Abstract
Purpose: To develop an age-dependent mathematical model of the zero-order shape of the isolated ex vivo human crystalline lens, using one mathematical function, that can be subsequently used to facilitate the development of other models for specific purposes such as optical modeling and analytical and numerical modeling of the lens. Methods: Profiles of whole isolated human lenses (n=30) aged 20-69, were measured from shadow-photogrammetric images. The profiles were fit to a 10th-order Fourier series consisting of cosine functions in polar-co-ordinate system that included terms for tilt and decentration. The profiles were corrected using these terms and processed in two ways. In the first, each lens was fit to a 10th-order Fourier series to obtain thickness and diameter, while in the second, all lenses were simultaneously fit to a Fourier series equation that explicitly include linear terms for age to develop an age-dependent mathematical model for the whole lens shape. Results: Thickness and diameter obtained from Fourier series fits exhibited high correlation with manual measurements made from shadow-photogrammetric images. The root-mean-squared-error of the age-dependent fit was 205μm. The age-dependent equations provide a reliable lens model for ages 20-60. years. Conclusion: The contour of the whole human crystalline lens can be modeled with a Fourier series. Shape obtained from the age-dependent model described in this paper can be used to facilitate the development of other models for specific purposes such as optical modeling and analytical and numerical modeling of the lens.
| Original language | English |
|---|---|
| Pages (from-to) | 1041-1047 |
| Number of pages | 7 |
| Journal | Vision Research |
| Volume | 50 |
| Issue number | 11 |
| DOIs | |
| State | Published - Jun 1 2010 |
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Keywords
- Accommodation
- Human crystalline lens shape
- Mechanical model
- Optical model
- Presbyopia
ASJC Scopus subject areas
- Ophthalmology
- Sensory Systems
Cite this
Age-dependent Fourier model of the shape of the isolated ex vivo human crystalline lens. / Urs, Raksha; Ho, Arthur; Manns, Fabrice; Parel, Jean-Marie A.
In: Vision Research, Vol. 50, No. 11, 01.06.2010, p. 1041-1047.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Age-dependent Fourier model of the shape of the isolated ex vivo human crystalline lens
AU - Urs, Raksha
AU - Ho, Arthur
AU - Manns, Fabrice
AU - Parel, Jean-Marie A
PY - 2010/6/1
Y1 - 2010/6/1
N2 - Purpose: To develop an age-dependent mathematical model of the zero-order shape of the isolated ex vivo human crystalline lens, using one mathematical function, that can be subsequently used to facilitate the development of other models for specific purposes such as optical modeling and analytical and numerical modeling of the lens. Methods: Profiles of whole isolated human lenses (n=30) aged 20-69, were measured from shadow-photogrammetric images. The profiles were fit to a 10th-order Fourier series consisting of cosine functions in polar-co-ordinate system that included terms for tilt and decentration. The profiles were corrected using these terms and processed in two ways. In the first, each lens was fit to a 10th-order Fourier series to obtain thickness and diameter, while in the second, all lenses were simultaneously fit to a Fourier series equation that explicitly include linear terms for age to develop an age-dependent mathematical model for the whole lens shape. Results: Thickness and diameter obtained from Fourier series fits exhibited high correlation with manual measurements made from shadow-photogrammetric images. The root-mean-squared-error of the age-dependent fit was 205μm. The age-dependent equations provide a reliable lens model for ages 20-60. years. Conclusion: The contour of the whole human crystalline lens can be modeled with a Fourier series. Shape obtained from the age-dependent model described in this paper can be used to facilitate the development of other models for specific purposes such as optical modeling and analytical and numerical modeling of the lens.
AB - Purpose: To develop an age-dependent mathematical model of the zero-order shape of the isolated ex vivo human crystalline lens, using one mathematical function, that can be subsequently used to facilitate the development of other models for specific purposes such as optical modeling and analytical and numerical modeling of the lens. Methods: Profiles of whole isolated human lenses (n=30) aged 20-69, were measured from shadow-photogrammetric images. The profiles were fit to a 10th-order Fourier series consisting of cosine functions in polar-co-ordinate system that included terms for tilt and decentration. The profiles were corrected using these terms and processed in two ways. In the first, each lens was fit to a 10th-order Fourier series to obtain thickness and diameter, while in the second, all lenses were simultaneously fit to a Fourier series equation that explicitly include linear terms for age to develop an age-dependent mathematical model for the whole lens shape. Results: Thickness and diameter obtained from Fourier series fits exhibited high correlation with manual measurements made from shadow-photogrammetric images. The root-mean-squared-error of the age-dependent fit was 205μm. The age-dependent equations provide a reliable lens model for ages 20-60. years. Conclusion: The contour of the whole human crystalline lens can be modeled with a Fourier series. Shape obtained from the age-dependent model described in this paper can be used to facilitate the development of other models for specific purposes such as optical modeling and analytical and numerical modeling of the lens.
KW - Accommodation
KW - Human crystalline lens shape
KW - Mechanical model
KW - Optical model
KW - Presbyopia
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UR - http://www.scopus.com/inward/citedby.url?scp=77952890643&partnerID=8YFLogxK
U2 - 10.1016/j.visres.2010.03.012
DO - 10.1016/j.visres.2010.03.012
M3 - Article
C2 - 20338192
AN - SCOPUS:77952890643
VL - 50
SP - 1041
EP - 1047
JO - Vision Research
JF - Vision Research
SN - 0042-6989
IS - 11
ER -