Comprehensive data on anterior corneal e values along both principal meridians across various chord lengths in pediatric and adolescent Chinese populations with moderate to high corneal astigmatism are limited. Our study provides a large-scale, detailed characterization of meridional e value patterns in this population, addressing an important gap in pediatric corneal morphology research. The sample size of 961 participants in our study was greater than previous studies examining corneal e values in this population [3, 5]. Specifically, Chui et al. [3] included 22 children aged 11.2 ± 2.2 years, and Li et al. [5] included 143 children aged 8–19 years with a mean astigmatism of − 0.78 ± 0.52 D. In the current study, the majority (99.48%) of participants exhibited with-the-rule astigmatism, which is consistent with the common occurrence of with-the-rule astigmatism in children and adolescents [29]. In our study, the flat K was 42.28 ± 1.50 D, and the steep K was 45.31 ± 1.59 D. Compared with previous studies [8, 17] the higher steep K in our cohort likely reflects the inclusion of participants with moderate-to-high astigmatism. This highlights that in patients with high corneal astigmatism, the increase in ΔK is primarily driven by steepening of the steep corneal meridian rather than flattening of the flatter meridian.

In our study, the mean flat and steep e values were 0.73 ± 0.10 and 0.51 ± 0.21, respectively. These values differ from prior studies primarily due to differences in the magnitude of astigmatism, sample size, and participant characteristics. For example, Li et al. [5] excluded participants with astigmatism greater than 1.50 D and reported mean flat and steep e values of 0.65 ± 0.08 and 0.45 ± 0.16, respectively. Differences in instrumentation, ethnicity, and age may also play a role. For example, Gruhl et al. [6] examined 106 German individuals aged 9 to 52 years, excluding participants with astigmatism greater than 1.50 D, and reported a mean flat e value of 0.54 ± 0.11 and a mean steep e value of 0.52 ± 0.13 using the Keratograph 5 M. These variations highlight the potential influence of study design, population characteristics, and measurement devices on corneal e values. A detailed summary of previous study designs is provided in Table S2 to contextualize these comparisons.

Notably, in our study, the e values at 1 mm along both principal meridians exceeded 1. This is because the Medmont E300 derives the measured e values by fitting the anterior corneal surface to theoretical surface shapes through a conic fitting approach (ellipse, parabola, or hyperbola, as described in the user manual). Although corneal e values generally range from 0 to 1, values greater than 1 may appear at very small chord lengths (~ 1 mm), reflecting a locally hyperbolic corneal profile.

Most previous studies have used a single e value to represent the overall corneal shape, typically obtained directly from the instrument software without any additional information. However, this study revealed that corneal e value varies substantially with chord length. Similar to the e value, the Q value measures the rate of change in corneal curvature [2] with Q = − e2. Previous research has demonstrated that the corneal Q value changes with chord length [1, 30,31,32,33]. For instance, Zhang et al. [33] reported Q values of − 0.09 ± 0.21, − 0.14 ± 0.16, − 0.15 ± 0.13, − 0.17 ± 0.11, and − 0.20 ± 0.11 at chord lengths of 3, 4, 5, 6, and 7 mm, respectively. This indicates a negative correlation between Q value and chord length, which corresponds to a positive relationship between e value and chord length.

In the corneal periphery, corneal astigmatism may either stabilize, increase, or decrease [29]. Our data revealed distinct meridian-specific patterns: the flat corneal meridian exhibited a smooth curvilinear pattern, characterized by a gradual reduction in e values from the central to the peripheral regions, eventually stabilizing, whereas the steep meridian showed a characteristic U-shaped progression.

No correlation was observed between age and the mean e values of both meridians. Previous cross-sectional studies [4, 15, 18, 34] have reported that e values decreased with age, while longitudinal studies [26, 35] have reported the opposite trend. Additionally, we observed sex-related differences, with females exhibiting higher e values than males, consistent with previous research [18, 26]. Further analysis revealed that the flat K (t = − 6.23, P < 0.001), steep K (t = − 6.39, P < 0.001), and ΔK (t = − 0.78, P < 0.001) varied significantly, indicating potential sex-related differences in corneal morphology. However, as with prior studies, the biological rationale for this association is not yet well understood and requires further exploration.

No significant correlations were found between the mean flat e or steep e and SE, which is consistent with some studies [1, 19, 36], but conflicting with others [4, 15, 35, 37]. This discrepancy may result from differences in population characteristics (e.g., the inclusion of participants with moderate to high astigmatism in our study), age, or measurement methods, warranting further investigation. Furthermore, we identified a significant negative correlation between mean flat e and flat K, but no correlation was found between mean steep e and steep K. Previous studies have suggested that a steeper cornea is associated with a greater rate of curvature change from the center to the periphery [15, 36] although others [34] found no such correlation.

A positive correlation was observed between mean flat e and ΔK, with no significant correlation for mean steep e. These results align with González-Méijome et al. [30], who also measured corneal Q values along the two principal meridians. Other studies [1, 15] have similarly reported associations between corneal shape factors and astigmatism, highlighting the complex interplay between corneal morphology and toricity.

While the observed changes in e values were small but statistically significant, their isolated clinical impact may be limited. Nevertheless, subtle variations in corneal e values might contribute cumulatively to corneal shape characterization and refractive outcomes, warranting further clinical investigation.

This study has several limitations. First, corneal data were available only up to 8 mm along the vertical meridian, the steeper meridian in most participants, due to eyelid obstruction. Second, the focus on participants with with-the-rule astigmatism may limit the generalizability of our findings to other types of astigmatism. Third, recruitment from a single center could introduce selection bias and restrict broader applicability. Future studies should develop improved tools for peripheral corneal measurements and include more diverse populations to enhance the generalizability of results.