BIOHEAT EQUATION WITH FOURIER AND NON-FOURIER HEAT TRANSPORT LAWS: APPLICABILITY TO HEAT TRANSFER IN HUMAN TISSUES

The paper is dedicated to mathematical problem formulations for the heat propagation in biological tissues based on the Fourier and non-Fourier laws at different boundary conditions. The heating of the tissues is provided by external heat sources like low intensity lasers or light-emitting diodes which are widely used in contemporary medical care. Numerical computations on the standard Pennes bioheat equation with Fourier heat conduction give the temperature curves for both heating and thermal relaxation processes that do not correspond to the in vivo measurement data on human skin tissue. It is shown the modified bioheat equation based on the Guyer-Krumhansl heat conduction with correct formulation of the boundary conditions produces realistic temperature curves when the distributed heat sources and sinks in the tissue are accounted for. The former corresponds to the metabolic heat and temperature dependent chemical reactions, while the latter is provided by the heat convection with blood microcirculation system. The proposed model gives realistic two time temperature curves. The perspective applications of the novel mathematical formulation are discussed.

Keywords:

Pennes Bioheat Equation, Non-Fourier Heat Transport Laws Heat Transfer in Biological Tissues, Mathematical Modeling,

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[1] Grossweiner, L. I. (2005). The Science of Phototherapy: An Introduction. Springer Science & Business Media.
[2] Gomer, Ch. J. (2010) Photodynamic Therapy: Methods and Protocols. Humana Press.
[3] Kizilova, N., & Korobov, A. (2018). On biomedical engineering techniques for efficient phototherapy. International Journal on Biosensors and Bioelectronics, 4(6), 289-295.
[4] Kizilova, N., & Korobov, A. (2016). Mechanisms of influence of the low-intense optical radiation on the microcirculatory system. A review. Photobiology and Photomedicine, 71(2), 79-93.
[5] Liu, K.-C. (2008). Thermal propagation analysis for living tissue with surface heating. International Journal of Thermal Sciences, 47, 507–513.
[6] Kumar, P., Kumar, D., Rai, K. N. (2015). A numerical study on dual-phase-lag model of bio-heat transfer during hyperthermia treatment. Journal of Thermal Biology, 49-50, 98–105.
[7] Ciesielski, M., Mochnacki, B., Piasecka-Belkhayat, A. (2016). Analysis of temperature distribution in the heated skin tissue under the assumption of thermal parameters uncertainty. 40th Solid Mechanics Conference, Book of Abstracts, Warsaw, IPPT, P048.
[8] Verma, S. K., Maheshwari, S., Singh, R. K., Chaudhari, P. K. (2012). Laser in dentistry: An innovative tool in modern dental practice. National Journal of Maxillofacial Surgery, 3(2), 124–132.
[9] Azadgoli, B., Baker, R. Y. (2016). Laser applications in surgery. Annals of Translational Medicine, 23(4), 452-458.
[10] Pennes, H. H. (1948). Analysis of tissue and arterial blood temperatures in the resting forearm. Journal f Applied Physiology, 1, 93–122.
[11] Xu, F., Lu, T. J., Seffen, K. A. (2008). Biothermomechanics of skin tissues. Journal of the Mechanics and Physics of Solids, 56, 1852–1884.
[12] Nóbrega, S., Coelho, P. J. (2017). A parametric study of thermal therapy of skin tissue. Journal of Thermal Biology, 63, 92–103.
[13] Lin, S.-M. (2013). Analytical solutions of bio-heat conduction on skin in Fourier and non-Fourier models. Journal on Mechanics in Medicine and Biology, 13 (4), 1350063.
[14] Kizilova, N., Korobov, A., Solovjova H. (2018). Heat transfer at local surface freezing of human tissues: experimental and theortical study. In: IX Internal Conference “Low temperature physics,” Abstracts book, Kharkiv, Ukraine, 148.
[15] Kizilova N., Korobov A. (2018). On bioheat equation and its modification. In: 3-rd International Conference “Differential equations and Control Theory,” Book of Abstracts, Kharkiv, Ukraine, 30-31.
[16] Tzou, D. Y. (1995). A unified field approach for heat conduction from macro- to microscales. Journal of Heat Transfer, 117(1), 8–16.
[17] Tzou, D. Y. (1997). Macro- to Microscale Heat Transfer: The Lagging Behavior, New York, Taylor and Francis.
[18] Cattaneo, C. (1948). Sulla conduzione del calore, Atti del Seminario Matematico e Fisico dell' Universita di Modena, 3, 83–101.
[19] Vernotte, P. (1958). Les paradoxes de la théorie continue de l’équation de la chaleur. Comptes rendus hebdomadaires des séances de l'Académie des sciences, 46, 3154–3155.
[20] Majchrzak, E., Turchan, Ł., Dziatkiewicz, J. (2015). Modeling of skin tissue heating using the generalized dual phase-lag equation. Archives of Mechanics, 67(6), 417-437.
[21] Rukolaine, S. A. (2014). Unphysical effects of the dual-phase-lag model of heat conduction. International Journal of Heat and Mass Transfer, 78, 58–63.
[22] Rukolaine, S. A. (2017). Unphysical effects of the dual-phase-lag model of heat conduction: higher-order approximations. International Journal of Thermal Sciences, 113, 83–88.
[23] Wang, M., Yang, N., Guo, Z.-Y. (2011). Non-Fourier heat conductions in nanomaterials. Journal of Applied Physics, 110(6), 064310.
[24] Kovács, R. (2017). Heat conduction beyond Fourier’s Law: theoretical predictions and experimental validation, Budapest University of Technology and Economics, Ph.D. Thesis.
[25] Ván, P., Berezovski, A., Fülöp, T., Gróf, G., Kovács, R., Lovas, Á., & Verhás, J. (2017). Guyer-Krumhansl–type heat conduction at room temperature. Europhysics Letters, 118, 50005.
[26] Tang, D. W., Araki, N. (2000). Non-Fourier heat condution behavior in finite mediums under pulse surface heating. Material Science Engineering A, 292, 173.
[27] Berezovski, V. A., Kolotylov, N. N. (1990). Biophysical characteristics of human tissues: A reference book, Kiev, Naukova Dumka.

Başlangıç: 2015
Yayıncı: YILDIZ TEKNİK ÜNİVERSİTESİ

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