An analytically solvable model that considers the elasticity of the cornea is developed for use in the current and novel corneal refractive surgery procedures. The model assumes that the cornea is a thin spheroid shell with an elastic response to intraocular pressure. The value of the Young’s modulus of the post-operative cornea and its dependence on the geometric parameters of the ablation zone are estimated employing “best-fit” approach to nomograms currently used in corneal refractive surgery. These elasticity parameters are applied for quantitative modeling of different types of refractive surgery for myopia.
Issue Section:
Technical Papers
1.
Trokel
, S. J.
, Srinivasan
, R.
, and Braren
, B.
, 1983
, “Excimer Laser Surgery of the Cornea
,” Am. J. Ophthalmol.
, 94
, p. 125
125
.2.
Marshall
, J.
, Trokel
, S.
, Rothery
, S.
, and Krueger
, R. R.
, 1986
, “Photoablative Reprofiling of the Cornea Using an Excimer Laser: Photorefractive Keratectomy
,” Lasers Ophthalmol.
, 1
, pp. 21
–48
.3.
Pallikaris
, I. G.
, and Saiganos
, D. S.
, 1994
, “Excimer Laser In-Situ Keratomileusis and Photorefractive Keratectomy for Correction of High Myopia
,” J. Refract. Corneal Surg.
, 10
, pp. 498
–510
.4.
Seiler
, T.
, 1993
, “HO:YAG Laser Thermokeratoplasty for Hyperopia
,” Ophthalmol. Clin. North Am.
, 5
, pp. 773
–780
.5.
Moreira
, H.
, Campos
, M.
, Sawusch
, M. R.
, et al., 1993
, “Holmium Laser Thermokeratoplasty
,” Ophthalmology
, 100
, pp. 752
–761
.6.
Schanzlin
, D. J.
, Asbell
, P. A.
, Burris
, T. E.
, and Durrie
, D. S.
, 1997
, “The Instrastromal Corneal Ring Segments: Phase II Results for the Correction of Myopia
,” Ophthalmology
, 104
, pp. 1067
–1078
.7.
Holmes-Higgin
, D. K.
, Baker
, P. C.
, et al., 1999
, “Characterization of the Aspheric Corneal Surface With Intrastromal Corneal Ring Segments
,” J. Refract. Surg.
, 15
, pp. 520
–528
.8.
Juhasz
, T.
, Loesel
, F. H.
, Kurtz
, R. M.
, Horvath
, C.
, Bille
, J. F.
, and Mourou
, G.
, 1999
, “Corneal Refractive Surgery With Femtosecond Lasers
,” IEEE J. Sel. Top. Quantum Electron.
, 5
, pp. 902
–910
.9.
Williams, S., and Grant, W., 1985, “Bending Resistance in Modeling the Cornea as a Thin Shell and the Effects in Radial Keratotomy,” ASME Biomechanics Symposium, ASME AMD-Vol. 68/FED-Vol. 21, pp. 81–84.
10.
Bryant, M. R., and Velinsky, S. A., 1989, “Design of Keratorefractive Surgical Procedures: Radial Keratotomy,” Advances in Design Automation, ASME DE-Vol. 19, pp. 383–391.
11.
Hanna
, K. D.
, Jouve
, F.
, Bercovier
, M. H.
, and Waring
, III, G. O.
, 1989
, “Computer Simulation of Lamellar Keratectomy and Laser Myopic Keratomileusis
,” J. Refract. Surg.
, 4
, pp. 222
–231
.12.
Huang
, T.
, Bisarnsin
, T.
, Schachar
, R. A.
, and Black
, T. D.
, 1988
, “Corneal Curvature Change Due to Structural Alteration by Radial Keratotomy
,” ASME J. Biomech. Eng.
, 110
, pp. 249
–253
.13.
Vito
, R. P.
, Shin
, T. J.
, and McCarey
, B. E.
, 1989
, “A Mechanical Model of the Cornea: The Effects of Physiological and Surgical Factors on Radial Keratotomy Surgery
,” Refract. Corneal Surg.
, 5
, pp. 82
–88
.14.
Mow
, C. C.
, 1968
, “A Theoretical Model of the Cornea for Use in Studies of Tonometry
,” Bull. Math. Biophys.
, 30
, pp. 437
–453
.15.
Rand
, R. H.
, Lubkin
, S. R.
, and Howland
, H. C.
, 1991
, “Analytical Model of Cornea Surgery
,” ASME J. Biomech. Eng.
, 113
, pp. 239
–241
.16.
Bryant
, M. R.
, Marchi
, V.
, and Juhasz
, T.
, 2000
, “Mathematical Model of Picosecond Laser Keratomileusis for High Myopia
,” J. Refract. Surg.
, 16
, pp. 155
–162
.17.
Timoshenko, S., and Woinowsky-Krieger, S., 1959, Theory of Plates and Shells, 2nd ed., McGraw-Hill, New York.
18.
Munnerlyn
, C. R.
, Koons
, S. J.
, and Marshall
, J.
, 1988
, “A Technique for Laser Refractive Surgery
,” J. Cataract Refract. Surg.
, 14
, pp. 46
–52
.19.
Blaker
, W. J.
, and Hersh
, P. S.
, 1994
, “Theoretical and Clinical Effects of Preoperative Corneal Curvature on Excimer Laser Photorefractive Keratectomy
,” J. Refract. Surg.
, 10
, pp. 571
–574
.20.
Colliac
, J. P.
, Shammas
, J. H.
, and Bart
, D. J.
, 1994
, “Photorefractive Keratectomy for the Correction of Myopia and Astigmatism
,” Am. J. Ophthalmol.
, 117
, pp. 369
–380
.21.
Woo
, S. L.-Y.
, Kobayashi
, A. S.
, Schlegel
, W. A.
, and Lawrence
, C.
, 1972
, “Nonlinear Material Properties of Intact Cornea and Sclera
,” Exp. Eye Res.
, 14
, pp. 29
–39
.22.
Bryant
, M. R.
, and McDonnel
, P. J.
, 1996
, “Constitutive Laws for Biomechanical Modeling of Refractive Surgery
,” ASME J. Biomech. Eng.
, 118
, pp. 473
–481
.23.
Le Grand Y., 1965, Optique physiologique, Tome 1. La Dioptrique de l’oeil et sa Correction, 2nd ed., Paris, Revue d’Optique, pp. 147–159.
24.
Colliac
, J. P.
, and Shammas
, H. J.
, 1993
, “Optics for Photorefractive Keratectomy
,” J. Cataract Refract. Surg.
, 19
, pp. 356
–363
.25.
Casebeer J. C., Lamellar Refractive Surgery, ISBN: 1-55642-286-5, Slack Incorp.
26.
Sletten
, K.
, Yen
, K.
, Sayegh
, F.
, et al., 1999
, “An in Vivo Model of Femtosecond Laser Intrastromal Refractive Surgery
,” J. Ophthalmic Laser Surgery
, 30
, pp. 742
–749
.Copyright © 2001
by ASME
You do not currently have access to this content.
