A boundary element model of the human eye undergoing laser thermokeratoplasty

In the present paper, a three-dimensional radially symmetric boundary element model of the human eye is proposed for simulating changes in corneal temperature during treatment of laser thermokeratoplasty. Energy absorption inside the cornea is modeled using the Beer-Lambert law. Heat transfer inside the eye is assumed to be governed by the classical heat diffusion equation. The resulting initial-boundary value problem is solved numerically using a time-stepping boundary element method. The temperature field is calculated for heating by both the pulsed laser and the continuous wave laser. The results obtained are compared with those from other models found in the literature.

[1]  Ralf Brinkmann,et al.  Corneal collagen denaturation in laser thermokeratoplasty , 1996, Photonics West.

[2]  E. Y. K. Ng,et al.  Bioheat transfer in the human eye: a boundary element approach , 2007 .

[3]  R Birngruber,et al.  Influence of temperature and time on thermally induced forces in corneal collagen and the effect on laser thermokeratoplasty. , 2000, Journal of cataract and refractive surgery.

[4]  S. Wu,et al.  Adler's Physiology of the Eye , 2002 .

[5]  R F Brubaker,et al.  Volume and depth of the anterior chamber in the normal aging human eye. , 1980, Archives of ophthalmology.

[6]  Carlos Alberto Brebbia,et al.  Dynamic analysis in solid mechanics by an alternative boundary element procedure , 2000 .

[7]  J. A. Scott,et al.  A finite element model of heat transport in the human eye. , 1988, Physics in medicine and biology.

[8]  Francis Heed Adler,et al.  Adler's Physiology of the eye;: Clinical application , 1976 .

[9]  G. I. Zheltov,et al.  Photodestructive effect of IR laser radiation on the cornea , 2007 .

[10]  S. Kanagasabay Safety with Lasers and Other Optical Sources—A Comprehensive Handbook , 1981 .

[11]  M A Mainster,et al.  Ophthalmic applications of infrared lasers -- thermal considerations. , 1979, Investigative ophthalmology & visual science.

[12]  Reginald Birngruber,et al.  Laser thermokeratoplasty: analysis of in-vitro results and refractive changes achieved in a first clinical study , 1997, European Conference on Biomedical Optics.

[13]  Arthur Ho,et al.  Ophthalmic Technologies XV , 2005 .

[14]  J H Tips,et al.  Corneal Thermal Response to the CO(2) Laser. , 1970, Applied optics.

[15]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[16]  Theo Oltrup,et al.  Depth-adjusted thermal keratoplasty using a cw diode laser and a new focusing handpiece , 1996, Photonics West.

[17]  Lee M. Jampol Adler's Physiology of the Eye: Clinical Application, 10th Edition, , 2003 .

[18]  James C. Lin,et al.  Microwave Induced Temperature Rises in Rabbit Eyes in Cataract Research , 1975 .

[19]  H. Stringer,et al.  Shrinkage Temperature of Eye Collagen , 1964, Nature.

[20]  Reginald Birngruber,et al.  Laser thermokeratoplasty by means of a continuously emitting laser diode in the mid IR , 1996, European Conference on Biomedical Optics.

[21]  R.M.M. Mattheij,et al.  Alternative DRM formulations , 2002 .

[22]  Jeffrey J. Heys,et al.  A Boussinesq Model of Natural Convection in the Human Eye and the Formation of Krukenberg's Spindle , 2002, Annals of Biomedical Engineering.

[23]  E. Y. K. Ng,et al.  FEM simulation of the eye structure with bioheat analysis , 2006, Comput. Methods Programs Biomed..

[24]  S. Mukherjee,et al.  Boundary element techniques: Theory and applications in engineering , 1984 .

[25]  P. Neelakantaswamy,et al.  Microwave-induced hazardous nonlinear thermoelastic vibrations of the ocular lens in the human eye. , 1979, Journal of biomechanics.

[26]  J J Lagendijk,et al.  A mathematical model to calculate temperature distributions in human and rabbit eyes during hyperthermic treatment. , 1982, Physics in medicine and biology.

[27]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[28]  N. Brown,et al.  Dimensions of the human eye relevant to radiation protection. , 1975, Physics in medicine and biology.

[29]  Fabrice Manns,et al.  Semianalytical thermal model for subablative laser heating of homogeneous nonperfused biological tissue: application to laser thermokeratoplasty. , 2003, Journal of biomedical optics.

[30]  Fabrice Manns,et al.  Calculation of corneal temperature and shrikage during laser thermokeratoplasty (LTK) , 2002, SPIE BiOS.

[31]  A Thesis COMPUTATIONAL MODEL FOR HEAT TRANSFER IN THE HUMAN EYE USING THE FINITE ELEMENT METHOD , 2003 .

[32]  Reginald Birngruber,et al.  Investigations on laser thermokeratoplasty , 1994 .

[33]  Thanassis Papaioannou,et al.  Spatiotemporal temperature profiling of corneal surface during LTK , 2002, SPIE BiOS.

[34]  N. A. Peppers,et al.  Corneal Damage Thresholds for CO(2) Laser Radiation. , 1969, Applied optics.