Abstract

The accommodating volume-constant age-dependent optical (AVOCADO) model of the crystalline lens is used to explore the age-related changes in ocular power and spherical aberration. The additional parameter m in the GRIN lens model allows decoupling of the axial and radial GRIN profiles, and is used to stabilise the age-related change in ocular power. Data for age-related changes in ocular geometry and lens parameter P in the axial GRIN profile were taken from published experimental data. In our age-dependent eye model, the ocular refractive power shows behaviour similar to the previously unexplained “lens paradox”. Furthermore, ocular spherical aberration agrees with the data average, in contrast to the proposed “spherical aberration paradox”. The additional flexibility afforded by parameter m, which controls the ratio of the axial and radial GRIN profile exponents, has allowed us to study the restructuring of the lens GRIN medium with age, resulting in a new interpretation of the origin of the power and spherical aberration paradoxes. Our findings also contradict the conceptual idea that the ageing eye is similar to the accommodating eye.

© 2017 Optical Society of America

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References

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  1. R. Navarro, “The optical design of the human eye: a critical review,” Journal of Optometry 2, 3–18 (2009).
    [Crossref]
  2. C. J. Sheil and A. V. Goncharov, “Accommodating volume-constant age-dependent optical (AVOCADO) model of the crystalline GRIN lens,” Biomed. Opt. Express 7, 1985–1999 (2016).
    [Crossref] [PubMed]
  3. M. Bahrami and A. V. Goncharov, “Geometry-invariant gradient refractive index lens: analytical ray tracing,” J. Biomed. Opt. 17, 055001 (2012).
    [Crossref] [PubMed]
  4. A. Sharma, D. V. Kumar, and A. K. Ghatak, “Tracing rays through graded-index media: a new method,” Appl. Opt. 21, 984–987 (1982).
    [Crossref] [PubMed]
  5. E. Martinez-Enriquez, P. Pérez-Merino, M. Velasco-Ocana, and S. Marcos, “Oct-based full crystalline lens shape change during accommodation in vivo,” Biomed. Opt. Express 8, 918–933 (2017).
    [Crossref] [PubMed]
  6. C. J. Sheil, M. Bahrami, and A. V. Goncharov, “An analytical method for predicting the geometrical and optical properties of the human lens under accommodation,” Biomed. Opt. Express 5, 1649–1663 (2014).
    [Crossref] [PubMed]
  7. R. Navarro and N. López-Gil, “Impact of internal curvature gradient on the power and accommodation of the crystalline lens,” Optica 4, 334–340 (2017).
    [Crossref]
  8. N. Brown, “The change in lens curvature with age,” Exp. Eye Res. 19, 175–183 (1974).
    [Crossref] [PubMed]
  9. J. F. Koretz and G. H. Handelman, “The ‘lens paradox’ and image formation in accommodating human eyes,” in “The lens: transparency and cataract: Proceedings of the EURAGE/BBS Symposium,” G. Duncan, ed. (Eurage, 1986), pp. 57–64.
  10. B. A. Moffat, D. A. Atchison, and J. M. Pope, “Explanation of the lens paradox,” Optom. Vis. Sci. 79, 148–150 (2002).
    [Crossref] [PubMed]
  11. T. Grosvenor, “Changes in spherical refraction during the adult years,” in “Refractive anomalies. Research and clinical applications,” T. Grosvenor and M. Flom, eds. (Butterworth-Heinemann, Boston, 1991), pp. 131–145.
  12. D. A. Atchison, E. L. Markwell, S. Kasthurirangan, J. M. Pope, G. Smith, and P. G. Swann, “Age-related changes in optical and biometric characteristics of emmetropic eyes,” J. Vis. 84, 29 (2008).
    [Crossref] [PubMed]
  13. K. Attebo, R. Q. Ivers, and P. Mitchell, “Refractive errors in an older population: The blue mountains eye study,” Ophthalmology 106, 1066–1072 (1999).
    [Crossref] [PubMed]
  14. H. Saunders, “Age-dependence of human refractive errors,” Ophthalmic Physiol. Opt. 1, 159–174 (1981).
    [Crossref] [PubMed]
  15. H. Saunders, “A longitudinal study of the age-dependence of human ocular refraction—i. age-dependent changes in the equivalent sphere,” Ophthalmic Physiol. Opt. 6, 39–46 (1986).
  16. C. Shufelt, S. Fraser-Bell, M. Ying-Lai, M. Torres, R. Varma, and the Los Angeles Latino Eye Study Group, “Refractive error, ocular biometry, and lens opalescence in an adult population: The Los Angeles latino eye study,” Invest. Ophthalmol. Vis. Sci. 46, 4450–4460 (2005).
    [Crossref] [PubMed]
  17. Q. Wang, B. E. Klein, R. Klein, and S. E. Moss, “Refractive status in the beaver dam eye study,” Invest. Ophthalmol. Vis. Sci. 35, 4344–4347 (1994).
    [PubMed]
  18. S.-Y. Wu, B. Nemesure, M. C. Leske, and for the Barbados Eye Study Group, “Refractive errors in a black adult population: The Barbados eye study,” Invest. Ophthalmol. Vis. Sci. 40, 2179–2184 (1999).
    [PubMed]
  19. N. A. Brown and A. R. Hill, “Cataract: the relation between myopia and cataract morphology,” Br. J. Ophthalmol. 71, 405–414 (1987).
    [Crossref] [PubMed]
  20. R. Lim, P. Mitchell, and R. G. Cumming, “Refractive associations with cataract: the blue mountains eye study,” Invest. Ophthalmol. Vis. Sci. 40, 3021 (1999).
    [PubMed]
  21. C. Younan, P. Mitchell, R. G. Cumming, E. Rochtchina, and J. J. Wang, “Myopia and incident cataract and cataract surgery: The blue mountains eye study,” Invest. Ophthalmol. Vis. Sci. 43, 3625 (2002).
    [PubMed]
  22. D. A. Atchison and G. Smith, Optics of the Human Eye (Butterworth-Heinemann, 2000).
  23. J. Tabernero, E. Berrio, and P. Artal, “Modeling the mechanism of compensation of aberrations in the human eye for accommodation and aging,” J. Opt. Soc. Am. A 28, 1889–1895 (2011).
    [Crossref]
  24. Y. Le Grand and S. G. El Hage, Physiological Optics (Springer-Verlag, 1980).
  25. M. Dubbelman and G. van der Heijde, “The shape of the aging human lens: curvature, equivalent refractive index and the lens paradox,” Vision Res. 41, 1867–1877 (2001).
    [Crossref] [PubMed]
  26. M. Dubbelman, G. van der Heijde, and H. Weeber, “The thickness of the aging human lens obtained from corrected scheimpflug images,” Optom. Vis. Sci. 78, 411–416 (2001).
    [Crossref] [PubMed]
  27. T. Oshika, S. D. Klyce, R. A. Applegate, and H. C. Howland, “Changes in corneal wavefront aberrations with aging,” Invest. Ophthalmol. Vis. Sci. 40, 1351–1355 (1999).
    [PubMed]
  28. A. Guirao, M. Redondo, and P. Artal, “Optical aberrations of the human cornea as a function of age,” J. Opt. Soc. Am. A 17, 1697–1702 (2000).
    [Crossref]
  29. R. Navarro, “Adaptive model of the aging emmetropic eye and its changes with accommodation,” J. Vis. 1413, 21 (2014).
    [Crossref] [PubMed]
  30. I. Escudero-Sanz and R. Navarro, “Off-axis aberrations of a wide-angle schematic eye model,” J. Opt. Soc. Am. A 16, 1881–1891 (1999).
    [Crossref]
  31. R. Navarro, F. Palos, and L. González, “Adaptive model of the gradient index of the human lens. I. formulation and model of aging ex vivo lenses,” J. Opt. Soc. Am. A 24, 2175–2185 (2007).
    [Crossref]
  32. L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of objective refraction from wavefront aberrations,” J. Vis. 4, 9 (2004).
    [Crossref]
  33. T. O. Salmon and C. van de Pol, “Normal-eye zernike coefficients and root-mean-square wavefront errors,” J. Cataract. Refract. Surg. 32, 2064–2074 (2006).
    [Crossref] [PubMed]
  34. C. E. Campbell, “Nested shell optical model of the lens of the human eye,” J. Opt. Soc. Am. A 27, 2432–2441 (2010).
    [Crossref]
  35. J. F. Koretz, C. A. Cook, and P. L. Kaufman, “Accommodation and presbyopia in the human eye. changes in the anterior segment and crystalline lens with focus,” Investigative Ophthalmol. Vis. Sci. 38, 569–578 (1997).
  36. J. Tabernero, A. Benito, E. Alcón, and P. Artal, “Mechanism of compensation of aberrations in the human eye,” J. Opt. Soc. Am. A 24, 3274–3283 (2007).
    [Crossref]

2017 (2)

2016 (1)

2014 (2)

2012 (1)

M. Bahrami and A. V. Goncharov, “Geometry-invariant gradient refractive index lens: analytical ray tracing,” J. Biomed. Opt. 17, 055001 (2012).
[Crossref] [PubMed]

2011 (1)

2010 (1)

2009 (1)

R. Navarro, “The optical design of the human eye: a critical review,” Journal of Optometry 2, 3–18 (2009).
[Crossref]

2008 (1)

D. A. Atchison, E. L. Markwell, S. Kasthurirangan, J. M. Pope, G. Smith, and P. G. Swann, “Age-related changes in optical and biometric characteristics of emmetropic eyes,” J. Vis. 84, 29 (2008).
[Crossref] [PubMed]

2007 (2)

2006 (1)

T. O. Salmon and C. van de Pol, “Normal-eye zernike coefficients and root-mean-square wavefront errors,” J. Cataract. Refract. Surg. 32, 2064–2074 (2006).
[Crossref] [PubMed]

2005 (1)

C. Shufelt, S. Fraser-Bell, M. Ying-Lai, M. Torres, R. Varma, and the Los Angeles Latino Eye Study Group, “Refractive error, ocular biometry, and lens opalescence in an adult population: The Los Angeles latino eye study,” Invest. Ophthalmol. Vis. Sci. 46, 4450–4460 (2005).
[Crossref] [PubMed]

2004 (1)

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of objective refraction from wavefront aberrations,” J. Vis. 4, 9 (2004).
[Crossref]

2002 (2)

C. Younan, P. Mitchell, R. G. Cumming, E. Rochtchina, and J. J. Wang, “Myopia and incident cataract and cataract surgery: The blue mountains eye study,” Invest. Ophthalmol. Vis. Sci. 43, 3625 (2002).
[PubMed]

B. A. Moffat, D. A. Atchison, and J. M. Pope, “Explanation of the lens paradox,” Optom. Vis. Sci. 79, 148–150 (2002).
[Crossref] [PubMed]

2001 (2)

M. Dubbelman and G. van der Heijde, “The shape of the aging human lens: curvature, equivalent refractive index and the lens paradox,” Vision Res. 41, 1867–1877 (2001).
[Crossref] [PubMed]

M. Dubbelman, G. van der Heijde, and H. Weeber, “The thickness of the aging human lens obtained from corrected scheimpflug images,” Optom. Vis. Sci. 78, 411–416 (2001).
[Crossref] [PubMed]

2000 (1)

1999 (5)

I. Escudero-Sanz and R. Navarro, “Off-axis aberrations of a wide-angle schematic eye model,” J. Opt. Soc. Am. A 16, 1881–1891 (1999).
[Crossref]

T. Oshika, S. D. Klyce, R. A. Applegate, and H. C. Howland, “Changes in corneal wavefront aberrations with aging,” Invest. Ophthalmol. Vis. Sci. 40, 1351–1355 (1999).
[PubMed]

K. Attebo, R. Q. Ivers, and P. Mitchell, “Refractive errors in an older population: The blue mountains eye study,” Ophthalmology 106, 1066–1072 (1999).
[Crossref] [PubMed]

S.-Y. Wu, B. Nemesure, M. C. Leske, and for the Barbados Eye Study Group, “Refractive errors in a black adult population: The Barbados eye study,” Invest. Ophthalmol. Vis. Sci. 40, 2179–2184 (1999).
[PubMed]

R. Lim, P. Mitchell, and R. G. Cumming, “Refractive associations with cataract: the blue mountains eye study,” Invest. Ophthalmol. Vis. Sci. 40, 3021 (1999).
[PubMed]

1997 (1)

J. F. Koretz, C. A. Cook, and P. L. Kaufman, “Accommodation and presbyopia in the human eye. changes in the anterior segment and crystalline lens with focus,” Investigative Ophthalmol. Vis. Sci. 38, 569–578 (1997).

1994 (1)

Q. Wang, B. E. Klein, R. Klein, and S. E. Moss, “Refractive status in the beaver dam eye study,” Invest. Ophthalmol. Vis. Sci. 35, 4344–4347 (1994).
[PubMed]

1987 (1)

N. A. Brown and A. R. Hill, “Cataract: the relation between myopia and cataract morphology,” Br. J. Ophthalmol. 71, 405–414 (1987).
[Crossref] [PubMed]

1986 (1)

H. Saunders, “A longitudinal study of the age-dependence of human ocular refraction—i. age-dependent changes in the equivalent sphere,” Ophthalmic Physiol. Opt. 6, 39–46 (1986).

1982 (1)

1981 (1)

H. Saunders, “Age-dependence of human refractive errors,” Ophthalmic Physiol. Opt. 1, 159–174 (1981).
[Crossref] [PubMed]

1974 (1)

N. Brown, “The change in lens curvature with age,” Exp. Eye Res. 19, 175–183 (1974).
[Crossref] [PubMed]

Alcón, E.

Applegate, R. A.

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of objective refraction from wavefront aberrations,” J. Vis. 4, 9 (2004).
[Crossref]

T. Oshika, S. D. Klyce, R. A. Applegate, and H. C. Howland, “Changes in corneal wavefront aberrations with aging,” Invest. Ophthalmol. Vis. Sci. 40, 1351–1355 (1999).
[PubMed]

Artal, P.

Atchison, D. A.

D. A. Atchison, E. L. Markwell, S. Kasthurirangan, J. M. Pope, G. Smith, and P. G. Swann, “Age-related changes in optical and biometric characteristics of emmetropic eyes,” J. Vis. 84, 29 (2008).
[Crossref] [PubMed]

B. A. Moffat, D. A. Atchison, and J. M. Pope, “Explanation of the lens paradox,” Optom. Vis. Sci. 79, 148–150 (2002).
[Crossref] [PubMed]

D. A. Atchison and G. Smith, Optics of the Human Eye (Butterworth-Heinemann, 2000).

Attebo, K.

K. Attebo, R. Q. Ivers, and P. Mitchell, “Refractive errors in an older population: The blue mountains eye study,” Ophthalmology 106, 1066–1072 (1999).
[Crossref] [PubMed]

Bahrami, M.

Benito, A.

Berrio, E.

Bradley, A.

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of objective refraction from wavefront aberrations,” J. Vis. 4, 9 (2004).
[Crossref]

Brown, N.

N. Brown, “The change in lens curvature with age,” Exp. Eye Res. 19, 175–183 (1974).
[Crossref] [PubMed]

Brown, N. A.

N. A. Brown and A. R. Hill, “Cataract: the relation between myopia and cataract morphology,” Br. J. Ophthalmol. 71, 405–414 (1987).
[Crossref] [PubMed]

Campbell, C. E.

Cook, C. A.

J. F. Koretz, C. A. Cook, and P. L. Kaufman, “Accommodation and presbyopia in the human eye. changes in the anterior segment and crystalline lens with focus,” Investigative Ophthalmol. Vis. Sci. 38, 569–578 (1997).

Cumming, R. G.

C. Younan, P. Mitchell, R. G. Cumming, E. Rochtchina, and J. J. Wang, “Myopia and incident cataract and cataract surgery: The blue mountains eye study,” Invest. Ophthalmol. Vis. Sci. 43, 3625 (2002).
[PubMed]

R. Lim, P. Mitchell, and R. G. Cumming, “Refractive associations with cataract: the blue mountains eye study,” Invest. Ophthalmol. Vis. Sci. 40, 3021 (1999).
[PubMed]

Dubbelman, M.

M. Dubbelman and G. van der Heijde, “The shape of the aging human lens: curvature, equivalent refractive index and the lens paradox,” Vision Res. 41, 1867–1877 (2001).
[Crossref] [PubMed]

M. Dubbelman, G. van der Heijde, and H. Weeber, “The thickness of the aging human lens obtained from corrected scheimpflug images,” Optom. Vis. Sci. 78, 411–416 (2001).
[Crossref] [PubMed]

El Hage, S. G.

Y. Le Grand and S. G. El Hage, Physiological Optics (Springer-Verlag, 1980).

Escudero-Sanz, I.

Fraser-Bell, S.

C. Shufelt, S. Fraser-Bell, M. Ying-Lai, M. Torres, R. Varma, and the Los Angeles Latino Eye Study Group, “Refractive error, ocular biometry, and lens opalescence in an adult population: The Los Angeles latino eye study,” Invest. Ophthalmol. Vis. Sci. 46, 4450–4460 (2005).
[Crossref] [PubMed]

Ghatak, A. K.

Goncharov, A. V.

González, L.

Grosvenor, T.

T. Grosvenor, “Changes in spherical refraction during the adult years,” in “Refractive anomalies. Research and clinical applications,” T. Grosvenor and M. Flom, eds. (Butterworth-Heinemann, Boston, 1991), pp. 131–145.

Guirao, A.

Handelman, G. H.

J. F. Koretz and G. H. Handelman, “The ‘lens paradox’ and image formation in accommodating human eyes,” in “The lens: transparency and cataract: Proceedings of the EURAGE/BBS Symposium,” G. Duncan, ed. (Eurage, 1986), pp. 57–64.

Hill, A. R.

N. A. Brown and A. R. Hill, “Cataract: the relation between myopia and cataract morphology,” Br. J. Ophthalmol. 71, 405–414 (1987).
[Crossref] [PubMed]

Hong, X.

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of objective refraction from wavefront aberrations,” J. Vis. 4, 9 (2004).
[Crossref]

Howland, H. C.

T. Oshika, S. D. Klyce, R. A. Applegate, and H. C. Howland, “Changes in corneal wavefront aberrations with aging,” Invest. Ophthalmol. Vis. Sci. 40, 1351–1355 (1999).
[PubMed]

Ivers, R. Q.

K. Attebo, R. Q. Ivers, and P. Mitchell, “Refractive errors in an older population: The blue mountains eye study,” Ophthalmology 106, 1066–1072 (1999).
[Crossref] [PubMed]

Kasthurirangan, S.

D. A. Atchison, E. L. Markwell, S. Kasthurirangan, J. M. Pope, G. Smith, and P. G. Swann, “Age-related changes in optical and biometric characteristics of emmetropic eyes,” J. Vis. 84, 29 (2008).
[Crossref] [PubMed]

Kaufman, P. L.

J. F. Koretz, C. A. Cook, and P. L. Kaufman, “Accommodation and presbyopia in the human eye. changes in the anterior segment and crystalline lens with focus,” Investigative Ophthalmol. Vis. Sci. 38, 569–578 (1997).

Klein, B. E.

Q. Wang, B. E. Klein, R. Klein, and S. E. Moss, “Refractive status in the beaver dam eye study,” Invest. Ophthalmol. Vis. Sci. 35, 4344–4347 (1994).
[PubMed]

Klein, R.

Q. Wang, B. E. Klein, R. Klein, and S. E. Moss, “Refractive status in the beaver dam eye study,” Invest. Ophthalmol. Vis. Sci. 35, 4344–4347 (1994).
[PubMed]

Klyce, S. D.

T. Oshika, S. D. Klyce, R. A. Applegate, and H. C. Howland, “Changes in corneal wavefront aberrations with aging,” Invest. Ophthalmol. Vis. Sci. 40, 1351–1355 (1999).
[PubMed]

Koretz, J. F.

J. F. Koretz, C. A. Cook, and P. L. Kaufman, “Accommodation and presbyopia in the human eye. changes in the anterior segment and crystalline lens with focus,” Investigative Ophthalmol. Vis. Sci. 38, 569–578 (1997).

J. F. Koretz and G. H. Handelman, “The ‘lens paradox’ and image formation in accommodating human eyes,” in “The lens: transparency and cataract: Proceedings of the EURAGE/BBS Symposium,” G. Duncan, ed. (Eurage, 1986), pp. 57–64.

Kumar, D. V.

Le Grand, Y.

Y. Le Grand and S. G. El Hage, Physiological Optics (Springer-Verlag, 1980).

Leske, M. C.

S.-Y. Wu, B. Nemesure, M. C. Leske, and for the Barbados Eye Study Group, “Refractive errors in a black adult population: The Barbados eye study,” Invest. Ophthalmol. Vis. Sci. 40, 2179–2184 (1999).
[PubMed]

Lim, R.

R. Lim, P. Mitchell, and R. G. Cumming, “Refractive associations with cataract: the blue mountains eye study,” Invest. Ophthalmol. Vis. Sci. 40, 3021 (1999).
[PubMed]

López-Gil, N.

Marcos, S.

Markwell, E. L.

D. A. Atchison, E. L. Markwell, S. Kasthurirangan, J. M. Pope, G. Smith, and P. G. Swann, “Age-related changes in optical and biometric characteristics of emmetropic eyes,” J. Vis. 84, 29 (2008).
[Crossref] [PubMed]

Martinez-Enriquez, E.

Mitchell, P.

C. Younan, P. Mitchell, R. G. Cumming, E. Rochtchina, and J. J. Wang, “Myopia and incident cataract and cataract surgery: The blue mountains eye study,” Invest. Ophthalmol. Vis. Sci. 43, 3625 (2002).
[PubMed]

K. Attebo, R. Q. Ivers, and P. Mitchell, “Refractive errors in an older population: The blue mountains eye study,” Ophthalmology 106, 1066–1072 (1999).
[Crossref] [PubMed]

R. Lim, P. Mitchell, and R. G. Cumming, “Refractive associations with cataract: the blue mountains eye study,” Invest. Ophthalmol. Vis. Sci. 40, 3021 (1999).
[PubMed]

Moffat, B. A.

B. A. Moffat, D. A. Atchison, and J. M. Pope, “Explanation of the lens paradox,” Optom. Vis. Sci. 79, 148–150 (2002).
[Crossref] [PubMed]

Moss, S. E.

Q. Wang, B. E. Klein, R. Klein, and S. E. Moss, “Refractive status in the beaver dam eye study,” Invest. Ophthalmol. Vis. Sci. 35, 4344–4347 (1994).
[PubMed]

Navarro, R.

Nemesure, B.

S.-Y. Wu, B. Nemesure, M. C. Leske, and for the Barbados Eye Study Group, “Refractive errors in a black adult population: The Barbados eye study,” Invest. Ophthalmol. Vis. Sci. 40, 2179–2184 (1999).
[PubMed]

Oshika, T.

T. Oshika, S. D. Klyce, R. A. Applegate, and H. C. Howland, “Changes in corneal wavefront aberrations with aging,” Invest. Ophthalmol. Vis. Sci. 40, 1351–1355 (1999).
[PubMed]

Palos, F.

Pérez-Merino, P.

Pope, J. M.

D. A. Atchison, E. L. Markwell, S. Kasthurirangan, J. M. Pope, G. Smith, and P. G. Swann, “Age-related changes in optical and biometric characteristics of emmetropic eyes,” J. Vis. 84, 29 (2008).
[Crossref] [PubMed]

B. A. Moffat, D. A. Atchison, and J. M. Pope, “Explanation of the lens paradox,” Optom. Vis. Sci. 79, 148–150 (2002).
[Crossref] [PubMed]

Redondo, M.

Rochtchina, E.

C. Younan, P. Mitchell, R. G. Cumming, E. Rochtchina, and J. J. Wang, “Myopia and incident cataract and cataract surgery: The blue mountains eye study,” Invest. Ophthalmol. Vis. Sci. 43, 3625 (2002).
[PubMed]

Salmon, T. O.

T. O. Salmon and C. van de Pol, “Normal-eye zernike coefficients and root-mean-square wavefront errors,” J. Cataract. Refract. Surg. 32, 2064–2074 (2006).
[Crossref] [PubMed]

Saunders, H.

H. Saunders, “A longitudinal study of the age-dependence of human ocular refraction—i. age-dependent changes in the equivalent sphere,” Ophthalmic Physiol. Opt. 6, 39–46 (1986).

H. Saunders, “Age-dependence of human refractive errors,” Ophthalmic Physiol. Opt. 1, 159–174 (1981).
[Crossref] [PubMed]

Sharma, A.

Sheil, C. J.

Shufelt, C.

C. Shufelt, S. Fraser-Bell, M. Ying-Lai, M. Torres, R. Varma, and the Los Angeles Latino Eye Study Group, “Refractive error, ocular biometry, and lens opalescence in an adult population: The Los Angeles latino eye study,” Invest. Ophthalmol. Vis. Sci. 46, 4450–4460 (2005).
[Crossref] [PubMed]

Smith, G.

D. A. Atchison, E. L. Markwell, S. Kasthurirangan, J. M. Pope, G. Smith, and P. G. Swann, “Age-related changes in optical and biometric characteristics of emmetropic eyes,” J. Vis. 84, 29 (2008).
[Crossref] [PubMed]

D. A. Atchison and G. Smith, Optics of the Human Eye (Butterworth-Heinemann, 2000).

Swann, P. G.

D. A. Atchison, E. L. Markwell, S. Kasthurirangan, J. M. Pope, G. Smith, and P. G. Swann, “Age-related changes in optical and biometric characteristics of emmetropic eyes,” J. Vis. 84, 29 (2008).
[Crossref] [PubMed]

Tabernero, J.

Thibos, L. N.

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of objective refraction from wavefront aberrations,” J. Vis. 4, 9 (2004).
[Crossref]

Torres, M.

C. Shufelt, S. Fraser-Bell, M. Ying-Lai, M. Torres, R. Varma, and the Los Angeles Latino Eye Study Group, “Refractive error, ocular biometry, and lens opalescence in an adult population: The Los Angeles latino eye study,” Invest. Ophthalmol. Vis. Sci. 46, 4450–4460 (2005).
[Crossref] [PubMed]

van de Pol, C.

T. O. Salmon and C. van de Pol, “Normal-eye zernike coefficients and root-mean-square wavefront errors,” J. Cataract. Refract. Surg. 32, 2064–2074 (2006).
[Crossref] [PubMed]

van der Heijde, G.

M. Dubbelman, G. van der Heijde, and H. Weeber, “The thickness of the aging human lens obtained from corrected scheimpflug images,” Optom. Vis. Sci. 78, 411–416 (2001).
[Crossref] [PubMed]

M. Dubbelman and G. van der Heijde, “The shape of the aging human lens: curvature, equivalent refractive index and the lens paradox,” Vision Res. 41, 1867–1877 (2001).
[Crossref] [PubMed]

Varma, R.

C. Shufelt, S. Fraser-Bell, M. Ying-Lai, M. Torres, R. Varma, and the Los Angeles Latino Eye Study Group, “Refractive error, ocular biometry, and lens opalescence in an adult population: The Los Angeles latino eye study,” Invest. Ophthalmol. Vis. Sci. 46, 4450–4460 (2005).
[Crossref] [PubMed]

Velasco-Ocana, M.

Wang, J. J.

C. Younan, P. Mitchell, R. G. Cumming, E. Rochtchina, and J. J. Wang, “Myopia and incident cataract and cataract surgery: The blue mountains eye study,” Invest. Ophthalmol. Vis. Sci. 43, 3625 (2002).
[PubMed]

Wang, Q.

Q. Wang, B. E. Klein, R. Klein, and S. E. Moss, “Refractive status in the beaver dam eye study,” Invest. Ophthalmol. Vis. Sci. 35, 4344–4347 (1994).
[PubMed]

Weeber, H.

M. Dubbelman, G. van der Heijde, and H. Weeber, “The thickness of the aging human lens obtained from corrected scheimpflug images,” Optom. Vis. Sci. 78, 411–416 (2001).
[Crossref] [PubMed]

Wu, S.-Y.

S.-Y. Wu, B. Nemesure, M. C. Leske, and for the Barbados Eye Study Group, “Refractive errors in a black adult population: The Barbados eye study,” Invest. Ophthalmol. Vis. Sci. 40, 2179–2184 (1999).
[PubMed]

Ying-Lai, M.

C. Shufelt, S. Fraser-Bell, M. Ying-Lai, M. Torres, R. Varma, and the Los Angeles Latino Eye Study Group, “Refractive error, ocular biometry, and lens opalescence in an adult population: The Los Angeles latino eye study,” Invest. Ophthalmol. Vis. Sci. 46, 4450–4460 (2005).
[Crossref] [PubMed]

Younan, C.

C. Younan, P. Mitchell, R. G. Cumming, E. Rochtchina, and J. J. Wang, “Myopia and incident cataract and cataract surgery: The blue mountains eye study,” Invest. Ophthalmol. Vis. Sci. 43, 3625 (2002).
[PubMed]

Appl. Opt. (1)

Biomed. Opt. Express (3)

Br. J. Ophthalmol. (1)

N. A. Brown and A. R. Hill, “Cataract: the relation between myopia and cataract morphology,” Br. J. Ophthalmol. 71, 405–414 (1987).
[Crossref] [PubMed]

Exp. Eye Res. (1)

N. Brown, “The change in lens curvature with age,” Exp. Eye Res. 19, 175–183 (1974).
[Crossref] [PubMed]

Invest. Ophthalmol. Vis. Sci. (6)

C. Shufelt, S. Fraser-Bell, M. Ying-Lai, M. Torres, R. Varma, and the Los Angeles Latino Eye Study Group, “Refractive error, ocular biometry, and lens opalescence in an adult population: The Los Angeles latino eye study,” Invest. Ophthalmol. Vis. Sci. 46, 4450–4460 (2005).
[Crossref] [PubMed]

Q. Wang, B. E. Klein, R. Klein, and S. E. Moss, “Refractive status in the beaver dam eye study,” Invest. Ophthalmol. Vis. Sci. 35, 4344–4347 (1994).
[PubMed]

S.-Y. Wu, B. Nemesure, M. C. Leske, and for the Barbados Eye Study Group, “Refractive errors in a black adult population: The Barbados eye study,” Invest. Ophthalmol. Vis. Sci. 40, 2179–2184 (1999).
[PubMed]

R. Lim, P. Mitchell, and R. G. Cumming, “Refractive associations with cataract: the blue mountains eye study,” Invest. Ophthalmol. Vis. Sci. 40, 3021 (1999).
[PubMed]

C. Younan, P. Mitchell, R. G. Cumming, E. Rochtchina, and J. J. Wang, “Myopia and incident cataract and cataract surgery: The blue mountains eye study,” Invest. Ophthalmol. Vis. Sci. 43, 3625 (2002).
[PubMed]

T. Oshika, S. D. Klyce, R. A. Applegate, and H. C. Howland, “Changes in corneal wavefront aberrations with aging,” Invest. Ophthalmol. Vis. Sci. 40, 1351–1355 (1999).
[PubMed]

Investigative Ophthalmol. Vis. Sci. (1)

J. F. Koretz, C. A. Cook, and P. L. Kaufman, “Accommodation and presbyopia in the human eye. changes in the anterior segment and crystalline lens with focus,” Investigative Ophthalmol. Vis. Sci. 38, 569–578 (1997).

J. Biomed. Opt. (1)

M. Bahrami and A. V. Goncharov, “Geometry-invariant gradient refractive index lens: analytical ray tracing,” J. Biomed. Opt. 17, 055001 (2012).
[Crossref] [PubMed]

J. Cataract. Refract. Surg. (1)

T. O. Salmon and C. van de Pol, “Normal-eye zernike coefficients and root-mean-square wavefront errors,” J. Cataract. Refract. Surg. 32, 2064–2074 (2006).
[Crossref] [PubMed]

J. Opt. Soc. Am. A (6)

J. Vis. (3)

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of objective refraction from wavefront aberrations,” J. Vis. 4, 9 (2004).
[Crossref]

R. Navarro, “Adaptive model of the aging emmetropic eye and its changes with accommodation,” J. Vis. 1413, 21 (2014).
[Crossref] [PubMed]

D. A. Atchison, E. L. Markwell, S. Kasthurirangan, J. M. Pope, G. Smith, and P. G. Swann, “Age-related changes in optical and biometric characteristics of emmetropic eyes,” J. Vis. 84, 29 (2008).
[Crossref] [PubMed]

Journal of Optometry (1)

R. Navarro, “The optical design of the human eye: a critical review,” Journal of Optometry 2, 3–18 (2009).
[Crossref]

Ophthalmic Physiol. Opt. (2)

H. Saunders, “Age-dependence of human refractive errors,” Ophthalmic Physiol. Opt. 1, 159–174 (1981).
[Crossref] [PubMed]

H. Saunders, “A longitudinal study of the age-dependence of human ocular refraction—i. age-dependent changes in the equivalent sphere,” Ophthalmic Physiol. Opt. 6, 39–46 (1986).

Ophthalmology (1)

K. Attebo, R. Q. Ivers, and P. Mitchell, “Refractive errors in an older population: The blue mountains eye study,” Ophthalmology 106, 1066–1072 (1999).
[Crossref] [PubMed]

Optica (1)

Optom. Vis. Sci. (2)

B. A. Moffat, D. A. Atchison, and J. M. Pope, “Explanation of the lens paradox,” Optom. Vis. Sci. 79, 148–150 (2002).
[Crossref] [PubMed]

M. Dubbelman, G. van der Heijde, and H. Weeber, “The thickness of the aging human lens obtained from corrected scheimpflug images,” Optom. Vis. Sci. 78, 411–416 (2001).
[Crossref] [PubMed]

Vision Res. (1)

M. Dubbelman and G. van der Heijde, “The shape of the aging human lens: curvature, equivalent refractive index and the lens paradox,” Vision Res. 41, 1867–1877 (2001).
[Crossref] [PubMed]

Other (4)

Y. Le Grand and S. G. El Hage, Physiological Optics (Springer-Verlag, 1980).

D. A. Atchison and G. Smith, Optics of the Human Eye (Butterworth-Heinemann, 2000).

T. Grosvenor, “Changes in spherical refraction during the adult years,” in “Refractive anomalies. Research and clinical applications,” T. Grosvenor and M. Flom, eds. (Butterworth-Heinemann, Boston, 1991), pp. 131–145.

J. F. Koretz and G. H. Handelman, “The ‘lens paradox’ and image formation in accommodating human eyes,” in “The lens: transparency and cataract: Proceedings of the EURAGE/BBS Symposium,” G. Duncan, ed. (Eurage, 1986), pp. 57–64.

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Figures (3)

Fig. 1
Fig. 1 Iso-indicial contours of lenses modelled at different ages. (a): age = 20, P = 2.87, m = 0.60; (b): age = 45, P = 3.30, m = 0.54; (c): age = 70, P = 5.49, m = 0.23. The “avocado” effect can be seen in (a), while the geometry-invariant shape is seen in (c).
Fig. 2
Fig. 2 Simulation of ocular power (a) and refractive error (b) vs age using the AVOCADO model, with the age-dependence of m = 0.6 − (age/90)4. Refractive error (b) is compared to the findings of Saunders [14,15], after [22].
Fig. 3
Fig. 3 Simulation of SA vs age with 5 mm pupil diameter, for comparison with the work of Tabernero et al. [23].

Tables (1)

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Table 1 Intraocular distances and lens radii used in modelling the ageing eye.

Equations (7)

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ρ 2 = 2 ζ 2 m + 1 R a ( ζ T a + z ) ζ 2 m ( 1 + K a ) ( ζ T a + z ) 2 + ζ 2 m 1 B a ( ζ T a + z ) 3 ,
n ( ζ ) | ρ = 0 = n c + ( n s n c ) ζ 2 P along z axis ,
n ( ζ ) | z = 0 = n c + ( n s n c ) ζ 2 P m + 1 perpendicular to z axis .
d C d z 2 m + 1 r ζ = 2 m + 1 r 2 m + 2 2 m + 1 .
Δ K a = + 0.03 / yr and Δ K p = + 0.07 / yr .
2 P ( age ) = 5.7 + ( age 46 ) 4 .
m ( age ) = 0.6 ( age 90 ) 4 .

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