Journal of Applied and Computational Mechanics

Analysis of a Hyperbolic Heat Transfer Model in Blood-perfused ‎Biological Tissues with Laser Heating

Document Type : Research Paper

Authors

Department of Mathematical and Computer Science, Physical Sciences and Earth Sciences, University of Messina,‎ Viale F. Stagno d’Alcontres 31, Messina, 98166, Italy

Abstract

This paper proposes a hyperbolic heat transport model for a homogeneously perfused biological tissue irradiated by a laser beam. In particular, involving two local energy equations, one for the blood vessel and the other for the tissue, a non-Fourier-like heat equation is introduced and solved analytically using the Laplace transform method. The generalized hyperbolic model obtained is reduced to Pennes' heat transport equation in case the thermal delay time is zero and the solution obtained is in accordance with the numerical and experimental data existing in the literature. In addition, the achieved results also show that the effects of thermal relaxation and blood perfusion on temperature distribution are similar; indeed the highest temperature is expected when the delay time tR increases during tissue cooling. Finally, the consequences of the change in the values of the physical parameters characterizing the model are described and the effect of thermal relaxation on the temperature profile in the tissue during and after laser application is investigated.

Keywords

Main Subjects

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[1] Chua, K.J., Chou, S.K., Ho, J.C., An analytical study on the thermal effects of cryosurgery on selective cell destruction, Journal of Biomechanics, 40, 2007, 100–116.
[2] Bischof, J.C., Rubinsky B., Microscale heat and mass transfer of vascular and intracellular freezing, Journal of Heat Transfer, 115, 1993, 1029–1035.
[3] Xu, F., Moon, S., Zhang, X., Shao, L., Song, Y.S., Demirci, U., Multi-scale heat and mass transfer modelling of cell and tissue cryopreservation, Philos. Trans. A. Math. Phys .Eng. Sci., 368(1912), 2010, 561–583.
[4] Kizilova, N., Bioheat equation with Fourier and non-Fourier heat transport laws: Applicability to heat transfer in human tissues, Journal of Thermal Engineering, 5, 2019, 149-161.
[5] Hooshmand, P., Moradi, A., Khezry, B., Bioheat transfer analysis of biological tissues induced by laser irradiation, International Journal of Thermal Sciences, 9, 2015, 214-223.
[6] Sudar, A., Futaki, G., Kovacs, R., Continuum Modeling Perspectives of Non-Fourier heat conduction in biological systems, Journal of Non-Equilibrium Thermodynamics, 46(4), 2021, 371-381.
[7] Lopez-Molina, J.A., Riviera, M.J., Trujillo, M., et al., Effect of the thermal wave in radiofrequency ablation modeling: an analytical study, Physics in Medicine & Biology, 53, 2008, 1447-1462.
[8] Pennes, H.H., Analysis of Tissue and Arterial Blood Temperature in the Resisting Human Foream, Journal of Applied Physiology, 1, 1948, 93-122.
[9] Kanafer, K., AlAmiri, A., Pop, I., Bull, J.L., Flow and Heat Transfer in Biological Tissues: Application of Porous Media Theory, Emerging Topics in Heat and Mass Transfer in Porous Media, 237, 2008, 237-259.
[10] Chen, M.M., Holmes, Microvascular Contributions in Tissue Heat Transfer, Annals of the New York Academy of Sciences, 335, 1980, 137-150.
11] Wulff, W., The Energy Conservation Equation for Living Tissue, IEEE Transactions on Biomedical Engineering, BME-21, 1974, 494-495.
[12] Klinger, Heat Transfer in Perfused Tissue: General Theory, Bulletin of Mathematical Biology, 36, 1974, 403-415.
[13] Nakayama, A., Kuwahara, F., Liu, W., A Macroscopic Model for Countercurrent Bioheat Transfer in a Circulatory System, Journal of Porous Media, 12, 2009, 289-300.
[14] Nakayama, A., Kuwahara, F., A general bioheat transfer model based on the theory of porous media, International Journal of Heat and Mass Transfer, 51, 2008, 3190-3199.
[15] Nakayama, A., Sano, Y., Yoshikawa, K., A rigorous derivation of the bioheat equation for local tissue heat transfer based on a volume averaging theory, Heat and Mass Transfer, 46, 2010, 739-746.
[16] Xuan, Y., Roetzel, W., Bioheat Equation of the Human Thermal System, Chemical Engineering & Technology, 20, 1997, 268-276.
[17] Yuan, P., Numerical analysis of temperature and thermal dose response of biological tissues to thermal non-equilibrium during hyperthermia therapy, Medical Engineering and Physics, 30, 2008, 135-143.
[18] Cattaneo, C., Sulla conduzione del calore, Atti Sem. Mat. Fis. Univ. Modena, 3, 1948, 83-101.
[19] Brinkmann, R., Droge, G., Koop, N., Wondermann, A., et al., Investigations on laser thermokeratoplasty, Lasers Light Opthalmol, 2079, 1994, 259-270.
[20] Loze, M.K., Wright, D.C., Temperature distributions in laser-heated biological tissue with application to birthmark removal, Journal of Biomedical Optics, 6(1), 2001, 74-85.
[21] Ahmadikia, H., Moradi, A., Fazlali, R., Basiri Parsa, A., Analytical solution of non-Fourier and Fourier bioheat transfer analysis during laser irradiation of skin tissue, Journal of Mechanical Science and Technology, 26, 2012, 1937-1947.
[22] Wongchadakula, P., Rattanadechob, P., Wessapanc, T., Implementation of a thermomechanical model to simulate laser heating in shrinkage tissue (effects of wavelength, laser irradiation intensity, and irradiation beam area), International Journal of Thermal Sciences, 134, 2018, 312-336.
[23] Shashi, K.M., Nanoparticles in modern medicine: State of the art and future challenges, International Journal of Nanomedicine, 2, 2007, 129-141.
[24] Waynant, R., Lasers in medicine, CRC Press LLC, 2002.
[25] Abramowitz, M., Stegun, I.A., Handbook of mathematical functions with Formulas, Graps, and Mathematical Tables, Dover, New York, 1972.
[26] Museux, N., Perez, L., Autrique, L., Agay, D., Skin burns after laser exposure: Histological analysis and predictive simulation, Burns, 38, 2012, 658-667.
[27] Kaminski, W., Hyperbolic heat conduction equation for materials with a nonhomogeneous inner structure, Journal of Heat Transfer, 112, 1990, 555–560.
[28] Zhou, J., Zhang, Y., Chen, J.K., Non-Fourier Heat Conduction Effect on Laser-Induced Thermal Damage in Biological Tissues, Numerical Heat Transfer, Part A: Applications, 54(1), 2008, 1-19.
[29] Kabin, A., Talaee, M.R., Thermal field and tissue damage analysis of moving laser in cancer thermal therapy, Lasers in Medical Sciences, 36(3), 2021, 583-597.
Journal of Applied and Computational Mechanics
Volume 8, Issue 4
October 2022
Pages 1398-1406