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Mathematical models for describing the shape of the in vitro unstretched human crystalline lens

Smith, George, Atchison, David A., Iskander, Robert, Jones, Catherine E., & Pope, James M. (2009) Mathematical models for describing the shape of the in vitro unstretched human crystalline lens. Vision Research, 49(20), pp. 2442-2452.

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Abstract

We developed orthogonal least-squares techniques for fitting crystalline lens shapes, and used the bootstrap method to determine uncertainties associated with the estimated vertex radii of curvature and asphericities of five different models. Three existing models were investigated including one that uses two separate conics for the anterior and posterior surfaces, and two whole lens models based on a modulated hyperbolic cosine function and on a generalized conic function. Two new models were proposed including one that uses two interdependent conics and a polynomial based whole lens model. The models were used to describe the in vitro shape for a data set of twenty human lenses with ages 7–82 years. The two-conic-surface model (7 mm zone diameter) and the interdependent surfaces model had significantly lower merit functions than the other three models for the data set, indicating that most likely they can describe human lens shape over a wide age range better than the other models (although with the two-conic-surfaces model being unable to describe the lens equatorial region). Considerable differences were found between some models regarding estimates of radii of curvature and surface asphericities. The hyperbolic cosine model and the new polynomial based whole lens model had the best precision in determining the radii of curvature and surface asphericities across the five considered models. Most models found significant increase in anterior, but not posterior, radius of curvature with age. Most models found a wide scatter of asphericities, but with the asphericities usually being positive and not significantly related to age. As the interdependent surfaces model had lower merit function than three whole lens models, there is further scope to develop an accurate model of the complete shape of human lenses of all ages. The results highlight the continued difficulty in selecting an appropriate model for the crystalline lens shape.

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10 citations in Scopus
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12 citations in Web of Science®

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ID Code: 29541
Item Type: Journal Article
Additional URLs:
Keywords: Asphericity, Bootstrap, In vitro, Lens, Merit function, Surface Shape
DOI: 10.1016/j.visres.2009.07.014
ISSN: 0042-6989
Subjects: Australian and New Zealand Standard Research Classification > MEDICAL AND HEALTH SCIENCES (110000) > OPTOMETRY AND OPHTHALMOLOGY (111300)
Australian and New Zealand Standard Research Classification > MEDICAL AND HEALTH SCIENCES (110000) > OPTOMETRY AND OPHTHALMOLOGY (111300) > Vision Science (111303)
Divisions: Current > QUT Faculties and Divisions > Faculty of Health
Past > QUT Faculties & Divisions > Faculty of Science and Technology
Current > Institutes > Institute of Health and Biomedical Innovation
Current > Schools > School of Optometry & Vision Science
Past > Schools > School of Physical & Chemical Sciences
Copyright Owner: Copyright 2009 Elsevier
Deposited On: 08 Jan 2010 11:09
Last Modified: 01 Mar 2012 00:08

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