Model biomedyczny ludzkiej gałki ocznej

Śródka, W.

Artykuł - szczegóły

Tytuł artykułu

Model biomedyczny ludzkiej gałki ocznej

Autorzy

Śródka W.

Identyfikatory

Warianty tytułu

Biomechanical model of human eyeball

Języki publikacji

Abstrakty

Przedmiotem badań jest model strukturalny gaiki ocznej oraz możliwość symulowania za jego pomocą funkcji optycznych oka. Analizie poddano także aspekty mechaniczne pomiaru ciśnienia wewnątrzgałkowego (IOP) techniką określaną jako tonometria. Opracowanie jest próbą stworzenia podstaw teoretycznych mechaniki powłok oka w obu wymienionych zakresach. Obliczenia oparte są na trzech podstawowych założeniach: samonastawności optycznej modelu gałki ocznej, równości ciśnień po obu stronach strefy aplanacji rogówki kalibracyjnej dla ciśnienia nominalnego i dla nienormalnej izotropii materiału. Rozwiązania, osiągane metodą elementów skończonych, uwzględniają fizyczną i geometryczną nieliniowość konstrukcji. Przyjęta strategia obliczeń umożliwia badanie stateczności powłoki rogówkowej w tonometrii aplanacyjnej Goldmanna. Wyznaczone w drodze obliczeń numerycznych ciśnienie aplanacji okazuje się nieliniową funkcją IOP, znacznie odbiegającą od przewidywań Goldmanna. Przeprowadzono szczegółową krytykę tej metody oraz zaproponowano nowy opis teoretyczny pomiaru, a także wynikający z niego formalizm umożliwiający korygowanie odczytu ze względu na grubość rogówki i promień jej krzywizny. Zbadane zostały także pokrewne techniki pomiaru ciśnienia wewnątrzgałkowego nazywane tonometria dynamiczną (DCT) i tonometria rezonansową (ART). Wykorzystanie hipotezy samonastawności oka pozwoliło zintegrować elementy składowe gałki ocznej w jeden spójny układ optyczny. Badanie funkcji optycznych modelu wykazało ścisłą relację zachodzącą pomiędzy materiałem rogówki, rąbka i twardówki. Dla zachowania samonastawności modelu, sieczny moduł sprężystości twardówki musi być około pięciu razy większy od modułu rogówki. Określony metodą odwrotną moduł sieczny rogówki zbliżony jest do 0,27 MPa dla ciśnienia nominalnego. Parametry mechaniczne powłok gałki ocznej nie są wzajemnie niezależne, powiązania między nimi są narzucane przez funkcje optyczne. Zależności te ułatwiają identyfikację strukturalną oka. Odkryte za pomocą modelu efekty nieliniowe w tonometrii aplanacyjnej falsyfikują teorię Goldmanna, a także wynikającą z niej procedurę korekcji wyniku pomiaru IOP. Skutki te obejmują również DCT i ART, oparte na postulatach Goldmanna.

Refraction surgery, tonometry and eye optical system theory are the fields of ophthalmology, in which a biomechanical model of the eyeball could play a significant research and utilitarian role. Attempts at creating such a model have been made since the 1970s. Today when highly sophisticated systems using most advanced methods of structural analysis are available, such problems can be relatively easily solved. Unfortunately, pre-information era assumptions and ways of thinking are still underlying the biomechanical model of the eyeball. This clash of outdated ideas and modern computing tools leads to results which do not find practical application - up to this day the effects of cornea surgeries are empirically predicted, similarly IOP reading corrections in applanation tonometry are experimentally determined. The aim of this research was to diagnose the condition of eye biomechanics, to carry out a critical assessment of the binding formal foundations and to attempt to solve selected problems. The invars process was used to identify the material parameters of the cornea, the sclera and the corneal limbus. In this method, the eyeball model is so designed that its functioning is in agreement with the commonly known experimental results. The results available today relate to tonometry, eyeball stiffness and the cornea. Also the original idea of the optical self-adjustment of the eyeball was used. The number of model assumptions was considerably reduced and the latter were well-founded. The assumptions boil down to the three postulates: abnormal anisotropy of the material, optical self-adjustment of the model and Goldman's postulate that the (nominal) pressures on both sides of the calibration cornea are equal. The calculation eyeball model was solved using the finite element method. Its optical system was built according to the rules predicted by the self-adjustment hypothesis. This new approach to the applanation problem has enabled the investigation of corneal shell stability in GAT. As a result, the hitherto unnoticed influence of IOP on the correction value for the pressure measured by the Goldmann tonometer has been revealed. A detailed critique of the method is presented. A new measurement theory is proposed and a formalism making it possible to correct readings disturbed by cornea thickness and curvature radius variation among people is derived from this theory. Also the IOP measuring techniques: DCT and ART were tested. Numerical simulations showed, contrary to the authors of the techniques, that intraocular pressure measurement results are not in agreement with GAT and need to be corrected as well. Thanks to the eye self-adjustment hypothesis the components of the eyeball could be integrated into one coherent optical system. The examination of the model's optical functions revealed the relationship which must exist between the materials of the cornea, the corneal limbus and the sclera: in order to preserve the self-adjustment of the model, the secant modulus of elasticity of the sclera must be about five times larger than the modulus of the cornea, and the latter is close to 0.27 MPa under natural stress. The investigations showed that above the pressure of 16 mmHg the Goldmann tonometer readings are understated and the deviation from the real IOP value increases with pressure, to as much as 10 mmHg. The same is observed for a cornea with calibration dimensions. This contradicts the Imbert-Fick law. The causes of this phenomenon, until now associated with surface tension in the lacrimal fluid, should be linked with corneal shell stability during flattening. On this basis an applanation pressure function in GAT for the cornea of any dimensions has been developed. The correction formulas for CCT and cornea curvature have been found to depend on IOP and to be mutually dependent. Their analytical form has, besides the empirical basis, a theoretical basis now. Contrary to the common belief, the numerical simulations of DCT suggest that the pressure measured by the tonometer clearly depends on CCT -like in GAT.

Słowa kluczowe

układ optyczny oka tonometria chirurgia refrakcyjna eksperyment numeryczny stateczność konstrukcji powłoka nieliniowa

human eyeball opthalmology tonometry numerical simulation

Wydawca

Oficyna Wydawnicza Politechniki Wrocławskiej

Czasopismo

Prace Naukowe Instytutu Konstrukcji i Eksploatacji Maszyn Politechniki Wrocławskiej. Monografie

Rocznik

2010

Tom

Vol. 91, nr 34

Strony

242--242

Opis fizyczny

Bibliogr. 157 poz.

Twórcy

autor

Śródka W.

Politechnika Wrocłąwska ul. Smoluchowskiego 25, 50-370 Wrocław, Wydziałowy Zakład Wytrzymałośći Materiałów

Bibliografia

1. Adler 's Physiology of the Eye, Tenth Edition, Elsevier, Mosby Published, 2002, Editor: Paul Kaufman, Albert Alm (F.H. Adler, Physiology of the Eye, Mosby, St. Louis, 1965).
2. Alastrue V., Calvo B., Pena E., Doblare M., Biomechanical modeling of refractive corneal surgery. Journal of Biomechanical Engineering-Transactions of the ASME, 2006, 128(1), 150 -160.
3. van Alphen G.W.H.M., Graebel W.P., Elasticity of tissues involved in accommodation. Vision Research, 1991, 31, 1417-1438.
4. Anderson K., El-Sheikh A., Newson, T., Application of structural analysis to the mechanical behavior of the cornea. Journal of Royal Society Interface, 2004, 1(1), 3-15.
5. Andreassen T.T., Simonsen A.J., Oxlund, H., Biomechanical properties of keratoconus and normal corneas. Experimental Eye Research, 1980, 31, 435^141.
6. Asejczyk-Widlicka M., Środka W., Kasprzak H., The modelling of effect of refractive surgery on the physically linear model of human eyeball. Influence of IOP on the geometrical and biomechanical properties of the model of the eye globe. An International Conference on Astigmatism, Aberrations and Vision. Mopane 2003. [Ed. by] Alan Rubin. Mopani Camp, South Africa, August 1-6, 2003. Auckland Park: Optometric Science Research Group Department of Optometry Rand Afrikaans University 2003,221-224.
7. Asejczyk-Widlicka M., Środka W., Kasprzak H., Iskander D.R., Influence of intraocular pressure on geometrical properties of a linear model of the eyeball: Effect of optical self-adjustment. Optik - International Journal for Light and Electron Optics, 2004, 115(11), 517-524.
8. Asejczyk-Widlicka M., Środka W., Kasprzak H., Pierścionek B.K., Modeling the elastic properties of the anterior eye and their contribution to maintenance of image quality: the role of the limbus. Eye, 2006, advance online publication, June 23; doi: 10.1038/sj.eye.6702464.
9. Atchison D.A., Jones C.E., Schmid K.L., Pritchard N., Pope J.M., Strugnell W.E., Riley R.A., Eye shape in emmentropia and myopia. Investigative Ophthalmology & Visual Science, 2004, 45(10), 3380-3386.
10. Beers A.P.A., van der Heijde G.L., In vivo determination of the biomechanical properties of the component elements of the accommodation mechanism. Vision Research., 1994, 34(21), 2897 -2905.
11. Belaidi A., Pierścionek B.K., Modelling internal stress distributions in the human lens: can opponent theories coexist!, Journal of Vision, 2007, 7(11), 1-12
12. Benedek G.B., Theory of the transparency of the eye. Applied Optics, 1971, 10, 459 473.
13. Bettelheim F.A., Physical basis of lens transparency. The Ocular Lens (ed. by H. Maisel), 265-300, New York, Marcel Dekker Inc., 1985.
14. Bier N., Lowther G.E., Contact lens correction, London, Butterworths, 1977.
15. Boote C, Dennis S., Newton R.H., Puri H., Meek K.M., Collagen fibrils appear more closely packed in the prepupillary cornea: Optical and biomechanical implications, Investigative Ophthalmology & Visual Science, 2003, 44, 2941-2948.
16. Borcherding M.S., Blacik L.J., Sittig R.A., Bizzell J.W., Breen M., Weinstein H.G., Proteoglycans and collagen fiber organization in human corneoscleral tissue. Experimental Eye Research, 1975, 21, 59-70.
17. Borja D., Manns F., Lamar P., Rosen A., Fernandez V., Parel, J.M., Preparation and hydration control of corneal tissue strips for experimental use. Cornea, 2004, 23, 61-66.
18. Bryant M.R., McDonnell P. J., Constitutive laws for biomechanical modeling of refractive surgery, Journal of Biomechanical Engineering, 1996, 118, 473—481.
19. Buzard K.A., Introduction to biomechanics of the cornea. Refractive and Corneal Surgery, 1992, 8, 127-138.
20. Cheng H-M, Singh O.S., Kwong K.K., Xiong J., Woods B.T., Brady T.J., Shape of the myopic eye as seen with high-resolution magnetic resonance imaging. Optometry and Vision Science 1992, 69, 698-701.
21. Clark J.I., Fourier and power law analysis of structural complexity in cornea and lens, Micron, 2001,32(3), 239-249.
22. Coleman D.J., Trokel S., Direct-recorded IOP variations in a human subject. Archives of Ophthalmology, 1969, 82, 637-640.
23. Collins R., Van Der Werff T.J., Mathematical models of the dynamics of the human eye. Springer-Verlag, 1980. Part of the Lecture Notes in Biomafhematics series, No. 34.
24. Damji K.F., Munger R., Influence of central corneal thickness on applanation intraocular pressure, Journal of Glaucoma, 2000, 9, 205-207.
25. Danielsen C.C., Tensile mechanical and creep properties of Descemet's membrane and lens capsule, Experimental Eye Research, 2004, 79, 343-350.
26. Daxer A., Fratzl P., Collagen fibril orientation in the human corneal stroma and its implication in keratoconus, Investigative Ophthalmology & Visual Science, 1997, 38, 121-129.
27. Deenadayalu C, Mobasher B., Rajan S.D., Hall G.W., Refractive Change Induced by the LASIK Flap in a Biomechanical Finite Element Model. Journal of Refractive Surgery, 2006, 22(2).
28. Doughty M.J., Zaman M.L., Human corneal thickness and its impact on intraocular pressure measures: a review and meta-analysis approach, Survey of Ophthalmology, 2000, 44, 367-408.
29. Doyle A., Lachkar Y., Comparison of dynamic contour tonometry with goldman applanation tonometry over a wide range of central corneal thickness, Journal of Glaucoma, 2005, 14(4), 288-292.
30. Ehlers N., Bramsen T., Sperling S., Applanation tonometry and central corneal thickness. Acta Ophthalmologics (Copenh), 1975, 53, 34-43.
31. Eklund A., Resonator sensor technique for medical use—an intraocular pressure measurement system. Umea, Umea University, 2002.
32. Elsheikh A., Alhasso D., Rama P., Assessment of the epithelium's contribution to corneal biomechanics. Experimental Eye Research, 2008a, 86, 445-561.
33. Elsheikh A., Anderson K., Comparative study of corneal strip extensometry and inflation tests. Journal of the Royal Society Interface, 2005, 2, 177-185.
34. Elsheikh A., Wang D., Numerical modelling of corneal biomechanical behaviour. Computer Methods in Biomechanics and Biomedical Engineering, 2007, 10(2), 85-95.
35. Elsheikh A., Wang D., Kotecha A., Brown M., Garway-Heath G., Evaluation of Goldmann applanation tonometry using a nonlinear finite element ocular model, Annals of Biomedical Engineering, 2006, 34(10), 1628-1640.
36. Elsheikh A., Wang D., Rama P., Campanelli M., Garway-Heath D., Experimental assessment of human corneal hysteresis, Current Eye Research, 2008b, 33, 205-213.
37. Ethier C.R., Johnson M., Ruberti J., Ocular biomechanics and biotransport. Annual Review of Biomedical Engineering, 2004, 6, 249-73.
38. Feltgen N., Leifert D., Funk J., Correlation between central corneal thickness, applanation tonometry, and direct intracameral IOP readings, British Journal of Ophthalmology, 2001, 85, 85-87.
39. Feuk T., On the transparency of the stroma in the mammalian cornea. IEEE Transactions on Biomedical Engineering, 1970, BME-17, 186-190.
40. Fick A., Ober Messung des Druckes im Auge, Archiv. Fur Die Gesammte Physiologie Des Menschen und Der Thiere, 1888, 42, 86-90.
41. Fisher R.F., Elastic constants of the human lens capsule. Journal of Physiology, 1969a, 201, 1-19.
42. Fisher R.F., Tlie significance of the shape of the lens and capsular energy changes in accommodation. Journal of Physiology, 1969b, 201, 21-17.
43. Fisher R.F., The ciliary body in accommodation. Transactions of the Ophthalmology Society U.K., 1986,105,208-219.
44. Francis B.A., Hsieh A., Lai M.Y., Chopra V., Pena F., Azen S., Varma R., Effects of corneal thickness, corneal curvature, and intraocular pressure level on Goldmann applanation tonometry and dynamic contour tonometry, Ophthalmology, 2007, 114(1), 20-26.
45. Franklin R.J., Morelande M.R., Iskander D.R.I., Collins M.J., Davis B.A., Combining central and peripheral videokeratoscope maps to investigate total corneal topography. Eye Contact Lens, 2006, 32, 27-32.
46. Freund D.E., McCally R.L., Farrell R. A., et al. Ultrastructure in the anterior and posterior stroma of perfused human and rabbit corneas. Investigative Ophthalmology & Visual Science, 1995, 36, 1508-1523.
47. Friedenwald J.S., Contribution to the theory and practice of tonometry. American Journal of Ophthalmology, 1937, 20, 985-1024.
48. Fung Y.C., Biomechanics: mechanical properties of living tissues. New York, Springer-Verlag, 1993.
49. Fung Y.C., Podstawy mechaniki ciała stałego, Warszawa, PWN, 1969. {Foundations of solid mechanics. New Jersey, Prentice-Hall, Inc., 1965)
50. Garzozi H.J., Chung H.S., Lang Y., Kagemann L., Harris A., Intraocular Pressure and Photorefractive Keratectomy: A Comparison of Three Different Tonometers. Cornea, 2001, 20(1), 33-36.
51. Ghista D.N., Kobayashi A.S., Davis N., Ray G., Finite Element Analysis in Biomedicine. 1st Int. Conf. on Variational Methods in Engineering (C.A. Brebbia and H. Tottenham, Eds.), Southampton University Press, 1972.
52. Gierek-Łapińska A., Kałużny J., Chirurgia refrakcyjna rogówki. Volumed, 1993.
53. Goldman J.N., Benedek G.B., Dohlman C.H., Kravitt A., Structural alteration affecting transparency in swollen human corneas, Investigative Ophthalmology, 1968, 7, 501-519.
54. Goldmann H., Schmidt T., Ober Applanations-tonometrie. Ophthalmologica, 1957, 134, 221 -242.
55. Goldmann H., Schmidt T., Weiterer beitrag zur applanationstonometrie. Ophthalmologica, 1961, 141,441^56.
56. Gonzales G., Fitt A., The mathematical modelling of human eyes - a PhD study. Mathematics Today, February 2003, 20-25.
57. Graebel W.P., van Alphen G.W.H.M., The elasticity of sclera and choroid of the human eye, and its implications on scleral rigidity and accommodation. Journal of Biomechanical Engineering, 1977, 99, 203-208.
58. Guirao A., Tiieoretical elastic response of the cornea to refractive surgery: risk factors for keratectasia. Journal of Refractive Surgery, 2005, 21, 176-185.
59. Gunvant P., O'Leary D.J., Baskaran M., Broadway D.C., Watkins R.J., Vijaya L., Evaluation of tonometric correction factors, Journal of Glaucoma, 2005, 14(5), 337-343.
60. Hachoł A., Środka W., Model biomechaniczny gaiki ocznej oparty na zjawisku samonastawności optycznej weryfikowany w tonometiycznym pomiarze IOP. Pomiary Autom. Kontr., 2006, 5bis wyd. spec. dod., 55-60. Referat z VIII Sympozjum Modelowanie i Pomiary w Medycynie MPM 2006, Krynica, 14-18 maja 2006.
61. Hallberg P., Eklund A., Santala K, Koskela T., Lindahl O., Linden C, Underestimation of intraocular pressure after photorefractive keratectomy: a biomechanical analysis, Medical & Biological Engineering & Computing, 2006, 44, 609-618.
62. Hamilton K.E., Pye D.C., Young's Modulus in Normal Corneas and the Effect on Applanation Tonometry. Optometry & Vision Science, 2008, 85(6), 445-450.
63. Hart R.W., Farrell R.A., Light scattering in the cornea. Journal of the Optical Society of America, 1969, 59, 766-774.
64. Hibbard R.R., Lyon C.S., Shepherd M.D., McBain E. H., McEwen W.K., Immediate rigidity of an eye: whole, segments and strips. Experimental Eye Research., 1970, 9, 137-143.
65. Hjortdal J.0., Regional elastic performance of the human cornea. Journal of Biomechanics, 1996, 29(7), 931-942.
66. Hjortdal J.0., On the biomechanical properties of the cornea with particular reference to refractive surgery. Acta Ophthalmol Scand Suppl, 1998, 225, 1-23.
67. Hjortdal J.0. Ehlers N., Effect of excimer laser kertectomy on the mechanical performance of the human cornea. Acta Ophthalmologica Scandinavica, 1995, 73, 18-24.
68. Hoeltzel D.A., Altman P., Buzard K., Choe K.-I., Strip extensometry for comparison of the mechanical response of bovine, rabbit and human corneas. Journal of Biomechanical Engineering, 1992, 14, 202-215.
69. Hogan M.J., Alvardo J.A., Weddell J., Histology of the human eye. W.B. Sanders Co., Philadelphia PA, 1971.
70. Iskander D.R., Kasprzak H.T., Dynamics in longitudinal eye movements and corneal shape. Ophthalmic and Physiological Optics, 2006, 26, 572-579.
71. Jakus M.A., Studies on the cornea. II. The fine structure of Descemet's membrane. Journal of Biophysical and Biochemical Cytology, 1956, 2, 243-252.
72. Jayasuriya A.C., Ghosh S., Scheinbeim J.I., Lubkin V., Bennett G., Kramer P., A study ofpiezoelectric and mechanical anisotropics of the human cornea. Biosensors and Bioelectronics, 2003, 18, 381-387.
73. Jester J.V., Venet T., Lee J., Schanzlin D.J., Smith R.E., A statistical analysis of radial keratotomy in human cadaver eyes. American Journal of Ophthalmology, 1981, 92(2), 172-177.
74. Jue B., Maurice D.M. The mechanical properties of the rabbit and human cornea, Journal of Biomechanics, 1986, 19(10), 847-853.
75. Kamppeter B.A., Jonas J.B., Dynamic contour tonometry for intraocular pressure measurement, American Journal of Ophthalmology, 2005, 140(2), 318-320.
76. Kaneko M., Tokuda K., Kawahara T., Dynamic Sensing of Human Eye. Proceedings of the 2005 IEEE, International Conference on Robotics and Automation, Barcelona, Spain, April 2005.
77. Kanngiesser H.E., Dynamic contour tonometry simulation on the human cornea using finite element methods. The theoretical foundations of dynamic contour tonometry (part II), ARVO 2004, Poster.
78. Kanngiesser H.E., Nee M., Kniestedt C, Inversini C, Stamper R.L., Simulation of dynamic contour tonometry compared to in-vitro study revealing minimal influence of corneal radius and astigmatism. The theoretical foundations of dynamic contour tonometry, ARVO 2003, Poster.
79. Kanngiesser H.E., Robert Y.C.A., Dynamic contour tonometry - DCT: A new method for the direct and continuous measurement of intraocular pressure (IOP), ARVO 2002, Poster.
80. Kasprzak H., A model of inhomogeneous expansion of the cornea and stability of its focus. Ophthalmic and Physiological Optics, 1997, 17, 133-136.
81. Kasprzak H.T., Iskander D.R., Spectral characteristics of longitudinal corneal apex velocities and their relation to the cardiopulmonary system, Eye, 2007, 21, 1212-1219; doi:10.1038/sj.eye.6702578.
82. Kasprzak H., Jankowska-Kuchta E., A new analytical approximation of corneal topography. Journal of modern optics, 1996, 43, 1135-1148.
83. Kaufmann C, Bachmann L.M., Thiel M.A., Comparison of dynamic contour tonometry with goldmann applanation tonometry, Investigative Ophthalmology & Visual Science, 2004, 45(9), 3118-21.
84. Kempf R., Kurita Y., Iida Y., Kaneko M., Mishima H., Tsukamoto H., Sugimoto E., Dynamic properties of human eyes, Proceedings of the 2005 IEEE, Engineering in Medicine and Biology 27th Annual Conference, Shanghai, China, September 1^1, 2005.
85. Kirstein E.M., Husler A. Evaluation of the Orssengo-Pye IOP corrective algorithm in LASIK patients with thick corneas. Optometry, 2005, 76(9), 536-43.
86. Klein S.A., Corzione J., Corbin J.A., Wechsler S., Wide-angle cornea-sclera (ocular) topography. Proc SPIE - International Society for Optical Engineering, 2002, 4611, 149-158.
87. Kniestedt C, Lin S., Choe J., Nee M., Bostrom A., Stunner J., Stamper R.L., Correlation between intraocular pressure, central corneal thickness, stage of glaucoma, and demographic patient data: prospective analysis of biophysical parameters in tertiary glaucoma practice populations, Journal of Glaucoma, 2006, 15(2), 91-97.
88. Kohlhaas M., Boehm A.G., Spoerl E., Piirsten A., Grein H. I, Pillunat, L. EEffect of Central Corneal Thickness, Corneal Curvature, and Axial Length on Applanation Tonometry, Archives of Ophthalmology, 2006, 124(4), 471-476.
89. Komai Y., Ushiki T., The three-dimensional organization of collagen fibres in the human cornea and sclera. Investigative Ophthalmology & Visual Science, 1991, 32, 2244-2258.
90. Le Grand Y., El Hage S.G., Physiological Optics. Springer Series in Optical Sciences, Vol. 13, Springer-Verlag, Berlin, Heidelberg, New York, 1980.
91. Levy Y., Zadok D., Glovinsky Y., Krakowski D., Nemet P., Tono-Pen versus Goldmann tonometry after excimer laser photorefractive keratectomy. Journal of Cataract and Refractive Surgery, 1999,25(4), 486-191.
92. Liu J., Roberts C.J., Influence of corneal biomechanical properties on intraocular pressure measurement, Journal of Cataract and Refractive Surgery, 2005, 31, 146-155.
93. Lynn M.J., Waring G.O., Sperduto R.D., PERK Study Group: Factors affecting outcome and predictability of radial keratotomy in the PERK Study. Archives of Ophthalmology, 1987, 105, 42-51.
94. Maurice D.M., The cornea and sclera. In: Davson H., ed, The Eye. London, London Academic Press, 1984.
95. Maurice D.M., Mechanics of the cornea, The cornea: Transactions of the world congress on the cornea III, edited by H. Dwight Cavanagh. Raven Press. Ltd., NY 1988.
96. McBain E.H., Tonometer Calibration II. Ocular Rigidity. Archives of Ophthalmology, 1958, 60(6), 1080-1091.
97. McMonnies C.W., Pulsating vision [letter], Australian Journal of Optometry, 1970, 53, 257.
98. McMonnies C.W., Boneham G.C., Experimentally increased intraocular pressure using digital forces, Eye Contact Lens, 2007, 33, 124-129.
99. Meek K.M., Blamires T., Elliot G.F., Gyi T.J., Nave C, The organization of collagen fibrils in the human corneal stroma: a synchrotron x-ray diffracrion study, Current Eye Research, 1987, 6, 841-846.
100. Meek K.M., Fullwood N.J., Corneal and scleral collagens—a microscopist's perspective, Micron, 2001,32(3), 261-272.
101. Meek K.M., Newton R.H., Organization of collagen fibrils in the corneal stroma in relation to mechanical properties and surgical practice, Journal of Refractive Surgery, 1999, 15, 695-699.
102. Mejia-Barbosa Y., Malacara-Hernandez D., A review of methods for measuring corneal topography. Optometry and Vision Science, 2001, 78, 240-53.
103. Miller D., Pressure of the lid on the eye. Archives of Ophthalmology, 1967, 78, 328-330.
104. Min H.K., Choi Y.I., Ghim D.G., Effect of Excimer Laser Photorefractive Keratectomy on Goldmann Applanation Tonometry. Journal of Korean Ophthalmological Society, 1995, 2022-2028.
105. Munnerlyn C, Koons S.J., Mearshall J., Photorefractive Qeratectomy: A Technique for Laser Refractive Surgery. Journal of Cataract & Refractive Surgery, 1988, 14, 46-52.
106. Nash L.S., Greene P.R., Foster C.S., Comparison of mechanical properties of keratoconus and normal corneas, Experimental Eye Research, 1982, 35, 413^423.
107. Nestorov A.P., Bunin A.Y., Kantselson L.A., Ciśnienie wewnątrzgałkowe [po rosyjsku], Nauka, 1974.
108. Nestorov A.P., Vurgaft M.B., Tablice kalibracyjne do elastometru Filatowa-Kalfy [po rosyjsku], Vestnik Oftalmologii, 1972, 2, 20-25.
109. Newton R.H., Meek K.M., Circumcorneal annulus of collagen fibrils in the human limbus, Investigative Ophthalmology & Visual Science, 1998a, 39, 1125-1134.
110. Newton R.H., Meek K.M., The integration of the corneal and limbal fibrils in the human eye, Biophysical Journal, 1998b, 75, 2508-2512.
111. Orłowski W.J. - redakcja, Okulistyka współczesna, Tl, Warszawa, Państwowy Zakład Wydawnictw Lekarskich, 1986.
112. Orssengo G.J., Pye D.C., Determination of the true intraocular pressure and modulus of elasticity of the human cornea, Bulletin of Mathematical Biology, 1999, 61(3), 551-572.
113. Pallikaris I.G., Kymionis G.D., Ginis H.S., Kounis G.A., Tsilimbaris M.K., Ocular rigidity in living human eyes. Investigative Ophthalmology and Visual Science, 2005, 46(2), 409^14.
114. Pache M., Wilmsmeyer S., Lautebach S., Funk J., Dynamic contour tonometry versus Goldmann applanation tonometry: a comparative study, Graefe's Archive for Clinical and Experimental Ophthalmology, 2005, 243(8), 763-767.
115. Pandolfi A., Manganiello F., A model for the human cornea: constitutive formulation and numerical analysis, Biomechanics and Modeling in Mechanobiology, 2006, 5(4), 237-246.
116. Pinsky P.M., Heide D., Chernyak D., Computational modeling of mechanical anisotropy in the cornea and sclera, Journal of Cataract and Refractive Surgery, 2005, 31, 136-145.
117. Popper K., The logic of scientific discovery, London and New York, Routledge, 2002.
118. Radner W., Zehetmayer M., Aufreiter R., Mallinger R., Interlacing and cross angle distribution of collagen lamellae in the human cornea, Cornea, 1998, 17, 537-543.
119. Roberts C, Biomechanics of the cornea and wavefront-guided laser refractive surgery, Journal of Refractive Surgery, 2002, 18, 589-592.
120. Rowsey J.J., Balyeat H.D., Rabinovitch B., Burns T.E., Hays J.C., Predicting the results of radial keratotomy, Ophthalmology, 1983, 90(6), 642-654.
121. Salz J., Lee J.S., Jester J.V., Steel D., Villasenor R.A., Nesburn A.B., Smith R.E., Radial keratotomy in fresh human cadaver eyes. Ophthalmology. 1981, 88(8), 742-746.
122. Sawada H., Konomi H., Hirosawa K., Characterization of the collagen in the hexagonal lattice of Descemet's membrane: its relation to type VIII collagen, Journal of Cell Biology, 1990, 110, 219-227.
123. Schachar R.A., Zonular function. A new hypothesis with clinical implications. Annals of Ophthalmology, 1994, 26, 36-38.
124. Schachar R.A., Is Helmholtz theory of accommodation correct!, Annals of Ophthalmology, 1999, 31, 10-17.
125. Schachar R., Pierścionek B.K., Proper controls are required for determining the mechanism of accommodation. Investigative Ophthalmology and Visual Science (E-letter), 9th April 2009.
126. Schuman J.S., Massicotte E.C., Connolly S., et al. Increased intraocular pressure and visual field defects in high resistance wind instruments players. Ophthalmology, 2000, 107, 127-133.
127. Schutte S., van den Bedem S.P.W., van Keulen F., van der Helm F.C.T., Simonsz H.J., A finite-element analysis model of orbital biomechanics. Vision Research, 2006, 46, 1724-1731.
128. Schwartz N.J., Mackay R.S., Sackman J.L., A theoretical and experimental study of the mechanical behavior of the cornea with application to the measurement of intraocular pressure. Bulletin of Mathematical Biophysics, 1966, 28, 585-643.
129. Seiler T., Matallana M., Sendler S., Bende T., Does Bowman's layer determine the biomechanical properties of the cornea!, Journal of Refractive Corneal Surgery, 1992, 8(2), 139-142.
130. Serrao S., Lombardo G., Lombardo M., Differences in nasal and temporal responses of the cornea after photorefractive keratectomy, Journal of Cataract and Refractive Surgery, 2005, 31, 30 38.
131. Shah S., Accurate intraocular pressure measurement - the myth of modern ophthalmology!, Ophthalmology, 2000, 107, 1805-1807.
132. Shah S., Chatterjee A., Mathai M., et al., Relationship between corneal thickness and measured intraocular pressure in a general ophthalmology clinic, Ophthalmology, 1999, 106, 2154-2160.
133. Shin T.J., Vito R.P., Johnson L.W., McCarey B.E., The distribution of strain in the human cornea. Journal of Biomechanics, 1997, 30, 497-503.
134. Shuttleworth C.A., Molecules in focus. Type VIII collagen. International Journal of Biochemistry & Cell Biology, 1997, 29, 1145-1148.
135. Silver D.M., Geyer O., Pressure-volume relation for the living human eye, Current Eye Research, 2000, 20, 115-120.
136. Sjontoft E., Edmund C, In vivo determination of Young's modulus for the human cornea. Bulletin of Mathematical Biology, 1987, 49, 217-232.
137. Stodtmeister R., Applanation tonometry and correction according to corneal thickness, Acta Ophthalmologica Scandinavica, 1998, 76, 319-324.
138. Środka W., Effect of kinematic boundary conditions on optical and biomechanical behaviour of eyeball model. Acta of Bioengineering and Biomechanics, 2006, 8(2), 69-77.
139. Środka W., Biomechanical model of human eyeball and its applications. Optica Applicata, 2009, 39(2), 401-413.
140. Środka W., Asejczyk-Widlicka M., Kasprzak H., Jamrozy-Witkowska A., The effect of optical self-adjustment in the linear eyeball model with the crystalline lens and without lens. 13th Polish-Czech-Slovak Conference on Wave and Quantum Aspects of Contemporary Optics. Eds Jerzy Nowak, Marek Zając, Jan Masajada. Krzyżowa, 9-13 September 2002. Bellingam, Wash.: SPIE-The International Society for Optical Engineering 2003, s. 323-329.
141. Środka W., Iskander D.R., Optically inspired biomechanical model of the human eyeball, Journal of Biomedical Optics, 2008, 13(4), 044034.
142. Środka W., Kasprzak H., Identification of mechanical parameters of incised cornea by means of finite element method. Optica Applicata, 1996, 26(1), 9-17.
143. Środka W., Kasprzak H., Wpływ aproksymacji profilu rogówki na dynamiczne zmiany jej refrakcji. Biology of Sport, 1997, 14 suppl. 7, 324-328, Referat z XIV Szkoły Biomechaniki. Spała, 10-12 września 1997.
144. Środka W., Pierścionek B.K., Effect of material properties of the eyeball coat on optical image stability, Journal of Biomedical Optics, 2008, 13(5), 054013.
145. Uchio E., Ohno S., Kudoh J., Aoki K., Kisielewicz L.T., Simulation model of an eyeball based on finite element analysis on a supercomputer. British Journal of Ophthalmology, 1999, 83, 1106-1111.
146. Vaezy S., Clark J.I., A quantitative analysis of transparency in human sclera and cornea using Fourier methods. Journal of Microscopy, 1991, 163, 85-94.
147. Vaezy S., Clark J.I., Quantitative analysis of the microstructure of the human cornea and sclera using 2-D Fourier methods, Journal of Microscopy, 1994, 175, 93-99.
148. Viestenz A., Langenbucher A., Seitz B., Viestenz A., Evaluation of dynamic contour tonometry in penetrating keratoplasties, Ophthalmology, 2006, 103(9), 773-776.
149. Vito R.P., Carnell P.H., Finite element based mechanical models of the cornea for pressure and indenter loading. Refractive & Corneal Surgery, 1992, 8, 146-151.
150. Wang X., Shen J., McCulley J., Bowman R.W., Petroll W.M., Cavanagh H.D., Intraocular Pressure Measurement ąfterHyperopic LASIX. CLAO Journal, 2002, 28(3), 136-139.
151. Whitacre M.M., Stein R.A., Hassanein K., The effect of corneal thickness on applanation tonometry. American Journal of Ophthalmology, 1993, 115, 592-596.
152. Wollensak G., Stress-strain measurements of human and porcine corneas after riboflavin-ultra-violet-A-induced cross-linking, Journal of Cataract & Refractive Surgery, 2003, 29, 1780-1785.
153. Woo S.L., Kobayashi A.S., Lawrence C, Schlegel W.A., Mathematical model of the corneoscleral shell as applied to intraocular pressure-volume relations and applanation tonometry. Annals of Biomedical Engineering, 1972a, 1(1), 87-98.
154. Woo S.L.-Y., Kobayashi A.S., Schlegel W.A., Lawrence C, Nonlinear material properties of intact cornea and sclera, Experimental Eye Research, 1972b, 14(1), 29-39.
155. Yeh H.-L., Huang T., Schachar R.A., A closed shell structured eyeball model with application to radial keratotomy. Journal of Biomechanical Engineering, 2000, 122(5), 504-510.
156. Young W.C., Roark's formulas for stress and strain, International Editions: McGraw-Hill. 6th Edn., 1989.
157. Ytteborg J., 77ie effect of intraocular pressure on rigidity coefficient in the human eye. Acta Ophthalmologica, 1960, 38, 548-561.

Typ dokumentu

Bibliografia

Identyfikator YADDA

bwmeta1.element.baztech-article-BPW7-0013-0049