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Mechanism of human accommodation as analyzed by nonlinear finite element analysis

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Annals of Ophthalmology

Abstract

Results of nonlinear finite element analysis support the Schachar theory of accommodation and demonstrate that the long-held Helmholtz theory of accommodation is impossible.

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References

  1. Young, T. On the mechanism of the eye. Philos Trans Roy Soc Lond. 1801;92:23–88.

    Article  Google Scholar 

  2. Tscherning M. Physiological Optics, Philadelphia, Pa: Keystone; 1904;160–189.

    Google Scholar 

  3. Fincham EF. Mechanism of accommodation. Br J Ophthalmol. 1937;8(suppl):5–80.

    Google Scholar 

  4. Ivanoff A. On the influence of accommodation on spherical aberration in the human eye: an attempt to interpret night myopia. J Opt Soc Am. 1947;37:730–731.

    Google Scholar 

  5. Kooman M, Tousey R, Scolnik R. The spherical aberration of the eye. J Opt Soc Am. 1949;39:370–376.

    Article  Google Scholar 

  6. von Helmholtz H. Uber die Akkommodation des Auges. Graefes Arch Clin Exp Ophthalmol. 1855;1:1–89.

    Google Scholar 

  7. Schachar RA. Cause and treatment of presbyopia with a method for increasing the amplitude of accommodation. Ann Ophhthamol. 1992;24:445–452.

    CAS  Google Scholar 

  8. Schachar RA. Zonular function: a new hypothesis with clinical implications. Ann Ophthalmol 1994;26:36–38.

    PubMed  CAS  Google Scholar 

  9. Schachar RA, Anderson DA. The mechanism of ciliary muscle function. Ann Ophthalmol. 1995;27:126–132.

    Google Scholar 

  10. Schachar RA. Histology of the ciliary muscle-zonular connections. Ann Ophthalmol. 1999;31:10–17.

    Google Scholar 

  11. Schachar RA, Cudmore DP, Black TD. A revolutionary variable focus lens. Ann Ophthalmol. 1996;28:11–18.

    Google Scholar 

  12. Schachar RA, Cudmore DP, Black TD, et al. Paradoxical optical power increase of a deformable lens by equatorial stretching. Ann Ophthalmol. 1998;30:10–18.

    Google Scholar 

  13. Fisher RF. Elastic constants of the human lens capsule. J Physiol [Lond]. 1969;201:1–19.

    CAS  Google Scholar 

  14. van Alphen GWHM, Graebel WP. Elasticity of tissues involved in accommodation. Vision Res. 1991;31:1417–1438.

    Article  PubMed  Google Scholar 

  15. Krag S, Olsen T, Andreassen TT. Biomechanical characteristics of the human anterior lens capsule in relation to age. Invest Ophthalmo Vis Sci. 1997;38:357–363.

    CAS  Google Scholar 

  16. Hogan MJ, Alvardo JA, Weddell JE. Histology of the Human Eye. Philadelphia, Pa: WB Saunders Co; 1971:667–673.

    Google Scholar 

  17. Duke-Elder S, Gloster J, Weale RA. The physiology of the eye and of vision. In: Duke-Elder S. ed., System of Ophthalmology Vol 4. London, England: Henry Kimpton: 1968:365–366.

    Google Scholar 

  18. Burd HJ, Judge SJ, Flavell MJ. Mechanics of accommodation of the human eye. Vision Res. 1999;39:1591–1595.

    Article  PubMed  CAS  Google Scholar 

  19. Baughman RH, Dantas SO, Stafrom S, Zakhidov AA, Mitchell TB, Dubin DHE. Negative Poisson's ratios for extreme states of matter. Science. 2000;288:2018–2022.

    Article  PubMed  CAS  Google Scholar 

  20. Chen JS, Pan C. A pressure projection method for nearly incompressible rubber hyperelasticity. Part I: Theory. J Appl Mech. 1996; 63:862–868.

    Google Scholar 

  21. Chen JS, Wu CT, Pan C. A pressure projection method for nearly incompressible rubber hyperelasticity. Part II: Applications. J Appl Mech. 1996;63:869–876.

    Google Scholar 

  22. Brown N. The change in shape, and internal form of the lens of the eye on accommodation. Exp Eye Res. 1973;15:441–459.

    Article  PubMed  CAS  Google Scholar 

  23. Farnsworth PN, Shyne SE. Anterior zonular shifts with age. Exp Eye Res. 1979;28:291–297.

    Article  PubMed  CAS  Google Scholar 

  24. McCulloch C. The zonule of Zinn: its origin, course, and its relation to neighboring structures. Trans Am Ophthalmol Soc. 1954; 52:525–585.

    PubMed  Google Scholar 

  25. Brown N. The shape of the lens equator Exp Eye Res. 1974;19:571–576.

    Article  PubMed  CAS  Google Scholar 

  26. ANSYS 5.6. User's Manual & Theory Reference. Cannonsburg, Pa: ANSYS Inc; 1999.

    Google Scholar 

  27. Born W, Wolf E. Principles of Optics. 4th ed. Oxford, England: Pergamon Press; 1970:161–163.

    Google Scholar 

  28. Zemax Optical Design Program: User's Guide. Version 9.0. Tucson, Ariz: Focus Software Inc; 2000.

  29. Donders FO, On the Anomalies of Accommodation and Refraction of the Eye. London, England: New Sydenham Society; 1864:204–214.

    Google Scholar 

  30. van Alphen GWHM, Robinett SL, Macri FJ. Drug effects on ciliary muscle and choroid preparations in vitro. Arch Ophthalmol. 1962;68:111–123.

    Google Scholar 

  31. Fisher RF. The force of contraction of the humna ciliary muscle during accommodation. J Physiol. 1977;270:51–74.

    PubMed  CAS  Google Scholar 

  32. Fukasaku H. The Correction of Presbyopia [film]. Seattle, Wash: American Society of Cataract and Refractive Surgery; May 1999.

    Google Scholar 

  33. Schachar RA, Tello C, Cudmore DP, et al. In vivo increase of the human lens equatorial diameter during accommodation. Am J Physiol (Regulatory Integrative Comp Physiol 40). 1996;271:R670-R676.

    CAS  Google Scholar 

  34. Schachar RA, Cudmore DP, Torti R, et al. A physical model demonstrating Schachar's hypothesis of accommodation. Ann Ophthalmol. 1994;26:4–9.

    PubMed  CAS  Google Scholar 

  35. Emery JM, Paton D. Current Concepts in Cataract Surgery. St Louis, Mo. CV Mosby Co; 1976:182–189.

    Google Scholar 

  36. Streeten BW. Zonular apparatus. In: Jakobiec FA, ed. Ocular Anatomy, Embryology and Teratology. Philadelphia, Pa: Harper & Row Publishers; 1982:331–353.

    Google Scholar 

  37. Schachar RA, Huang T, Huang X. Mathematic, proof of Schachar's hypothesis of accommodation. Ann Ophthalmol 1993;25:5–9.

    PubMed  CAS  Google Scholar 

  38. Ganem SP, Stubler S. The mechanism of human accommodation: an analytical mathematical model [abstract]. Presented at: American Society of Cataract and Refractive Surgery meeting; May 2000; Boston, Mass.

  39. Neider MW, Crawford K, Kaufman PL, Bito LZ. In vivo videography of the rheusus monkey accommodative apparatus: age-related loss of ciliary muscle response to central stimulation. Arch Ophthalmol. 1990;108:69–74.

    PubMed  CAS  Google Scholar 

  40. Koretz JF, Bertasso AM, Neider MW, True-Gabelt B, Kaufman PL. Slit-lamp studies of the Rhesus monkey eye. II. Changes in crystalline lens shape, thickness and position during accommodation and aging. Exp Eye Res. 1987;45:317–326.

    Article  PubMed  CAS  Google Scholar 

  41. Wilson RS. Does the lens diameter increase or decrease during accommodation? Human accommodation studies: a new technique using infrared retro-illumination video photography and pixel unit measurements. Trans Am Ophthalmol Soc. 1997;95:261–270.

    PubMed  CAS  Google Scholar 

  42. Le Grand Y. Optique Physiologique I. 2nd ed. Paris, France: Editions de la Revue D'Optoque; 1952:45.

    Google Scholar 

  43. Gullstrand A In: von Helmholtz H, ed. Physiological Optics, 3rd ed. Mineola, NY, Dover Publications; 1962:56,396.

    Google Scholar 

  44. Enoch JM, Hope GM. An analysis of retinal orientation. IV. Center of the entrace pupil and the center of convergence of orientation and directional sensitivity. Invest Ophthalmol. 1972;11:1017–1021.

    PubMed  CAS  Google Scholar 

  45. Glasser A, Kaufman PL. The mechanism of accommodation in primates. Ophthalmology. 1999;106:863–872.

    Article  PubMed  CAS  Google Scholar 

  46. Levy NS. The mechanism of accommodation in primates [letter]. Ophthalmology. 2000;107:625.

    Article  PubMed  CAS  Google Scholar 

  47. Glasser A, Kaufman PL. The mechanism of accommodation in primates [letter]. Ophthalmology. 2000;107:626.

    Article  Google Scholar 

  48. Strenk SA, Semmlow JL, Strenk LM, et al. Age-related changes in human ciliary muscle and lens: a magnetic resonance imaging study. Invest Ophthalmol Vis Sci. 1999;40:1162–1169.

    PubMed  CAS  Google Scholar 

  49. Levy NS. Age-related changes in human ciliary muscle and lens: a magnetic resonance imaging study [letter] Invest Ophthalmol Vis Sci [online]. 2000. Available at: http://www.iovs.org/cgi/eletters/ 40/6/1162#ELO3.

  50. Strenk SA, Krishnan A, Semmlow, Strenk LS, DeMarco JK. Volume changes in the in vivo associated with accommodation [abstract]. Invest Ophthalmol Vis Sci. 2001;42:S9.

    Google Scholar 

  51. Tripathi RC, Tripathi BJ. Anatomy, orbit and adnexa of the human eye. In: Davson H, ed. The Eye. Vol 1A. 3rd ed. Orlando, Fla: Academic Press; 1984:56–57.

    Google Scholar 

  52. Rafferty NS. Structure, function and pathology. In: Maisel H, ed. The Ocular Lens. New York, NY: Marcel Dekker: 1985:2–5.

    Google Scholar 

  53. Sakabe I, Oshika T, Lim SJ, Apple DJ. Anterior shift of zonular insertion onto the anterior surface of human crystalline lens with age. Ophthalmology. 1998;105:295–299.

    Article  PubMed  CAS  Google Scholar 

  54. Lim SJ, Shin JK, Kim HB, Kurata Y, Sakabe I, Apple DJ. Analysis of zonular-free zone and lens size in relation to axial length of eye with age. J Cataract Refract Surg. 1998;24:390–396.

    PubMed  CAS  Google Scholar 

  55. Coulombe JL, Coulombe AJ. Lens development. IV. Size. shape and orientation. Invest Ophthalmol. 1969;8:251–257.

    Google Scholar 

  56. Marshall J, Bauconsfield M, Rothery S. The anatomy and development of the human lens and zonules. Trans Ophthalmol Soc UK. 1982;102:423–440.

    PubMed  Google Scholar 

  57. Kleinman NJ, Worgul BV. The lens. In: Tasman W, ed. Duane's Foundations of Clinical Ophthalmology. Vol 1. Philadelphia, Pa: JB Lippincott; 1994: chap 15.

    Google Scholar 

  58. Duke-Elder S, Waybar KC. Anatomy of the visual system. In: Duke-Elder S, ed. System of Ophthalmology, Vol. 2. London, England: Henry Kimpton; 1962:312–313.

    Google Scholar 

  59. Schachar RA, Black TD, Huang T. Understanding Radial Keratotomy. Denison, Tex: LAL Publishing; 1981:100–102.

    Google Scholar 

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Authors and Affiliations

  1. Presby Corp., Dallas, Tex.

    Ronald A. Schachar MD, PhD

  2. DRD Technology Corp., Tulsa, Okla

    Andrew J. Bax MS, PE

Authors
  1. Ronald A. Schachar MD, PhD
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  2. Andrew J. Bax MS, PE
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Correspondence to Ronald A. Schachar MD, PhD.

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Schachar, R.A., Bax, A.J. Mechanism of human accommodation as analyzed by nonlinear finite element analysis. Ann Ophthalmol 33, 103–112 (2001). https://doi.org/10.1007/s12009-001-0002-4

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