Perpetual eye model with accommodation

Abstract

Purpose : To develop a paraxial model of the changes in ocular biometry and refractive error during natural, non-myopic growth and other age-related changes that occur between 0 to 80 years, combined with an age-appropriate accommodative range.

Methods : The perpetual eye model is based on a series of previously published bi-exponential regressions of ocular biometry and refractive error as a function of age that were derived from 294 papers in the literature (Figure 1). These regressions were modified for mutual consistency, so that e.g. all intraocular distances would add up to the axial length. Next, the equivalent refractive index of the crystalline lens was optimized to match the difference between the total ocular power and the axial power with the age-normal mean refractive error. This optimized lens refractive index was then also fitted by a bi-exponential function to complete the aging eye model. To add accommodation, the biometric data of accommodating eyes of all ages were taken from 46 additional papers. From these the age-normal accommodative response to a stimulus was determined, along with the biometry changes per diopter of accommodative response. Again, the corresponding lens refractive index was estimated and fitted with a polynomial function. This accommodation model was then combined with the age model by simple addition.

Results : Examples of the model are shown in Figure 2. The regression derived for the lens refractive index closely matched the optimized values (r² > 0.999; fit error range [-3.09, +2.07] x 10^–4), corresponding with refractive error differences with the target refraction of [-0.087, +0.034]D over the entire age range. For the accommodated model, a similarly good agreement was seen (r² > 0.999; fit error range between 3 - 80 years [-4.23, +4.21] x 10^-4) corresponding with refractive error differences ranging between [-0.19, +0.01]D. The fit errors grow considerably below the age of 3 years, making the accommodation model unreliable at those ages, mostly due to a lack of data.

Conclusions : The proposed equations appear to accurately describe normal ocular biometry changes over the entire human life span. This model may be useful in myopia research.

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

 

Overview of the modelling process.

 

Eye model for different ages for distance vision (top panel, red lines) and under 6D of accommodative demand (bottom panel, blue lines).