Mathematical Estimation of Axial Length Increment in the Control of Myopia Progression

Abstract

This study aims to evaluate the existing mathematical approach for the theoretical estimation of axial length (AL) in a cross-sectional study, developing a new mathematical model and testing it in a longitudinal sample. Many professionals do not have a device to measure the AL due to clinic space and cost of equipment. However, this parameter plays an important role in the assessment of myopia progression to monitor treatment effects with myopia control strategies. First, a cross-sectional study based on the mathematical equation proposed by Morgan was performed. The AL was estimated based on the mean values of keratometry and spherical equivalent in 1783 subjects (52% female), aged 14.6 ± 4.6 years (6 to 25 years), of whom 738 were myopic, 770 emmetropic and 275 hyperopic. On average, the AL estimated with the Morgan formula was 0.25 ± 0.48 mm larger than the real AL value (95% limits of agreement: +0.70 to −1.20 mm). The study by gender, ametropia, type of astigmatism and age showed statistically significant differences between the real AL and predicted AL_Morgan (r > 0.750, spearman). Based on the previous sample, a multiple linear regression was applied, and a new mathematical model was proposed. The model was tested on a longitudinal sample of 152 subjects whose mean age was 13.3 ± 3.1 years (9 to 24 years) and of whom 96 were female (64%). The sample consisted of 46 myopes, 82 emmetropes and 24 hyperopes. The longitudinal study of the differences in axial length at one year between the models showed no statistically significant differences and that the mathematical equations are valid for estimating differences in axial increment for ages between 9 and 24 years, despite errors in the predicted value for axial length.