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ANALYSIS OF THE DPL BIO-HEAT TRANSFER EQUATION WITH CONSTANT AND TIME-DEPENDENT HEAT FLUX CONDITIONS ON SKIN SURFACE

ABSTRACT
This article focuses on temperature response of skin tissue due to time-dependent surface heat fluxes. Analytical solution is constructed for DPL bio-heat transfer equation with constant, periodic and pulse train heat flux conditions on skin surface. Separation of variables and Duhamel’s theorem for a skin tissue as a finite domain are employed. The transient temperature responses for constant and time-dependent boundary conditions are obtained and discussed. The results show that there is major discrepancy between the predicted temperature of parabolic (Pennes bio-heat transfer), hyperbolic (thermal wave) and DPL bio-heat transfer models when high heat flux accidents on the skin surface with a short duration or propagation speed of thermal wave is finite. The results illustrate that the DPL model reduces to the hyperbolic model when τT approaches zero and the classic Fourier model when both thermal relaxations approach zero. However for τq = τT the DPL model anticipates different temperature distribution with that predicted by the Pennes model. Such discrepancy is due to the blood perfusion term in energy equation. It is in contrast to results from the literature for pure conduction material, where the DPL model approaches the Fourier heat conduction model when τq = τT . The burn injury is also investigated.
KEYWORDS
PAPER SUBMITTED: 2014-01-28
PAPER REVISED: 2014-04-08
PAPER ACCEPTED: 2014-04-09
PUBLISHED ONLINE: 2014-05-04
DOI REFERENCE: https://doi.org/10.2298/TSCI140128057Z
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2016, VOLUME 20, ISSUE 5, PAGES [1457 - 1472]
REFERENCES
  1. Cho, Y.I., Bioengineering Heat Transfer, Advances in Heat Transfer, Academic, London, 22 (1992).
  2. Xu, F., Lu, T.J., Seffen, K.A., Ng, E.Y.K., Mathematical modeling of skin bioheat transfer., Appl. Mech. Rev., 62 (2009): p. 050801.
  3. Kumar Jha, K., Narasimhan, A., Three-dimensional bio-heat transfer simulation of sequential and simultaneous retinal laser irradiation, Int. J. Thermal Sciences 50 (2011), pp. 1191-1198.
  4. Zhu, L., Xu, L.X., Chencinski, N., Quantification of the3-D electromagnetic power absorption rate in tissue during transurethral prostatic microwave thermotherapy using heat transfer model., IEEE Tran. Biomed. Eng., 45 (1998), pp. 1163-1172.
  5. Deng, Z.S., Liu, J., Computational study on temperature mapping over skin surface and its implementation in disease diagnostic, Computers in Biology and Medicine, 34 (2004), pp. 495-521.
  6. Pennes, H.H., Analysis of tissue and arterial blood temperature in the resting forearm, Journal of Applied Physiology, 1 (1948), pp. 93-122.
  7. Peshkov, V., Second sound in helium II. Journal of Physics 381 (1994), 3.
  8. Cattaneo, C. A., form of heat conduction equation which eliminates the paradox of instantaneous propagation, Compte Rendus, 247 (1958), pp. 431-433.
  9. Vernotte, P., Les paradoxes de la theorie continue de l'equation de la chaleur, Compte Rendus, 246 (1958), pp. 3154-3155.
  10. Liu, J., Ren, Z., Wang, C., Interpretation of living tissue's temperature oscillations by thermal wave theory, Chinese Science Bulletin, 40 (1995), pp. 1493-1495.
  11. Durkee Jr, J.W., Antich, P.P., Lee, C.E., Exact solutions to the multiregion time-dependent bioheat equation. I: Solution development, Phys. Med. Biol., 35 (1990), 7, pp. 847-867.
  12. Foster, K.R., Nieto, A.L., Riu, P.J., Ely, T.S., Heating of tissues by microwaves: A model analysis, Bioelectromagnetics, 19 (1998), pp. 420-428.
  13. Shen, W., Zhang, J., Modeling and numerical simulation of bioheat transfer and biomechanics in soft tissue, Mathematical and Computer Modeling, 41 (2005), pp. 1251-1265.
  14. Mitra, K., Kumar, S., Vedavarz, A., Moallemi, M.K., Experimental evidence of hyperbolic heat conduction in processed meat, Journal of Heat Transfer Transactions of the ASME 117 (1995), 3, pp. 568-573.
  15. Liu, J., Chen, X., Xu, L.X., New thermal wave aspects on burn evaluation of skin subjected to instantaneous heating, IEEE Transaction on Biomedical Engineering, 46 (1999), pp. 4420-428.
  16. Xu, F., Lu, T.J., Seffen, K.A., Biothermomechanics of skin tissues, Journal of the Mechanics and Physics of Solids, 56 (2008), pp. 1852-1884.
  17. Liu, K.C., Cheng, P.J., Wang, Y.N., Analysis of non-Fourier thermal behavior for multi-layer skin model, Thermal Science, 15 (2011), 1, pp. 61-67.
  18. Tzou, D.Y., Macro-to microscale heat transfer: The lagging behavior, Taylor & Francis, Washington, DC; (1997).
  19. Tzou, D.Y., A Unified field approach for heat conduction from micro- to macro-scales, ASME J. Heat Transfer, 117 (1995), pp. 8-16.
  20. Ozisik, M.N., Tzou, D.Y., On the wave theory in heat conduction, ASME J. Heat Transfer 116 (1994), pp. 526-535.
  21. Xu, F., Seffen, K.A., Lu, T.J., Non-Fourier analysis of skin biothermomechanics, Int. J. Heat and Mass Transfer, 51 (2008), pp. 2237-2259.
  22. Liu, K.C., Chen, H.T., Investigation for the dual phase lag behavior of bio-heat transfer, Int. J. Thermal Sci., 49 (2010), pp. 1138-1146.
  23. Liu, K.C., Chen, H.T., Analysis for the dual-phase-lag bio-heat transfer during magnetic hyperthermia treatment, Int. J. Heat and Mass Transfer, 52 (2009), pp. 1185-1192.
  24. Zhang, Y., Generalized dual-phase lag bioheat equations based on nonequilibrium heat transfer in living biological tissues, Int. J. Heat and Mass Transfer, 52 (2009), pp. 4829-4834.
  25. Liu, K.C., Wang, Y.N., Chen, Y.S., Investigation on the bio-heat transfer with the dual phase-lag effect, Int. J. Thermal Sci., 58 (2012), pp.29-35.
  26. Liu, J., Xu, L.X., Estimation of Blood Perfusion Using Phase Shift in Temperature Response to Sinusoidal Heating at the Skin Surface, IEEE Trans. Biomed. Eng., 46 (9) (1999), pp. 1037-1043.
  27. Shih, T.C., Yuan, P., Lin, W.L., Kou, H.S., Analytical analysis of the Pennes bioheat transfer equation with sinusoidal heat flux condition on skin surface., Medical Engineering & Physics, 29 (2007), pp. 946-953.
  28. Ahmadikia, H., Fazlali, R., Moradi, A., Analytical solution of the parabolic and hyperbolic heat transfer equations with constant and transient heat flux conditions on skin tissue, Int. Commun. Heat and Mass Transfer, 39 (2012), pp.121-130.
  29. Horng, T.L., Lin, W.L., Liauh, C.T., Shih, T.C., Effects of pulsatile blood flow in large vessels on thermal dose distribution during thermal therapy, Med. Phys. 34 (4) (2007), pp. 1312-1320.
  30. Shih, T.C., Horng, T.L., Huang, H.W., Ju, K.C., Huang, T.C., Chen, P. Y., Ho, Y.J., Lin, W.L., Numerical analysis of coupled effects of pulsatile blood flow and thermal relaxation time during thermal therapy, Int. J. Heat Mass Transfer, 55 (2012), pp. 3763-3773.
  31. Arpaci, V.C., Conduction Heat Transfer, Addisson Wesley Publication, (1966).
  32. Torvi, D.A., Dale, J.D., A finite element model of skin subjected to a flash fire, ASME J. Biomech. Eng., 116 (1994), pp. 250-255.
  33. Moritz, A.R., Henriques, F.C., Study of thermal injuries II. The relative importance of time and source temperature in the causation of cutaneous burns, American Journal of Pathology, 23 (1947), pp. 695-720.

© 2019 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence