An Analytical Solution of the Hyperbolic Bioheat Model of the Cornea Subjected to Laser Irradiation

Ram Autar
Department of Mathematics, Harcourt Butler Technical University, Kanpur, India

Anuj Kumar (Login required)
Department of Mathematics, Harcourt Butler Technical University, Kanpur, India

Paper #3463 received 10 Nov 2021; revised manuscript received 11 Jul 2022; accepted for publication 12 Jul 2022; published online 6 Aug 2022.

DOI: 10.18287/JBPE22.08.030302


The thermal effects occurring in a cornea subjected to short-pulsed laser irradiation during laser thermokeratoplasty (LTK) are investigated. The transient bioheat transfer is described by the hyperbolic model and solved analytically using the finite Fourier transform technique and the method of variation of parameters. The computational results predicted by the hyperbolic model show that the degree of damage in the corneal tissue induced by Ho: YAG laser irradiation under LTK surgery increases linearly with time. An increase in the convection coefficient of the anterior corneal surface causes an insignificant reduction in the corneal temperature, whereas an increase in the value of phase lag in the heat flux vector causes a rise in the corneal temperature.


temperature; laser; cornea; refractive error; LTK; Finite Fourier transform technique; hyperbolic model

Full Text:



1. P. Hooshmand, A. Moradi, and B. Khezry, “Bioheat transfer analysis of biological tissues induced by laser irradiation,” International Journal of Thermal Sciences 90, 214–223 (2015).

2. J. E. Fulton, T. Barnes, “Collagen shrinkage (selective dermatoplasty) with the high-energy pulsed carbon dioxide laser,” Dermatologic Surgery 24, 37–41 (1998).

3. A. D. Hobiny, I. A. Abbas, “Theoretical analysis of thermal damages in skin tissue induced by an intense moving heat source,” International Journal of Heat and Mass Transfer 124, 1011–1014(2018).

4. F. S. Alzahrani, I. A. Abbas, “Analytical estimations of temperature in a living tissue generated by laser irradiation using experimental data,” Journal of Thermal Biology 85, 10241(2019).

5. I. Abbas, A.Hobiny, and F. Alzahrani, “An analytical solution of the bioheat model in a spherical tissue due to laser irradiation,” Indian Journal of Physics 94, 1329–1334 (2019).

6. A.Hobiny, I. Abbas, “Thermal response of cylindrical tissue induced by laser irradiation with experimental study,” International Journal of Numerical Methods for Heat & Fluid flow 22(8), 4013–4023 (2019).

7. A. Ghanmi, I. A. Abbas, “An analytical study on the fractional transient heating within the skin tissue during the thermal therapy,” Journal of Thermal Biology 82, 229–233(2019).

8. A. Hobiny, I. Abbas, “Analytical solutions of fractional bioheat model in a spherical Tissue,” An International Journal of Mechanics Based Design of Structures and Machines 49(3), 430–439 (2019).

9. A. Hobiny, F. Alzahrani, I. Abbas, and M. Marin, “The effect of fractional time derivative of bioheat model in skin tissue induced to laser irradiation,” Symmetry 12(4), 602 (2020).

10. A. D. Hobiny, I. A. Abbas, “Nonlinear analysis of dual-phase lag bio-heat model in living tissues induced by laser irradiation,” Journal of Thermal Stresses 43(4), 503–511(2020).

11. E. H. Ooi, W.-T. Ang, and E. Y. K Ng, “A boundary element model of the human eye undergoing laser thermoKeratoplasty,” Computers in Biology and Medicine 38(6), 727–737 (2008).

12. D. Singh, K. Firouzbakhsh, and M. T. Ahmadian, “Laser Keratoplasty in Human Eye Considering the Fluid Aqueous Humor and Vitreous Humor Fluid Flow,” International Journal of Me-chanical and Mechatronics Engineering 11(4), 776–786 (2017).

13. N. A. Peppers, “Corneal damage threshold for CO2 laser irradiation,” Applied Optics 8(2), 377–381(1969).

14. K. Mitra, S. Kumar, A. Vedevarz, and M. K. Moallemi, “Experimental evidence of hyperbolic heat conduction in processed meat,” Journal of Heat Transfer 117(3), 568–573(1995).

15. W. Kaminski, “Hyperbolic heat conduction equation for materials with a nonhomogeneous inner structure,” Journal of Heat Transfer 112(3), 555–560 (1990).

16. A. M. Gheitaghy, B. Takabi, and M. Alizadeh, “Modeling of ultrashort pulsed laser irradiation in the cornea based on parabolic and hyperbolic heat equations using an electrical analogy,” International Journal of Modern Physics C 25(9), 1450039 (2014).

17. A. Narasimhan, S. Sadasivam, “Non-Fourier bioheat transfer modelling of thermal damage during retinal laser irradiation,” International Journal of Heat and Mass Transfer 60, 591–597(2013).

18. S. N. Fyodorov, V. V. Durnev, “Operation of dosages dissection of the corneal circular ligament in cases of myopia of mild degree,” Annals of Ophthalmology 11(12), 1885–1890 (1979).

19. W. W. Haw, E. E. Manche, “Conductive keratoplasty and laser thermal keratoplasty,” International Ophthalmology Clinics 42(4), 99–106 (2002).

20. P. A. Asbell, R. K. Maloney, J. M. Davidorf, P. S. Hersh, M. B. Mcdonald, and E. E. Manche, “Conductive keratoplasty for the correction of hyperopia,” Transactions of the American Ophthalmological Society 99, 79–87 (2001).

21. A. Aksan, J. J. McGrath, “Thermomechanical analysis of soft tissue thermo-therapy,” Journal of Biomechanical Engineering 125(5), 700–708 (2003).

22. T. L. Naoumidi, I. G. Pallikaris, I. Naoumidi, and N. I. Astyrakakis, “Conductive Keratoplasty: Histological Study of Human Corneas,” American Journal of Ophthalmology 140(6), 984–992 (2005).

23. B. Jo, A. Aksan, “Prediction of the extent of thermal damage in the cornea during conductive keratoplasty,” Journal of Thermal Biology 35(4), 167–174 (2010).

24. H. Moosavi, A. Moradi, and M. Parastarfeizabadi, “Investigation on the dual-phase lag effects in biological tissues during laser irradiation,” International Journal of Mechanic Systems Engineering 4(4), 33–46 (2014).

© 2014-2024 Samara National Research University. All Rights Reserved.
Public Media Certificate (RUS). 12+