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Articles

Nonlinear parameter identification in a corneal geometry model

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Pages 443-456 | Received 13 Sep 2013, Accepted 04 May 2014, Published online: 05 Jun 2014

References

  • Mejía-Barbosa Y, Malacara-Hernández D. A review of methods for measuring corneal topography. Optom. Vision Sci. 2001;78:240–253.
  • Trattler W, Majmudar P, Luchs JI, Swartz T. Cornea handbook. Slack Incorporated, Thorofare; 2010.
  • von Helmholtz H, Southall H, James PC, editors. Helmholtz’s treatise on physiological optics. Dover Publications, New York; 1924.
  • Canning CR, Dewynne JN, Fitt AD, Greaney MJ. Fluid flow in the anterior chamber of a human eye. IMA J. Math. Appl. Med. Biol. 2002;19:31–60.
  • Ismail Z, Fitt AD. Mathematical modelling of flow in Schlemm’s Canal and its influence on primary open angle glaucoma. International Conference on Science and Technology (ICSTIE): Applications in Industry and Education, 1967–1973; 2008; Universiti Teknologi MARA Penang.
  • Braun RJ, Usha R, McFadden GB, Driscoll TA, Cook LP, King-Smith PE. Thin film dynamics on a prolate spheroid with application to the cornea. J. Eng. Math. 2012;73:121–138.
  • Braun RJ. Dynamics of the tear film. Annu. Rev. Fluid Mech. 2012;44:267–297.
  • Braun RJ, Fitt AD. Modelling drainage of the precorneal tear film after a blink. Math. Med. Biol. 2003;20:1–28.
  • Kasprzak H, Iskander DR. Approximating ocular surfaces by generalized conic curves. Ophthal. Physiol. Opt. 2006;26:602–609.
  • Rosales MA, Juárez-Aubry M, López-Olazagasti E, Ibarra J, Tepichín E. Anterior corneal profile with variable asphericity. Appl. Opt. 2009;48:6594–6599.
  • Kiely PM, Smith G, Carney LG. The mean shape of the human cornea. Optica Acta. 1982;29:1027–1040.
  • Anderson K, El-Sheikh A, Newson T. Application of structural analysis to the mechanical behaviour of the cornea. J. R. Soc. Interface. 2004;1:3–15.
  • Ahmed E. Finite element modeling of corneal biomechanical behavior. J. Refract. Surg. 2010;26:289–300.
  • Iskander DR, Collins MJ, Davis B. Optimal Modeling of Corneal Surfaces by Zernike Polynomials. IEEE Trans. Biomed. Eng. 2001;48:87–95.
  • Schneider M. Iskander DR, Collins MJ, Modeling corneal surfaces with rational functions for high-speed videokeratoscopy data compression. IEEE Trans. Biomed. Eng. 2009;56:493–499.
  • Schwiegerling J, Greivenkamp JE, Miller JM. Representation of videokeratoscopic height data with Zernike polynomials. J. Opt. Soc. Am. A. 1995;12:2105–2113.
  • Schwiegerling J. Cone dimensions in keratoconus using Zernike polynomials. Optom. Vision Sci. 1997;74:963–969.
  • Trevino JP, Gómez-Correa JE, Iskander DR, Chávez-Cerda S. Zernike vs. Bessel circular functions in visual optics. Ophthalmic Physiol. Opt. 2013;33:394–402. doi:10.1111/opo.12065.
  • Martínez-Finkelshtein A, Ramos-López D, Castro-Luna GM, Alió JL. Adaptive cornea modeling from keratometric data. Invest. Ophthalmol. Visual Sci. 2011;52:4963–4970.
  • Okrasiński W, Płociniczak Ł. A nonlinear mathematical model of the corneal shape. Nonlinear Anal.: Real World Appl. 2012;13:1498–1505.
  • Okrasiński W, Płociniczak Ł. Bessel function model of corneal topography. Appl. Math. Comput. 2013;223:436–443.
  • Płociniczak Ł, Okrasiński W. Regularization of an ill-posed problem in corneal topography. Inverse Prob. Sci. Eng. 2013;21:1090–1097.
  • Groetsch CW. Inverse problems in the mathematical sciences. Braunschweig: Vieweg; 1993.
  • Hofman B. On ill-posedness and local ill-posedness of operator equations in Hilbert spaces. Fakultät für Mathematik: Technische Universität Chemnitz; 1998.
  • Kirsch A. An introduction to the mathematical theory of inverse problems. New York (NY): Springer; 1996.
  • Engl HW. Regularization methods for the stable solutions of inverse problems. Surv. Math. Ind. 1993;3:71–143.
  • Hadamard J. Le problème de Cauchy et les équation aux dérivée partielle linéaires hyperboliques. Paris: Hermann; 1932.
  • Hanke M, Neubauer A, Scherzer O. A convergence analysis of the Landweber iteration for nonlinear ill-posed problems. Numer. Math. 1995;72:21–37.

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