Delicate balance: the relationship between internal astigmatism and lens astigmatism [version 2; peer review: 1 approved with reservations, 1 not approved]

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


Introduction
Astigmatism is the most common refractive error in the world, which may come from congenital or acquired factors 1 .Astigmatism can change from birth, and its development is influenced by many factors such as heredity, extraocular muscle tension, visual feedback and eyelid pressure 2 .According to World Health Organisation (WHO) statistics in 2018, the prevalence rates of astigmatism in children and adults are 14.9% and 40.4%, respectively 3 .Similarly, studies have found that 47% of cataract patients suffer from astigmatism ≥1 diopter 4 .Uncorrected ametropia is the second leading cause of blindness in the world, and astigmatism is a major factor that damages human vision 5 .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 reproducibility 6,7 .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.

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 studies 8 [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)].

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 years 11 .Figure 1 shows the inclusion of the research object.

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, 12, 29).

Any further responses from the reviewers can be found at the end of the article
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).

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.

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.

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 astigmatism 12 , 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 astigmatism 12 .Internal astigmatism compensates for corneal astigmatism from birth, but the efficiency of its decreases with age 13 .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 refraction 14,15 .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 lens 16 .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 astigmatism 17 .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 astigmatism 19 .
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 age 21,22 .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 accommodation 24 , 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 astigmatism 23 .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 distribution 26 , 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 out 27 .The unity of changes among corneal astigmatism, lens astigmatism and refractive astigmatism, do not occur individually 28 .The axis of astigmatism is fluctuating, and the distinctive mechanisms may account for the different astigmatism axis orientations 29 .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.

Introduction:
"Similarly, studies have found that 47% of cataract patients suffer from astigmatism≥1 degree".What do you mean by "degree"?It seems that it should be changed to "diopter".

Method:
Subjects: How were the subjects screened to reduce bias?Please clarify more.

○
Please add the inclusion criteria.For instance, is there any age limit for the study?

Procedures:
What are the other measurements that the authors measured using CASIA and what is the standardized optometry?
○ Due to the effect of accommodation on the lens and even on corneal curvature, cyclorefraction and comparing changes before and after cycloplegia seems useful.

Outcome parameters:
As a general rule, all non-standard abbreviations/acronyms should be written out in full on first use (in both the abstract and the paper itself) and followed by the abbreviated form in parentheses.Please consider this point throughout the manuscript.
○ related to adjustment before and after mydriasis are very important, which is worth our next research direction.
3.5 As a general rule, all non-standard abbreviations/acronyms should be written out in full on first use (in both the abstract and the paper itself) and followed by the abbreviated form in parentheses.Please consider this point throughout the manuscript.
Author response: It has been added in the abstract.
3.6 Do the authors consider the curvature of the anterior and posterior surface of the lens as AAL and PAL? Astigmatism is the difference between the main curvatures, not just the curvature.
Author response: We are discussing the main curvature, which has been made clear.Thanks again.
3.7 Statistical analysis: Please cite the reference that is used for the calculation of the sample size.

Binzhong Li (on behalf of all authors)
Competing Interests: The authors declare that they have no competing interests.
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Figure 2 .
Figure 2. Linear regression graph of the internal astigmatism (IA) and the anterior astigmatism (AAL) of the lens.

Table 2 . Comparison of all parameters by age.
* 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.

Table 3 . Correlation analysis among all parameters.
* 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.

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)
* 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.