Age-dependent Fourier model of the shape of the isolated ex vivo human crystalline lens

PURPOSE To develop an age-dependent mathematical model of the isolated ex-vivo human crystalline lens shape to serve as basis for use in computational modeling. METHODS Profiles of whole isolated human lenses (n=27) aged 6 to 82, were measured from shadow-photogrammetric images. Two methods were used to analyze the lenses. In the two curves method (TCM) the anterior and posterior surfaces of the lens were fit to 10th-order even polynomials and in the one curve method (OCM) the contour of one half-meridional section of the lens was fit to 10th-order polynomials. 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. RESULTS The root mean squared errors for the fits ranged from 11 to 70 microm for the OCM, 9 to 27 microm for the posterior surface of the TCM and 8 to 134 microm for the anterior surface of the TCM. The coefficients of the OCM did not display a significant trend with age. The 2nd-, 6th- and 10th-order coefficients of the anterior surface of the TCM decreased with age while the 8th-order coefficient increased. For the posterior surface of the TCM, the 8th-order coefficient significantly decreased with age and the 10th-order coefficient increased. The age-dependent equations of both the models provide a reliable model from age 20 to 60. The OCM model can be used for lenses older than 60 as well. CONCLUSION The shape of the whole human crystalline lens can be accurately modeled with 10th-order polynomial functions. These models can serve to improve computational modeling, such as finite element (FE) modeling of crystalline lenses.

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