### 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 |
---|---|

Pages (from-to) | 74-83 |

Number of pages | 10 |

Journal | Vision Research |

Volume | 49 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2009 |

### Fingerprint

### Keywords

- Accommodation
- Finite element modeling
- Lens geometry
- Presbyopia

### ASJC Scopus subject areas

- Ophthalmology
- Sensory Systems

### Cite this

*Vision Research*,

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

**Shape of the isolated ex-vivo human crystalline lens.** / Urs, Raksha; Manns, Fabrice; Ho, Arthur; Borja, David; Amelinckx, Adriana; Smith, Jared; Jain, Rakhi; Augusteyn, Robert; Parel, Jean-Marie A.

Research output: Contribution to journal › Article

*Vision Research*, vol. 49, no. 1, pp. 74-83. https://doi.org/10.1016/j.visres.2008.09.028

}

TY - JOUR

T1 - Shape of the isolated ex-vivo human crystalline lens

AU - Urs, Raksha

AU - Manns, Fabrice

AU - Ho, Arthur

AU - Borja, David

AU - Amelinckx, Adriana

AU - Smith, Jared

AU - Jain, Rakhi

AU - Augusteyn, Robert

AU - Parel, Jean-Marie A

PY - 2009/1/1

Y1 - 2009/1/1

N2 - 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.

AB - 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.

KW - Accommodation

KW - Finite element modeling

KW - Lens geometry

KW - Presbyopia

UR - http://www.scopus.com/inward/record.url?scp=57049089924&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=57049089924&partnerID=8YFLogxK

U2 - 10.1016/j.visres.2008.09.028

DO - 10.1016/j.visres.2008.09.028

M3 - Article

C2 - 18950656

AN - SCOPUS:57049089924

VL - 49

SP - 74

EP - 83

JO - Vision Research

JF - Vision Research

SN - 0042-6989

IS - 1

ER -