Ocular biometry in children and adolescents from 4 to 17 years: a cross‐sectional study in central Germany

To evaluate ocular biometry in a large paediatric population as a function of age and sex in children of European descent.


Introduction
Measurement of ocular biometry has become increasingly important in the paediatric population in order to assess the refractive status of the eye in children and adolescents. Exact data on ocular biometry during the growth of the eye is needed to understand the process of emmetropization and describe the development of refractive errors such as myopia. Myopia prevalence is increasing around the world, 1 which can lead to potentially blinding complications in adulthood. It is therefore important to identify the factors involved in emmetropization and the development of refractive error in general. 2,3 The distribution of refractive errors in the population is leptokurtic, with a bias towards emmetropia in adults. 3 Variations in axial length account for much of the observed change in refractive error. Emmetropization is an active mechanism in which the eye modulates its growth to minimise the mismatch between its size and the focal length of its optics. 4,5 Findings from animal studies show this mechanism is local and visually guided, and can be experimentally manipulated. [6][7][8][9] Knowledge of changes in refraction and biometry during childhood is essential to identify the failure of the emmetropization process. Therefore, data on ocular biometry is needed while the eye grows during childhood. Occurring during the first years of life, the most important factor in emmetropization is axial length growth in response to an initial refractive error leading to a change in refractive state; this process is guided by visual feedback. 4,5,8,10 Previous work investigated ocular parameters in the early years of life, mainly using A-scan ultrasound supported by keratometry and phakometry. 11 Newborn babies presented with axial lengths between 16.50 and 17.70 mm, 12 or in a different study between 16.60 to 19.04 mm for boys (mean 17.7 mm) and 16.70 to 18.50 mm for girls (mean 17.5 mm). 13 A summary study on children after their first, second and third birthdays observed axial lengths of 20.19 mm, 21.31 mm and 22.07 mm, respectively. 14 Other data show a similar trend, with mean values in newborns and at 3 years of age of 16.08 mm and 23.60 mm, repectively. 15 Similarly, Mutti et al. reported mean axial lengths at 3 and 9 months of age of 19.03 mm and 20.23, respectively. 5 The cornea and crystalline lens reduce their dioptric power substantially, although Mutti and co-workers stated that the reduction is not sufficient to prevent emmetropization, nor does it play a passive role in this process. 5 The observed change in corneal curvature was highest in newborns, with mean keratometry values at 2, 4 and 8 weeks of age being 49.01 D, 45.98 D and 44.60 D, respectively, 16 followed by a 1 D change from 3 to 9 months (43.90 D to 42.83). 5 Previous work concluded that corneal radii reach adult values at 3 years of age. 17 Central corneal thickness reduced from 541 µm in newborns to 520 µm in young childhood, after which no further change was observed. Lens power reduced markedly from newborns to 2 years of age. 11 Lens thickness in newborns was measured at 3.4 mm, 12 and in an alternative investigation 3.6 mm (girls) or 3.7 mm (boys). 13 Mutti and co-workers recorded lens thickness values of 3.92 and 3.86 mm at 3 and 9 months, respectively. 5 Geographic region and place of origin is important when comparing ocular biometry data because differences have been shown to exist both in the prevalence of refractive error and value of biometric components. 1,18 Differences in eye development are based on both genetic predisposition and environmental factors. In order to detect subtle changes in biometry throughout childhood and adolescence, a wide age range and narrow age groups are needed. A 1961 study in the UK investigated 1430 children 3-14 years of age. This work by Sorsby and co-workers presented corneal radii by keratometry and axial length using a conjugate foci method; the depth of the anterior chamber and lens thickness and radii were quantified from photographs. 19 Larsen examined ocular biometry by ultrasound in a sample of 846 children in Norway aged 5-13. [20][21][22][23] Twelker et al. examined ocular biometry in 6-14 years old children in the USA by assessing corneal curvature (keratometry), axial dimensions (ultrasound) and lens curvature (videophakometry). They included 835 white children 6 years or younger and 866 white children between 7 and 14 years. 18 Hashemi and colleagues examined 683 Iranian children between 6 and 18 years. 24 They employed optical low coherence reflectometry, summarising their data in two-year intervals. Others have investigated axial length, corneal radii and anterior chamber depth by using partial coherence interferometry. For example, two UK studies, Logan et al. 25 and McCullough et al. 26 evaluated children from two age groups, namely 7 and 13 years, both combining female and male participants; while a study from Norway examined adolescents between 16 and 19 years of age separated by sex. 27 Previously, only A-scan ultrasound biometers enabled measurements of axial length, anterior chamber depth, lens thickness and central corneal thickness. Today, other methods are available for the measurement of ocular biometry with better precision than A-scan ultrasound; for background of those methods see the review by Koumbo Mekountchou et al. 28 Non-contact optical methods provide highly repeatable measurements, 29-31 offering a major advantage when assessing ocular biometry components in childhood.
The aim of the current study is to report normative ocular biometry data for a large sample of children in Germany over a wide age range, i.e., 3.5-17.5 years. With a view to extending knowledge from the aforementioned studies on children during infancy, we investigate children across a large age span into adulthood. Data will be presented by year, enabling analysis for ocular growth in detail. Further objectives are to describe sexrelated differences and to report on the change in these variables with age and the relationship of each respective variable with axial length. Data were filtered by a quality criterion based on repeatability prior to analysis. 29

Setting
Children were examined as part of the LIFE Child Study (Leipzig Centre for Civilization Diseases) in the city of Leipzig, Germany. The LIFE Child Study is a network of various medical subspecialties investigating the reasons behind civilisation diseases and examining children from womb to adulthood. LIFE aims to unravel the interplay between genetic predisposition, metabolism, environment and individual lifestyle. 32 Processes are identical across different age groups. Recruitment of participants between 3 months and 16 years of age was carried out by advertisement at different institutions by media or word of mouth. 32 Children and adolescents are included at various ages. Household income and the education of parents suggests a selection towards higher socioeconomic status. 32 In order to counter-balance this, the LIFE Child Study recruits whole school classes (29% of all participants) throughout Leipzig, a city in central Germany with more than 550 000 inhabitants. Inclusion into the LIFE Child Study is described as "children not suffering from any chronic, chromosomal and syndromal diseases"; for details see Poulain et al. 32 Written informed consent was obtained from the parents of all individual participants included in the study. Oral consent is additionally obtained from all children, and from age 12 onwards, written consent was provided by the participating adolescents. Participants have the right to withdraw from the study at any point. The LIFE Child Study adheres to the tenets of the Declaration of Helsinki and approval for the study was obtained from the Ethics Committee of the Medical Faculty of the University of Leipzig (Reg. No. 264- ; ethical approval for the optometric examination (Reg. No. 089-13-11032013) was also obtained. The study was registered at ClinicalTrials.gov, trial number NCT02550236.
Autorefraction and biometric examination of the eye were introduced into the study in 2014 in order to investigate eye development. Objective refraction was measured with the ZEISS i. Profiler plus wavefront-based autorefractor (Carl Zeiss Vision, zeiss.com). Ocular biometry was investigated using the Lenstar LS 900 (Haag Streit, haagstreit.com). Utilising optical low coherence reflectometry (OLCR) technology, this device measures biometric variables in a non-contact manner with fast examination time. 33 The corneal radii for the steep and flat meridians can also be determined.
In the present cross-sectional study, ocular biometry and refraction data were collected at the base-line visit of all children examined between January 2014 and June 2018. All data were collected without cycloplegia.

Participants
Participants originated from the city of Leipzig, and data presented here were restricted to participants of European descent. Data from at least one Lenstar LS 900 measure output (at least one variable) were required for the child to be included. Children and adolescents were required to be free of ocular disease. Only children between 3.5 and 17.5 years of age were included. This resulted in a total of 1907 children.

Variables
Variables assessed in the present study were central corneal thickness (CCT), aqueous depth (AD) indicating the physiological length of the anterior chamber from the corneal endothelium to the anterior surface of the crystalline lens, lens thickness (LT) and axial length of the eye (AL). Vitreous depth (VD) was calculated as AL minus CCT, AD and LT, and indicates the distance from the posterior surface of the lens to the retina. The flat (R1) and steep radii (R2) of the anterior surface of the cornea were also obtained. Derived from these radii and appropriate refractive index, corneal astigmatism was computed in dioptres, see Figures S1 and S2. In order to allow averaging across subjects per year (age), corneal astigmatism was converted into astigmatic vector components, i.e., J 0 and J 45 computed by the following formula: C (dioptres) = À2 *(J 0 2 + J 45 2 ) ½ . 34 The average axis as a function of age in years, as presented in Figure S1, was converted back to degrees using the following formula A (degrees) = 0.5 * tan À1 (J 45 /J 0 ). 34

Refraction
Wavefront-based autorefraction was analysed for the spherical equivalent (M) and astigmatic components J 0 and J 45 . 34 For three consecutive measurements per eye obtained by the iProfiler we carried out the following steps, prior to analysis: for M, the most positive measure output was carried forward for analysis; as described previously. 35 For J 0 and J 45 , the average of three consecutive measure outputs was used. The median value for M, J 0 , and J 45 was computed for each year of age; this is displayed in Figure 1 with numerical values presented in Table S1. Based on a common definition of emmetropia (À1.0 D to +1.0 D), 85% of the children were emmetropes, about 8% hyperopes and 7% were myopes. As shown in Figure 1a, the median value of M indicated low hyperopia for younger children and low myopia for older children. As depicted in Figure 1b, children with shorter axial lengths tended to have low hyperopia, whereas children with longer axial length were myopic. Note that this figure does not display the differences in axial length with age (see Figure 2a). The median astigmatic components, i.e., J 0 ( Figure 1c) and J 45 ( Figure 1d) showed minor variations with age. Corneal astigmatism ( Figure S1) exceeded refractive astigmatism 17

Data source
All data for the study variables were obtained with the Lenstar LS 900. The device measures ocular distances (CCT, AD, LT and AL) by low coherence optical reflectometry employing an 820 nm superluminescent diode with a Gaussian-shaped spectrum. The device obtains the curvature of the front surface of the cornea (R1, R2) by analysing the anterior corneal curvature at 32 reference points orientated in two circles, with optical zones at 2.30 mm and 1.65 mm.
Participants were seated with their head stabilised using a chin rest and brow bar. During the examination, participants were asked to fixate the internal fixation light while the Lenstar data capture was aligned and executed by the operator. The instrument is aligned using an image of the eye on the computer monitor. Subjects were asked to blink just before each Lenstar data capture. The device has a proprietary quality check mechanism which may withhold parts of the measure output for some variables. For example, there may be cases where it saves a measure for AL, but not for LT. This in-built proprietary quality check mechanism was not evaluated in the present study. . Axial length and lens thickness as a function of age (a, c), body height as a function of age (b) and lens thickness as a function of axial length (d). For better visualisation, data is shifted sideways to allow differentiation of measurements for boys and girls. Reported data depicts the mean for the respective group and the 95% confidence interval.

Data evaluation and statistics
For analysis, each individual data capture (per variable) was termed a measure output. We considered only variables of children with at least three consecutive measure outputs by the Lenstar device. The first step was the calculation of the mean and standard deviation from the first three consecutive Lenstar measure outputs for the variable in question. This mean of three measure outputs represents our "measurement". Second, a quality criterion was applied as follows.
The calculated standard deviation needed to be smaller than the repeatability limit estimated in a previous study. 29 These repeatability limits were available for three different age bands: i.e., from 3.50 to 6.49 years, 6.50 to 10.49 years and 10.50 to 17.49 years, and were applied accordingly to our present data. Readings with standard deviations larger than the respective repeatability limit were excluded. Subsequent analyses were separated by sex and age. Fourteen age groups were formed, spanning 12 month intervals from 3.5 to 17.5 years of age. For example, the "4 year age group" included cases from 3.50 to 4.49 years of age. There were about the same number of cases for both sexes (Table 1), and age was approximately normally distributed inside each age group. Data were analysed by axial length into six groups. This was based on the need to include sufficient number of cases per group, and to have equal group width for the most common values of axial length. The six groups were formed in the following way: one group with all values below 22 mm, four groups between 22 and 24 mm, each interval 0.5 mm wide, and one group above 24 mm.
A two-way analysis of variance (ANOVA) was performed for all biometry variables with age and sex as factors. This was followed by a one-way ANOVA for each sex to compare the effects of age separately for girls and boys. ANOVA contrasts for four a priori selected age pairs were calculated (4 vs 7 years, 7 vs 10 years, 10 vs 14 years and 14 vs 17 years). The same approach was adopted with a two-way ANOVA with axial length and sex as factors, followed by a one-way ANOVA and the difference between the six axial length groups separately for girls and boys. ANOVA contrasts for five a priori selected axial length pairs were calculated. These pairs always comprised neighbouring axial length groups. All ANOVA a priori contrasts had an orthogonal design.
Significance level was set to p < 0.05. All figures depict the mean and 95% confidence intervals. Statistical calculations were carried out using SPSS v.22 software (IBM, ibm.com).

Number of cases per variable
Of the 1907 cases included, the Lenstar was able to output the following number of successful measurements: for AL and CCT: 1841; R1 and R2: 1800; AD: 1626 and LT: 1279. After applying the repeatability limit as a quality cut-off to accept a measurement for succeeding analyses, the following number of measurements were available: AL: 1744; CCT: 1727; R1: 1747; R2: 1777; AD: 1582; LT: 1261. These measurements were used to calculate the ocular biometry findings (Table 1).

Axial length (AL)
Axial length differed statistically significantly between girls and boys ( Table 2 Table 2). Children's height with respect to age is depicted in Figure 2b. Here, a continuous increase until 14 years of age is observed; after that, girls level off in mean height while boys continue to grow steadily in the sample investigated.

Central corneal thickness (CCT)
Central corneal thickness differed statistically significantly between girls and boys ( Table 2, Factor sex). CCT in girls did not change statistically significantly between 4 and 7 years of age. There was a statistically significant increase between 7 and 10 years and, thereafter, no statistically significant change until 17 years. CCT at 4 and 17 years of age was 548 and 549 µm, respectively; the overall mean was 550 µm (Figure 4a). CCT in boys did not change statistically significantly between 4 and 17 years ( Table 2, Oneway ANOVA). CCT at 4 and 17 years of age was 546 and 552 µm, respectively; the overall mean was 554 µm (Table 1 and Figure 3).
When CCT was plotted against AL groups (Figure 4b), the only statistically significant change found between neighbouring AL groups was for girls with short eyes, 542 µm (AL < 22.0 mm) compared with 550 µm in the somewhat longer eyes (AL 22.0-22.5 mm). There were no sex differences for CCT when compared according to AL groups (Table 3, Factor sex).

Corneal flat (R1) and steep radius (R2)
There was a statistically significant difference between girls and boys for R1 and R2, respectively (Table 2, Factor sex). Comparing all age groups with ANOVA, R1 and R2 changed statistically significantly in girls, but there was no statistically significant change between our pre-established age group comparisons. For R1 and R2 in boys, there was no statistically significant age-related change. At 4 years of age, R1 was 7.70 mm in girls and 7.89 mm in boys (Figure 4c). At 17 years of age, mean values were 7.82 mm for girls and 7.89 mm for boys. Findings for R2 were very  Table 2). When plotted against axial length (Figure 4d), R1 was flatter with longer AL, with mean R1s of 7.61 mm (short eyes) to 7.97 mm (long eyes) in girls, and mean R1s of 7.68 mm (short eyes) to 8.10 mm (long eyes) in boys. Results for R2 were similar (Figure 4f). There was a statistical significant difference between girls and boys for R1 and R2, respectively, when compared according to AL groups (Table 3, Factor sex).   Table 1 and statistical results from Table 2. Mean values for five selected ages (4, 7, 10, 14 and 17 years) are given if there was a statistically significant difference between them; based on one-way ANOVA a priori contrasts for four age pairs: 4 vs 7 years, 7 vs 10 years, 10 vs 14 years and 14 vs 17 years (lower part of Table 2). The average change per year for the respective variable is given for age intervals where statistical significance was found.

Aqueous depth (AD)
Aqueous depth differed statistically significantly between girls and boys ( Table 2, Factor sex). AD increased in girls with age, from 2.73 mm (4 years) up to 3.01 mm (10 years), with a 0.046 mm increase per year. Between 10 and 17 years of age, no further statistically significant increase was noted, resulting in a mean AD at 17 years of 3.06 mm. AD increased in boys from 2.86 mm (4 years) to 3.14 mm (10 years), with a 0.047 mm increase per year. Between 10 and 17 years, there was no further statistically significant increase, resulting in a mean AD at 17 years of 3.20 mm (Figures 3 and 5a and Table 2). AD increased in eyes with longer AL, see Figure 5b, with mean AD of 2.76 mm (short eyes) to 3.25 mm (long eyes) in girls, and mean AD of 2.79 mm (short eyes) to 3.31 mm (long eyes) in boys. For AD there was a statistically significant difference for sex in the respective AL groups (Table 3, Factor sex).

Lens thickness (LT)
For LT, there was an overall statistically significant difference found between girls and boys (Table 2, Factor sex). LT decreased in girls from 3.75 mm (4 years) to 3.47 mm (10 years), with a 0.046 mm decrease per year. Between 10 and 17 years, there was no further statistically significant change, resulting in a mean LT at 17 years of 3.52 mm. LT decreased in boys from 3.73 mm (4 years) to 3.44 mm (10 years), with a 0.047 mm decrease per year. Between 10 and 17 years, there was no further statistically significant change, resulting in a mean LT at 17 years of 3.50 mm (Figures 2c and 3 and Table 2). Girls showed the lowest LT at 11 years of age (3.46 mm) and boys at 12 years of age (3.43 mm).
Shorter eyes had thicker lenses, see Figure 2d. LT was higher (3.69 mm for girls and 3.70 mm for boys) in short eyes, and lower in longer eyes (3.41 mm for girls and 3.40 mm for boys). There was no statistically significant difference for sex for LT when compared according to AL groups (Table 3, Factor sex).

Vitreous depth (VD)
Vitreous depth was statistically significantly different between girls and boys ( Table 2 (Figures 3 and 5c and Table 2). Vitreous depth increased with axial length from 14.5 mm (short eyes) to 17.3 mm (long eyes) for girls and from 14.5 mm (short eyes) to 17.3 mm (long eyes) for Table 3. Two-way ANOVA with axial length and sex as factors and one-way ANOVA with axial length, split for female and male boys. There was no statistically significant difference for sex for VD when compared according to AL groups (Table 3, Factor sex).

Influence of astigmatism
Corneal astigmatism for children between 3.5 and 17.5 years of age is presented in Figure S1. Median J 0 was 0.34 D for boys and 0.39 D for girls; median J 45 was 0.03 D for boys and 0 D for girls. There was no apparent change with age. It is of interest to investigate the influence of corneal astigmatism on ocular components. As displayed in Figure S2, children with more corneal astigmatism had shorter eyes (axial length, aqueous depth) compared to children with low corneal astigmatism. A trend for thinner CCT in the group with higher corneal astigmatism was observed. LT and flat corneal radius did not differ between astigmatic groups. However, different corneal astigmatism groups exhibit strong differences in the steep corneal radius (R2).

Discussion
This is the first report of biometry measured in a large cohort of children and adolescents in Germany. For (c) (d) Figure 5. Aqueous depth (a, b) and vitreous depth (c, d) as a function of age (a, c) and axial length (b, d). For better visualisation, data is shifted sideways to allow differentiation of measurements for boys and girls. Reported data depicts the mean for the respective group and the 95% confidence interval.
comparison, other data from individuals of European descent are used.

Limitations
It has to be taken into account that the current analysis is based on cross-sectional data, which means that generational effects cannot be entirely excluded. However, we considered the difference of 14 years between our youngest and oldest participants was acceptable for comparisons based on age. Axial length, corneal radii and central corneal thickness were measured successfully in 94%-97% of cases. For aqueous depth, 85% of cases could be measured, although some difficulties arose due to non-detection of the anterior lens surface. Lens thickness was measured successfully in 66% of the cases across all ages. Here, non-detection of anterior and/or posterior lens surfaces was probably an issue. The number of cases obtained per variable for all ages is shown in the lower part of Table 1. Details for different age bands are provided in the accompanying paper. 29 Axial length (AL) As seen in Figure 2a, girls have shorter eyes than boys of the same age. At 4 years of age, girls exhibit on average 0.63 mm shorter axial length than boys. Girls' eyes then grow at a very similar rate to boys until 14 years of age. The AL in 10-year-old boys has the same mean value as for 14-year-old girls (23.3 mm). Between 10 and 17 years of age, the AL in boys increased from 23.3 to 23.9 mm, although this change was not statistically significant in our study.
Hashemi et al. 24 found very similar AL values in their population of Iranian children between 6 and 18 years of age (n = 648). This is also true for the findings of Twelker et al. 18 for white US children from 6 to 14 years (6 years and below, n = 835; 7-14 years, n = 866). The mean AL findings from those two studies differ from our values by between +0.4 and À0.2 mm for the respective ages. Additionally, Larsen 21 observed mean values that were 0.4 to 0.6 mm shorter than our results. Since both Larsen 21  It is of interest to compare the current results with studies of ocular growth. Tideman and colleagues found axial length increased in all percentiles until the age of 9, while percentiles below the median increased until the age of 15. These median percentiles were associated with >50% risk of developing myopia in adulthood. 37 Their median percentile between ages 6 and 15 increased by 1.09 and 1.06 mm in girls and boys, respectively. This is similar to the increase in mean AL between ages 6 and 15 found in the present study (1.25 mm in girls and 1.07 mm in boys). Likewise, Jones et al. presented growth curves for AL in different refractive groups. Data both above and below 10.5 years of age were similar to the current study; however, they did not separate girls and boys. 38 Similar findings have also been shown for Asian eyes. 39 In both emmetropes and hyperopes, AL growth was faster in younger children and decreased with age. However, prevalent and new myopes demonstrated much faster AL growth. 39

Central corneal thickness (CCT)
We found no clinically significant change in CCT between 4 and 17 years of age, with mean findings of 550 µm in girls and 554 µm in boys, see Table 1 and Figures 3 and 4a. Very similar values were found for children 24,40 and adults examined in Leipzig, Germany. 36 When CCT is compared with axial length, girls have statistically significantly thinner (10 µm) corneas compared with boys, but only in short eyes (<22.0 mm). For longer eyes, no statistically significant difference between girls and boys in CCT was observed ( Figure 4b and Table 3).

Corneal anterior radii (R1, R2)
We found very slight, and non-significant changes in corneal curvature (R1 and R2) in girls from 4 to 13 years of age, e.g., R1 from 7.70 to 7.79 mm, see Table 1 and Figures 3 and 4c,e. However, analysis for sex found statistically significant differences between girls and boys for all age groups up to 11 years, and also at 13 years. At 17 years of age, R1 was 7.82 mm in girls and 7.89 mm in boys. Our results for R2 are also in accordance with these findings.
The same trend for girls was reported by Hashemi et al., 24 with mean corneal radius increasing in girls from 6 to about 12 years of age, and reaching the values in boys at 17 years, with no increase for boys between 6 and 17 years of age. Twelker et al. 18 did not find a change in corneal power for boys and girls between 6 and 14 years.
These sex-related differences may be linked to the smaller size of the globe in young girls, which reach the value of axial length in boys by about 14 years of age. Our results disagree with the findings of York and Mandell, 41 who found that corneal radii increased from birth to age 1, at which time they claimed corneal radii had reached adult values. However, they did not account for sex differences in the data. Furthermore, York and Mandell employed photokeratoscopy, which has measurement bias (0.57 D flatter) compared with keratometry, and may miss clinically significant corneal astigmatism, as shown by Zadnik et al. 42 Further, we found that corneal radii increased linearly with axial length (Figures 4d and 4f). The mean flat corneal radius was 7.77 mm in short eyes (22.0-22.5 mm) and 7.98 mm in long eyes (23.5-24.0 mm). This results in less corneal power in longer eyes, as was also reported by Scott and Grosvenor. 43 Aqueous depth (AD) Aqueous depth increased at the same rate in girls and boys between 4 and 10 years of age, but girls presented with lower values, being 0.13 mm shorter at age 4 compared to boys. At age 17 a sex-related difference of 0.14 mm remains, see Table 1 and Figures 3 and 5a.
An increase in AD (Figure 5a) is driven by two aspects, firstly a decrease in lens thickness (LT) as noted below, and furthermore by an increase in AL (Figure 5b). Because of these two effects, AD increases up to 10 years of age, matching the decrease in LT observed in Figure 2c. After age 10, AD follows the combined effect of the plateau and increase in LT combined with the continuous growth of the AL (Figure 2a).
In the literature, confusion may exist between the aqueous depth (AD: not including CCT) and anterior chamber depth (ACD: often, but not always, including CCT). When we add CCT to our AD values, the ACD data are very similar to those of Hashemi et al., 24 i.e., within approximately AE 0.1 mm for boys and girls of the same age groups. Our ACD data is even closer to the findings of Larsen 20 (AE0.05 mm), although about 0.1mm lower than Twelker et al. 18 Both Hashemi et al. 24 and Twelker et al. 18 found that girls have a 0.1 mm shorter AD than boys, which corresponds well with our difference of 0.09 mm at 6 years and 0.14 mm at 17 years. Indeed, our AD values at 17 years of age in girls and boys (3.06 and 3.20 mm, respectively), are very similar to the findings of Shammas et al. 44 and Kunert et al. 31 who reported adult values for women and men combined of 3.08 and 3.06 mm, respectively.

Lens thickness (LT)
When comparing age groups, LT did not differ statistically significantly between girls and boys except for the age of 15 years. Further, LT decreased at the same rate in girls and boys between 4 and 10 years. For all ages, LT was 0.03 mm thicker in girls, as was also found by Hashemi et al. 24 between 6 and 18 years (0.05 mm). For analysis, see Tables 1 and 2 and Figure 2c. Both Twelker et al. 18 and Larsen 23 described this pattern of lens thinning in children with a minimum LT at 11 and 14 years of age, respectively. Their findings are consistent with our minimum LT for girls and boys at 11 and 12 years of age, respectively. The lens probably flattens during eye growth because of zonular tension, as suggested by Zadnik et al. 45 and Mutti et al. 46 However, the gradient refractive index may also change during eye development. 47,48 Hashemi et al. 24 showed a wider plateau in boys (8-16 years) than in girls (11-13 years). A study of 11 656 Taiwanese children and adolescents aged 7-18 years confirmed the aforementioned decrease in LT for East Asian eyes, showing a decrease in lens thickness until 11 years of age, after which point the lens thickened. 49 Our LT findings at 17 years of age of 3.52 and 3.50 mm for girls and boys, respectively, also agrees with the mean of 3.5mm in young adults (20-30 years of age). 50,51 Additionally, we found a linear trend for lens thickness as function of axial length (Figure 2d). Mean lens thickness was 3.62 mm in short eyes and 3.42 mm in long eyes. A thinner lens results in less optical power in longer eyes.
It is of interest to compare the current results with studies of ocular growth. Jones et al. 38 presented growth curves for LT in different refractive groups. Their data showed thinning of the lens until 9.5 years of age, which is similar to the present findings, although they did not separate girls and boys. 38 This two-phase growth of the lens was also shown in Asian eyes, although not separated by sex. 39 Vitreous depth (VD) Vitreous depth increased with age at about the same rate in girls and boys between 4 and 14 years, but girls presented with a statistically significantly lower value (mean = 0.6 mm) at 4 years. By 17 years of age, the remaining difference of 0.3 mm was not statistically significant ( Figure 5c). Our values of VD are very similar to those of Hashemi et al. 24 and Twelker et al., 18 with only small differences (around AE 0.2 mm) being observed.
When AD, LT and VD are plotted against axial length, a linear correlation was seen (Figures 2d, 5b and d). AD increases concurrent with LT decrease. There is also less variation in the VD data, which is expected as the latter distance is critical for clear focusing of an image on the retina. The higher variation in AD and LT values may indicate that both dimensions compensate for one another to keep a stable VD.

Influence of astigmatism
Corneal astigmatism, as displayed in Figure S1, exceeded refractive astigmatism (Figure 1), which confirms previous findings. 52,53 The prevalence of refractive and corneal astigmatism is stable with age, which has also been shown previously. 52,54 However, these findings should be confirmed by longitudinal data, as it has been demonstrated that the values of astigmatism change in around 10% of children with age. 54 We found most corneal astigmatism for the J 0 parameter (i.e., vertical/horizontal astigmatism) with a minor contribution of J 45 (oblique astigmatism), see Figure S1. When converting the axes to degrees, most children presented with-the-rule corneal astigmatism. Further, high corneal astigmatism was associated with both shorter axial length and aqueous depth ( Figure S2). In addition, it can be observed that the steep corneal radius was responsible for corneal astigmatism. It is relevant to investigate the influence of corneal astigmatism on ocular components, as it has been suggested that infantile astigmatism may disrupt the focusing mechanisms of the eye or that ocular growth could induce astigmatism. 55

Summary
Girls presented with 0.63 mm shorter eyes than boys at 4 years of age. However, in this cross-sectional dataset, girls' eyes elongated at a similar rate to boys, reaching the same axial length about 4 years after the boys. Lens thickness decreased with increasing age, reaching a minimum at ages 11 and 12 for girls and boys, respectively. The trend for girls to have thicker lenses was statistically significant for all age groups. With regard to eye elongation and lens thinning, a longer aqueous depth was associated with shorter lens thickness and increasing age. The mean vitreous chamber depth was 0.60 mm smaller in girls at 4 years of age, but almost equal for girls and boys by age 17. Corneal radii were 0.20 mm steeper in girls. While corneal radii flattened with increasing age in girls between 4 and 10 years of age, they did not change statistically significantly with age in boys. Central corneal thickness remained unchanged between 4 and 17 years of age for both girls and boys.
In conclusion, the current dataset presents the first biometric measurements in a large cohort of children and adolescents in Germany. These data may serve as normative values for the assessment of eye growth in central European children, and will provide a basis for monitoring refractive error development. Furthermore, by conveying data for an unprecedented age range, the current study demonstrates cross-sectional data and their relationship with age and sex during important phases of eye growth.

Supporting Information
Additional Supporting Information may be found in the online version of this article: Table S1. Objective refraction presented as spherical equivalent M and astigmatic components J 0 and J 45 by age. Table S2. Corneal astigmatism presented as astigmatic components J 0 and J 45 by age. Figure S1. Corneal astigmatism by age. Figure S2. Biometry by age stratified by the amount of corneal astigmatism.