Adaptive model of the gradient index of the human lens. I. Formulation and model of aging ex vivo lenses.

A simple, parametric adaptive model of the refractive index distribution of the ex vivo crystalline lens is presented. It assumes conicoid (or nonrevolution quadric in 3D) iso-indical surfaces, concentric with the external surfaces of the lens. The model uses a minimum number of internal structural parameters, while the shape of the iso-indical surfaces adapts automatically to the external geometry. In this way, it is able to adapt and fit individual distributions as well as adapt to the changes of the lens shape and structure with age and accommodation. The model is fit to experimental data for individual eyes spanning ages 7 to 82 years, where for each eye the crystalline lens dimensions and iso-indical index data are known. The analysis demonstrates that only one age-dependent structural parameter is needed to replicate the internal iso-indical index structure, given age-dependent models for the external surfaces. An age-dependent-parameter global model is derived and is shown to predict age-dependent changes in the ex vivo lens power and longitudinal spherical aberration with age.

[1]  Melanie C. W. Campbell,et al.  Measurement of refractive index in an intact crystalline lens , 1984, Vision Research.

[2]  Damian Siedlecki,et al.  Schematic eye with a gradient-index lens and aspheric surfaces. , 2004, Optics letters.

[3]  N A Brennan,et al.  Anatomically accurate, finite model eye for optical modeling. , 1997, Journal of the Optical Society of America. A, Optics, image science, and vision.

[4]  R. Navarro,et al.  Optics of the average normal cornea from general and canonical representations of its surface topography. , 2006, Journal of the Optical Society of America. A, Optics, image science, and vision.

[5]  David A. Atchison,et al.  Continuous gradient index and shell models of the human lens , 1995, Vision Research.

[6]  A. Popiolek Masajada,et al.  Numerical study of the influence of the shell structure of the crystalline lens on the refractive properties of the human eye , 1999 .

[7]  J. M. Pope,et al.  Refractive index distribution and optical properties of the isolated human lens measured using magnetic resonance imaging (MRI) , 2005, Vision Research.

[8]  M. Dubbelman,et al.  Changes in the internal structure of the human crystalline lens with age and accommodation , 2003, Vision Research.

[9]  George Smith,et al.  Tomographic method for measurement of the gradient refractive index of the crystalline lens. II. The rotationally symmetrical lens. , 2006, Journal of the Optical Society of America. A, Optics, image science, and vision.

[10]  Adrian Glasser,et al.  Wave aberrations of the isolated crystalline lens. , 2004, Journal of vision.

[11]  L. Garner,et al.  Change with age of the refractive index gradient of the human ocular lens. , 1994, Investigative ophthalmology & visual science.

[12]  George Smith,et al.  The gradient index and spherical aberration of the lens of the human eye , 2001, Ophthalmic & physiological optics : the journal of the British College of Ophthalmic Opticians.

[13]  M. Dubbelman,et al.  Change in shape of the aging human crystalline lens with accommodation , 2005, Vision Research.

[14]  R. Navarro,et al.  Accommodation-dependent model of the human eye with aspherics. , 1985, Journal of the Optical Society of America. A, Optics and image science.

[15]  Pablo Artal,et al.  Contribution of the cornea and internal surfaces to the change of ocular aberrations with age. , 2002, Journal of the Optical Society of America. A, Optics, image science, and vision.

[16]  J F Koretz,et al.  Aging of the human lens: changes in lens shape at zero-diopter accommodation. , 2001, Journal of the Optical Society of America. A, Optics, image science, and vision.

[17]  N. Brown,et al.  The change in lens curvature with age. , 1974, Experimental eye research.

[18]  C. A. Cook,et al.  Accommodation and presbyopia in the human eye. Changes in the anterior segment and crystalline lens with focus. , 1997, Investigative ophthalmology & visual science.

[19]  D A Atchison,et al.  Modeling the power of the aging human eye. , 1992, Journal of the Optical Society of America. A, Optics and image science.

[20]  J. W. Blaker,et al.  Toward an adaptive model of the human eye. , 1980, Journal of the Optical Society of America.

[21]  Fabrice Manns,et al.  In vitro dimensions and curvatures of human lenses , 2006, Vision Research.

[22]  D A Atchison,et al.  The optical modelling of the human lens , 1991, Ophthalmic & physiological optics : the journal of the British College of Ophthalmic Opticians.

[23]  J. Sivak,et al.  Spherical aberration of the crystalline lens , 1983, Vision Research.

[24]  M. Campbell,et al.  Biometric, optical and physical changes in the isolated human crystalline lens with age in relation to presbyopia , 1999, Vision Research.

[25]  H. Kasprzak.  New approximation for the whole profile of the human crystalline lens. , 2000 .

[26]  J. Parker,et al.  Aspheric curvatures for the human lens , 1977, Vision Research.

[27]  B K Pierscionek,et al.  Refractive Index Gradient of Human Lenses , 1989, Optometry and vision science : official publication of the American Academy of Optometry.