Impact of Ocular Residual Astigmatism On Anterior Corneal Astigmatism In Children With Low And Moderate Myopia

Background: To assess the inuence of ocular residual astigmatism to anterior corneal astigmatism in children with low and moderate myopia. Methods: Refractive astigmatism was obtained by subjective manifest refraction. Anterior corneal astigmatism was obtained by IOL Master. Using Thibos vector analysis to calculate ocular residual astigmatism. Correlation analysis was used to assess the relationship between the magnitude of ocular residual astigmatism and anterior corneal astigmatism. The inuence of ocular residual astigmatism to anterior corneal astigmatism was evaluated by Physical method. Results: The study analyzed 241 right eyes of 241 children aged 8 to 18 years old. In this study, the median magnitude of ocular residual astigmatism was 1.02 D, with interquartile range was 0.58 D. Against-the-rule ocular residual astigmatism was seen in 232 eyes (96.3%). There was a signicant and moderate correlation between ocular residual astigmatism and anterior corneal astigmatism (r = 0.50, P < 0.001). The ocular residual astigmatism in 240 eyes (99.6%) had a compensatory effects on anterior corneal astigmatism. The mean compensation value was 1.00 ± 0.41 D (rang 0.02 D to 2.34 D). Based on this effect, 37 eyes had different axial classication of anterior corneal astigmatism and refractive astigmatism. By contrast, one eye (0.4%) had oblique ocular residual astigmatism and superimposed with-the-rule anterior corneal astigmatism. Conclusions: The magnitude of ocular residual astigmatism was relatively huge in myopia children and predominantly compensated anterior corneal astigmatism. The ocular residual astigmatism should be assessed rst tting


Background
Astigmatism is a common optical defect and prevails in human eyes. [1][2][3] It is de ned as the difference in power between the steep and at ocular meridians, which causes each point from an object is refracted into two line foci with speci c orientations. 2 Signi cant astigmatism ( ≥1.0 D) reduces visual acuity, interferes with visual development and causes various symptoms like glare, monocular diplopia, asthenopia, and distortion. 2,4 Children with against-the-rule (ATR) astigmatism had higher risk of myopia than those with with-the-rule (WTR) astigmatism. 5 It is more di cult 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. 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 was mainly WTR astigmatism, 3 whereas most of the ORA Page 3/13 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 are few detailed informations 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 speci c, 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 signi cantly. [17][18][19] As a result, the ORA was exposed after orthokeratology treatment. As mentioned previously, ORA is mainly ATR astigmatism, which has higher risk of myopia than RA (mainly WTR astigmatism). On the other hand, it's important to understand 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 speci c effect 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 at 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 J 0 and J 45 were the horizontal/vertical and oblique components of astigmatism, respectively, and β was the positive-cylinder axis.
The components of ORA were determined as: So the magnitude and axis (β ORA ) of ORA were calculated 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 (β ORA ) was de ned. 20 For describing the distribution of astigmatic axes, with-the-rule astigmatism was determined as positivecylinder 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 de ned as positive-cylinder axes from 31° to 59°or 121° to 149°.

Analysis Process Of The Effect 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 coe cients (Pearson or Spearman depending if normality condition could be assumed) were used to assess the correlation between ORA and ACA, ORA and RA. Correlations were considered to be statistically signi cant 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 SER 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 effects 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 but lower than Hong Kong (28.4%) 23 and Taiwan (32.6%). 24 Whereas, the prevalence of ACA (85.5%) and ORA (51.5%) were signi cantly 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 reason for this result is that the magnitude of ACA and ORA of myopia was signi cantly larger than that of emmetropia and hyperopia. Another possibility is the compensation effects of ORA to ACA in myopia were more signi cantly than other refractive states.
The prevailing wisdom was that the ORA compensated ACA. [8][9][10] Although our recent work evaluated the contribution of ORA to ACA in 5-year-old children, 20 but there are still no detailed information on the compensation effects in myope children. There was a signi cant and moderate correlations between the magnitude of ORA and ACA (r =0.50, P < 0.001  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 speci c in uence 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 classi cation of ACA and RA after the compensation effects. The ORA were exposed after orthokeratology treatment. So, the ocular residual astigmatism should be assessed rst before the completion of a course of orthokeratology. In addition, more attention should be paid to the speci c in uence of ORA to the effective of orthokeratology. Committee of Lianyungang Maternal and Child Health Hospital. The authors con rm that the research followed the tenets of the Declaration of Helsinki and that informed consent was obtained from the subjects after explanation of the nature and possible consequences of the study.

Consent for publication
Not applicable Availability of data and materials The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request. Figure 1 Calculation process of the compensation values. Distributions of different types of astigmatism.

Figure 3
Correlation between the magnitude of ORA and ACA.