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R. Urs, D. Borja, A. Amelinckx, J. Smith, R. Augusteyn, F. Manns, J.-M. Parel; Model of the Isolated Human Crystalline Lens Shape Using Polynomial Functions. Invest. Ophthalmol. Vis. Sci. 2008;49(13):3791. doi: https://doi.org/.
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© ARVO (1962-2015); The Authors (2016-present)
To develop an age dependent mathematical model of the isolated ex-vivo human crystalline lens shape for use in finite element modeling.
Profiles of whole isolated human lenses (n=22) aged 26 to 82, were measured from shadow-photographs and fit to tenth order polynomials. Two methods were used to analyze the lenses. The Two Curves Method (TCM) used separate equations for the anterior and posterior surfaces of the lens. The One Curve Method (OCM) assumed symmetry around the optical axis and fit half of the contour of the lens. The age dependence of the polynomial coefficients was assessed. The analysis was used to produce an age-dependent polynomial model of the whole lens shape.
The root mean squared errors for the fits ranged from 41 to 122 µm for the OCM, 8 to 30 µm for the posterior surface of the TCM and 11 to 41 µm for the anterior surface of the TCM. Coefficients of the first, fifth and ninth term of the anterior surface of the TCM decreased with age. Coefficients of the third and seventh terms of the anterior surface and the eight term of the posterior surface increased with age. The coefficients of all other terms did not show any significant trend with age. The age dependent equation of the OCM provides a reliable model from age 20 to 70.
The shape of the whole human crystalline lens can be accurately modeled with tenth order polynomial functions. This model can serve to improve FE-models of the lens.Support: NIH Grants 2R01EY14225, 5F31EY15395 (Borja), P30EY14801 (Center Grant); the Florida Lions Eye Bank; AMO Inc, Santa Ana, CA; an unrestricted grant from Research to Prevent Blindness; Australian Federal Government CRC Scheme through the Vision Cooperative Research; Henri and Flore Lesieur Foundation.
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