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Fabrice Manns, Arthur Ho, Jean-Marie Parel; Prediction of human crystalline lens power and spherical aberration using an anatomically-based discrete shell model. Invest. Ophthalmol. Vis. Sci. 2013;54(15):4269.
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© ARVO (1962-2015); The Authors (2016-present)
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.
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 tK=tlens/K, is located at position zi = i*tK, radius Ri=R(zi), asphericity Qi=Q(zi), and is surrounded by refractive indices ni-1=n(zi-1) and ni=n(zi). 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 Psum. The power Psum was compared to the effective power Peff.
The spherical aberration coefficient and lens power converge as the number of shell increases. The asymptotic values were W040=0.053mm-3, Psum=22.2D, and Peff=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.
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.
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