Significant Loss of Coordination Among Astigmatism Components in Young Chinese Adults With High Myopia

Abstract

Purpose: To investigate the coordination among astigmatism components, including refractive astigmatism (RA), corneal astigmatism (CA), and internal astigmatism (IA), across refractive statuses in a large cycloplegic sample of Chinese young adults.

Methods: This cross-sectional study included 7971 undergraduate students in China. Cycloplegic refraction and ocular biometric were measured using an autorefractor and optical biometry. IA was calculated as the vector difference between RA and CA. Relationships among astigmatism components, refractive errors, and ocular parameters were analyzed using generalized additive models, smoothed curve fitting, and threshold effect analysis.

Results: A total of 7315 young adults (mean age = 20.2 ± 1.5 years; 37.0% male) were included. The prevalence rates of RA, CA, and IA (≥1.0 D) were 16.4%, 36.7%, and 12.2%, respectively. RA and CA were significantly higher in the high myopia, moderate myopia, and moderate hyperopia groups compared to the emmetropia group, while IA was significantly smaller only in the high myopia group (P < 0.001). Piecewise relationships among RA, CA, and IA with refractive errors were identified. RA and CA showed a significant increase, whereas IA decreased in moderate and high myopia. Furthermore, the compensatory effect of IA was significantly reduced in the high myopia group.

Conclusions: The components of astigmatism demonstrated coordination from low myopia to low hyperopia, but this coordination was reduced in high myopia.

Translational Relevance: Greater attention should be paid to changes in astigmatism components and their coordination in high myopia.

Introduction

Astigmatism is a common refractive error resulting from variations in refractive power along different meridians of the eye.^1,2 Previous meta-analysis has identified astigmatism as the most prevalent refractive error, with a global pooled prevalence of 40% in adults over 30 years old.³ Astigmatism reduces visual quality, impairing visual acuity and contrast sensitivity, and may cause discomfort, such as glare and halos, while also affecting the speed and accuracy of vision-dependent tasks.^2,4,5 Additionally, it can impose a significant economic burden and reduce productivity, particularly among working-age adults.¹ 

Refractive astigmatism (RA) arises from the combined effects of corneal astigmatism (CA) and internal astigmatism (IA).⁶ IA includes astigmatism originating from the posterior corneal surface, crystalline lens, and aqueous humor.^2,7 Previous studies have shown that both the magnitude and axis of astigmatism can influence myopia progression.⁸ A comprehensive understanding of RA, CA and IA is essential for gaining insights into the development and progression of ocular refraction, which is critical for constructing accurate refractive models and managing astigmatism effectively, particularly in corneal refractive surgery.^9–12 

Numerous studies have examined the relationship between astigmatism and refractive errors, often observing that RA values increase as refractive errors worsen,^9,10,13 especially in myopic patients.^14–20 Some studies also report a compensatory role of IA^10,13; however, findings on IA's relationship with refractive error have been inconsistent. Although some studies have indicated that IA remains constant across refractive statuses,^9,18 other studies suggest a positive association with refractive status.^10,19,21,22 Despite these findings, few studies have focused on cycloplegic refractive measurements in young adults,²³ a crucial age group representing the final stage of childhood myopia progression. This study therefore aimed to investigate the coordination among astigmatism components, specifically RA, CA, and IA, across different refractive statuses. 

Methods

Study Population

This report is a part of the Anyang University Students Eye Study (AUSES), whose detailed methodology has been previously described.^24–28 Briefly, AUSES is a cross-sectional study conducted between September 2016 and June 2017 at two universities in Anyang City, Henan Province, central China, involving 7971 students. Students with systemic diseases, or any past or present eye diseases or injuries, were excluded. Comprehensive cycloplegic eye examinations were performed on all participants. The study was approved by the Ethics Committee of Beijing Tongren Hospital, Capital Medical University, and informed consent was obtained from all participants in accordance with the principles of the Declaration of Helsinki. 

Ocular Examination

Participants underwent comprehensive and standardized eye examinations at the university clinic. Cycloplegic refractive errors were measured three times using an autorefractor (HUVITZ HRK-7000A; Huvitz, Gunpo, South Korea), and the average value was recorded. The procedure for achieving full cycloplegia has been described previously.²⁹ Briefly, two drops of 1% cyclopentolate (Alcon, Geneva, Switzerland) were administered, followed by one drop of Mydrin P (Santen, Japan) at five-minute intervals. If, after 30 minutes, the pupillary light reflex persisted or the pupil size was less than 6.0 mm, a third drop of 1% cyclopentolate was given. Axial length (AL) and keratometry were measured using optical biometry (Lenstar LS900; Haag-Streit, Koeniz, Switzerland), with five measurements averaged for each parameter.²⁵ 

Definitions

RA, CA, and IA were calculated as negative corrective cylinders. RA was derived from the cycloplegic autorefractor output (vertex distance 12 mm), whereas CA was calculated as the difference between the corneal powers of the principal meridians, as measured via optical biometry, with the CA axis set along the meridian of least power. RA at the spectacle plane (12 mm vertex distance) was converted to corneal-plane equivalent power (RA_c) through vergence transformation of both steep and flat principal meridians using:  

\begin{eqnarray*} F\!c = \frac{{F\!s}}{{1 - d \cdot F\!s}} \end{eqnarray*}

where Fc was the corneal plane power (D), Fs was the spectacle plane power (D), and d was the vertex distance (0.012 m). The magnitude of RA_c was determined by the dioptric difference between transformed meridians, preserving the original cylindrical axis orientation. RA_c and CA were converted to power vector notation using the vector method, resulting in horizontal/vertical (J0) and oblique (J45) vectors according to the following formulas³⁰:  

\begin{eqnarray*} {{J}_0} = - \frac{C}{2}\cos \left( {2\alpha } \right) \end{eqnarray*}

 

\begin{eqnarray*} {{J}_{45}} = - \frac{C}{2}\sin \left( {2\alpha } \right) \end{eqnarray*}

where C is the cylinder power and α is the cylinder axis. The J0 vector represents a cylinder with axes at 180° and 90°, whereas the J45 vector represents a cylinder with axes at 45° and 135°. The vector of IA was computed as the difference between RA_c and CA:  

\begin{eqnarray*} {{J}_{0\left( {IA} \right)}} = {{J}_{0\left( {RA\_c} \right)}} - {{J}_{0\left( {CA} \right)}} \end{eqnarray*}

 

\begin{eqnarray*} {{J}_{45\left( {IA} \right)}} = {{J}_{45\left( {RA\_c} \right)}} - {{J}_{45\left( {CA} \right)}} \end{eqnarray*}

J_0(IA) and J_45(IA) were then combined to determine IA as a negative corrective cylinder along the IA axis using the following formulas:  

\begin{eqnarray*} IA = - 2\sqrt {{{J}_{45\left( {IA} \right)}}^2 + {{J}_{45\left( {IA} \right)}}^2} \end{eqnarray*}

 

\begin{eqnarray*}{{\alpha }_{IA}} = \frac{1}{2}{{\tan }^{ - 1}}\frac{{{{J}_{45\left( {IA} \right)}}}}{{{{J}_{0\left( {IA} \right)}}}}\end{eqnarray*}

 

\begin{eqnarray*}0^\circ < {{\alpha }_{IA}} \le 180^\circ \end{eqnarray*}

 

The compensation factor (CF) was calculated with the following formulas:  

\begin{eqnarray*}C{{F}_0} = ({{J}_{0\left( {CA} \right)}} - {{J}_{0\left( {RA\_c} \right)}})/{{J}_{0\left( {CA} \right)}}\end{eqnarray*}

 

\begin{eqnarray*}C{{F}_{45}} = ({{J}_{45\left( {CA} \right)}} - {{J}_{45\left( {RA\_c} \right)}})/{{J}_{45\left( {CA} \right)}}\end{eqnarray*}

 

The CF values were classified into six categories: (1) same-axis augmentation (CF < −0.1); (2) no compensation (−0.1 ≤ CF ≤ 0.1); (3) undercompensation (0.1 < CF < 0.9); (4) full compensation (0.9 ≤ CF ≤ 1.1); (5) overcompensation (1.1 < CF ≤ 2); and (6) opposite-axis augmentation (CF > 2). 

Astigmatism was initially recorded in negative cylinder format, but for further analysis, the sign was disregarded. RA was measured at the spectacle plane (vertex distance 12 mm) and converted to the corneal plane (vertex distance 0 mm) as RA_c, ensuring RA_c, CA, and IA were all referenced to the same corneal plane. To enable comparisons with other studies, the prevalence of RA, CA, and IA was assessed at thresholds of ≥0.50 D, ≥0.75 D, ≥1.00 D, and ≥1.50 D.^9,11,31 The spherical equivalent (SE) refractive error was calculated as the spherical power plus half the cylinder power, while the axial length-to-corneal radius (AL/CR) ratio was determined as the axial length divided by the average corneal radius across the two principal meridians.³² Refractive status was categorized as follows: high myopia (SE ≤ −6.00 D), moderate myopia (−6.00 D < SE ≤ −3.00 D), low myopia (−3.00 D < SE ≤ −0.50 D), emmetropia (−0.50 D < SE < 0.50 D), low hyperopia (0.50 D ≤ SE < 2.00 D), and moderate hyperopia (2.00 D ≤ SE < 5.00 D).³³ Astigmatism types were defined as follows: with-the-rule (WTR) when the flat meridian was within 180° ± 30°, against-the-rule (ATR) within 90° ± 30°, and oblique when the axis fell outside these ranges. 

Statistical Analysis

Data from the right eyes were presented, given the similar distribution patterns between the right and left eyes.^24–27 Group differences for continuous and categorical variables were analyzed using independent t-tests and χ² tests, respectively. To examine the relationships between refractive errors and astigmatism components, generalized additive models (GAMs) and smoothed curve fitting were applied, excluding any outliers with values exceeding three standard deviations from the mean. If a nonlinear relationship was detected, threshold effect analysis was performed using a two-piecewise linear regression model (segmented regression). The presence of a threshold was assessed with a log-likelihood ratio test, comparing a one-line (nonsegmented) model to the two-piecewise model. The inflection point was determined using a two-step recursive approach. A two-sided P value < 0.05 indicated statistical significance, with a 95% confidence interval. 

Results

Characteristics of the Study Population

Of the 7971 university students recruited for the AUSES, 178 (2.2%) did not undergo cycloplegic refraction, 249 (3.1%) missed one or more required examinations, and 233 (2.9%) were identified as potential outliers, with ocular measurements exceeding three standard deviations from the mean. Ultimately, 7315 students (91.8%) were included in the analysis. The average age of participants was 20.2 ± 1.5 years, with 2704 (37.0%) male. 

The mean cycloplegic SE was −2.88 ± 2.32 D (range −10.00 D to 4.38 D; male −2.67 ± 2.32 D; female −3.00 ± 2.32 D). The mean AL was 24.77 ± 1.17 mm (males 25.10 ± 1.17 mm, females 24.58 ± 1.13 mm). The mean AL/CR was 3.18 ± 0.14 for both males and females. The prevalence for refractive errors was as follows: high myopia (10.1%), moderate myopia (37.8%), low myopia (35.4%), emmetropia (9.7%), low hyperopia (6.5%), and moderate hyperopia (0.5%). 

Average Values, Prevalence Rates, and Axes of RA, CA, and IA

The mean values for RA, CA, and IA were 0.48 ± 0.40 D, 0.85 ± 0.50 D, and 0.62 ± 0.31 D, respectively (Table 1). The mean value of CA was significantly higher compared to RA and IA. Males exhibited significantly but slightly higher RA values (mean difference of 0.04 D, P < 0.001), whereas females had higher IA values (mean difference: 0.11 D, P < 0.001). No significant gender difference was observed for CA (P = 0.706). RA and CA decreased with age (P < 0.001), whereas IA remained stable (P = 0.502). As shown in Figure 1, RA was most frequently observed within the range of 0–0.5 D, whereas CA and IA were most common within the range of 0.5–1.0 D. Table 2 summarizes the prevalence rates of RA, CA, and IA across different thresholds (≥0.5 D, ≥0.75 D, ≥1.0 D, and ≥1.5 D). Applying the criterion for astigmatism (≥1.0 D), the prevalence rates of RA, CA, and IA were 16.4%, 36.7%, and 12.2%, respectively. RA and CA were predominantly WTR, whereas IA was primarily ATR. 

Table 1.

 

Mean Values of RA, CA, and IA Stratified by Sex, Age, and Refraction Groups

 

Figure 1.

 

Distribution profiles of RA, CA, and IA values. RA was most frequently observed within the range of 0–0.5 D, whereas CA and IA were most common within the range of 0.5–1.0 D.

Table 2.

 

Prevalences at Different Magnitudes and Axis of RA, CA, and IA

 

Diverse Astigmatism Components Among Refractive Statuses

As shown in Table 1, the high myopia, moderate myopia, and moderate hyperopia groups had significantly higher mean RA and CA values than the emmetropia group (P < 0.001 for all, independent t tests). For IA, only the high myopia group had a significantly lower value than the emmetropia group (P = 0.03). Figure 2 presents the prevalence rates of RA, CA, and IA (≥1.00 D) across different refractive error groups. RA and CA (≥1.00D) prevalence remained stable in low myopia and low hyperopia compared to emmetropia, with a significant increase in moderate and high myopia and moderate hyperopia (P < 0.05). In contrast, IA (≥1.00D) prevalence was consistent across refractive groups, except for a reduced rate in the high myopia group compared to emmetropia (P < 0.05). 

Figure 2.

 

Prevalence rates of RA, CA, and IA (≥1.00 D) across different refraction groups. The prevalence rates of RA and CA (≥1.00 D) remained stable in low myopia and low hyperopia, with significant increases in moderate myopia, high myopia and moderate hyperopia. In contrast, the prevalence of IA (≥1.00 D) was consistent across refractive groups, except for a reduced rate in the high myopia compared with emmetropia (P < 0.05). *Statistical significance compared to the emmetropia group (P < 0.05). HM, high myopia (SE ≤ −6.00 D); MM, moderate myopia (−6.00 D < SE ≤ −3.00 D); LM, low myopia (−3.00 D < SE ≤ −0.50 D); EM, emmetropia (−0.50 D < SE < 0.50 D); LH, low hyperopia (0.50 D ≤ SE < 2.00 D); MH, moderate hyperopia (2.00 D ≤ SE < 5.00 D).

Figure 3.

 

Two-piecewise relationships between SE and astigmatism components. GAM and smoothed curve fitting were applied. (A) All astigmatism components, with inflection points identified at −3.62 D, −1.38 D, and −3.50 D for RA, CA, and IA. Individual component relationships of (B) RA, (C) CA, and (D) IA are shown. The solid lines denote the estimated values, whereas the dotted lines represent the corresponding 95% confidence intervals (CIs), with β values adjusted for age and sex. *Statistical significance (P < 0.001).

Figure 4.

 

Two-piecewise relationships between AL and astigmatism components. GAM and smoothed curve fitting were used. (A) All astigmatism components, with inflection points at 24.91 mm, 23.95 mm, and 22.92 mm for RA, CA, and IA. Relationships for each component (B) RA, (C) CA, and (D) IA are shown. The solid lines denote the estimated values, whereas the dotted lines represent the corresponding 95% confidence interval (CIs), with β values adjusted for age and sex. *Statistical significance (P < 0.001).

Two-Piecewise Relationships Between Refractive Error and RA, CA, and IA

Figures 2 through 5 display the results of the generalized additive models and smoothed curve fitting adjusted for age and sex, revealing nonlinear relationships of SE, AL, and AL/CR with RA, CA, and IA. The piecewise linear regression model, adjusted for age and sex, provided a better fit than the linear regression model (all log-likelihood ratio P values < 0.001). As shown in Table 3 threshold effect analysis revealed inflection points for RA, CA, and IA: for SE at −3.62 D, −1.38 D, and −3.50 D; for AL at 24.91 mm, 23.95 mm, and 22.92 mm; and for AL/CR at 3.20, 3.14, and 3.20, respectively. Significant threshold effects were observed in the relationships between refractive error and astigmatism components. When myopia severity exceeded the inflection points, RA was negatively associated with SE (β = −0.11, P < 0.01) but positively associated with AL (β = 0.12, P < 0.01) and AL/CR (β = 1.71, P < 0.01). Below these inflection points, no significant correlations were found between SE, AL, or AL/CR and RA (all P > 0.05). For CA, significant increases were observed both below and above the inflection points for SE and AL (all P < 0.01). For IA, on the myopic side of the inflection points (SE < −3.50 D, AL > 22.92 mm), IA decreased with increasing myopia (P < 0.01); however, on the opposite side, no significant associations were found (P > 0.05). 

Figure 5.

 

Two-piecewise relationships between AL/CR and astigmatism components. GAM and smoothed curve fitting were used. (A) All astigmatism components, with inflection points at 3.20, 3.14, and 3.20 for RA, CA, and IA. The relationships for each component (B) RA, (C) CA, and (D) are shown. The solid lines denote the estimated values, whereas the dotted lines represent the corresponding 95% confidence interval (CIs), with β values adjusted for age and sex. *Statistical significance (P < 0.001).

Table 3.

 

Threshold Effect Analysis of SE, AL, and AL/CR on RA, CA, and IA

 

Significant Loss of Astigmatism Component Coordination in High Myopia

On the myopic side of these inflection points (SE < inflection points, as well as AL and AL/CR > inflection points), RA and CA increased significantly with worsening myopia, with CA increasing more rapidly, whereas IA decreased. This suggested a significant loss of coordination among astigmatism components once myopia exceeds the identified threshold. Furthermore, as shown in Figure 6, the percentages of overall compensation (under, full, and over compensation) and full compensation in both J0 and J45 components were significantly lower in the high myopia group compared to the emmetropia group (all P < 0.05). The compensatory effect of IA on CA was reduced in the high myopia group, suggesting a significant loss of astigmatism component coordination in high myopia. 

Figure 6.

 

Compensation levels in different refraction groups. Overall Compensation categories included under compensation(0.1 < CF < 0.9), full compensation(0.9 ≤ CF ≤ 1.1), and over-compensation(1.1 < CF ≤ 2). Both overall compensation and full compensation rates were significantly lower in the high myopia group. *Statistical significance compared to the emmetropia group (P < 0.05). HM, high myopia (SE ≤ −6.00 D); MM, moderate myopia (−6.00 D < SE ≤ −3.00 D); LM, low myopia (−3.00 D < SE ≤ −0.50 D); EM, emmetropia (−0.50 D < SE < 0.50 D); LH, low hyperopia (0.50 D ≤ SE < 2.00 D); MH, moderate hyperopia (2.00 D ≤ SE < 5.00 D).

Discussion

To our knowledge, this study represents the first large-scale investigation of the coordination among astigmatism components, including RA, CA, and IA, across different refractive statuses in a large, cycloplegic sample of young adults in China. The prevalence rates of RA, CA, and IA with magnitudes ≥1.0 D were found to be 16.4%, 36.7%, and 12.2%, respectively. Notably, our findings reveal that RA, CA, and IA exhibit piecewise relationships with refractive error. In individuals with moderate and high myopia, RA and CA showed a significant increase, while IA decreased with worsening myopia. Furthermore, the compensatory effect of IA was significantly reduced in the high myopia group. 

Prevalence, Distribution, and Axis Orientation of RA, CA and IA

The prevalence of astigmatism in this study was comparable to or lower than that reported in previous studies^{10,22,34–38} (Supplementary Table S1). Compared to studies on minors from the same city,^9,31 the prevalence rate of RA was similar, whereas the prevalence rates of CA and IA were lower in the current study. Astigmatism tends to decrease through the emmetropization process from childhood to adulthood, while in older adults, it typically increases with age.³⁹ Because young adults represent an intermediate-age group, their astigmatism levels may be comparatively lower.⁴⁰ In line with findings from other studies, RA and CA were predominantly WTR astigmatism, whereas IA was mainly ATR, consistent across both child and adult populations.^9,10,31 

Two-Piecewise Relationships Between Refractive Error and RA, CA, and IA

Previous studies have observed that RA values tend to increase as refractive errors worsen, generally following a symmetric U-shaped relationship, with RA increasing as refractive status deviates from the emmetropic range,^9,10,13 particularly in patients with myopia.^14–20 Similar trends have been reported for RA and CA in earlier studies.^9,10 Our findings align with these observations; however, this study identified that CA reached its minimum at low myopia (SE = −1.38 D, AL = 23.95 mm). In the ACES study,⁹ IA was found to remain constant (IA = 0.72D), and Hashemi et al.¹⁸ also reported minimal changes in IA across different SE levels. By contrast, Kam et al.¹⁰ found a positive association between IA and SE. In the present study, when SE > −3.5 D, the IA did not significantly change and could be considered to remain constant. However, when SE < −3.5 D, there was a positive association between IA and SE. The current findings aligned with those of previous studies within a specific range of refractive errors,^9,10,18 which was primarily due to differences in the refractive error ranges of the study populations. Compared to our study, previous studies included fewer individuals with high myopia.^9,18 

Significant Loss of Astigmatism Component Coordination in High Myopia

The current study found that individuals with high myopia exhibited greater RA and CA but lower IA, with these changes becoming more pronounced as refractive error increased. The compensatory effect among astigmatism components was markedly weaker in this group, indicating a significant loss of coordination among astigmatism components in high myopia. The elevated prevalence and values of RA in patients with high myopia were associated not only with increased CA but also with diminished coordination among astigmatism components.¹³ 

A study in children (mean age 9.2 years) found that the rate of full astigmatism compensation decreased as refractive error increased.¹³ In contrast, our study identified a significant decline in full compensation primarily in the high myopia group. This discrepancy is likely due to differences in refractive error distribution, as high myopia accounted for only 1.8% of cases in the pediatric study compared to 10.1% in ours. Additionally, age-related declines in compensatory mechanisms may partly contribute to this difference.¹³ Supporting this, another study reported that children (7.5 ± 1.0 years) exhibited a significantly higher rate of compensation via IA compared to adults (mean age 41.1 ± 7.5 years).¹⁰ 

By focusing on young adults—an underrepresented population in prior research—our study helps bridge the gap in understanding the evolution of astigmatism compensation mechanisms in early adulthood. Moreover, the inflection points identified in our study have critical clinical implications. At these points, RA and CA reached their minimal values, whereas IA peaked. Notably, the relationship between astigmatism components and refractive error differed significantly on either side of the inflection points. Therefore, when analyzing the association between refractive error and astigmatism, it is essential to account for these inflection points to ensure accurate interpretation. 

A limitation of the current study is its cross-sectional design. Longitudinal research, especially during the onset of myopia, is necessary to track the progression of refractive error and astigmatism components, thus establishing causal relationships between them, and identifying potential inflection points in the development of myopia and astigmatism where their interrelationships become more prominent. The limited number of participants with moderate hyperopia and the absence of high hyperopia cases in our study may introduce bias. Future research should investigate astigmatism components and their coordination in hyperopic individuals, particularly those with moderate-to-high hyperopia. Given the higher prevalence of hyperopia in preschool-aged children compared to adults, future studies should focus on this population. The school-based sampling framework of this study, rather than population-based sampling, may introduce selection bias in prevalence estimates. This potential bias should be taken into account when comparing findings with population-based studies. In this study, CA represented anterior corneal astigmatism, while IA included posterior corneal astigmatism. To achieve a more accurate assessment of intraocular astigmatism and the compensatory roles of different structures, further investigations should carefully examine the individual components of IA. 

Conclusions

In summary, our study, conducted in a large cycloplegic sample of young adults from central China, found that the components of astigmatism demonstrated coordination from low myopia to low hyperopia. However this coordination was significantly lost in high myopia. 

Acknowledgments

The authors thank all the participants of this study. 

Supported by the Integration, translation and development on Ophthalmic technology (Jingyiyan 2016-5), the Major International (Regional) Joint Research Project of the National Natural Science Foundation of China (81120108007), and the National Natural Science Foundation of China (82301250). 

Disclosure: W. An, None; S. Wei, None; S.-M. Li, None; K. Cao, None; J. Hu, None; C. Lin, None; W. Bai, None; J. Fu, None; Y. Sun, None; N. Wang, None