A machine learning-based algorithm used to estimate the physiological elongation of ocular axial length in myopic children

Abstract

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 AL _predicted -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 R ² value of 0.87 and relatively minimal averaged errors between the predicted AL and true AL. Based on the partial derivatives of the AL _predicted -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.

Keywords: Machine learning; Myopia; Myopia progression; Ocular axial length; Orthokeratology; Physiological elongation.

Fig. 1

Flow chart of our proposed method. a Data inclusion criteria. b Data processing procedure. c Machine learning models used to predict the axial length and estimate the physiological axial length elongation. The best-performing prediction model was applied to predict the axial length and estimate the physiological axial length elongation by considering the partial derivatives of AL_predicted-age curves. K-mean: mean K reading; CCT: central corneal thickness; ACD: anterior chamber depth; WTW: white-to-white corneal diameter; SER: spherical equivalent refraction error; AL: axial length; SVM: support vector machine; R: the coefficient of determination; MAEs: mean absolute errors; MSEs: mean squared errors; RMSE: root mean square error; N: number of patients

Fig. 2

Final axial length prediction using machine learning with baseline input variables. Scatterplot of the predicted axial length vs. the true axial length. The solid line represents the perfect correlation regression line. The dashed line represents the perfect line without error prediction

Fig. 3

Growth curves of predicted axial length elongation vs. age and rate of predicted axial length elongation vs. age. Left panel: Growth charts (predicted axial length elongation vs. age). Right panel: Growth charts (rate of predicted axial length elongation vs. age) with the spherical equivalent refraction error fixed at − 1.00 D, − 2.00 D, − 3.00 D, − 4.00 D, − 5.00 D and − 6.00 D and the mean K reading fixed at 40.00 D, 42.00 D, 44.00 D and 46.00 D. Males are indicated by dashed lines, and females are indicated by solid lines

Fig. 4

Scatterplots of the calculated lens powers, anterior chamber depth, mean K reading and age. a Calculated lens powers vs. age. b Anterior chamber depths vs. age. c Mean K readings vs. age. The lens power and K-mean were negatively correlated with age, while ACD was positively correlated with age