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TECHNICAL PAPERS

A Closed Shell Structured Eyeball Model With Application to Radial Keratotomy

[+] Author and Article Information
Hsien-Liang Yeh

Department of Civil Engineering, I-Shou University, Kaohsiung County, Taiwan 84008

Tseng Huang

Department of Civil Engineering, The University of Texas at Arlington, Arlington, TX 76019

Ronald A. Schachar

Presby Corp., 5910 N. Central Expway, Ste. 1770, Dallas, TX 75206

J Biomech Eng 122(5), 504-510 (Jan 23, 2000) (7 pages) doi:10.1115/1.1289626 History: Received March 17, 1999; Revised January 23, 2000
Copyright © 2000 by ASME
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References

Schachar, R. A., Black, T. D., and Huang, T., 1980, “A Physicist View of Radial Keratotomy With Practical Surgical Implications,” in: Keratofraction, Schachar, R. A., Levy, N. S., and Schachar, L., eds., LAL Publishing, Denison, TX, pp. 195–220.
Schachar, R. A., Black, T. D., and Huang, T., 1981, Understanding Radial Keratotomy, LAL Publishing, Denison, Texas.
Bisarnsin, T., 1983, “Predicting the Effects of Radial Keratotomy,” Ph.D. Dissertation, The University of Texas at Arlington, May.
Huang,  T., Bisarnsin,  T., Schachar,  R. A., and Black,  T. D., 1988, “Corneal Curvature Change Due to Structural Alternation by Radial Keratotomy,” ASME J. Biomech. Eng., 110, pp. 249–253.
Chen, J.-S., 1983, “A Finite Element Formulation for Geometrically Nonlinear Problems With Application to Radial Keratotomy,” Master thesis, The University of Texas at Arlington, May.
Williams, S., and Grant, W., 1985, “Bending Resistance in Modeling the Cornea as a Thin Shell and the Effects in Radial Keratotomy,” Proc. Joint ASCE/ASME Mechanics Conference, Albuquerque, NM, June 24–26, pp. 81–84.
Bryant, M. R., and Velinsky, S. A., 1989, “Design of Keratorefractive Surgical Procedures: Radial Keratotomy,” Advances in Design Automation—1989, Vol. 1, ASME DE-Vol. 19-1, pp. 383–391.
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, No. 2,pp.82–88.
Kobayashi,  A. S., Woo,  S. L.-Y., Lawrence,  C., and Schlegel,  W. A., 1971, “Analysis of the Corneo-Scleral Shell by Method of Direct Stiffness,” J. Biomech., 4, pp. 323–330.
Woo,  S. L.-Y., Kobayshi,  A. S., Schlegel,  W. A., and Lawrence,  C., 1972, “Nonlinear Material Properties of Intact Cornea and Sclera,” Exp. Eye Res., 14, pp. 29–39.
Wray, W. D., Best, E. D., and Cheng, L. Y., 1989, “Development of a Continuum Finite-Element Model for Radial Keratotomy,” presented at the The Winter Annual Meeting of The Americal Society of Mechanical Engineers, San Francisco, CA, Dec. 10–15.
Chen, Y.-L., 1990, “Transverse Shear Deformation in an Impaired Thin Shell,” Ph.D. Dissertation, The University of Texas at Arlington, Aug.
Vito,  R. P., and Carnell,  P. H., 1992, “Finite Element Based Mechanical Models of the Cornea for Pressure and Indenter Loading,” Refract. Corneal Surg., 8, No. 2, March/April, pp. 146–151.
Howland,  H. C., Rand,  R. H., and Lubkin,  S. R., 1992, “A Thin-Shell Model of the Cornea and Its Application to Corneal Surgery,” Refract. Corneal Surg., 8, No. 2, March/April, pp. 183–186.
Pinsky,  P. M., and Datye,  D. V., 1992, “Numerical Modeling of Radial, Astigmatic, and Hexagonal Keratotomy,” Refract. Corneal Surg., 8, No. 2, March/April, pp. 164–172.
Thomas, C. I., 1955, The Cornea, Thomas, Springfield.
Jones, R. M., 1975, Mechanics of Composite Materials, Scripta Bood Co., Washington, D. C.
Langhaar, H. L., 1964, Foundations of Practical Shell Analysis, Univ. of Illinois.
Yeh, H.-L., 1990, “A 3-D model for Predicting the Effects of Radial Keratotomy,” Ph.D. Dissertation, The University of Texas at Arlington, Aug.
Yeh,  H.-L., Huang,  T., and Schachar,  R. A., 1992, “A Solid Element for the Shell Structured Eyeball With Application to Radial Keratotomy,” Int. J. Numer. Methods Eng., 33, No. 9, pp. 1875–1890.
Haisler,  W. E., and Stricklin,  J. A., 1967, “Rigid-Body Displacements of Curved Elements in the Analysis of Shells by the Matrix-Displacement Method,” AIAA J., 5, pp. 1525–1527.

Figures

Grahic Jump Location
Geometric parameters of the eyeball model
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(a) Mean value of Q22 versus E2/E1 for ν12=0.20,0.01≤G12/E1≤0.10,N=40, and M=25; (b) mean value of Q22 versus E2/E1 for ν12=0.20,0.1≤G12/E1≤1.0,N=40, and M=25
Grahic Jump Location
(a) Standard deviation of Q22 versus E2/E1 for ν12=0.20,0.01≤G12/E1≤0.10,N=40, and M=25; (b) standard deviation of Q22 versus E2/E1 for ν12=0.20,0.1≤G12/E1≤1.0,N=40, and M=25
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Three shell coordinates (x, y, z),(X, Y, z), and (X, Y, z) for a spherical shell
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A solid shell element of an ellipsoidal shell in the pole region associated with shell coordinates (X, Y, z) and (X, Y, z)
Grahic Jump Location
Side view of the coarse mesh for the spherical corneo-scleral shell
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Geometric parameters of the spherical corneo-scleral shell with shell coordinates (X, Y, z) and (X, Y, z)
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Displacement, u, at x=45 deg for the spherical corneo-scleral shell
Grahic Jump Location
Displacement, w, at x=45 deg for the spherical corneo-scleral shell

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