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Research Article
Revised

Delicate balance: the relationship between internal astigmatism and lens astigmatism

[version 2; peer review: 1 approved with reservations, 1 not approved]
* Equal contributors
PUBLISHED 20 Sep 2021
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This article is included in the Eye Health gateway.

Abstract

Background: Due to lack of equipment for directly measuring crystal morphology, there has been little research on lenticular astigmatism. The purpose of this study was to accurately explore the correlation between internal astigmatism and lens astigmatism in patients with ametropia.
Methods: This is a cross-sectional study conducted in the Affiliated Hospital of North Sichuan Medical College, China, in September 2020. Diopter values (refractive astigmatism, RA) of patients with ametropia was recorded, and the corneal and lens biological parameters were measured by CASIA2 (corneal/anterior segment optical correlation tomography analyzer). Biometric parameters, including the total corneal astigmatism (total corneal astigmatism, TCA), anterior and posterior curvature radius of the lens (anterior curvature radius of the lens, ACL;  posterior curvature radius of the lens, PCL), internal astigmatism (internal astigmatism, IA), anterior and posterior astigmatism of the lens (anterior astigmatism of the lens, AAL;  posterior astigmatism of the lens, PAL) were measured. Grouping and comparisons were made according to gender and age.
Results: In total, 151 participants (293 eyes) were included in the analysis. There were significant ( P<0.05) differences in the IA ( Z=-2.194, P=0.028) according to gender, but not in the other parameters. By age group, there were statistically significant differences in the TCA ( H=10.609, P=0.005), IA ( F=3.722, P=0.025), and PAL ( H=8.254, P=0.016), but not in the others. The IA was positively correlated with the age ( r=0.155, P=0.008), RA ( r=0. 534, P<0.001), AAL ( r=0.308, P<0.001), and was negatively correlated with the TCA ( r=-0.244, P<0.001). The regression equation between the IA and AAL was: Y (IA) =-0.626 +0.447 X (AAL).
Conclusions:  Internal astigmatism is mainly related to the anterior astigmatism of the lens, and the higher the anterior astigmatism of the lens, the higher the internal astigmatism; At the same time, internal astigmatism increases with age.

Keywords

Astigmatism, Internal astigmatism, Lens astigmatism, Corneal astigmatism, Refractive error

Revised Amendments from Version 1

According to the opinion of Professor Samira Heydarian, the article is revised, the specific changes are as follows: 1) we modified the inclusion criteria to make the research object more clear; 2) We modified the procedure to make the outcome indicators more clear; 3) We added the analysis of astigmatism axis in the result section, and Table 4 is the added content; 4) In the discussion section, we discuss the contents added in the results section, and at the same time, we add a description of the limitations of the article and discuss the direction for further research; 5) There has been an increase in the reference section( reference 10, 11, 28).

See the authors' detailed response to the review by Samira Heydarian

Introduction

Astigmatism is the most common refractive error in the world, which may come from congenital or acquired factors1. Astigmatism can change from birth, and its development is influenced by many factors such as heredity, extraocular muscle tension, visual feedback and eyelid pressure2. According to World Health Organisation (WHO) statistics in 2018, the prevalence rates of astigmatism in children and adults are 14.9% and 40.4%, respectively3. Similarly, studies have found that 47% of cataract patients suffer from astigmatism ≥1 diopter4. Uncorrected ametropia is the second leading cause of blindness in the world, and astigmatism is a major factor that damages human vision5. At present, we have a clear understanding of the detection of refractive astigmatism and corneal astigmatism, but due to the lack of methods to observe crystal morphology, there are few studies on lens astigmatism. The CASIA2 (Tomey Corp., Nagoya, Japan) system is a new type of anterior segment scanner. This novel device can provide accurate measurement of anterior segment parameters, and has good repeatability and reproducibility6,7. Based on the advantages of the CASIA2 system, this paper combines corneal and lens parameters and optometry data to analyze the correlation between internal astigmatism and lens astigmatism.

Methods

Subjects

All the subjects were ametropia patients who came to the Affiliated Hospital of North Sichuan Medical College naturally. The experimenter (Meng Liu) explained this study and examined it with the permission of the patients. Since this research does not infringe on any rights and interests of patients, it can be conducted with the authorization of the Ethics Committee of North Sichuan Medical College. In order to reduce bias, we carefully screened the subjects. The screening criteria for the subjects included in the study are as follows: 1) Include the subjects under 40 years old who have clear refractive media through slit lamp examination,the best corrected visual acuity is above 20/20; 2) The subjects who can cooperate well with the detection; 3) The subjects with simple ametropia and no other organic diseases, such as cataract, glaucoma, retinal diseases, etc.; 4) Exclude the subjects with previous binocular surgery history.

Ethical considerations

Written informed consent was provided by the patient or their family/guardian if under the age of 18 years. As this study is an extended retrospective study of relevant prospective approved studies8 [approval number 2020ER(A) 068] and does not harm the interests of patients, it received an exemption by the Ethics Committee of North Sichuan Medical College.

Procedure

Biometric parameters of the lens were measured by the same experimenter (ML). An ARK-510A autorefractor (NIDEK, Co., Ltd, Gamagori, Japan) and DK-700 optometry system (Topcon, Japan) were used to perform optometry, and the CASIA2 system (Tomey Corp., Nagoya, Japan) was applied to obtain other measurements [the total corneal astigmatism (TCA), anterior and posterior curvature radius of the lens (ACL, PCL)].

Outcome parameters

Outcome parameters included the following: (1) Sex and age; (2) RA: The refractive astigmatism obtained by optometry; (3) TCA, ACL and PCL directly recorded by the CASIA2 system; (4) IA calculated by RA minus TCA; (5) AAL, PAL: Convert radius of curvature to curvature by formula9 (Ø=n-nr, Ø = curvature; n’=Exit square refractive index; n=Incident square refractive index; r=the radius of curvature).The default refractive index of CASIA2 crystal is 1.4085, and the refractive index of aqueous humor is 1.336.The radius of the anterior and posterior curvature of the lens can be obtained directly from CASIA2.

Statistical analysis

The sample size was estimated by Stata 16.0 software. The test efficiency β= 0.1, α=0.05, bilateral test, and the correlation coefficient is 0.310. The calculated sample size is estimated to be 112. SPSS 25.0 statistical software was used for analysis. All data were first tested by the Kolmogorov-Smirnov (K-S) goodness-of-fit normality test before comparisons. Data with a normal distribution were compared using a paired sample t test or ANOVA analysis. If the distribution was not normal, a nonparametric test was used for comparison. In the correlation analysis(Internal astigmatism with Age, Refractive astigmatism, Total corneal astigmatism, Anterior astigmatism of the lens, Posterior astigmatism of the lens), data with a normal distribution are presented as the mean±standard deviation (X±S), a Pearson correlation analysis was applied, and a scatter plot was used to describe the correlation. If the data did not conform to a normal distribution, the median±quartile spacing (M±Q) was used, and a Spearman correlation analysis was carried out. Multivariate linear regression analysis was performed for parameters with multiple correlations. P < 0.05 was considered to indicate statistical significance.

Results

Participants

This was a cross-sectional study of 151 patients (293 eyes, 77 males and 74 females), the average age is 11± 13, including 93 patients with 179 eyes aged 4–12 years, 17 patients with 32 eyes aged 13–18 years and 41 patients with 82 eyes aged 19–40 years11. Figure 1 shows the inclusion of the research object.

b9b90bb6-2856-4be5-8821-63a4f914be3d_figure1.gif

Figure 1. Inclusion of research objects.

Comparison of all parameters by gender

Table 1 shows the comparison results of all parameters grouped by gender. It can be seen that there is no statistical difference in other parameters except IA (Z=-2. 194, P=0. 028).

Table 1. Comparison of all parameters by gender.

Gender(eyes)Age
(M±Q)
RA
(M±Q)
TCA
(M±Q)
IA
(M±Q)
AAL
(M±Q)
PAL
(M±Q)
Male(149)12±120.50±0.750.95±0.74-0.27±0.500.69±0.360.95±0.85
Female(144)11.00±120.50±0.500.98±0.65-0.41±0.570.67±0.480.88±0.74
Z/P-0.028/0.977-1.744/0.081-0.553/0.58-2.194/0.028*-0.581/0.561-1.935/0.053

* indicates that the comparison is statistically significant. RA: refractive astigmatism; TCA: total corneal astigmatism; IA: internal astigmatism; AAL: anterior astigmatism of the lens; PAL: posterior astigmatism of the lens.

Comparison of all parameters by age

Comparison of all parameters by age group is shown in Table 2. It can be seen that there are statistically significant differences in TCA (H=10. 609, P=0. 005), IA (F=3. 722, P=0. 025), and PAL (H=8. 254, P=0. 016), and others have no statistically significant differences.

Table 2. Comparison of all parameters by age.

Years(eyes)RA
(M±Q)
TCA
(X±S/M±Q)
IA
(X±S)
AAL
(X±S/M±Q)
PAL
(M±Q)
≤12(179)0.50±0.500.99±0.60-0.35±0.040.69±0.020.94±0.77
13–18(32)0.75±0.501.06±0.07-0.35±0.040.68±0.041.15±0.99
≥19(82)0.50±0.750.80±0.73-0.19±0.050.70±0.450.80±0.87
P0.2560.005*0.025*0.7130.016*

* indicates that the comparison is statistically significant. RA: refractive astigmatism; TCA: total corneal astigmatism; IA: internal astigmatism; AAL: anterior astigmatism of the lens; PAL: posterior astigmatism of the lens.

Correlation analysis between internal astigmatism and lens astigmatism

After K-S test, the IA and the AAL showed normal distribution, so Pearson correlation analysis was used to analyze the correlation between them. Other parameters had non-normal distribution, so Spearman correlation analysis was used, and the results are shown in Table 3.

Table 3. Correlation analysis among all parameters.

Age(r/P)RA(r/P)TCA(r/P)AAL(r/P)PAL(r/P)
IA0.155/0.008*0.534/<0.001*-0.244/<0.001*0.308/<0.001*0.032/0.591

* indicates that the comparison is statistically significant. RA: refractive astigmatism; TCA: total corneal astigmatism; IA: internal astigmatism; AAL: anterior astigmatism of the lens; PAL: posterior astigmatism of the lens.

Internal astigmatism axis was positively correlated with age (r=0. 119, P=0. 041), total astigmatism axis (r=0. 764, P < 0.001), total corneal astigmatism axis (r=0. 791, P < 0.001), but negatively correlated with anterior surface astigmatism axis (r=-0. 124, P=0. 034) (Table 4).

Table 4. Correlation analysis between internal astigmatism axis and various astigmatism axes.

Age (r/P)RA axis (r/P)TCA axis (r/P)AAL axis (r/P)PAL axis (r/P)
IAA0.119/0.041*0.764/<0.001*0.791/<0.001*-0.124/0.034*-0.068/0.244

* indicates that the comparison is statistically significant. IAA:internal astigmatism axis; RA: refractive astigmatism; TCA: total corneal astigmatism; IA: internal astigmatism; AAL: anterior astigmatism of the lens; PAL: posterior astigmatism of the lens.

The IA was positively correlated with the age (r=0.155, P=0. 008), RA (r=0.534, P < 0.001), and was negatively correlated with the TCA (r=-0.244, P < 0.001). It can be seen that in the correlation analysis between IA and lens astigmatism, IA was positively correlated with AAL (r=0. 308, P < 0.001), but not with other lens astigmatism parameters. Therefore, for the regression analysis of IA and AAL, the regression equation is Y (IA) =-0.626 +0.447 X (AAL) (F=30. 461, P < 0.001, R2=0. 095) (Figure 2).

b9b90bb6-2856-4be5-8821-63a4f914be3d_figure2.gif

Figure 2. Linear regression graph of the internal astigmatism (IA) and the anterior astigmatism (AAL) of the lens.

Discussion

The types of astigmatism in human eyes include refractive astigmatism, corneal astigmatism, internal astigmatism and lens astigmatism. The astigmatism obtained by optometry is refractive astigmatism12, and the total corneal astigmatism is a comprehensive index of CASIA2 system combined with the anterior and posterior corneal surfaces. We regard the difference between the above two as internal astigmatism, which mainly includes lens astigmatism and other possible physiological astigmatism12. Internal astigmatism compensates for corneal astigmatism from birth, but the efficiency of its decreases with age13. The active compensation between corneal astigmatism and internal astigmatism in childhood helps maintain refractive stability, which is mainly due to the high convergence of the wavefront incident on the lens due to corneal refraction14,15. However, due to the lack of precise equipment for observing anterior segment, the relationship between internal astigmatism and lens is still controversial. For instance, one study found that internal astigmatism gradually increases with age, and it mainly comes from lens16. Nevertheless, some studies believe that the prevalence rate of astigmatism increases with age, and the refractive and corneal astigmatism shift to ATR (against-the-rule). But the continuous corneal changes seem to be the cause of the age trend of refractive astigmatism, and the severity of lens opacity plays a small role in the change of internal astigmatism17. Therefore, based on the advantages of the CASIA2 system, this paper comprehensively analyzed the correlation between internal astigmatism and lens astigmatism by combining corneal and lens parameters. Inevitably, our research also has certain limitations: 1) Because of the complexity and instability of astigmatism, the power and axis of astigmatism are analyzed separately; 2) Physiological astigmatism from the vitreous and retina cannot be measured and estimated despite strict inclusion criteria and exclusion of opacity in the refractive media. However, through this article, we have made clear the quantitative relationship between internal astigmatism and lens astigmatism, and lens astigmatism mainly comes from the anterior surface of the lens. This can provide reference and ideas for more accurate research on astigmatism.

According to gender, there were statistical differences in internal astigmatism, which were lower in boys than girls, but not in other parameters. Li et al.18 found that corneal astigmatism and internal astigmatism seemed to be higher in girls than in boys. Similarly, Liu et al.13 also found that girls had greater internal astigmatism than boys. This may be due to the fact that girls' physical development is earlier than boys', and the difference caused by the growth rate of the axial length. Gender is highly correlated with the growth of the axial length, and the growth of the axial length has also been proved to be related to internal astigmatism19.

Then, we found that corneal astigmatism, internal astigmatism and posterior astigmatism of lens were different according to age. Firstly, corneal astigmatism has been changing since birth. Naeser et al.20 proved that corneal astigmatism is not stable until the age of 50. Under normal circumstances, corneal astigmatism changes regularly by 0.25 D every 10 years. Secondly, the compensation effect of internal astigmatism on reducing corneal astigmatism is very significant among preschool children, and then this compensation effect gradually weakens with age21,22. Finally, we found that there were differences in the posterior astigmatism of lens, but there was not in the anterior. Birkenfeld et al.23 have also found that with the increase of age, the astigmatism of the lens changes significantly, but the difference is that they have significant changes in the anterior lens. We all know that the curvature of the anterior lens changes more than posterior in the process of accommodation24, but this is not completely equivalent to the greater astigmatism of the anterior surface with the change of age, which is the direction for further research.

It can be seen that internal astigmatism is highly correlated with the anterior astigmatism of the lens, but not with the posterior and the internal astigmatism increases with the increase of anterior astigmatism of the lens. Although the refractive index of lens is gradient, its astigmatism is close to anterior surface astigmatism23. However, this does not mean an absolute correlation between internal astigmatism and the anterior astigmatism of the lens, because the state of the lens is unstable. For example, Pérez et al.25 found that in the relaxed state, spherical terms account for the majority of anterior lens surface irregularity (47%) and posterior lens astigmatism (70%); however, in the accommodation lens, astigmatism is the main irregularity of anterior lens surface (90%). The optical characteristics of the lens depend on its shape and refractive index distribution26, which can affect its astigmatism to a great extent, thus further causing internal astigmatism to change. It seems that corneal and internal astigmatism cancel each other out27. The unity of changes among corneal astigmatism, lens astigmatism and refractive astigmatism, do not occur individually28. The axis of astigmatism is fluctuating, and the distinctive mechanisms may account for the different astigmatism axis orientations29. We find that the axis of internal astigmatism also changes with age, and the internal astigmatism is related to the axis of the anterior astigmatism of the lens. However, unlike the power, the higher the axis of internal astigmatism, the lower the astigmatism on the anterior astigmatism of the lens. This seems to further confirm the compensation and balance of lens astigmatism, which is also the direction worthy of further study.

To sum up, we found that there are gender and age differences in some astigmatism parameters and the relationship between internal astigmatism and lens astigmatism is clarified. Internal astigmatism increases with the increase of lens astigmatism, and the source of lens astigmatism is mainly the anterior. However, further research is required to determine whether lens astigmatism can be equated with internal astigmatism, and the correlation between internal astigmatism and anterior astigmatism of the lens is related to the mechanism of accommodation.

Data availability

Underlying data

Open Science Framework: Delicate balance: relationship between internal astigmatism and lens astigmatism. https://doi.org/10.17605/OSF.IO/7X9FD11.

Data are available under the terms of the Creative Commons Zero "No rights reserved" data waiver (CC0 1.0 Public domain dedication).

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Liu M, Dai C, Zhou G et al. Delicate balance: the relationship between internal astigmatism and lens astigmatism [version 2; peer review: 1 approved with reservations, 1 not approved]. F1000Research 2021, 10:527 (https://doi.org/10.12688/f1000research.54045.2)
NOTE: If applicable, it is important to ensure the information in square brackets after the title is included in all citations of this article.
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Current Reviewer Status: ?
Key to Reviewer Statuses VIEW
ApprovedThe paper is scientifically sound in its current form and only minor, if any, improvements are suggested
Approved with reservations A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit.
Not approvedFundamental flaws in the paper seriously undermine the findings and conclusions
Version 2
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PUBLISHED 20 Sep 2021
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Reviewer Report 28 Sep 2021
Samira Heydarian, Department of Rehabilitation Science, School of Allied Medical Sciences, Mazandaran University of Medical Sciences, Sari, Iran 
Approved with Reservations
VIEWS 7
There are still some comments that require more clarification as given below:
  • Internal astigmatism is the difference between total refractive and corneal astigmatism, what about intra-ocular astigmatism? It is still vague.
     
... Continue reading
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Heydarian S. Reviewer Report For: Delicate balance: the relationship between internal astigmatism and lens astigmatism [version 2; peer review: 1 approved with reservations, 1 not approved]. F1000Research 2021, 10:527 (https://doi.org/10.5256/f1000research.77535.r94737)
NOTE: it is important to ensure the information in square brackets after the title is included in all citations of this article.
Version 1
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PUBLISHED 01 Jul 2021
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Reviewer Report 01 Nov 2021
Hu Liu, Department of Ophthalmology, The First Affiliated Hospital with Nanjing Medical University, Nanjing, China 
Not Approved
VIEWS 4
Although this manuscript raised an interesting topic, i.e. the relationship between lens astigmatism and internal astigmatism, it had multiple mistakes in the methods and failed to provide convincing results and logical discussion to prove this relationship. Here are some examples: ... Continue reading
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CITE
HOW TO CITE THIS REPORT
Liu H. Reviewer Report For: Delicate balance: the relationship between internal astigmatism and lens astigmatism [version 2; peer review: 1 approved with reservations, 1 not approved]. F1000Research 2021, 10:527 (https://doi.org/10.5256/f1000research.57490.r91892)
NOTE: it is important to ensure the information in square brackets after the title is included in all citations of this article.
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Reviewer Report 07 Sep 2021
Samira Heydarian, Department of Rehabilitation Science, School of Allied Medical Sciences, Mazandaran University of Medical Sciences, Sari, Iran 
Not Approved
VIEWS 11
Here are some comments that require clarification as given below.

Abstract:
  • It is better to use lenticular astigmatism instead of crystal astigmatism.
     
  • Please clarify what the difference is
... Continue reading
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HOW TO CITE THIS REPORT
Heydarian S. Reviewer Report For: Delicate balance: the relationship between internal astigmatism and lens astigmatism [version 2; peer review: 1 approved with reservations, 1 not approved]. F1000Research 2021, 10:527 (https://doi.org/10.5256/f1000research.57490.r92837)
NOTE: it is important to ensure the information in square brackets after the title is included in all citations of this article.
  • Author Response 20 Sep 2021
    Binzhong Li, School of Basic Medicine, North Sichuan Medical College, nanchong, China
    20 Sep 2021
    Author Response
    Dear Professor Samira Heydarian,

    Thank you very much for your many meaningful comments on this article, so as to make changes according to your suggestions. The changes are as ... Continue reading
COMMENTS ON THIS REPORT
  • Author Response 20 Sep 2021
    Binzhong Li, School of Basic Medicine, North Sichuan Medical College, nanchong, China
    20 Sep 2021
    Author Response
    Dear Professor Samira Heydarian,

    Thank you very much for your many meaningful comments on this article, so as to make changes according to your suggestions. The changes are as ... Continue reading

Comments on this article Comments (0)

Version 2
VERSION 2 PUBLISHED 01 Jul 2021
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Alongside their report, reviewers assign a status to the article:
Approved - the paper is scientifically sound in its current form and only minor, if any, improvements are suggested
Approved with reservations - A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit.
Not approved - fundamental flaws in the paper seriously undermine the findings and conclusions
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