Prediction of human crystalline lens power and spherical aberration using an anatomically-based discrete shell model

Abstract

Purpose: To develop an anatomically-correct aspheric discrete model of the human crystalline lens that predicts power and spherical aberration and the contribution of the refractive index gradient.

Methods: A continuous and a discrete model of a 30 year old relaxed human lens were developed. The shape was modeled using data from Dubbelman et al (Vis Res, 2001): Ant Radius=11.10mm; Ant Asphericity=-3.05; Post Radius = -5.82mm; Post Asphericity=-0.795; Thickness=3.69mm. In the continuous model, the refractive index gradient is represented as a set of aspheric iso-indicial surfaces with radius of curvature R(z) and asphericity Q(z) that vary linearly from the lens equator to the value at the surface. The axial refractive index follows a power-dependence in each half of the lens (Kasthurirangan et al, IOVS 2008): n(z)=1.41-0.032×(z/t)⁴, where t is the anterior or posterior half-thickness and z is the distance, both measured from the equator. The discrete shell model was created by sampling iso-indicial surfaces of the continuous model at regularly spaced intervals. The ith shell of a model with K shells has thickness t_K=t_lens/K, is located at position z_i = i*t_K, radius R_i=R(z_i), asphericity Q_i=Q(z_i), and is surrounded by refractive indices n_i-1=n(z_i-1) and n_i=n(z_i). The number of shells ranged from K=6 to K=3000. The contribution of each surface to lens power and Seidel primary spherical aberration was calculated from a paraxial ray trace. The contributions were plotted as a function of axial position and summed to provide the Seidel wavefront aberration coefficient W₀₄₀, and total power contribution P_sum. The power P_sum was compared to the effective power P_eff.

Results: The spherical aberration coefficient and lens power converge as the number of shell increases. The asymptotic values were W₀₄₀=0.053mm^-3, P_sum=22.2D, and P_eff=22.3D. For lens power, the number of shells required to reach 90%, 95% and 99% of the asymptote are 20, 40, and 200. For spherical aberration the values are 160, 320, and approx. 1000. The contributions of the anterior and posterior halves of the lens were -0.015mm^-3 and 0.068mm^-3.

Conclusions: The power and spherical aberration of the crystalline lens can be predicted using a discrete model with tightly packed shells.The discrete model allows calculation of contributions of specific regions of the lens to total spherical aberration from a paraxial ray trace.

Keywords: 626 aberrations • 630 optical properties • 404 accommodation