Abstract

A hypothesis is presented that may explain why the aging eye does not become myopic with age. The power of the eye lens is predicted with a modeling approach to determine how the form of the refractive-index gradient within the lens can change to maintain a constant power in spite of age-related curvature increase. Methods used include published age-dependent data on the optical parameters of the eye, a mathematical model of the lens based on elliptical isoindicial contours, and a refractive-index profile that can be expressed as a power series in the distance from the lens center. The kinds of change in profile required to prevent the eye from becoming myopic as its lens grows are shown.

© 1992 Optical Society of America

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References

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  1. N. Brown, “The change in lens curvature with age,” Exp. Eye Res. 19, 175–183 (1974).
    [CrossRef] [PubMed]
  2. F. J. Slataper, “Age norms of refraction and vision,” Arch. Ophthalmol. N.Y. 43, 466–481 (1950).
    [CrossRef]
  3. H. Saunders, “Age dependence of human refractive errors,” Ophthalmol. Physiol. Opt. 1, 159–174 (1981).
    [CrossRef]
  4. R. A. Weale, A Biography of the Eye; Development, Growth, Age (Lewis, London, 1982), pp. 185–230.
  5. O. Pomerantzeff, P. Dufault, R. Goldstein, “Wide-angle optical model of the eye,” in Advances in Diagnostic Visual Optics, G. M. Breinin, I. M. Siegel, eds. (Springer-Verlag, Berlin, 1983), pp. 12–21.
    [CrossRef]
  6. B. K. Pierscionek, D. Y. C. Chan, “Refractive index gradient of human lenses,” Optom. Vision Sci. 66, 822–829 (1989).
    [CrossRef]
  7. R. Barer, S. Joseph, “Refractometry of living cells. Part 1. Basic principles.” J. Microsc. Sci. 95, 399–423 (1954).
  8. B. K. Pierscionek, “The effects of development and ageing on the structure and function of the crystalline lens,” Ph.D. dissertation (University of Melbourne, Melbourne, Australia, 1988).
  9. P. P. Fagerholm, B. T. Philipson, B. Lindstrom, “Normal human lens; the distribution of protein,” Exp. Eye Res. 33, 615–620 (1981).
    [CrossRef] [PubMed]
  10. B. K. Pierscionek, “Presbyopia—effect of refractive index,” Clin. Exp. Optom. 73, 23–30 (1990).
    [CrossRef]
  11. G. Smith, B. K. Pierscionek, D. A. Atchison, “The optical modelling of the human lens,” Ophthal. Physiol. Opt. 11, 359–369 (1991).
    [CrossRef]
  12. J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye—aging of the anterior segment,” Vision Res. 29, 1685–1692 (1989).
    [CrossRef]
  13. A. Sharma, D. V. Kumar, A. K. Ghatak, “Tracing rays through graded index media,” Appl. Opt. 21, 984–987 (1982).
    [CrossRef] [PubMed]
  14. S. Nakao, S. Fujimoto, R. Nagata, K. Iwata, “Model of refractive-index distribution in the rabbit crystalline lens,” J. Opt. Soc. Am. 58, 1125–1130 (1968).
    [CrossRef] [PubMed]
  15. M. C. W. Campbell, “Measurement of refractive index of an intact crystalline lens,” Vision Res. 24, 409–415 (1984).
    [CrossRef]
  16. B. K. Pierscionek, “Growth and ageing effects on the refractive index in the equatorial plane of the bovine lens,” Vision Res. 29, 1759–1766 (1989).
    [CrossRef] [PubMed]
  17. W. S. Jagger, “The refractive structure and optical properties of the isolated crystalline lens of the cat,” Vision Res. 30, 723–738 (1990).
    [CrossRef] [PubMed]
  18. S. Nakao, T. Ono, R. Nagata, K. Iwata, “Model of refractive indices in the human crystalline lens, J. J. Clin. Ophthalmol. 23, 903–906 (1969).
  19. D. T. Moore, “Design of singlets with continuously varying indices of refraction,” J. Opt. Soc. Am. 61, 886–894 (1971).
    [CrossRef]
  20. A. Gullstrand, “Procedure of rays in the eye. Imagery-laws of first order,” in H. von Helmholtz, Handbuch der Physiologischen Optik, 3rd ed., English translation edited byJ. P. Southall (Dover, New York, 1962), Vol. 1, App. II, pp. 351–352.
  21. J. W. Blaker, “Toward an adaptive model of the human eye,” J. Opt. Soc. Am. 70, 220–223 (1980).
    [CrossRef] [PubMed]
  22. R. F. Fisher, B. E. Pettet, “Presbyopia and the water content of the human crystalline lens,” J. Physiol. (London) 234, 443–447 (1973).
  23. J. Bours, H. J. Fodisch, O. Hockwin, “Age related changes in water and crystallin content of the fetal and adult human lens, demonstrated by a microsectioning technique,” Ophthalmol. Res. 19, 235–239 (1987).
    [CrossRef]

1991

G. Smith, B. K. Pierscionek, D. A. Atchison, “The optical modelling of the human lens,” Ophthal. Physiol. Opt. 11, 359–369 (1991).
[CrossRef]

1990

B. K. Pierscionek, “Presbyopia—effect of refractive index,” Clin. Exp. Optom. 73, 23–30 (1990).
[CrossRef]

W. S. Jagger, “The refractive structure and optical properties of the isolated crystalline lens of the cat,” Vision Res. 30, 723–738 (1990).
[CrossRef] [PubMed]

1989

B. K. Pierscionek, “Growth and ageing effects on the refractive index in the equatorial plane of the bovine lens,” Vision Res. 29, 1759–1766 (1989).
[CrossRef] [PubMed]

J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye—aging of the anterior segment,” Vision Res. 29, 1685–1692 (1989).
[CrossRef]

B. K. Pierscionek, D. Y. C. Chan, “Refractive index gradient of human lenses,” Optom. Vision Sci. 66, 822–829 (1989).
[CrossRef]

1987

J. Bours, H. J. Fodisch, O. Hockwin, “Age related changes in water and crystallin content of the fetal and adult human lens, demonstrated by a microsectioning technique,” Ophthalmol. Res. 19, 235–239 (1987).
[CrossRef]

1984

M. C. W. Campbell, “Measurement of refractive index of an intact crystalline lens,” Vision Res. 24, 409–415 (1984).
[CrossRef]

1982

1981

H. Saunders, “Age dependence of human refractive errors,” Ophthalmol. Physiol. Opt. 1, 159–174 (1981).
[CrossRef]

P. P. Fagerholm, B. T. Philipson, B. Lindstrom, “Normal human lens; the distribution of protein,” Exp. Eye Res. 33, 615–620 (1981).
[CrossRef] [PubMed]

1980

1974

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

1973

R. F. Fisher, B. E. Pettet, “Presbyopia and the water content of the human crystalline lens,” J. Physiol. (London) 234, 443–447 (1973).

1971

1969

S. Nakao, T. Ono, R. Nagata, K. Iwata, “Model of refractive indices in the human crystalline lens, J. J. Clin. Ophthalmol. 23, 903–906 (1969).

1968

1954

R. Barer, S. Joseph, “Refractometry of living cells. Part 1. Basic principles.” J. Microsc. Sci. 95, 399–423 (1954).

1950

F. J. Slataper, “Age norms of refraction and vision,” Arch. Ophthalmol. N.Y. 43, 466–481 (1950).
[CrossRef]

Atchison, D. A.

G. Smith, B. K. Pierscionek, D. A. Atchison, “The optical modelling of the human lens,” Ophthal. Physiol. Opt. 11, 359–369 (1991).
[CrossRef]

Barer, R.

R. Barer, S. Joseph, “Refractometry of living cells. Part 1. Basic principles.” J. Microsc. Sci. 95, 399–423 (1954).

Blaker, J. W.

Bours, J.

J. Bours, H. J. Fodisch, O. Hockwin, “Age related changes in water and crystallin content of the fetal and adult human lens, demonstrated by a microsectioning technique,” Ophthalmol. Res. 19, 235–239 (1987).
[CrossRef]

Brown, N.

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

Campbell, M. C. W.

M. C. W. Campbell, “Measurement of refractive index of an intact crystalline lens,” Vision Res. 24, 409–415 (1984).
[CrossRef]

Chan, D. Y. C.

B. K. Pierscionek, D. Y. C. Chan, “Refractive index gradient of human lenses,” Optom. Vision Sci. 66, 822–829 (1989).
[CrossRef]

Dufault, P.

O. Pomerantzeff, P. Dufault, R. Goldstein, “Wide-angle optical model of the eye,” in Advances in Diagnostic Visual Optics, G. M. Breinin, I. M. Siegel, eds. (Springer-Verlag, Berlin, 1983), pp. 12–21.
[CrossRef]

Fagerholm, P. P.

P. P. Fagerholm, B. T. Philipson, B. Lindstrom, “Normal human lens; the distribution of protein,” Exp. Eye Res. 33, 615–620 (1981).
[CrossRef] [PubMed]

Fisher, R. F.

R. F. Fisher, B. E. Pettet, “Presbyopia and the water content of the human crystalline lens,” J. Physiol. (London) 234, 443–447 (1973).

Fodisch, H. J.

J. Bours, H. J. Fodisch, O. Hockwin, “Age related changes in water and crystallin content of the fetal and adult human lens, demonstrated by a microsectioning technique,” Ophthalmol. Res. 19, 235–239 (1987).
[CrossRef]

Fujimoto, S.

Ghatak, A. K.

Goeckner, P. A.

J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye—aging of the anterior segment,” Vision Res. 29, 1685–1692 (1989).
[CrossRef]

Goldstein, R.

O. Pomerantzeff, P. Dufault, R. Goldstein, “Wide-angle optical model of the eye,” in Advances in Diagnostic Visual Optics, G. M. Breinin, I. M. Siegel, eds. (Springer-Verlag, Berlin, 1983), pp. 12–21.
[CrossRef]

Gullstrand, A.

A. Gullstrand, “Procedure of rays in the eye. Imagery-laws of first order,” in H. von Helmholtz, Handbuch der Physiologischen Optik, 3rd ed., English translation edited byJ. P. Southall (Dover, New York, 1962), Vol. 1, App. II, pp. 351–352.

Hockwin, O.

J. Bours, H. J. Fodisch, O. Hockwin, “Age related changes in water and crystallin content of the fetal and adult human lens, demonstrated by a microsectioning technique,” Ophthalmol. Res. 19, 235–239 (1987).
[CrossRef]

Iwata, K.

S. Nakao, T. Ono, R. Nagata, K. Iwata, “Model of refractive indices in the human crystalline lens, J. J. Clin. Ophthalmol. 23, 903–906 (1969).

S. Nakao, S. Fujimoto, R. Nagata, K. Iwata, “Model of refractive-index distribution in the rabbit crystalline lens,” J. Opt. Soc. Am. 58, 1125–1130 (1968).
[CrossRef] [PubMed]

Jagger, W. S.

W. S. Jagger, “The refractive structure and optical properties of the isolated crystalline lens of the cat,” Vision Res. 30, 723–738 (1990).
[CrossRef] [PubMed]

Joseph, S.

R. Barer, S. Joseph, “Refractometry of living cells. Part 1. Basic principles.” J. Microsc. Sci. 95, 399–423 (1954).

Kaufman, P. L.

J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye—aging of the anterior segment,” Vision Res. 29, 1685–1692 (1989).
[CrossRef]

Koretz, J. F.

J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye—aging of the anterior segment,” Vision Res. 29, 1685–1692 (1989).
[CrossRef]

Kumar, D. V.

Lindstrom, B.

P. P. Fagerholm, B. T. Philipson, B. Lindstrom, “Normal human lens; the distribution of protein,” Exp. Eye Res. 33, 615–620 (1981).
[CrossRef] [PubMed]

Moore, D. T.

Nagata, R.

S. Nakao, T. Ono, R. Nagata, K. Iwata, “Model of refractive indices in the human crystalline lens, J. J. Clin. Ophthalmol. 23, 903–906 (1969).

S. Nakao, S. Fujimoto, R. Nagata, K. Iwata, “Model of refractive-index distribution in the rabbit crystalline lens,” J. Opt. Soc. Am. 58, 1125–1130 (1968).
[CrossRef] [PubMed]

Nakao, S.

S. Nakao, T. Ono, R. Nagata, K. Iwata, “Model of refractive indices in the human crystalline lens, J. J. Clin. Ophthalmol. 23, 903–906 (1969).

S. Nakao, S. Fujimoto, R. Nagata, K. Iwata, “Model of refractive-index distribution in the rabbit crystalline lens,” J. Opt. Soc. Am. 58, 1125–1130 (1968).
[CrossRef] [PubMed]

Neider, M. W.

J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye—aging of the anterior segment,” Vision Res. 29, 1685–1692 (1989).
[CrossRef]

Ono, T.

S. Nakao, T. Ono, R. Nagata, K. Iwata, “Model of refractive indices in the human crystalline lens, J. J. Clin. Ophthalmol. 23, 903–906 (1969).

Pettet, B. E.

R. F. Fisher, B. E. Pettet, “Presbyopia and the water content of the human crystalline lens,” J. Physiol. (London) 234, 443–447 (1973).

Philipson, B. T.

P. P. Fagerholm, B. T. Philipson, B. Lindstrom, “Normal human lens; the distribution of protein,” Exp. Eye Res. 33, 615–620 (1981).
[CrossRef] [PubMed]

Pierscionek, B. K.

G. Smith, B. K. Pierscionek, D. A. Atchison, “The optical modelling of the human lens,” Ophthal. Physiol. Opt. 11, 359–369 (1991).
[CrossRef]

B. K. Pierscionek, “Presbyopia—effect of refractive index,” Clin. Exp. Optom. 73, 23–30 (1990).
[CrossRef]

B. K. Pierscionek, D. Y. C. Chan, “Refractive index gradient of human lenses,” Optom. Vision Sci. 66, 822–829 (1989).
[CrossRef]

B. K. Pierscionek, “Growth and ageing effects on the refractive index in the equatorial plane of the bovine lens,” Vision Res. 29, 1759–1766 (1989).
[CrossRef] [PubMed]

B. K. Pierscionek, “The effects of development and ageing on the structure and function of the crystalline lens,” Ph.D. dissertation (University of Melbourne, Melbourne, Australia, 1988).

Pomerantzeff, O.

O. Pomerantzeff, P. Dufault, R. Goldstein, “Wide-angle optical model of the eye,” in Advances in Diagnostic Visual Optics, G. M. Breinin, I. M. Siegel, eds. (Springer-Verlag, Berlin, 1983), pp. 12–21.
[CrossRef]

Saunders, H.

H. Saunders, “Age dependence of human refractive errors,” Ophthalmol. Physiol. Opt. 1, 159–174 (1981).
[CrossRef]

Sharma, A.

Slataper, F. J.

F. J. Slataper, “Age norms of refraction and vision,” Arch. Ophthalmol. N.Y. 43, 466–481 (1950).
[CrossRef]

Smith, G.

G. Smith, B. K. Pierscionek, D. A. Atchison, “The optical modelling of the human lens,” Ophthal. Physiol. Opt. 11, 359–369 (1991).
[CrossRef]

Weale, R. A.

R. A. Weale, A Biography of the Eye; Development, Growth, Age (Lewis, London, 1982), pp. 185–230.

Appl. Opt.

Arch. Ophthalmol. N.Y.

F. J. Slataper, “Age norms of refraction and vision,” Arch. Ophthalmol. N.Y. 43, 466–481 (1950).
[CrossRef]

Clin. Exp. Optom.

B. K. Pierscionek, “Presbyopia—effect of refractive index,” Clin. Exp. Optom. 73, 23–30 (1990).
[CrossRef]

Exp. Eye Res.

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

P. P. Fagerholm, B. T. Philipson, B. Lindstrom, “Normal human lens; the distribution of protein,” Exp. Eye Res. 33, 615–620 (1981).
[CrossRef] [PubMed]

J. J. Clin. Ophthalmol.

S. Nakao, T. Ono, R. Nagata, K. Iwata, “Model of refractive indices in the human crystalline lens, J. J. Clin. Ophthalmol. 23, 903–906 (1969).

J. Microsc. Sci.

R. Barer, S. Joseph, “Refractometry of living cells. Part 1. Basic principles.” J. Microsc. Sci. 95, 399–423 (1954).

J. Opt. Soc. Am.

J. Physiol. (London)

R. F. Fisher, B. E. Pettet, “Presbyopia and the water content of the human crystalline lens,” J. Physiol. (London) 234, 443–447 (1973).

Ophthal. Physiol. Opt.

G. Smith, B. K. Pierscionek, D. A. Atchison, “The optical modelling of the human lens,” Ophthal. Physiol. Opt. 11, 359–369 (1991).
[CrossRef]

Ophthalmol. Physiol. Opt.

H. Saunders, “Age dependence of human refractive errors,” Ophthalmol. Physiol. Opt. 1, 159–174 (1981).
[CrossRef]

Ophthalmol. Res.

J. Bours, H. J. Fodisch, O. Hockwin, “Age related changes in water and crystallin content of the fetal and adult human lens, demonstrated by a microsectioning technique,” Ophthalmol. Res. 19, 235–239 (1987).
[CrossRef]

Optom. Vision Sci.

B. K. Pierscionek, D. Y. C. Chan, “Refractive index gradient of human lenses,” Optom. Vision Sci. 66, 822–829 (1989).
[CrossRef]

Vision Res.

J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye—aging of the anterior segment,” Vision Res. 29, 1685–1692 (1989).
[CrossRef]

M. C. W. Campbell, “Measurement of refractive index of an intact crystalline lens,” Vision Res. 24, 409–415 (1984).
[CrossRef]

B. K. Pierscionek, “Growth and ageing effects on the refractive index in the equatorial plane of the bovine lens,” Vision Res. 29, 1759–1766 (1989).
[CrossRef] [PubMed]

W. S. Jagger, “The refractive structure and optical properties of the isolated crystalline lens of the cat,” Vision Res. 30, 723–738 (1990).
[CrossRef] [PubMed]

Other

A. Gullstrand, “Procedure of rays in the eye. Imagery-laws of first order,” in H. von Helmholtz, Handbuch der Physiologischen Optik, 3rd ed., English translation edited byJ. P. Southall (Dover, New York, 1962), Vol. 1, App. II, pp. 351–352.

B. K. Pierscionek, “The effects of development and ageing on the structure and function of the crystalline lens,” Ph.D. dissertation (University of Melbourne, Melbourne, Australia, 1988).

R. A. Weale, A Biography of the Eye; Development, Growth, Age (Lewis, London, 1982), pp. 185–230.

O. Pomerantzeff, P. Dufault, R. Goldstein, “Wide-angle optical model of the eye,” in Advances in Diagnostic Visual Optics, G. M. Breinin, I. M. Siegel, eds. (Springer-Verlag, Berlin, 1983), pp. 12–21.
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Diagrammatic representation of the lens of the eye in the sagittal section, based on the asymmetric-ellipse model 2 of Smith et al.11 Z is the optical axis. Y(1) is the position of the Y axis for the front ellipse; Y(2) is the position of the Y axis for the rear ellipse. The posterior curvature is greater than the anterior curvature.

Fig. 2
Fig. 2

Equivalent power of a symmetric lens for various forms of the refractive-index profile that are specified by the value of p given in Eq. (7). For this lens, c0 = 1.4037 and cp = −0.0611, giving ncenter = 1.4037 and nedge = 1.3426. The lens has the shape specified by a1 = a2 = 2.4 and b = 4.6, giving R1 = 8.438 and R2 = −R1. Drawn from the data of Smith et al.11

Fig. 3
Fig. 3

Effect of the value of the order p in Eq. (7) on the refractive-index profile specified in Fig. 2.

Fig. 4
Fig. 4

Refractive-index profiles for lenses of three ages that give the same ocular power of 56.03 D. See Table 4 for details.

Tables (4)

Tables Icon

Table 1 Values of Relevant Ocular Parameters As a Function of Agea

Tables Icon

Table 2 Equivalent Power of the Eye, the Difference Being Due to the Change in the Ocular Parameters Shown in Table 1a

Tables Icon

Table 3 The Values of c1c2 and c3 That Are Required to Give an Equivalent Power of 62.12 D for All Agesa

Tables Icon

Table 4 The Values of c1c2, c3, and c4 That Are Required to Give an Equivalent Power of 56.03 D for All Ages a

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

( Z a 1 ) 2 a 1 2 + Y 2 b 2 = 1 ,
Z 2 a 2 2 + Y 2 b 2 = 1 ,
R 1 = b 2 / a 1 , R 2 = b 2 / a 2 .
N ( r ) = c 0 + c 1 r 2 + c 2 r 4 + c 3 r 6 + c 4 r 8 + ,
N ( Y , Z ) = c 0 + c 1 f ( Y , Z ) + c 2 f 2 ( Y , Z ) + c 3 f 3 ( Y , Z ) + .
f ( Y , Z ) = ( Z a 1 ) 2 a 1 2 + Y 2 b 2 ,
f ( Y , Z ) = Z 2 a 2 2 + Y 2 b 2 .
N ( r ) = c 0 + c p r p ,
anterior chamber depth ( mm ) = 3.64 0.013 * age .
lens thickness ( mm ) = 3.46 + 0.013 * age .
R 1 ( mm ) = 16.815 0.104 * age ( anterior ) ,
R 2 ( mm ) = ( 8.719 0.015 * age ) ( posterior ) .
c 0 = n center ,
c 0 + c 1 + c 2 + c 3 + = n edge .

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