Background Axial myopia is the most common type of myopia. However, due to the high incidence of myopia in Chinese children, few studies estimating the physiological elongation of the ocular axial length (AL), which does not cause myopia progression and differs from the non-physiological elongation of AL, have been conducted. The purpose of our study was to construct a machine learning (ML)-based model for estimating the physiological elongation of AL in a sample of Chinese school-aged myopic children. Methods In total, 1011 myopic children aged 6 to 18 years participated in this study. Cross-sectional datasets were used to optimize the ML algorithms. The input variables included age, sex, central corneal thickness (CCT), spherical equivalent refractive error (SER), mean K reading (K-mean), and white-to-white corneal diameter (WTW). The output variable was AL. A 5-fold cross-validation scheme was used to randomly divide all data into 5 groups, including 4 groups used as training data and one group used as validation data. Six types of ML algorithms were implemented in our models. The best-performing algorithm was applied to predict AL, and estimates of the physiological elongation of AL were obtained as the partial derivatives of ALpredicted-age curves based on an unchanged SER value with increasing age. Results Among the six algorithms, the robust linear regression model was the best model for predicting AL, with a R2 value of 0.87 and relatively minimal averaged errors between the predicted AL and true AL. Based on the partial derivatives of the ALpredicted-age curves, the estimated physiological AL elongation varied from 0.010 to 0.116 mm/year in male subjects and 0.003 to 0.110 mm/year in female subjects and was influenced by age, SER and K-mean. According to the model, the physiological elongation of AL linearly decreased with increasing age and was negatively correlated with the SER and the K-mean. Conclusions The physiological elongation of the AL is rarely recorded in clinical data in China. In cases of unavailable clinical data, an ML algorithm could provide practitioners a reasonable model that can be used to estimate the physiological elongation of AL, which is especially useful when monitoring myopia progression in orthokeratology lens wearers.

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Background The goal of this study was to reproduce a three-dimensional representation of corneal defocus characteristics after orthokeratology (Ortho-K) treatment via an indicator defined as the weighted Zernike defocus coefficient of the treatment zone (Cweighted defocus). This could be used to predict the effectiveness of Ortho-K treatment quantitatively in a timely manner after the one-month visit. Methods Seventy myopic children with axial length (AL) elongation after Ortho-K treatment (group A) and 63 myopic children with AL shortening after Ortho-K treatment (group B) were included in this one-year retrospective study. The proposed indicator was calculated by a customized MATLAB program. Multivariate binomial logistic regression and multivariate linear regression analyses were used to explore the association between AL change and the Cweighted defocus, age, sex, and other ocular biometric parameters. Results The 12-month AL change, age, pupil diameter, and vertical decentration of the Ortho-K lens were significantly different between the two groups. Multivariate logistic regression analysis showed that a larger Cweighted defocus (≥ 0.35 D/mm2) (OR: 0.224; 95% CI: 0.078–0.646; P = 0.006) was correlated with the emergence of AL shortening after orthokeratology treatment. A multivariate linear regression model showed that a greater Cweighted defocus was associated with slower 12-month AL elongation (β =  − 0.51, P = 0.001). Conclusions The Cweighted defocus is an effective predictive indicator of myopia control, and a larger Cweighted defocus may lead to slower elongation of AL. This meaningful indicator may help in the evaluation and adjustment of Ortho-K lens parameters in a timely manner and minimize the cost of clinical trial and error.