Non-Fourier analysis of skin biothermomechanics

International Journal of Heat and Mass Transfer

Volumn 51, Issue 9-10, 2008, Pages 2237-2259

  Xu, F ^a   Seffen, K A ^a   Lu, T J ^b  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b XI'AN JIAOTONG UNIVERSITY   (China)

Author keywords

Bioheat transfer; Non Fourier analysis; Numerical method; Skin tissue; Temperature; Thermal pain; Thermal stress

Indexed keywords

HEAT TRANSFER; NUMERICAL METHODS; RELAXATION PROCESSES; THERMAL STRESS; TISSUE;

BIOHEAT TRANSFER; NON-FOURIER ANALYSIS; SKIN TISSUE; THERMAL PAIN;

SKIN;

HEAT TRANSFER; NUMERICAL METHODS; RELAXATION PROCESSES; SKIN; THERMAL STRESS; TISSUE;

EID: 41649101655     PISSN: 00179310     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijheatmasstransfer.2007.10.024     Document Type: Article

References (100)

1. Peshkov V. Second sound in helium II. J. Phys. VIII 381 (1944)
2. Brown J.B., Chung D.Y., and Matthews P.W. Heat pulse at low temperature. Phys. Rev. Lett. 21 (1966) 241
3. Glass D.E., Ozisik M.N., and Vick B. Hyperbolic heat conduction with surface radiation. Int. J. Heat Mass Transfer 28 10 (1985) 1823-1830
4. Banerjee A., Ogale A.A., Das C., Mitra K., and Subramanian C. Temperature distribution in different materials due to short pulse laser irradiation. Heat Transfer Eng. 26 8 (2005) 41-49
5. Kaminski W. Hyperbolic heat conduction equation for materials with a nonhomogeneous inner structure. J. Heat Transfer, Trans. ASME 112 3 (1990) 555-560
6. Grassmann A., and Peters F. Experimental investigation of heat conduction in wet sand. Heat Mass Transfer/Waerme- und Stoffuebertragung 35 4 (1999) 289-294
7. Herwig H., and Beckert K. Experimental evidence about the controversy concerning Fourier or non-Fourier heat conduction in materials with a nonhomogeneous inner structure. Heat Mass Transfer/Waerme- und Stoffuebertragung 36 5 (2000) 387-392
8. Herwig H., and Beckert K. Fourier versus non-Fourier heat conduction in materials with a nonhomogeneous inner structure. J. Heat Transfer-Trans. ASME 122 2 (2000) 363-365
9. Roetzel W., Putra N., and Das S.K. Experiment and analysis for non-Fourier conduction in materials with non-homogeneous inner structure. Int. J. Therm. Sci. 42 6 (2003) 541-552
10. Richardson A.W., Imig C.G., Feucht B.L., and Hines H.M. Relationship between deep tissue temperature and blood flow during electromagnetic irradiation. Arch. Phys. Med. Rehabil. 31 (1950) 19-25
11. Roemer R.B., Oleson J.R., and Cetas T.C. Oscillatory temperature response to constant power applied to canine muscle. Am. J. Physiol. 249 2 (1985) R153-R158
12. Mitra K., Kumar S., Vedavarz A., and Moallemi M.K. Experimental evidence of hyperbolic heat conduction in processed meat. J. Heat Transfer, Trans. ASME 117 3 (1995) 568-573
13. E.V. Davydov, I.A. Lubashevsky, V.A. Milyaev, R.F. Musin, Nondiffusive heat transfer in muscle tissue 1 (1) (2001), preliminary results, arXiv:cond-mat/0102006.
14. Tilahun M., Scott E.P., and Vick B. The question of thermal waves in heterogeneous and biological materials. Am. Soc. Mech. Eng., Bioeng. Div. (Publ.) BED 44 (1999) 145-152
15. Antaki P.J. New interpretation of non-Fourier heat conduction in processed meat. J. Heat Transfer 127 2 (2005) 189-193
16. Liu J., Chen X., and Xu L.X. New thermal wave aspects on burn evaluation of skin subjected to instantaneous heating. IEEE Trans. Biomed. Eng. 46 4 (1999) 420-428
17. L.X. Xu, J. Liu, Discussion of non-equilibrium heat transfer in biological systems, in: Advances in Heat and Mass Transfer in Biotechnology, Proceedings of the 1998 ASME International Mechanical Engineering Congress and Exposition, Anaheim, CA, USA, 1998, pp. 13-17.
18. Tharp H.S., and Zhang W. Analytical study of temperature oscillations in living tissue. IEEE Trans. Biomed. Eng. 40 1 (1993) 108-110
19. Deng Z.S., and Liu J. Blood perfusion-based model for characterizing the temperature fluctuations in living tissue. Phys. A STAT Mech. Appl. 300 3-4 (2001) 521-530
20. Chen C., and Roemer R.B. A thermo-pharmacokinetic model of tissue temperature oscillations during localized heating. Int. J. Hyperther. 21 2 (2005) 107-124
21. Liu J., Zhang X.X., Wang C.C., and Lu W.Q. Engineering investigation on medical application approaches f or the thermal wave effects in living tissue. Space Med. Med. Eng. 10 2 (1997) 135-139
22. Liu J., Ren Z.P., and Wang C.C. Simulating experimental study on the mechanisms of temperature oscillation in living tissue. J. Basic Sci. Eng. 4 2 (1996) 173-182
23. Liu J., Wang C.C., and Ren Z.P. Theory and experiments on temperature oscillations effects in living tissue. J. Tsinghua Univ. (Sci & Tech) 2 (1997) 91-95
24. Shih T.-C., Kou H.-S., Liauh C.-T., and Lin W.-L. The impact of thermal wave characteristics on thermal dose distribution during thermal therapy: A numerical study. Med. Phys. 32 9 (2005) 3029-3036
25. Moritz A.R., and Henriques F.C. Study of thermal injuries II. The relative importance of time and source temperature in the causation of cutaneous burns. Am. J. Pathol. 23 (1947) 695-720
26. Pennes H.H. Analysis of tissue and arterial blood temperatures in the resting human forearm. J. Appl. Physiol. 1 (1948) 93-122
27. J. Herivel, Joseph Fourier: Face aux objections contre sa theorie de la chaleur: Bibliotheque Nationale, Paris, 1980.
28. M.N. Ozisik, D.Y. Tzou, On the Wave Theory in Heat Conduction, Anaheim, CA, USA, 1992, pp. 13-27.
29. Qiu T.Q., and Tien C.L. Short-pulse laser heating on metals. Int. J. Heat Mass Transfer 35 3 (1992) 719-726
30. Vedavarz A., Kumar S., and Moallemi M.K. Significance of non-Fourier heat waves in conduction. J. Heat Transfer, Trans. ASME 116 1 (1994) 221-224
31. Antaki P.J. Importance of nonFourier heat conduction in solid-phase reactions. Combust. Flame 112 3 (1998) 329-341
32. Liu J., and Lu W.Q. Dual reciprocity boundary element method for solving thermal wave model of bioheat transfer. Space Med. Med. Eng. 10 6 (1997) 391-395
33. Lu W.-Q., Liu J., and Zeng Y. Simulation of the thermal wave propagation in biological tissues by the dual reciprocity boundary element method. Eng. Anal. Boundary Elem. 22 3 (1998) 167-174
34. Lu W.-Q., Liu J., and Zeng Y. Extension of the dual reciprocity boundary element method to simulate thermal wave propagation in biological tissu. J. Eng. Thermophys. 19 6 (1998) 728-731
35. Morse P.M., and Feshbach H. Methods of Theoretical Physics vol. 1 (1953), McGraw-Hill, New York
36. Cattaneo C. A form of heat conduction equation which eliminates the paradox of instantaneous propagation. Comp. Rend. 247 (1958) 431-433
37. Vernotte P. Les paradoxes de la theorie continue de l'equation de la chaleur. Comp. Rend. 246 (1958) 3154-3155
38. Chester M. Second sound in solid. Phvs. Rev. 131 (1963) 2013-2015
39. Weymann H.D. Finite speed of propagation in heat conduction, diffusion and viscous shear motion. Am. J. Phys. 35 (1967) 488-496
40. Tzou D.Y. Macro- to Micro-scale Heat Transfer: The Lagging Behavior (1997), Taylor and Francis, Washington, DC
41. Yu Tzou D. An engineering assessment to the relaxation time in thermal wave propagation. Int. J. Heat Mass Transfer 36 7 (1993) 1845-1851
42. Ozisik M.N., and Tzou D.Y. On the wave theory in heat conduction. ASME J. Heat Transfer 116 (1994) 526-535
43. Tzou D.Y. An engineering assessment to the relaxation time in thermal wave propagation. Int. J. Heat Mass Transfer 36 7 (1993) 1845-1851
44. Tzou D.Y. Thermal shock phenomena under high-rate response in solids. In: Tien C.L. (Ed). Annual Review of Heat Transfer (1992), Hemisphere, Washington, DC 111-185
45. Sieniutycz S. The variational principles of classical type for non-coupled non-stationary irreversible transport processes with convective motion and relaxation. Int. J. Heat Mass Transfer 20 11 (1977) 1221-1231
46. Taitel Y. On the parabolic, hyperbolic and discrete formulation of the heat conduction equation. Int. J. Heat Mass Transfer 15 2 (1972) 369-371
47. Antonishyn N.V., Geller M.A., and Parnas A.L. Hyperbolic heat conduction equation for disperse system. Inzhenerno Fiz. Zh. 26 3 (1974) 503-508
48. Raspopov B.M. Control of some transfer processes. Inzhenerno Fiz. Zh. 12 (1967) 444
49. Brazhnikov A.M., Karpychev V.A., and Luikova A.V. One engineering method of calculating heat conduction processes. Inzhenerno Fiz. Zh. 28 4 (1975) 677-680
50. Michalowski S., Mitura E., and Kaminski W. The application of mathematical method to describe the kinetics of drying. Hungarian J. Indus. Chem. 10 (1982) 387
51. Mitura E., Michalowski S., and Karnlnski W. A mathematical model of convection drying in Falling drying rate period. Dry. Technol. 6 (1988) 113-137
52. Luikov A.V. Application of irreversible thermodynamics methods to investigation of heat and mass transfer. Int. J. Heat Mass Transfer 9 2 (1966) 139-152
53. Stratigos A.J., and Dover J.S. Overview of Lasers and Their Properties vol. 13 (2000) 2-16
54. Tang D.W., and Araki N. The wave characteristics of thermal conduction in metallic films irradiated by ultra-short laser pulses. J. Phys. D: Appl. Phys. 29 (1996) 2527
55. Liu J., Zhang X.X., Lu W.Q., and Wang C.C. The thermal pulse decay method for invasive measurement of blood perfusion of tissue in vivo. Progr. Nat. Sci. 9 2 (1999) 179-184
56. Zhu T.C., and Feng X.Z. Numerical analysis of the relationship between blood flow coefficient and living tissue thermal behavior. Chin. J. Hemorheol. 11 3 (2001) 182-183
57. Deng Z.S., and Liu J. Non-Fourier heat conduction effect on prediction of temperature transients and thermal stress in skin cryopreservation. J. Therm. Stress. 26 8 (2003) 779-798
58. Chato J.C., and Lee R.C. The future of biothermal engineering. Ann. N.Y. Acad. Sci. 858 (1998) 1-17
59. Liu J. Preliminary survey on the mechanisms of the wave-like behaviors of heat transfer in living tissues. Forsch. Ingenieurwesen/Eng. Res. 66 1 (2000) 1-10
60. Ma N., Jiang S., Li H., and Zhang X. Analysis of non-flourier effect and laser-induced thermal damage of laser-irradiated layered human skin tissue. Space Med. Med. Eng. 16 2 (2003) 133-137
61. Y. Bayazitoglu, G.P. Peterson, Fundamental issues in hyperbolic heat conduction, ASME HTD, 1992, p. 227.
62. Tzou D.Y., Ozisik M.N., and Chiffelle R.J. The lattice temperature in the microscopic two-step model. J. Heat Transfer 116 (1994) 1034-1038
63. Koerner C., and Bergmann H.W. Physical defects of the hyperbolic heat conduction equation. Appl. Phys. A: Mater. Sci. Process. 67 4 (1998) 397-401
64. Godoy S., and Garci{dotless}́a-Coli{dotless}́n L.S. Nonvalidity of the telegrapher's diffusion equation in two and three dimensionsfor crystalline solids. Phys. Rev. E 55 (1997) 2127-2131
65. Tzou D.Y. A unified field approach for heat conduction from macro- to micro-scales. J. Heat Transfer, Trans. ASME 117 1 (1995) 8-16
66. Tzou D.Y. Experimental support for the lagging behavior in heat propagation. J. Thermophys. Heat Transfer 9 (1995) 686-693
67. Quintanilla R., and Racke R. A note on stability in dual-phase-lag heat conduction. Int. J. Heat Mass Transfer 49 7-8 (2006) 1209-1213
68. Tzou D.Y., and Chiu K.S. Temperature-dependent thermal lagging in ultrafast laser heating. Int. J. Heat Mass Transfer 44 9 (2001) 1725-1734
69. Henriques F.C., and Moritz A.R. Studies of thermal injury, 1. The conduction of heat to and through skin and the temperatures attained therein. A theoretical and an experimental investigation. Am. J. Pathol. 23 (1947) 531-549
70. Henriques F.C. Study of thermal injuries V., The predictability and the significance of thermally induced rate processes leading to irreversible epidermal injury. Arch. Pathol. 43 (1947) 489-502
71. Wright N.T. On a relationship between the Arrhenius parameters from thermal damage studies. J. Biomech. Eng. 125 (2003) 300-304
72. Diller K.R., and Pearce J.A. Issues in modeling thermal alterations in tissues. Ann. N.Y. Acad. Sci. 888 (1999) 153-164
73. Despa F., Orgill D.P., Neuwalder J., and Lee R.C. The relative thermal stability of tissue macromolecules and cellular structure in burn injury. Burns 31 (2005) 568-577
74. F. Xu, Thermomechanical analysis of skin tissue, PhD First Year Report, Cambridge, UK Engineering Department, Cambridge University, 2005.
75. Xu F., Wen T., Seffen K.A., and Lu T.J. Biothermomechanics of skin tissue. J. Mech. Phys. Solids (2007)
76. Rigal J.D., and Leveque J. In vivo measurement of the stratum corneum elasticity. Bioeng. Skin 1 (1985) 13-23
77. Magnenat-Thalmann N., Kalra P., Leveque J.L., Bazin R., Batisse D., and Querleux B. A computational skin model: fold and wrinkle formation. IEEE Trans. Inf. Technol. Biomed. 6 4 (2002) 317-323
78. Patapoutian A., Peier A.M., Story G.M., and Viswanath V. Thermo TRP channels and beyond: mechanisms of temperature sensation. Nat. Rev. Neurosci. 4 8 (2003) 529-539
79. Kruger L., Perl E.R., and Sedivec M.J. Fine structure of myelinated mechanical nociceptor endings in cat hairy skin. J. Comp. Neurol. 198 1 (1981) 137-154
80. James N.C., and Richard A.M. Neurobiology of Nociceptors (1996), Oxford University Press, Oxford
81. Van H.J., and Gybels J. C nociceptor activity in human nerve during painful and non painful skin stimulation. J. Neurol. Neurosurg. Psychiatr. 44 7 (1981) 600-607
82. Reuck A.V.S., and Knight J. Touch, Heat and Pain (1966), Churchill Ltd.
83. Liu K.-C. Analysis of dual-phase-lag thermal behaviour in layered films with temperature-dependent interface thermal resistance. J. Phys. D: Appl. Phys. 38 19 (2005) 3722-3732
84. Duck F.A. Physical Properties of Tissue: A Comprehensive Reference Book (1990), Academic Press
85. Torvi D.A., and Dale J.D. A finite element model of skin subjected to a flash fire. J. Biomech. Eng. 116 3 (1994) 250-255
86. Delalleau A., Josse G., Lagarde J.M., Zahouani H., and Bergheau J.M. Characterization of the mechanical properties of skin by inverse analysis combined with the indentation test. J. Biomech. 39 9 (2006) 1603-1610
87. Hendriks F.M., Brokken D., Oomens C.W., Bader D.L., and Baaijens F.P. The relative contributions of different skin layers to the mechanical behavior of human skin in vivo using suction experiments. Med. Eng. Phys. 28 3 (2006) 259-266
88. W. Elkins, J.G. Thomson, Instrumented Thermal Manikin, Acurex Corporation, Aerotherm Division Report AD-781, 1973, p. 176.
89. Roetzel W., and Xuan Y. Transient response of the human limb to an external stimulus. Int. J. Heat Mass Transfer 41 1 (1998) 229-239
90. Sejrsen P. Measurement of cutaneous blood flow by freely diffusible radioactive isotopes. Dan. Med. Bull. 18 (1972) 1-38
91. Dahan S., Lagarde J.M., Turlier V., Courrech L., and Mordon S. Treatment of neck lines and forehead rhytids with a nonablative 1540-nm Er:glass laser: A controlled clinical study combined with the measurement of the thickness and the mechanical properties of the skin. Dermatol. Surg. 30 6 (2004) 872-879
92. Whitton J.T., and Everall J.D. The thickness of the epidermis. Brit. J. Dermatol. 89 (1973) 467-476
93. C.E. Fugitt, A rate process of thermal injury, Armed Forces Special Weapons Project AFSWP-606, 1955.
94. Stoll A.M., and Greene L.C. Relationship between pain and tissue damage due to thermal radiation. J. Appl. Phys. 14 3 (1959) 373-382
95. Weaver J.A., and Stoll A.M. Mathematical model of skin exposed to thermal radiation. Aerosp. Med. 40 1 (1969) 24-30
96. Mehta A.K., and Wong F.C. Measurement of Flammability and Burn Potential of Fabrics (1973), Massachusetts Institute of Technology, Cambridge, Massachusetts
97. Takata A.N., Rouse J., and Stanley T. Thermal Analysis Program (1973), I.I.T., Chicago
98. Wu Y.C. A Modified Criterion for Predicting Thermal Injury (1982), National Bureau of Standards, Washington
99. J.A. Pearce, W.-F. Cheong, K. Pandit, T.J. McMurray, S.L. Thomsen, Kinetic models for coagulation processes: determination of rate coefficients in vivo, in: Lasers in Dermatology and Tissue Welding, Los Angeles, CA, USA, 1991, pp. 27-33.
100. J.A. Pearce, S. Thomsen, H. Vijverberg, T. Magnusen, Quantitative Measurement of Thermal Damage: Birefringence Changes in Thermally Coagulated Collagen, New Orleans, LA, USA, 1993, pp. 141-144.