volume | PIER Journals

Abstract

In this paper we present the three-dimensional finite element time domain model of the human eye exposed to pulsed holmium: YAG laser radiation used in thermokeratoplasty procedure. The model is based on the Pennes' bioheat transfer equation and takes into account the focusing action of the lens. The absorption of laser energy inside the eye tissues is modeled using the Lambert-Beer's law. Model takes into account the pulse temporal profile. The maximum temperature values obtained from steady state and transient analysis are compared against those reported from other papers. Finally, sensitivity analysis of several parameters on the calculated temperature field is carried out.

1. Niemz, M. H., Laser-Tissue Interactions: Fundamentals and Applications, 3rd Ed., Springer-Verlag, 2003.

2. Carroll, L. and T. R. Humphreys, "LASER-tissue interactions," Clin. in Dermatol., Vol. 24, 2-7, 2006. Google Scholar

3. Thompson, K., Q. Ren, and J. Parel, "Therapeutic and diagnostic application of lasers in ophthalmology," Proceedings of the IEEE, Vol. 80, No. 6, 838-860, 1992. Google Scholar

4. Taove, A. and M. Brodwin, "Computation of the electromagnetic fields and induced temperatures within a model of the microwave-irradiated human eye," IEEE Trans. on Microw. and Theory, Vol. 23, No. 11, 888-896, Jan. 1975. Google Scholar

5. Emery, A., P. Kramar, A. Guy, and J. Lin, "Microwave induced temperature rises in rabbit eyes in cataract research," J. of Heat Transf., Vol. 97, 123-128, 1975. Google Scholar

6. Scott, J., "A finite element model of heat transport in the human eye," Phys. Med. Biol., Vol. 33, No. 2, 227-241, 1988. Google Scholar

7. Scott, J., "The computation of temperature rises in the human eye induced by infrared radiation," Phys. Med. Biol., Vol. 33, No. 2, 243-257, 1988. Google Scholar

8. Lagendijk, J., "A mathematical model to calculate temperature distributions in human and rabbit eyes during hyperthermic treatment," Phys. Med. Biol., Vol. 27, No. 11, 1301-1311, 1982. Google Scholar

9. Mainster, M. A., "Ophthalmic applications of infrared lasers --- Thermal considerations," Invest. Ophth. Vis. Sci., Vol. 18, No. 4, 414-420, Apr. 1979. Google Scholar

10. Amara, E. H., "Numerical investigations on thermal effects of laser-ocular media interaction," Int. J. Heat and Mass Tran., Vol. 38, No. 13, 2479-2488, 1995. Google Scholar

11. Sbirlea, G. and J. P. L'Huillier, "A powerful finite element for analysis of argon laser iridectomy: Influence of natural convection on the human eye," WIT Tr Biomed Health, Vol. 4, 67-79, Apr. 1997. Google Scholar

12. Chua, K. J., J. C. Ho, S. K. Chou, and M. R. Islam, "On the study of the temperature distribution within a human eye subjected to a laser source," Int. Commun. in Heat and Mass Trans., Vol. 32, 1057-1065, 2005. Google Scholar

13. Ng, E. Y. K., E. H. Ooi, and U. R. Archarya, "A comparative study between the two-dimensional and three-dimensional human eye models," Math. Comput. Model., Vol. 48, No. 5--6, 712-720, 2008. Google Scholar

14. Narasimhan, A., K. Jha, and L. Gopal, "Transient simulations of heat transfer in human eye undergoing laser surgery," Int. Commun. in Heat and Mass Trans., Vol. 53, 482-490, Jan. 2010. Google Scholar

15. Manns, F., D. Borja, J. M. Parel, W. Smiddy, and W. Culbertson, "Semianalytical thermal model for subablative laser heating of homogeneous nonperfused biological tissue: Application to laser thermokeratoplasty," J. Biomed. Opt., Vol. 8, No. 2, 288-297, Apr. 2003. Google Scholar

16. Pustovalov, V., B. Jean, T. Bende, and A. Smetannikov, "Investigations and computer modeling of the optical and thermal processes of laser thermal keratoplasty," Laser Phys., Vol. 14, No. 10, 1334-1341, 2004. Google Scholar

17. Podol'tsev, A. and G. Zheltov, "Photodestructive effect of IR laser radiation on the cornea," Opt. Spectrosc., Vol. 102, No. 1, 142-146, 2007. Google Scholar

18. Ooi, E. H., W. T. Ang, and E. Y. K. Ng, "A boundary element model of the human eye undergoing laser thermokeratoplasty," Comput. Biol. Med., Vol. 38, 727-737, 2008. Google Scholar

19. Esquenazi, S., V. Bui, and O. Bibas, "Surgical correction of hyperopia," Surv. Ophthalmol., Vol. 51, No. 4, 381-418, 2006. Google Scholar

20. Pennes, H. H., "Analysis of tissue and arterial blood temperatures in the resting human forearm, 1948," J. Appl. Physiol., Vol. 85, No. 1, 5-34, Jul. 1998. Google Scholar

21. Smerdon, D., "Anatomy of the eye and orbit," Curr. Anaesth. & Crit. Care, Vol. 11, No. 6, 286-292, Jan. 2000. Google Scholar

22. DeMarco, S. C., G. Lazzi, W. Liu, J. D. Weiland, and M. S. Humayun, "Computed SAR and thermal elevation in a 0.25-mm 2-D model of the human eye and head in response to an implanted retinal stimulator --- Part I: Models and methods," IEEE Transactions on Antennas and Propagation, Vol. 51, No. 9, 2274-2285, 2003. Google Scholar

23. Makous, W. L. and J. D. Gould, "Effects of lasers on the human eye," IBM J. Res. and Dev., Vol. 12, No. 3, 257-271, 1968. Google Scholar

24. Krauss, J., C. Puliafito, and R. Steinert, "Laser interactions with the cornea," Surv. Ophthalmol., Vol. 31, No. 1, 37-51, Jan. 1986. Google Scholar

25. Cvetkovic, M., A. Peratta, and D. Poljak, "Thermal modelling of the human eye exposed to infrared radiation of 1064nm Nd:YAG and 2090nm Ho:YAG lasers," Wit Tr Biomed Health, Vol. 14, 221-231, 2009. Google Scholar

26. Poljak, D., A. Peratta, and C. A. Brebbia, "The boundary element electromagnetic --- Thermal analysis of human exposure to base station antennas radiation," Eng. Anal. with Bound. Elem., Vol. 28, 763-770, Jan. 2004. Google Scholar

27. Ibrahiem, A., C. Dale, W. Tabbara, and J. Wiart, "Analysis of the temperature increase linked to the power induced by RF source," Progress In Electromagnetics Research, Vol. 52, 23-46, 2005. Google Scholar

28. Hirata, A., H. Sugiyama, and O. Fujiwara, "Estimation of core temperature elevation in humans and animals for whole-body averaged SAR," Progress In Electromagnetics Research, Vol. 99, 53-70, 2009. Google Scholar

29. Ooi, E., W. Ang, and E. Y. K. Ng, "A boundary element model for investigating the effects of eye tumor on the temperature distribution inside the human eye," Comput. Biol. Med., Vol. 39, 667-677, Jan. 2009. Google Scholar

30. Mahillo-Isla, R., M. J. Gonzáles-Morales, and C. Dehesa-Martínez, "Plane wave spectrum of 2D complex beams," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 8--9, 1123-1131, 2009. Google Scholar

31. Gonźales-Morales, M. J., R. Mahillo-Isla, E. Gago-Ribas, and C. Dehesa-Martínez, "3D complex beams in the spatial and the spectral domains," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 8--9, 1103-1112, 2010. Google Scholar

32. Cember, H., Introduction to Health Physics, 3rd Ed., McGraw Hill, Inc., 1996.

33. Träger, F., Springer Handbook of Lasers and Optics, Springer Science + Business Media, 2007.

34. Cvetkovic, M., D. Cavka, D. Poljak, and A. Peratta, "3D FEM temperature distribution analysis of the human eye exposed to laser radiation," Proc. Biomed., 2009. Google Scholar

35. Acharya, R. U., E. Y. K. Ng, and J. S. Suri, Image Modeling of the Human Eye, Vol. 11, 229-252, Artech House, Inc., 2008.

36. Ng, E. Y. K. and E. H. Ooi, "FEM simulation of the eye structure with bioheat analysis," Comput. Meth. Prog. Bio., Vol. 82, 268-276, 2006. Google Scholar

37. Ooi, E. H., W. T. Ang, and E. Y. K. Ng, "Bioheat transfer in the human eye: A boundary element approach," Eng. Anal. eight Bound. Elem., Vol. 31, No. 6, 494-500, 2007. Google Scholar

38. Ng, E. Y. K. and E. H. Ooi, "Ocular surface temperature: A 3D FEM prediction using bioheat equation," Comput. Biol. Med., Vol. 37, 829-835, 2007. Google Scholar

39. Stringer, H. and J. Parr, "Shrinkage temperature of eye collagen,", Vol. 204, No. 4965, 1307-1307, Dec. 1964. Google Scholar

40. Brinkmann, R., J. Kampmeier, U. Grotehusmann, A. Vogel, N. Koop, M. Asiyo-Vogel, and R. Birngruber, "Corneal collagen denaturation in laser thermokeratoplasty," P. Soc. Photo.-Opt. Ins., Vol. 2681, No. 56, 56-63, Jan. 1996. Google Scholar

41. Cvetkovic, M., D. Poljak, and A. Peratta, "Thermal modelling of the human eye exposed to laser radiation," Proc. SoftCOM, Vol. 10, 16-20, 2008. Google Scholar

42. Jansen, E. D., T. G. van Leeuwen, M. Motamedi, C. Borst, and A. J. Welch, "Temperature dependence of the absorption coefficient of water for midinfrared laser radiation," Laser Surg. Med., Vol. 14, No. 3, 258-268, 1994. Google Scholar

43. Lange, B., T. Brendel, and G. Hüuttmann, "Temperature dependence of light absorption in water at holmium and thulium laser wavelengths," Appl. Optics, Vol. 41, No. 27, 5797-5803, Sep. 2002. Google Scholar

44. Zhou, J., J. K. Chen, and Y. Zhang, "Simulation of laser-induced thermotherapy using a dual-reciprocity boundary element model with dynamic tissue properties," IEEE on Trans. Bio. Eng., Vol. 57, No. 2, 238-245, Jan. 2010. Google Scholar

45. Jha, K. and A. Narasimhan, "Three-dimensional bio-heat transfer simulation of sequential and simultaneous retinal laser irradiation," Int. J. Therm. Sci., Vol. 50, No. 7, 1191-1198, 2011. Google Scholar

Dr. Mario Cvetković

Dr. Dragan Poljak

Dr. Andres Peratta