Estimating the biometric contributions to variations in refractive error by means of error propagation

Abstract

Purpose : The source of refractive errors of an eye lies in its components. This work uses error propagation to evaluate the contribution of each component to the variation in spherical equivalent (SE) during infancy and childhood.

Methods : This work considers two methods to estimate the biometric contributions. The first uses the thick lens formula and starts by considering SE as the difference between axial power and the whole eye power. This simple eye model, given in Fig 1a includes the vitreous refractive index n, axial length L, corneal power K, lens power P_L, and total anterior chamber depth ACD_tot, along with several age-adjusted principal plane positions pp considered as constants. The second method uses more accurate ray transfer matrices, but requires uses more parameters, such as the corneal and lenticular radii of curvature, the gradient index power of the lens P_G, the refractive indices and thicknesses of all optical media, the image principal plane, and the inverse of image focal length. For both methods, the partial derivatives of SE of all the parameters were determined by manual calculation and verified using the Matlab toolbox. Finally, the contribution of each parameter X_i and its standard deviation ΔX_i was calculated as a percentage using the absolute error propagation of each parameter (Fig 1b). These methods are applied to the mean ocular biometry data for infants and children published by Mutti et al. (OVS 2018) and Twelker, et al. (OVS 2009).

Results : Most ocular components change rapidly during the first years of life, but their percentage contributions to the variation in SE are stable (Fig 2a & b). For the Mutti infant data, the largest contributions are given by L, P_L and K for the first model (68, 23%, 9%, respectively), and by L, P_G and the anterior corneal curvature r_ac for the eye matrix model (55%, 21%, 14%, respectively). The Twelker data, sees the influence of myopization (Fig 2c), with the contribution of L increasing from 54.7% to 73.6%, and that of K decreasing from 10% to 6.33%.

Conclusions : Error propagation analysis is an interesting tool to understand the interactions between ocular components on a population level during emmetropization, refractive homeostasis and myopization.

This abstract was presented at the 2023 ARVO Annual Meeting, held in New Orleans, LA, April 23-27, 2023.

 

Figure 1: Formulas used for calculation.

 

Figure 2. The percentage contribution of ocular parameters for the Mutti (a,b) and Twelker (c) data.