With respect to the relationship of ORA and ACA, the prevailing wisdom was that the ORA compensated ACA. [8][9][10] Although our recent work evaluates the contribution of ORA to ACA in 5-year-old children with significant astigmatism, 20 but there are still no detailed information on the compensation effects in myope children. In this group of data, 235 eyes (97.6%) had WTR ACA, 2 eyes (0.8%) were ATR ACA, and 4 eyes (1.6%) shown oblique ACA. In comparison, ATR ORA was seen in 232 eyes (96.3%), WTR ORA was observed in 2 eyes (0.8%), and oblique ORA was discovered in 7 eyes (2.9%). There was a significant and moderate correlations between the magnitude of ORA and ACA (r =0.50, P < 0.001). The ORA in 240 eyes (99.6%) had a compensatory effects on ACA. The compensation values of 6.7% (16 / 240) eyes exceeded that of ACA. The distribution of astigmatic axes of 15.4% (37 / 240) eyes changed after the compensation effects (ie. the axial classification of ACA and RA were different). For 235 eyes with WTR ACA, 99.6% (234 / 235) ORA worked to offset it. Both ATR and oblique ORA can counteract WTR ACA, while oblique ORA also can superimposed it. The results was similar to our recent study in in 5-year-old children with significant astigmatism. 20 With regard to ATR ACA, both WTR and oblique ORA had a compensatory effects on it. WTR and ATR ORA can counteract oblique ACA.
Multiple studies have demonstrated that orthokeratology causes significant changes in corneal astigmatism. [17][18][19] Mountford and Pesudovs 17 stated 87.0% of patients with reverse geometry orthokeratology lenses had some reduction of ACA in their study. Chan 18 reported reductions in ACA of up to -2.50 D three weeks after toric orthokeratology treatment(1.5D). Chen et al. 19 investigated 35 myopic children with moderate-to-high astigmatism, and found a 79 percent reduction in ACA after one month of toric orthokeratology. As mentioned previous, orthokeratology did not change the posterior cornea radius. [15][16] Consequently, the ORA were exposed after orthokeratology treatment. Relatively large amounts of ORA which is mainly against-the-rule astigmatism existed in 12-year-old children with orthokeratology indications, it may one of the reasons to degrade visual quality after orthokeratology. As Sorbara et al. 26 found that the proportion of subjects with spectacles reaching 6/6 or better visual acuity was higher than those wearing orthokeratology lens ( 89% vs 83%). Unfortunately, there is no study on the relationship between ORA and orthokeratology up to now. Future research needs to be done in the correlation between ORA and residual astigmatism after shaping with orthokeratology, and in the specific influence of ORA to visual quality after orthokeratology.
In conclusion, for low and moderate myopia eyes, we found the prevalence of ORA (≥ 1.0 D) was relatively high and the magnitude was huge, nearly all (99.6%) ORA compensate ACA, the magnitude of CV/ACA exceeded 1.00 in 6.7%(16/240) eyes, and 15.4% (37/240) eyes had different axial classification of ACA and RA after the compensation effects. The ORA were exposed after orthokeratology treatment. So, the ocular residual astigmatism should be assessed first before the completion of a course of orthokeratology. In addition, more attention should be paid to the specific influence of ORA to the effective of orthokeratology.