Quanti cation of Ocular Parameters To Create An Anatomical Eye Model for The Japanese Population

Takushi Kawamorita (  kawa2008@kitasato-u.ac.jp ) Kitasato University School of Allied Health Sciences Hiroshi Uozato Tokyo Optometric College Tetsuro Oshika University of Tsukuba Kazuno Negishi Keio University School of medicine Takashi Fujikado Osaka University Graduate School of Medicine Akira Murakami Juntendo University Graduate School of Medicine Kazutaka Kamiya Kitasato University School of Allied Health Sciences Naoyuki Maeda Osaka University Graduate School of Medicine Yuta Ueno University of Tsukuba Kazuhiro Onuma Chiba University Masakazu Hirota Teikyo University Rie Hoshikawa Kitasato University School of Allied Health Sciences Sachiko Masui Keio University School of medicine Masahiro Yamaguchi Juntendo University Graduate School of Medicine Toshifumi Mihashi Teikyo University


Introduction
Gullstrand's eye model, a representative eye model created with reference to anatomical data, plays an important role in the optimal design of eyeglasses, contact lenses, intraocular lenses, and lasers for vision correction. While many historical eye models have been reported [1,2], recent improvements in the measurement and evaluation techniques of the shape of the eye have made it possible to create models that are more accurate than the previously reported conventional models. In fact, in addition to Gullstrand's eye model, there are other models of the eye that take into account focal adjustment [3], age-related changes that re ect biometrics [4] among other parameters. Liou and Brennan proposed a new model that is closer to anatomical, biometric, and optical realities, including those previously reported [5]. Recently, in Europe, a study called Project Gullstrand -European Project for the Determination of Average Biometric Values of Human Eyes (Gullstrand) was conducted by the European Vision Institute Clinical Research Network and reported by Zocher et al. [6]. Furthermore, the Bigaussian model was reported by Rozema et al. in Europe [7].
While there is a famous eye model, refractive errors in Japanese and East Asian eyes are often myopic because of genetic and environmental in uencing factors [8,9]; this may require corrections to the eye model. In myopic eyes, the anterior chamber depth (ACD), which is the distance from the cornea to the lens, is deeper and the length of the ocular axial length (AL) is longer [10]. These ndings suggest that the standard eye shapes are different from Japanese and East Asian eye shapes. Various studies have been conducted on this, including the Tajimi and Nagahama studies in Japan [11,12] and the Liwan study in China [13]. We compared the present study with these previous studies [11,13] and our eye model with other famous eye models, such as the Gullstrand [2], Navarro [3], and Liou and Brennan eye models [5]. This multicenter study was conducted at institutions belonging to the Japanese Society of Ophthalmology to obtain data on the average Japanese eye shape. The purpose of this project was to compile a database of the shape of the eyes of Japanese people and create a Japanese eye model, thereby allowing optimization of eyeglasses, contact lenses, intraocular lenses, and laser correction, and to apply this information to various elds.

Results
Two hundred and fty eyes from 250 participants (mean age = 46.5 ± 18.0 years, range: 20-90 years) were included in this study (126 females and 124 males with mean ages of 46.74 ± 18.41 and 46.25 ± 17.56 years, respectively, P = 0.905) ( Table 1). The descriptive statistics are shown in Table 1. While the mean log minimum angle of resolution (logMAR) value for best corrected distance visual acuity (CDVA) was -0.08 ± 0.09, indicating good vision, the mean logMAR value for uncorrected distance visual acuity (UDVA) was 0.68 ± 0.53, indicating a high degree of variability and a tendency for many participants to have insu cient vision. Owing to the variation in the normality of the various eye shape parameters, a non-parametric test was used. The mean and distribution results of the subjective and objective spherical equivalent values (SE) of ocular refraction revealed mild myopia and astigmatism (Tables 1). The spherical power (Sph), cylindrical power (Cyl), SE, power vector J180, and power vector J45 for differences between the subjective and objective measurements were 0.180 ± 0.463 D, 0.122 ± 0.329 D, 0.241 ± 0.469 D, -0.033 ± 0.222, and 0.025 ± 0.154, respectively ( Table 1). The posterior corneal curvature (PCC) / anterior corneal curvature (ACC) and AL/ACC ratios were 0.82 ± 0.02 and 3.19 ± 0.17, respectively. In the normality analyses, the hypothesis "This variable is normally distributed" was rejected for age, UDVA, CDVA, and all subjective and objective refractive parameters (P < 0.05), while AL, ACD, ACC, PCC, central corneal thickness (CCT), posterior corneal asphericity (PCA), PCC/ACC ratio, and AL/ACC ratio were accepted (P > 0.05).    A comparison between these results and results from the previous reports is presented in Table 2. Compared to the Gullstrand's model eye, the posterior surface of the cornea was 0.5 mm steeper and the cornea was 0.05 mm thicker. In the Liou and Brennan's model eye, the anterior corneal asphericity (ACA) and PCA were -0.18 and -0.60, respectively, while in this study, the ACA and PCA were -0.12 and 0.21, respectively; the corneal radius of curvature and thickness were almost the same. Compared to that in the Nagahama study [11], the ACC was 0.10 mm atter and the ACD was 0.24 mm shallower. Compared to that in the German study [6], the ACC and PCC were 0.05 mm and 0.14 mm steeper, respectively and the ACD was 0.13 mm deeper. In addition, the AL in the present study was longer than that of any ocular model [2,3,5] and ALs reported in the previous studies [6, 11,13].
Concerning visual acuity, the UDVA improved with age (P = 0.000 for both subjective SE and objective SE, Figure 1), although there was a large variability. The CDVA decreased slightly with age (P= 0.000, Figure 1). For refraction, both subjective SE and objective SE changed to the positive side with age (P = 0.000, Figure 1). Furthermore, the J180 shifted to the minus side with increasing age, i.e., from with-the-rule astigmatism to against-the-rule astigmatism (P= 0.000 for both subjective J180 and objective J180, Figure 1). For J45, there was a trend towards greater variability with age; while no age-related changes were observed in the objective values (P= 0.067), a positive change toward 135° was noted in the subjective values (P= 0.013, Table 3). Furthermore, the the observation test power (OTP) was almost equal to 1 ( Figure   1).
Furthermore, the OTP in the univariate general linear model was almost equal to 1 (Figures 1 and 2).
Regarding sex-based differences, male participants had a slightly worse UDVA compared to that of female participants (P= 0.03) due to negative shifts in the subjective and objective SE (P= 0.014, P = 0.020, respectively; Figure 1 and Table  3).
Regarding ocular parameters, male participants had a slightly longer ocular AL (P < 0.001), deeper ACD (P < 0.001), atter corneal shape (ACC, P < 0.001; PCC, P < 0.001), and different ACA (positive side) as compared those of the female participants (P = 0.012; Figure 2 and Table 3). The anterior corneal power (ACP) and total corneal power (TCP) were signi cantly more refractive, and the posterior corneal power (PCP) was signi cantly more negative in female participants than in male participants (P = 0.000 for ACP, TCP, and PCP; Figure 3 and Table 3). The parameters that did not differ signi cantly were the CDVA (P = 0.  Table 3).

Discussion
We conducted a multicenter study on visual function and eye shape to create a Japanese myopic eye model. Results showed that the values of refraction were slightly myopic, and there were age-related changes and sex-based differences in many parameters.
The results of the descriptive statistics regarding refraction showed the low myopia, which could be related to the higher myopia rate among East Asians. Morgan et al. [8] showed that myopia was common among East Asians and reported that 80-90% of middle school graduates were affected. It has also been reported that the curvature of the corneal radius attens with increasing myopia [15]. Compared to the other model eyes [2,3,5,6,11], in this study the anterior surface of the cornea was similar, the posterior surface was slightly steeper, and the asphericity was on the positive side. This may be due to the unique structure of the Japanese eye, where only the AL of the eye is slightly longer. In fact, this result was similar to the result of the large-scale Nagahama study conducted by Nakao et al. [11]. The results of the present study showed that the AL was about 0.7 mm longer than that in the Nagahama Study [11], about 1.7 mm longer than that in the Liwan Eye study [13], and about 1.0 mm more myopic than that in the above-mentioned German study [6]; however, the difference in Nagahama study and Liwan eye study may be because our study also included people in their 20s. The shallower ACD of our model, as compared to that of some previous models [1-3, 5, 11], could be due to the higher average age of the participants and the inclusion of older individuals.
With regards to age-related changes, previous reports have shown that refractive values become hyperopic with increasing age [16]. In addition, the corneal radius of curvature becomes slightly steeper and the asphericity changes slightly [4]. Dubbelman et al. [17] showed that the corneal radius of curvature does not change with age in either the anterior or posterior surfaces, while the asphericity changes slightly. The AL of the eye is slightly reduced [18], and the lens are reported to experience steepening and have a decreased refractive index [19]. In this study, the refraction values became more hyperopic, the corneal radius of curvature became steeper, and the ocular AL became shorter with age, each with statistically signi cant correlations. Therefore, these age-related changes were similar to those in Nagahara's study for refraction [11] and in Navarro's study for the corneal radius of curvature [4]. The decrease in the ACD with increasing age appears to be mainly due to an increase in the lens thickness, which was in line with the ndings of a previous report [20]. Although the age-related changes in the eye shape were similar to those previously reported [4,11,20], the average height difference between 20-year-olds was about 10 cm higher than that between 80-year-olds [21], which may have affected the difference in the ocular AL. Zocher et al. [6] reported that there is a relationship between height and ocular AL; the regression equation is 0.0393 mm longer per 1 cm of the height.
Regarding sex-based differences, Roters et al. [22] reported that women have a slightly shorter ocular AL and ACD than men. Dubbelman et al. [17] reported that the anterior and posterior corneal surfaces of men were atter than those of women. For all other parameters, including asphericity and trends with age, no sex-based differences have been observed. The results of the present study showed sex-based differences in the SE, corneal shape, ocular AL, and ACD.
These differences between men and women could be related to a correlation between height and ocular shape [23,24]. This is consistent with the results of previous studies. A comparison of the results between the present study and those obtained by Zocher et al.
[6] regarding age-and sex-based differences showed that the results of this study were on the myopic side for all ages. The male eye showed more myopic refraction and an elongated myopic eye shape than the female eye.
Thus, race, age, and sex differences need to be considered when using an eye model to optimize refractive correction.
The most commonly used eye models include the Gullstrand's eye model and the LeGrand's precision eye model, which are spherical proximal axis models [1]. The Navarro's eye model is an aspheric model that can consider the effects of offaxis aberration and more closely resembles the shape of the human eye [3]. The Liou and Brennan eye model takes into account the distribution of the lens' refractive index [5]. The Arizona eye model by Schwiegerling can control the accommodation level with longitudinal chromatic aberration of the eye and longitudinal spherical aberration [25].
Furthermore, Atchison and Thibos have reviewed, in detail, the eye models reported in the past [26]. As biometric techniques develop, new ocular models are emerging, and the role of these models will become increasingly important in elucidating the functional role of ocular structures and in developing new refractive correction methods. Eye models based on biometric data should also be actively applied to the development of corrective methods (which are applicable to the majority of cases) and to the selection of appropriate corrective methods that are customizable, in order to meet the needs of individual patients and address the individual differences in refraction.
A possible limitation of this study was the inclusion of some variability due to differences in the autorefractometers used at the ve different institutions. However, the trend of the objective refractive data was similar to that of the subjective data, and we believe that the study conclusion would remain unchanged. In addition, the results provided in this study are from a sample size of 250, which is not su cient to re ect the whole of Japan. However, we believe that the reliability of the results can be ensured, because the measurements were conducted by specialists using instruments with high accuracy and reproducibility. Further studies are needed that address the limitations. The study ndings on the model should be interpreted as being re ective of the characteristics of the Japanese eye rather than of the Japanese population. In addition, it would be desirable to examine the statistical differences between the present model eyes and the model eyes reported previously; however, due to the unavailability of raw data, only simple comparisons of the means and medians were made rather than of the statistical tests of differences. Due to racial, regional, and chronological biases, caution should be exercised in interpreting the data, and it is important to conduct future studies to compare the data statistically.
In conclusion, we have obtained eye shape data that are representative of the Japanese population, although the limitations of the study described above must be considered and interpreted with caution. The results can be used to optimize standard optical designs and laser treatments, such as new eyeglasses, contact lenses, and intraocular lenses, for the Japanese and East Asian population. The model eye can be applied to other elds such as oncology or elds related to vision, such as electronic displays and lighting, and to provide comparative data when epidemiological studies are conducted in the future. In the future, it is important to collect data from a larger sample size and to also investigate data outside the scope of this study, including eyes with intense myopia and diseases, to compare with the data from other countries.

Methods
This was a multicenter, prospective observational study and a cross-sectional survey involving ve institutions: The UDVA and CDVA in the logMAR unit, subjective manifest refraction (spherical and minus cylindrical powers and axis), and objective refraction (spherical and minus cylindrical powers and axis) were evaluated using the autorefractometer. The AL was evaluated using optical low-coherence re ectometry (IOLMaster 500 or 700, Carl Zeiss Meditec AG, Jen, Germany). The radii of the ACC and PCC, ACA and PCA, CCT, and ACD expressed as the distance from the posterior surface of the cornea to the front surface of the lens were estimated using the Pentacam HR (Oculus, Wetzlar, Germany) with rotating Scheimp ug photography. The SE and power vectors, J180 and J45, were calculated from the subjective manifest refraction and objective refraction as follows (equation 1) [14]: where, Sph is the sphere power, Cyl is the minus cylinder power, and α is the minus cylinder axis.
The total corneal power (TCP) was calculated using the follow formula (equation 2): where, ACP is the anterior corneal power; PCP is the posterior corneal power; CCT is the central corneal thickness; ACC is the radius of the anterior corneal curvature; PCC is the radius of the posterior corneal curvature; and n1, n2, and n3 are the refractive indices of air (1.000), cornea (1.376), and aqueous humor (1.336), respectively. The PCC/ACC ratio and the AL / ACC ratio were also calculated.
These measurements were performed under non-mydriatic and non-cycloplegic conditions.
Statistical analyses were performed using the IBM SPSS Statistics software (version 25.0, SPSS, Inc., Chicago, IL, USA) and Microsoft® Excel® for O ce 365 (Microsoft Co., Ltd, Redmond, WA, USA). Descriptive statistics (mean, standard deviation, median, minimum value, maximum value, and percentage) were computed and tests of normality, Shapiro-Wilk test, was performed. A regression analysis of age for each parameter was performed to assess changes associated with age. Regression equations were either linear or curve estimations based on the height of the adjusted coe cient of determination. To know if the amount of data was su cient, we calculated the OTP using α = 0.05. The OTP takes a value between 0 and 1; the closer the value is to 1, the more likely that the analysis of variance (ANOVA) is based on su cient data.
Non-parametric analyses using the Mann-Whitney U test (for two groups) and the Kruskal-Wallis test (for independent samples) were performed to evaluate the sex-based differences in each parameter between the age groups. Furthermore, an ANOVA and the Games-Howell post-hoc test for multiple comparisons were performed to compare the parameters between the refractive data groups. A P value of less than 0.05 was considered statistically signi cant.
In addition, the results of this study were compared with those of previous reports and eye models [2, 3, 5, 6, 11]. Figure 1 Age-Associated changes in visual acuity and refraction for each study parameter (only signif-icant correlations have been extracted from Table 3 Ocular biometry. Age-associated changes for each study parameter (only signi cant correla-tions have been extracted from Table 3