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F. Manns, A. Ho, D. Borja, J.-M. Parel; Paraxial Optical Model of the Crystalline Lens With Continuous Refractive Index Gradient. Invest. Ophthalmol. Vis. Sci. 2008;49(13):3774.
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© ARVO (1962-2015); The Authors (2016-present)
To determine the effect of the refractive index profile and its changes with age on the crystalline lens power.
The paraxial differential equation for the ray path in a crystalline lens with continuous refractive index gradient was solved to derive an expression of the contribution of the gradient to the lens power. The crystalline lens was modeled using published values of the curvature, thickness (Rosen et al, Vis Res 2006) and refractive index profile (Jones et al, Vis Res, 2005) obtained on isolated lenses. The paraxial gradient is characterized by the axial variation of the refractive index, n(z), and curvatures of the isoindicial surfaces, K(z). The functions n(z) and K(z) were modeled as second (parabola), fourth, or higher even-degree power functions. The surface (1.371) and equatorial (1.418) refractive index were assumed to be independent of age. At the lens surface, the isoindicial curvatures were equal to the lens surface curvature. The equatorial isoindicial curvature was adjusted until the power of the lens model matched measurements on isolated lenses of age 20 (32D) and 40 years (24D) (Borja et al, ARVO 06).
The contribution of the gradient to lens power is dependent only on the difference between the equatorial and surface values of the index (Δn) and isoindicial curvature (ΔK), independent of the shape of the index profile. The model is consistent with the measurements when the isoindicial curvature increases from the surfaces to the equator. When Δn=0.047, the model matches the 20 year old lens when ΔK=0.287mm-1 (anterior) and 0.439mm-1 (posterior) and the 40 year old lens when ΔK=0.204mm-1 (anterior) and 0.347mm-1 (posterior).
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