The Guiding Significance of Ocular Biometry in Evaluating the Refractive Status of Preschool Children

The ocular refractive state in children is influenced by the coordination between the refractive components of the cornea and lens (Km, LP), anterior chamber depth (ACD), lens thickness (LT), and axial length (AL) during refractive development [1]. Previous studies reported AL, LP, and Km as the three main factors for refractive development in children [2]. Corneal curvature generally stabilizes after 3 years of age [3], and reduced LP in preschool children may prevent myopic progression caused by AL growth [4]. Therefore, studying the effects of LP changes on refractive states in children aged 3–6 years is crucial for understanding refractive changes in preschool-age groups.

One percent atropine sulfate eye ointment is routinely used for cycloplegic refraction in children under 6 years of age. However, because of its long metabolism time and because this method may cause a range of drug-related reactions such as poor near vision, photophobia, allergies, etc., the current report on the refraction state of the preschoolers is to use cyclopentone eye drops.

In this paper, the examination of cycloplegia was tested by 1% atropine sulfate eye ointment, which investigated the correlation between various ocular biological parameters and spherical equivalent (SE) in children aged 3–6 years more accurately, established a regression model correlating these parameters with SE, and provided guidance for clinical decision-making on children’s refractive status, thereby improving the accuracy of refractive screening in preschool children.

We collected data from 508 preschool children between 3 and 6 years admitted to Shijiazhuang Aier Eye Hospital between August 2021 and March 2023 with suspected ametropia requiring dilation optometry. Of the 508 children, 326 were included in the statistics group, examined from August 2021 to October 2022, and the remaining 182 children were included in the validation group, examined from November 2022 to March 2023.

The anterior segment was examined using a slit lamp (TOPCON SL-D4), and the fundus was examined using a direct ophthalmoscope (Suzhou 66 Vision YZ6f) to exclude organic lesions.

All the children underwent standardized point-eye dilation with 1% atropine sulfate ocular gel administered three times a day for three consecutive days after obtaining consent from their legal guardians. Following medication, the lacrimal sacs were pressed for 10 min. On the fourth day, optometry was performed to record the diopter number and the best corrected visual acuity during ciliary muscle paralysis.

Inclusion criteria: absence of organic eye disease; cooperation with the relevant inspection; presence of complete examination results; absence of shallow anterior chamber or other ocular abnormalities or diseases; patients without systemic contraindication of atropine sulfate; understanding of the purpose and significance of cycloplegia among parents and following doctor’s advice; conducting cycloplegic refraction within 1 week of ocular biometry.

Exclusion criteria are as follows: missing test results or parameters; allergic to atropine sulfate; abnormal intraocular pressure or previous diagnosis of glaucoma; participants with a history of head or heart disease or head trauma; presence of fever or acute conjunctivitis; failure to comply with the required cycloplegia protocol.

• (1) SE: SE = spherical mirror +1/2 column mirror

• (2) Mean corneal curvature (Km): Km = (K1 + K2)/2

• (3) Lens refractive power (LP): based on the data in the Gullstrand-Emsley model and calculated by Bennett formula [2], LP = −(1,000 n × [Sev + Km])/(1,000 n − [ACD + C1 × LT] × [Sev + Km]) + 1,000 n/(−C2LT + Vd). Sev = SE/(1 – 0.014 × SE), C1 = 0.596, C2 = −0.358, n = 1.336

• (4) The myopia group was defined as SE ≤−0.50 D, emmetropia as −0.50 D < SE < +0.50 D, and hyperopia as SE ≥+0.50 D.

IBM SPSS Statistics 25.0 was utilized for data analysis. The data normality assumption for SE, AL, Km, ACD, LT, CCT, and LP was tested using the Kolmogorov-Smirnov test. Independent sample t test and single-factor ANOVA were employed to determine gender, age, and refractive group differences for normally distributed data. Scatter plots were utilized for SE in linear relationships with other eye biological parameters, and those exhibiting linearity were analyzed using multiple linear regression. Paired t test was used to compare SE with predicted SE# in the validation group, and p > 0.05 was considered statistically consistent. Pearson correlation analysis confirmed the correlation between SE and SE#, where r > 0.975 and p < 0.05 indicated a high correlation.

A total of 508 participants were included in this study. In the statistics group, there were 156 boys and 170 girls. The validation group comprised 86 boys and 95 girls. A summary of the general characteristics of the participants is presented in Table 1.

A high consistency was found in the SE of both eyes (t = 0.062, p = 0.951). However, for statistical purposes, only the data from the right eye were used.

Comparisons of children’s eye biological parameters among different age groups are shown in Table 2, which demonstrated a statistically significant difference in SE (F = 23.84, p < 0.001), AL/CR (F = 34.34, p < 0.001), AL (F = 30.98, p < 0.001), ACD (F = 44.33, p < 0.001), LT (F = 35.36, p < 0.001), LP (F = 24.72, p < 0.001), but no significant difference in Km (F = 0.313, p = 0.816 > 0.05) or CCT (F = 2.306, p = 0.076 > 0.05).

The study examined the difference in eye biometric parameters between genders in the statistical group, with the results presented in Table 3. The analysis revealed significant differences between boys and girls, particularly in AL (t = 4.29, p < 0.001), ACD (t = 3.51, p < 0.05), LT (t = −2.14, p < 0.05), Km (t = −4.69, p < 0.001), and LP (t = −6.83, p < 0.001). Specifically, boys had longer AL, larger ACD, and smaller LT, Km, and LP than girls. However, no significant differences were observed in SE (t = −0.02, p = 0.986 > 0.05), AL/CR (t = 1.12, p = 0.264 > 0.05), and CCT (t = 0.81, p = 0.421 > 0.05).

As shown in Table 4, the biometric parameters of the eye were analyzed concerning the refractive status of participants. Among the groups, AL/CR (F = 193.27, p < 0.001), AL (F = 127.81, p < 0.001), ACD (F = 66.02, p < 0.001), LT (F = 35.39, p < 0.001), and LP (F = 7.76, p < 0.05) showed statistically significant differences. Specifically, patients who were more myopic had significantly larger AL/CR, longer AL, larger ACD, smaller LT, and smaller LP. However, no statistically significant difference was observed in Km (F = 1.67, p = 0.191 > 0.05) or CCT (F = 0.43, p = 0.649 > 0.05) among different refractive status groups.

Pearson’s correlation analysis was conducted to determine the relationship between SE and various parameters (Fig. 1a–g; Table 5). The results indicated that SE had a significant negative correlation with AL/CR (r = −0.936, p < 0.001), AL (r = −0.811, p < 0.001), ACD (r = −0.500, p < 0.001), age (r = −0.396, p < 0.001), and Km (r = −0.213, p < 0.001). In contrast, SE had a significant positive correlation with LT (r = 0.302, p < 0.001) and LP (r = 0.176, p < 0.05) but no correlation with gender (r = −0.01, p = 0.985 > 0.05) or CCT (r = 0.001, p = 0.989 > 0.05). Among these correlations, the highest was observed between SE and AL/CR, AL, and ACD.

Table 6 presents the multiple linear regression analysis results, which showed that the regression equation was significant (F = 13,938.065, p < 0.001). Among the variables, AL/CR (β = −1.380, p < 0.001), ACD (β = 0.159, p < 0.001), Km (β = −0.389, p < 0.001), LP (β = −0.374, p < 0.001), and LT (β = 0.075, p < 0.001) had significant effects on SE, while AL (β = −0.112, p = 0.126) and age (β = −0.004, p = 0.364) did not. To identify the most important variables, a stepwise selection method was used, resulting in the following optimal regression equation shown in Table 7: SE = 49.232 – 23.583 × AL/CR + 1.703 × ACD + 0.589 × Km − 0.609 × LP + 1.103 × LT (R² = 0.997). These variables accounted for 99.7% of the variation in SE.

Table 8 presents the results of the linear regression analysis of SE and AL/CR, which revealed a significant negative predictive effect of SE (F = 2,287.353, p < 0.001), with AL/CR accounting for 87.6% of the variation in SE. The prediction model for SE was established as follows: SE = 51.675 – 17.416 × AL/CR (R² = 0.876).

As shown in Table 9 and Figure 2, in the validation group, SE# predicted by the regression equation demonstrated a highly significant correlation with SE (r = 0.998, p < 0.001). Additionally, the consistency analysis revealed good consistency between them (t = 0.787, p > 0.05).

Km, ACD, LT, and AL can be measured directly by ophthalmic measurement instruments, while LP requires calculation. Currently, crystal calculations are mainly performed using the improved Stensrom method, Bennett-Rabbetts formula method, and Bennett formula method. According to Rozema et al. [5] (2011), the most optimal method for determining crystal diopter is using the Bennett formula with known crystal thickness. In this study, we measured the crystal thickness using Master700 and determined the crystal diopter (LP) utilizing the Bennett formula. Our findings showed significant differences in SE, AL/CR, AL, ACD, LP, and LT among various age groups, which suggested that older children aged 3–6 have smaller SE, LT, and LP values but larger AL/CR, AL, and ACD values. These findings align with prior Australian research results [6]. In children and adolescents, the lens power decreased as the AL increased [7]. We found significant differences in AL, ACD, LT, Km, and LP among various gender groups, where boys have longer AL, deeper ACD, thinner LT, flatter Km, and less LP. Li reported in 2019 that after multivariate analysis, preschool girls in Shanghai, China, had longer AL than boys [8]. There were statistically significant differences in ocular biological parameters, such as AL/CR, AL, ACD, LT, and LP, among groups with varying refractive states. The more it approached a negative mirror, the larger the values of AL/CR, AL, and ACD, and the smaller the values of LT and LP. These findings align with Muzyka-Wozniak et al. [9] that refractive errors have the most significant impact on anterior segment parameters and AL in children, especially on the values of AL, ACD, and LT.

Refraction is determined through the coordinated contributions of ocular biometric components, such as AL, ACD, Km, and LT [10, 11]. Our correlation analysis showed that SE has a negative correlation with variables such as AL/CR, AL, ACD, age, and Km and a positive association with LT and LP, with no correlation with gender and CCT. Our study found that the correlation coefficient between SE and ACD was −0.464, ranking third after AL/CR and AL. However, the effect of ACD on SE is currently inconsistent among studies. Hosny et al. [12] (2000) reported a negative correlation between ACD and SE (r = −0.623, p < 0.01), while Zhou et al. [13] (2013) found no correlation between ACD and SE in children aged 3–14 with hyperopia amblyopia. Moreover, Cai et al. [14] (2016) pointed out that ACD did not change significantly with a change in hyperopia diopter (r = 0.080, p < 0.05) in children (ages 3–8) with hyperopia. The reasons may be related to the study subjects’ age, refractive state, and ocular biometric methods, and further studies are needed in future work.

Generally, newborns have an average diopter of +2.50 ∼ +3.00 D [15]. Hyperopia reserve is a physical condition that diminishes with age. At age 6, the mean hyperopia reserve is +1.33 D [16]. Depletion of the hyperopia reserve before the age of 6 is likely to result in myopia during primary school. Therefore, hyperopia reserve is a relatively accurate predictor of myopia in children [17]. It is practically significant to establish a “prediction formula” for the refractive development of the eyeball to control myopia in children and adolescents. Children between 3 and 6 years of age experience critical eye development, which is often hindered by their high accommodation, leading to reduced accuracy of apparent refraction [18]. Olsen et al. [10] proposed that the simultaneous consideration of AL, LP, and K in multiple linear regression analysis can explain up to 96% of the variability in the population’s diopter. The establishment of a regression curve linking ocular diopter and biological parameters can facilitate rapid clinical judgment of children’s refractive status and improve the accuracy of refractive screening in preschool children. The regression equation for SE obtained in this study is as follows: SE = 49.232 – 23.583 × AL/CR + 1.703 × ACD + 0.589 × Km − 0.609 × LP + 1.103 × LT with an R² value of 0.997. By substituting AL/CR, ACD, Km, LP, and LT into the formula, the diopter of children can be obtained with relative accuracy. The regression model proposed by Chen et al. [19] for the static diopter of children aged 3–12 is SE = 110.56 – 2.51 × Al − 0.97 × Km − 0.44 × LP with an R² value of 0.95. In a study by Yu et al. [20], children and adolescents aged 4–13 were measured through an ultrasound, and the regression equation SE = 90.124 + 2.345 × ACD + 2.252 × CT − 2.477 × A − 0.978 × CD (where CT refers to central corneal thickness, A refers to AL, and CD refers to Km) was obtained, with an R value of 0.937. Based on varying studies, AL and Km are the two ocular biological factors strongly correlating with SE. Among ocular biological factors, AL and corneal Km correlate most strongly with SE [21]. To verify the accuracy of the SE regression curve, we substituted the biological values of children in the validation group into the regression curve, which resulted in the predicted SE#. We further analyzed the consistency between the SE under cycloplegia and the predicted SE# of the validation group, revealing high consistency (r = 0.998, p < 0.001).

Corneal refractive power is mostly determined by the radius of corneal curvature (CR). The smaller the CR, the greater the corneal refractive power. AL and CR are two important biological factors that determine the refractive status of the eye [22]. The correlation between AL/CR and ametropia was first proposed by Grosvenor [23]. The measurement of AL/CR is relatively objective, less influenced by subjective and regulatory factors, and easier for children to cooperate with during the examination. Notably, this method has some clinical significance in predicting the onset and progression of myopia in children who are unwilling or unable to receive dilated optometry [24]. In this paper, the SE prediction model established by AL/CR was SE = 51.675 – 17.416 × AL/CR (R² = 0.876), and AL/CR explained 87.6% of the variation in SE. When SE = −0.50 diopters, and AL/CR = 3.00, it confirmed the previous idea that myopia incidence significantly increases when AL/CR >3.0 [25].

Cycloplegic retinoscopy is the standard method for evaluating refractive errors in children [26, 27], and it is recommended that 1% atropine sulfate eye ointment or drops be used in children under 6 years of age [28]. However, because of its long metabolism time, this method may cause a range of drug-related reactions such as poor near vision, photophobia, allergies, etc. This can result in reduced acceptability by children and their guardians, making it unsuitable for sampling large populations. In preschool children, cyclopentolate eye drops are often used for cycloplegic refraction. In this study, to comply with ethical guidelines, 3–6-year-old children who were objectively diagnosed with ametropia and required mydriasis underwent cycloplegic refraction with 1% atropine sulfate eye ointment. The results reflected a more realistic relationship between the refractive error and ocular biological parameters, which is the main characteristic of this study.

Despite this, there are some limitations. As most hospitalized patients had ametropia, the sample size was small and could not demonstrate the true incidence of ametropia in children aged 3–6 years. Consequently, when examining the effect of age and gender on ocular biological parameters, there might be some deviations.

In conclusion, the 3–6 year age range marks a critical period for ocular development in children, and the refractive state is influenced by various factors. This study discussed the relevant ocular biological parameters associated with SE and conducted a regression analysis to obtain the SE prediction model. This model has significant clinical value in rapidly evaluating the refractive status of preschool-age children. Monitoring changes in these biological parameters is crucial to evaluating ocular refractive development. Using the SE regression equation, clinicians can assess the refractive status of 3–6-year-olds and develop targeted treatment plans, such as carrying out myopia prevention and control, cycloplegic refraction, or amblyopia diagnosis and treatment, to avoid unnecessary procedures and accurately evaluate ocular refractive development.

The main ocular biological factors of ocular diopter in children aged 3–6 years are AL/CR, ACD, Km, LP, and LT, which are jointly influenced by multiple factors. Ocular biometry is a reliable predictor of real refraction among children aged 3–6.

We thank all the colleagues in the Optometry Department of Shijiazhuang Aier Eye Hospital, and thanks to Yingchun Xian, Bei Hao, Xiaoying Jiao,Haiyan Lan, Zetong Li for sorting out the data.

Prior to the examination, the consent of each child and his/her parents/guardian should be obtained, and the wishes of parents and children should be respected. Due to the observational nature of this study, written consent of patients is no longer required. This consent protocol was reviewed and the need for written and informed consent was waived by the Medical Ethics Committee of Shijiazhuang Aier Eye Hospital. The study was designed and implemented in accordance with the Declaration of Helsinki (revised in 2013). This study protocol was reviewed and approved by the Medical Ethics Committee of Shijiazhuang Aier Eye Hospital, approval number [2021001]/date [20210112].

The research project does not involve personal privacy or commercial interests. The author has no conflict of interest to explain.

There is no funding for this study.

Ya Zhang and Lingling Liang were responsible for data collation and statistics; Ming Su was responsible for the project design; Bingjie Shi, Dongmei Gong, and Yidan Wu were responsible for optometry; Junying Zhang was responsible for eye biometric measurement; and Ming Wang was responsible for proofreading the whole document.