Bi-exponential description for different forms of refractive development

Abstract

Purpose : To demonstrate how a system of bi-exponential growth functions can be used to describe the different courses of refractive development identified from earlier studies, as well as the underlying changes in biometry.

Methods : The eye can be described as a simplified optical system that balances two components, P_ax and P_eye, the refractive power required by the eye for a sharp retinal image and the total refractive power of the eye, respectively. The difference between these two parameters corresponds with the refractive error S. A recent paper (Rozema, OPO 2023) reported that P_ax and P_eye may be described by a bi-exponential function as a function of time t (in years):
P_ax = a₀ + a₁ exp(a₂t) + a₃ exp(a₄t)
P_eye = a₅ + a₆ exp(a₇t) + a₈ exp(a₉t)
These equations contain 10 a_i parameters that can be adjusted to match various courses of refractive development based on the previous literature (Pennie et al. 2001), (Mutti et al. 2018), and (Jones, IOVS 2005) for the first years. Also, the refractive development courses of some pathologies were simulated, such as school-age myopia and infant pseudophakia. It is noted that for school-age myopia, the feedback factors a₃ and a₇ had to be modulated with a Gompertz function to simulate the onset of myopia.

Results : By making different combinations of the a_i parameters, the equations can simulate instant emmetropization, persistent hypermetropia, developing hypermetropia, myopia, instant homeostasis, and modulated development forms of refractive development. Examples are shown in Figure 1, along with the required values of the a_i parameters. The parameter values for the population average (Rozema, 2023) are provided as a reference. The equations can also be adjusted to show the refractive development of school-age myopia and pseudophakia in the age range of 20 years, along with the underlying changes in P_ax and P_eye (Figure 2). All these courses closely resemble those reported in the previous literature.

Conclusions : The proposed bi-exponential growth functions can be adjusted to describe a wide range of different courses of refractive development found in the literature, both for healthy and pathological eyes.

This abstract was presented at the 2024 ARVO Annual Meeting, held in Seattle, WA, May 5-9, 2024.

 

Figure 1. Simulated refractive development courses and the a_i parameters needed to simulate them.

 

Figure 2. Refractive development courses of school-age myopia (a) and infant pseudophakia (b), along with the underlying changes in P_ax and P_eye.