### Abstract

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 μm for the OCM, 9 to 27 μm for the posterior surface of the TCM and 8 to 134 μm 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.

Original language | English (US) |
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Pages (from-to) | 74-83 |

Number of pages | 10 |

Journal | Vision Research |

Volume | 49 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2009 |

### Keywords

- Accommodation
- Finite element modeling
- Lens geometry
- Presbyopia

### ASJC Scopus subject areas

- Ophthalmology
- Sensory Systems

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## Cite this

*Vision Research*,

*49*(1), 74-83. https://doi.org/10.1016/j.visres.2008.09.028