Advances in laser, microwave, and similar technologies have led to recent developments of thermal treatments for disease and injury involving skin tissue. In spite of the widespread use of heating therapies in dermatology, they do not draw upon the detailed understanding of the biothermomechanics of behavior, for none exists to date, even though each behavioral facet is well established and understood. It is proposed that a detailed understanding of the coupled biological-mechanical response under thermal agitation will contribute to the design, characterization, and optimization of strategies for delivering better treatment. For a comprehensive understanding on the underlying mechanisms of thermomechanical behavior of skin tissue, recent progress on bioheat transfer, thermal damage, thermomechanics, and thermal pain should be systematically reviewed. This article focuses on the transfer of heat through skin tissue. Experimental study, theoretical analysis, and numerical modeling of skin thermal behavior are reviewed, with theoretical analysis carried out and closed-form solutions obtained for simple one-layer Fourier theory based model. Non-Fourier bioheat transfer models for skin tissue are discussed, and various skin cooling technologies summarized. Finally, the predictive capacity of various heat transfer models is demonstrated with selected case studies.
Issue Section:
Review Articles
1.
Klavuhn
, K. G.
, 2001, Epidermal Protection: A Comparative Analysis of Sapphire Contact and Cryogen Spray Cooling
, Lumenis Inc.
, Santa Clara, CA
.2.
Klavuhn
, K. G.
, and Green
, D.
, 2002, “Importance of Cutaneous Cooling During Photothermal Epilation: Theoretical and Practical Considerations
,” Lasers Surg. Med.
0196-8092, 31
(2
), pp. 97
–105
.3.
Nahm
, W. K.
, Tsoukas
, M. M.
, Falanga
, V.
, Carson
, P. A.
, Sami
, N.
, and Touma
, D. J.
, 2002, “Preliminary Study of Fine Changes in the Duration of Dynamic Cooling During 755-nm Laser Hair Removal on Pain and Epidermal Damage in Patients With Skin Types III-V
,” Lasers Surg. Med.
0196-8092, 31
(4
), pp. 247
–251
.4.
Altshuler
, G. B.
, Zenzie
, H. H.
, Erofeev
, A. V.
, Smirnov
, M. Z.
, Anderson
, R. R.
, and Dierickx
, C.
, 1999, “Contact Cooling of the Skin
,” Phys. Med. Biol.
0031-9155, 44
(4
), pp. 1003
–1023
.5.
Anvari
, B.
, Tanenbaum
, B. S.
, Milner
, T. E.
, Kimel
, S.
, Svaasand
, L. O.
, and Nelson
, J. S.
, 1995, “A Theoretical Study of the Thermal Response of Skin to Cryogen Spray Cooling and Pulsed Laser Irradiation: Implications for Treatment of Port Wine Stain Birthmarks
,” Phys. Med. Biol.
0031-9155, 40
(9
), pp. 1451
–1465
.6.
Sturesson
, C.
, and Andersson-Engels
, S.
, 1996, “Mathematical Modelling of Dynamic Cooling and Pre-Heating, Used to Increase the Depth of Selective Damage to Blood Vessels in Laser Treatment of Port Wine Stains
,” Phys. Med. Biol.
0031-9155, 41
(3
), pp. 413
–428
.7.
Pfefer
, T. J.
, Smithies
, D. J.
, Milner
, T. E.
, van Gemert
, M. J.
, Nelson
, J. S.
, and Welch
, A. J.
, 2000, “Bioheat Transfer Analysis of Cryogen Spray Cooling During Laser Treatment of Port Wine Stains
,” Lasers Surg. Med.
0196-8092, 26
(2
), pp. 145
–157
.8.
Verkruysse
, W.
, Majaron
, B.
, Tanenbaum
, B. S.
, and Nelson
, J. S.
, 2000, “Optimal Cryogen Spray Cooling Parameters for Pulsed Laser Treatment of Port Wine Stains
,” Lasers Surg. Med.
0196-8092, 27
(2
), pp. 165
–170
.9.
Yamauchi
, P. S.
, Soriano
, T. T.
, and Lask
, G. P.
, 2000, “Treatment of Port Wine Stains Using the Pulsed-Dye Laser at 585 nm With the Dynamic Cooling Device
,” J. Cutan. Laser Ther.
, 2
(1
), pp. 33
–36
. 1462-883X10.
Huang
, P. S.
, and Chang
, C. J.
, 2001, “Cryogen Spray Cooling in Conjunction With Pulse Dye Laser Treatment of Port Wine Stains of the Head and Neck
,” Chang Gung Med. J.
, 24
(8
), pp. 469
–475
.11.
Chiu
, C. H.
, Chan
, H. H.
, Ho
, W. S.
, Yeung
, C. K.
, and Nelson
, J. S.
, 2003, “Prospective Study of Pulsed Dye Laser in Conjunction With Cryogen Spray Cooling for Treatment of Port Wine Stains in Chinese Patients
,” Dermatol. Surg.
1076-0512, 29
(9
), pp. 909
–915
.12.
Ahcan
, U.
, Zorman
, P.
, Recek
, D.
, Ralca
, S.
, and Majaron
, B.
, 2004, “Port Wine Stain Treatment With a Dual-Wavelength Nd:Yag Laser and Cryogen Spray Cooling: A Pilot Study
,” Lasers Surg. Med.
0196-8092, 34
(2
), pp. 164
–167
.13.
Tunnell
, J. W.
, Chang
, D. W.
, Johnston
, C.
, Torres
, J. H.
, Patrick
, C. W.
, Jr., Miller
, M. J.
, Thomsen
, S. L.
, and Anvari
, B.
, 2003, “Effects of Cryogen Spray Cooling and High Radiant Exposures on Selective Vascular Injury During Laser Irradiation of Human Skin
,” Arch. Dermatol.
0003-987X, 139
(6
), pp. 743
–750
.14.
Tunnell
, J. W.
, Wang
, L. V.
, and Anvari
, B.
, 2003, “Optimum Pulse Duration and Radiant Exposure for Vascular Laser Therapy of Dark Port-Wine Skin: A Theoretical Study
,” Appl. Opt.
0003-6935, 42
(7
), pp. 1367
–1378
.15.
Greve
, B.
, Hammes
, S.
, and Raulin
, C.
, 2001, “The Effect of Cold Air Cooling on 585 nm Pulsed Dye Laser Treatment of Port-Wine Stains
,” Dermatol. Surg.
1076-0512, 27
(7
), pp. 633
–636
.16.
Fader
, D. J.
, Sax
, D. S.
, and Hamilton
, T. A.
, 2000, “Quantifying Postoperative Pain Reduction Using the Dynamic Cooling Device to Treat Pediatric Patients With Port-Wine Stains
,” Arch. Dermatol.
0003-987X, 136
(11
), pp. 1416
–1417
.17.
Chang
, C. J.
, and Nelson
, J. S.
, 1999, “Cryogen Spray Cooling and Higher Fluence Pulsed Dye Laser Treatment Improve Port-Wine Stain Clearance While Minimizing Epidermal Damage
,” Dermatol. Surg.
1076-0512, 25
(10
), pp. 767
–772
.18.
Waldorf
, H. A.
, Alster
, T. S.
, McMillan
, K.
, Kauvar
, A. N.
, Geronemus
, R. G.
, and Nelson
, J. S.
, 1997, “Effect of Dynamic Cooling on 585-nm Pulsed Dye Laser Treatment of Port-Wine Stain Birthmarks
,” Dermatol. Surg.
1076-0512, 23
(8
), pp. 657
–662
.19.
Nelson
, J. S.
, Milner
, T. E.
, Anvari
, B.
, Tanenbaum
, B. S.
, Kimel
, S.
, Svaasand
, L. O.
, and Jacques
, S. L.
, 1995, “Dynamic Epidermal Cooling During Pulsed Laser Treatment of Port-Wine Stain. A New Methodology With Preliminary Clinical Evaluation
,” Arch. Dermatol.
0003-987X, 131
(6
), pp. 695
–700
.20.
Gilchrest
, B. A.
, Rosen
, S.
, and Noe
, J. M.
, 1982, “Chilling Port Wine Stains Improves the Response to Argon Laser Therapy
,” Plast. Reconstr. Surg.
0032-1052, 69
, pp. 278
–283
.21.
Kono
, T.
, Groff
, W. F.
, Sakurai
, H.
, Takeuchi
, M.
, Yamaki
, T.
, Soejima
, K.
, and Nozaki
, M.
, 2006, “Evaluation of Fluence and Pulse-Duration on Purpuric Threshold Using an Extended Pulse Pulsed-Dye Laser in the Treatment of Port Wine Stains
,” J. Dermatol.
0385-2407, 33
(7
), pp. 473
–476
.22.
Asahina
, A.
, Watanabe
, T.
, Kishi
, A.
, Hattori
, N.
, Shirai
, A.
, Kagami
, S.
, Watanabe
, R.
, Le Pavoux
, A.
, Maekawa
, T.
, Tamaki
, K.
, and Ohara
, K.
, 2006, “Evaluation of the Treatment of Port-Wine Stains With the 595-nm Long Pulsed Dye Laser: A Large Prospective Study in Adult Japanese Patients
,” J. Am. Acad. Dermatol.
0190-9622, 54
(3
), pp. 487
–493
.23.
Shafirstein
, G.
, Baumler
, W.
, Lapidoth
, M.
, Ferguson
, S.
, North
, P. E.
, and Waner
, M.
, 2003, Laser Tissue Interaction Modeling for Treatment Planning of Port-Wine Stain
, Institute of Electrical and Electronics Engineers Inc.
, Tucson, AZ
, pp. 313
–315
.24.
Pustovalov
, V. K.
, and Jean
, B.
, 2007, “Melanin Granule Models for the Processes of Laser-Induced Thermal Damage in Pigmented Retinal Tissues. I. Modeling of Laser-Induced Heating of Melanosomes and Selective Thermal Processes in Retinal Tissues
,” Bull. Math. Biol.
0092-8240, 69
(1
), pp. 245
–263
.25.
Kauvar
, A. N.
, Rosen
, N.
, and Khrom
, T.
, 2006, “A Newly Modified 595-nm Pulsed Dye Laser With Compression Handpiece for the Treatment of Photodamaged Skin
,” Lasers Surg. Med.
0196-8092, 38
(9
), pp. 808
–813
.26.
Hamilton
, M. M.
, 2004, “Laser Treatment of Pigmented and Vascular Lesions in the Office
,” Facial Plast. Surg.
0736-6825, 20
(1
), pp. 63
–69
.27.
Diette
, K. M.
, Bronstein
, B. R.
, and Parrish
, J. A.
, 1985, “Histologic Comparison of Argon and Tunable Dye Lasers in the Treatment of Tattoos
,” J. Invest. Dermatol.
0022-202X, 85
(4
), pp. 368
–373
.28.
Hoffman
, W. L.
, Anvari
, B.
, Said
, S.
, Tanenbaum
, B. S.
, Liaw
, L. H.
, Milner
, T.
, and Nelson
, J. S.
, 1997, “Cryogen Spray Cooling During Nd:YAG Laser Treatment of Hemangiomas. A Preliminary Animal Model study
,” Dermatol. Surg.
1076-0512, 23
(8
), pp. 635
–641
.29.
Chang
, C. J.
, Anvari
, B.
, and Nelson
, J. S.
, 1998, “Cryogen Spray Cooling for Spatially Selective Photocoagulation of Hemangiomas: A New Methodology With Preliminary Clinical Reports
,” Plast. Reconstr. Surg.
0032-1052, 102
(2
), pp. 459
–463
.30.
Chang
, C. J.
, Kelly
, K. M.
, and Nelson
, J. S.
, 2001, “Cryogen Spray Cooling and Pulsed Dye Laser Treatment of Cutaneous Hemangiomas
,” Ann. Plast. Surg.
0148-7043, 46
(6
), pp. 577
–583
.31.
Vlachakis
, I.
, Gardikis
, S.
, Michailoudi
, E.
, and Charissis
, G.
, 2003, “Treatment of Hemangiomas in Children Using a Nd:YAG Laser in Conjunction With Ice Cooling of the Epidermis: Techniques and Results
,” BMC Pediatr.
, 3
(2
), pp. 1
–6
. 1471-243132.
Anvari
, B.
, Tanenbaum
, B. S.
, Hoffman
, W.
, Said
, S.
, Milner
, T. E.
, Liaw
, L. H.
, and Nelson
, J. S.
, 1997, “Nd:YAG Laser Irradiation in Conjunction With Cryogen Spray Cooling Induces Deep and Spatially Selective Photocoagulation in Animal Models
,” Phys. Med. Biol.
0031-9155, 42
(2
), pp. 265
–282
.33.
Kelly
, K. M.
, Nelson
, J. S.
, Lask
, G. P.
, Geronemus
, R. G.
, and Bernstein
, L. J.
, 1999, “Cryogen Spray Cooling in Combination With Nonablative Laser Treatment of Facial Rhytides
,” Arch. Dermatol.
0003-987X, 135
(6
), pp. 691
–694
.34.
Goldberg
, D. J.
, Rogachefsky
, A. S.
, and Silapunt
, S.
, 2002, “Non-Ablative Laser Treatment of Facial Rhytides: A Comparison of 1450-nm Diode Laser Treatment With Dynamic Cooling as Opposed to Treatment With Dynamic Cooling Alone
,” Lasers Surg. Med.
0196-8092, 30
(2
), pp. 79
–81
.35.
Majaron
, B.
, Kelly
, K. M.
, Park
, H. B.
, Verkruysse
, W.
, and Nelson
, J. S.
, 2001, “Er:YAG Laser Skin Resurfacing Using Repetitive Long-Pulse Exposure and Cryogen Spray Cooling: I. Histological Study
,” Lasers Surg. Med.
0196-8092, 28
(2
), pp. 121
–130
.36.
Majaron
, B.
, Verkruysse
, W.
, Kelly
, K. M.
, and Nelson
, J. S.
, 2001, “Er:YAG Laser Skin Resurfacing Using Repetitive Long-Pulse Exposure and Cryogen Spray Cooling: II. Theoretical Analysis
,” Lasers Surg. Med.
0196-8092, 28
(2
), pp. 131
–137
.37.
Raulin
, C.
, and Grema
, H.
, 2004, “Single-Pass Carbon Dioxide Laser Skin Resurfacing Combined With Cold-Air Cooling: Efficacy and Patient Satisfaction of a Prospective Side-by-Side Study
,” Arch. Dermatol.
0003-987X, 140
(11
), pp. 1333
–1336
.38.
Paithankar
, D. Y.
, Ross
, E. V.
, Saleh
, B. A.
, Blair
, M. A.
, and Graham
, B. S.
, 2002, “Acne Treatment With a 1,450 nm Wavelength Laser and Cryogen Spray Cooling
,” Lasers Surg. Med.
0196-8092, 31
(2
), pp. 106
–114
.39.
Kono
, T.
, Erçöçen
, A. R.
, Nakazawa
, H.
, and Nozaki
, M.
, 2005, “Treatment of Hypertrophic Scars Using a Long-Pulsed Dye Laser With Cryogen-Spray Cooling
,” Ann. Plast. Surg.
0148-7043, 54
(5
), pp. 487
–493
.40.
Negishi
, K.
, Wakamatsu
, S.
, Kushikata
, N.
, Tezuka
, Y.
, Kotani
, Y.
, and Shiba
, K.
, 2002, “Full-Face Photorejuvenation of Photodamaged Skin by Intense Pulsed Light With Integrated Contact Cooling: Initial Experiences in Asian Patients
,” Lasers Surg. Med.
0196-8092, 30
(4
), pp. 298
–305
.41.
Parsons
, K. C.
, 1993, Human Thermal Environments
, Taylor & Francis
, London, UK
.42.
Silver
, F. H.
, Siperko
, L. M.
, and Seehra
, G. P.
, 2003, “Mechanobiology of Force Transduction in Dermal Tissue
,” Skin Res. Technol.
0909-752X, 9
(1
), pp. 3
–23
.43.
Braverman
, I. M.
, 1995, “Anatomy and Physiology of the Cutaneous Microcirculation
,” Bioengineering of the Skin: Cutaneous Blood Flow and Erythema
, E.
Berardesca
, P.
Elsner
, and H.
Maibach
, eds., CRC
, Boca Raton, FL
.44.
Sonksen
, J.
, and Craggs
, J.
, 1999, “Circulation of the Skin
,” Current Anaesthesia and Critical Care
, 10
, pp. 58
–63
.45.
Moschella
, S.
, and Harley
, H. J.
, 1985, Dermatology
, Saunders
, Philadelphia, PA
.46.
Greenfield
, A. D. M.
, 1963, “Circulation Through the Skin
,” Handbook of Physiology
, W. F.
Hamilton
, ed., American Physiological Society
, Washington
, p. 1325
.47.
Fagrell
, B.
, 1984, “Microcirculation of the Skin
,” The Physiology and Pharmacolcogy of the Microcircualtion
, B.
Fagrell
, ed., Academic
, London
, pp. 133
–180
.48.
Ong
, M. L.
, and Ng
, E. Y. K.
, 2005, “A Global Bioheat Model With Self-Tuning Optimal Regulation of Body Temperature Using Hebbian Feedback Covariance Learning
,” Medical Physics, American Association of Physicists in Medicine
, 3
(12
), pp. 3819
–3831
.49.
Yen
, A.
, and Braverman
, I. M.
, 1976, “Ultrastructure of the Human Dermal Microcirculation: The Horizontal Plexus of the Papillary Dermis
,” J. Invest. Dermatol.
0022-202X, 66
(3
), pp. 131
–142
.50.
Joyner
, M. J.
, and Dietz
, N. M.
, 1997, “Nitric Oxide and Vasodilation in Human Limbs
,” J. Appl. Physiol.
8750-7587, 83
, pp. 1785
–1796
.51.
Conrad
, M. C.
, Anderson
, J. L.
, and Garrett
, J. B.
, 1971, “Chronic Collateral Growth After Femoral Artery Occlusion in the Dog
,” J. Appl. Physiol.
8750-7587, 31
, pp. 550
–555
.52.
Hales
, J. R. S.
, Iriki
, M.
, Tsuchiya
, K.
, and Kozawa
, E.
, 1978, “Thermally Induced Cutaneous Sympathetic Activity Related to Blood Flow Through Capillaries and Arteriovenous Anastomoses
,” Eur. J. Phys.
0143-0807, 375
, pp. 17
–24
.53.
Garrido
, M. J.
, Williams
, M.
, and Argenziano
, M.
, 2004, “Minimally Invasive Surgery for Atrial Fibrillation: Toward a Totally Endoscopic, Beating Heart Approach
,” J. Card. Surg.
0886-0440, 19
(3
), pp. 216
–220
.54.
Gillett
, M. D.
, Gettman
, M. T.
, Zincke
, H.
, and Blute
, M. L.
, 2004, “Tissue Ablation Technologies for Localized Prostate Cancer
,” Mayo Clin. Proc.
0025-6196, 79
(12
), pp. 1547
–1555
.55.
Buchalla
, W.
, and Attin
, T.
, 2007, “External Bleaching Therapy With Activation by Heat, Light or Laser-A Systematic Review
,” Dent. Mater.
0109-5641, 23
(5
), pp. 586
–596
.56.
Cobb
, C. M.
, 2006, “Lasers in Periodontics: A Review of the Literature
,” J. Periodontol.
0022-3492, 77
(4
), pp. 545
–564
.57.
Nottingham
, L. K.
, and Ries
, W. R.
, 2004, “Update on Lasers in Facial Plastic Surgery
,” Curr. Opin. Otolaryngol. Head Neck Surg.
1068-9508, 12
(4
), pp. 323
–326
.58.
Bischof
, J. C.
, 2006, “Micro and Nanoscale Phenomenon in Bioheat Transfer
,” Heat Mass Transfer
0947-7411, 42
(10
), pp. 955
–966
.59.
Xu
, F.
, Wen
, T.
, Seffen
, K. A.
, and Lu
, T. J.
, 2008, “Biothermomechanics of Skin Tissue
,” J. Mech. Phys. Solids
0022-5096, 56
(5
), 1852
–1884
.60.
Brigham
, P. A.
, and McLoughlin
, E.
, 1996, “Burn Incidence and Medical Care Use in the United States: Estimates, Trends, and Data Sources
,” J. Burn Care Rehabil.
0273-8481, 17
, pp. 95
–107
.61.
Moritz
, A. R.
, and Henriques
, F. C.
, 1947, “Study of Thermal Injuries II. The Relative Importance of Time and Source Temperature in the Causation of Cutaneous Burns
,” Am. J. Pathol.
0002-9440, 23
, pp. 695
–720
.62.
Diller
, K. R.
, 1985, “Analysis of Skin Burns
,” Heat Transfer in Medicine and Biology: Analysis and Applications
, Plenum
, New York
, pp. 85
–134
.63.
Diller
, K. R.
, 1998, “Modeling Skin Burns on a Personal Computer
,” J. Burn Care Rehabil.
0273-8481, 19
, pp. 420
–429
.64.
Diller
, K. R.
, 1999, “Development and Solution of Finite Difference Equations for Burn Injury With Spreadsheet Software
,” J. Burn Care Rehabil.
0273-8481, 20
, pp. 25
–32
.65.
Ng
, E. Y. K.
, and Chua
, L. T.
, 2000, “Mesh-Independent Prediction of Skin Burns Injury
,” J. Med. Eng. Technol.
0309-1902, 24
(6
), pp. 255
–261
.66.
Ng
, E. Y.
, and Chua
, L. T.
, 2002, “Comparison of One- and Two-Dimensional Programmes for Predicting the State of Skin Burns
,” Burns
0305-4179, 28
(1
), pp. 27
–34
.67.
Ng
, E. Y.
, and Chua
, L. T.
, 2002, “Prediction of Skin Burn Injury. Part 2: Parametric and Sensitivity Analysis
,” Proc. Inst. Mech. Eng., Part H: J. Eng. Med.
0954-4119, 216
(3
), pp. 171
–183
.68.
Ng
, E. Y.
, and Chua
, L. T.
, 2002, “Prediction of Skin Burn Injury. Part 1: Numerical Modelling
,” Proc. Inst. Mech. Eng., Part H: J. Eng. Med.
0954-4119, 216
(3
), pp. 157
–170
.69.
Ng
, E. Y. K.
, and Chua
, L. T.
, 2001, “Quick Numerical Assessment of Skin Burn Injury With Spreadsheet in PC
,” International Journal of Mechanics Medical Biology
, 1
(1
), pp. 1
–10
.70.
Phetteplace
, G.
, 2000, “Integrating Cold Weather Impacts on Human Performance Into Army M&S Applications
,” Proceedings of the 2000 Winter Simulation Conference
, J. A.
Joines
, R. R.
Barton
, K.
Kang
, and P. A.
Fishwick
, eds.71.
Cohen
, M. L.
, 1977, “Measurement of the Thermal Properties of Human Skin. A Review
,” J. Invest. Dermatol.
0022-202X, 69
(3
), pp. 333
–338
.72.
Duck
, F. A.
, 1990, Physical Properties of Tissue: A Comprehensive Reference Book
, Academic
, New York
.73.
Chato
, J. C.
, 1987, “Thermal Properties of Tissues
,” Handbook of Bioengineering
, R.
Skalak
and S.
Chien
, eds., McGraw-Hill
, New York
.74.
Bowman
, H. F.
, Cravalho
, E. G.
, and Woods
, M.
, 1975, “Theory, Measurement, and Application of Thermal Properties of Biomaterials
,” Annu. Rev. Biophys. Bioeng.
0084-6589, 4
, pp. 43
–80
.75.
Cooper
, T. E.
, and Trezck
, G. J.
, 1971, “Correlation of Thermal Properties of Some Human Tissues With Water Content
,” Aerosp. Med.
0001-9402, 42
, pp. 24
–27
.76.
Draper
, J. W.
, and Boag
, J. W.
, 1971, “The Calculation of Skin Temperature Distributions in Thermography
,” Phys. Med. Biol.
0031-9155, 16
(2
), pp. 201
–211
.77.
Draper
, J. W.
, and Boag
, J. W.
, 1971, “Skin Temperature Distributions Over Veins and Tumours
,” Phys. Med. Biol.
0031-9155, 16
(4
), pp. 645
–654
.78.
Nilsson
, S. K.
, 1975, “Skin Temperature Over an Artificial Heat Source Implanted in Man
,” Phys. Med. Biol.
0031-9155, 20
(3
), pp. 366
–383
.79.
Nilsson
, S. K.
, and Gustafsson
, S. E.
, 1974, “Surface Temperature Over an Implanted Artificial Heat Source
,” Phys. Med. Biol.
0031-9155, 19
(5
), pp. 677
–691
.80.
Gustafsson
, S. E.
, Nilsson
, S. K.
, and Torell
, L. M.
, 1975, “Analytical Calculation of the Skin Temperature Distribution Due to Subcutaneous Heat Production in a Spherical Heat Source
,” Phys. Med. Biol.
0031-9155, 20
(2
), pp. 219
–224
.81.
Tabern
, D. L.
, Kearney
, I.
, and Dolbow
, A.
, 1966, “Experimental Studies on Thermal Measurements Over Animal and Human Tumors
,” Surgery (St. Louis)
0039-6060, 60
, pp. 1058
–1065
.82.
Lawson
, R. N.
, 1956, “Implications of Surface Temperatures in the Diagnosis of Breast Cancer
,” Can. Med. Assoc. J.
0008-4409, 75
, pp. 309
–310
.83.
Ng
, E. Y. K.
, and Sudharsan
, N. M.
, 2001, “Effect of Blood Flow, Tumour and Cold Stress in a Female Breast: A Novel Time-Accurate Computer Simulation
,” Proc. Inst. Mech. Eng., Part H: J. Eng. Med.
0954-4119, 215
(4
), pp. 393
–404
.84.
Cui
, Z. F.
, and Barbenel
, J. C.
, 1991, “The Influence of Model Parameter Values on the Prediction of Skin Surface Temperature: II. Contact Problems
,” Phys. Med. Biol.
0031-9155, 36
(12
), pp. 1607
–1620
.85.
Hodson
, D. A.
, Barbenel
, J. C.
, and Eason
, G.
, 1989, “Modelling Transient Heat Transfer Through the Skin and a Contact Material
,” Phys. Med. Biol.
0031-9155, 34
(10
), pp. 1493
–1507
.86.
Stoll
, A. M.
, Chianta
, M. A.
, and Piergallini
, J. R.
, 1982, “Prediction of Threshold Pain Skin Temperature From Thermal Properties of Materials in Contact
,” Aviat., Space Environ. Med.
0095-6562, 53
(12
), pp. 1220
–1223
.87.
Wang
, Y. M.
, Wang
, B. X.
, and Cai
, W. M.
, 1995, Temperature Response of Living Tissue Contacting a Cold Material
, ASME
, New York, NY
, pp. 125
–130
.88.
Chen
, F.
, Nilsson
, H.
, and Holmer
, I.
, 1994, “Cooling Responses of Finger in Contact With an Aluminum Surface
,” Am. Ind. Hyg. Assoc. J.
0002-8894, 55
(3
), pp. 218
–222
.89.
Stewart
, D. A.
, Gowrishankar
, T. R.
, and Weaver
, J. C.
, 2006, “Skin Heating and Injury by Prolonged Millimeter-Wave Exposure: Theory Based on a Skin Model Coupled to a Whole Body Model and Local Biochemical Release From Cells at Supraphysiologic Temperatures
,” IEEE Trans. Plasma Sci.
0093-3813, 34
(4
), pp. 1480
–1493
.90.
Stec
, B.
, Dobrowolski
, A.
, and Susek
, W.
, 2004, Multifrequency Microwave Thermograph for Oncological Applications
, Institute of Electrical and Electronics Engineers Inc.
, New York
, pp. 603
–606
.91.
Weiss
, R. A.
, Weiss
, M. A.
, Munavalli
, G.
, and Beasley
, K. L.
, 2006, “Monopolar Radiofrequency Facial Tightening: A Retrospective Analysis of Efficacy and Safety in Over 600 Treatments
,” J. Drugs Dermatol.
, 5
(8
), pp. 707
–712
. 1545-961692.
Sadick
, N. S.
, and Shaoul
, J.
, 2004, “Hair Removal Using a Combination of Conducted Radiofrequency and Optical Energies—An 18-Month Follow-Up
,” J. Cosmet. Laser Ther.
, 6
(1
), pp. 21
–26
. 1476-417293.
Goldberg
, D. J.
, 2007, “Laser- and Light-Based Hair Removal: An Update
,” Expert Rev. Med. Devices
, 4
(2
), pp. 253
–260
. 1743-444094.
Bernstein
, E. F.
, 2007, “The New-Generation, High-Energy, 595 nm, Long Pulse-Duration, Pulsed-Dye Laser Effectively Removes Spider Veins of the Lower Extremity
,” Lasers Surg. Med.
0196-8092, 39
(3
), pp. 218
–224
.95.
Tay
, Y. K.
, Kwok
, C.
, and Tan
, E.
, 2006, “Non-Ablative 1,450-nm Diode Laser Treatment of Striae Distensae
,” Lasers Surg. Med.
0196-8092, 38
(3
), pp. 196
–199
.96.
Pennes
, H. H.
, 1948, “Analysis of Tissue and Arterial Blood Temperatures in the Resting Human Forearm
,” J. Appl. Physiol.
8750-7587, 1
, pp. 93
–122
.97.
Lubashevsky
, I. A.
, and Gafiychuk
, V. V.
, 2004, “Mathematical Description of the Heat Transfer in Living Tissue (Part I)
,” Report No. adap-org/9911001.98.
Charny
, C. K.
, 1992, “Mathematical Models of Bioheat Transfer
,” Adv. Heat Transfer
0065-2717, 22
, pp. 19
–155
.99.
Arkin
, H.
, Xu
, L. X.
, and Holmes
, K. R.
, 1994, “Recent Developments in Modeling Heat Transfer in Blood Perfused Tissues
,” IEEE Trans. Biomed. Eng.
0018-9294, 41
(2
), pp. 97
–107
.100.
Crezee
, J.
, Mooibroek
, J.
, Lagendijk
, J. J.
, and van Leeuwen
, G. M.
, 1994, “The Theoretical and Experimental Evaluation of the Heat Balance in Perfused Tissue
,” Phys. Med. Biol.
0031-9155, 39
(5
), pp. 813
–832
.101.
Stanczyk
, M.
, and Telega
, J. J.
, 2002, “Modelling of Heat Transfer in Biomechanics—A Review. Part I. Soft Tissues
,” Acta Bioeng. Biomech.
, 4
(1
), pp. 31
–61
. 1509-409X102.
Khaled
, A. R. A.
, and Vafai
, K.
, 2003, “The Role of Porous Media in Modeling Flow and Heat Transfer in Biological Tissues
,” Int. J. Heat Mass Transfer
0017-9310, 46
(26
), pp. 4989
–5003
.103.
Song
, W. J.
, Weinbaum
, S.
, Jiji
, L. M.
, and Lemons
, D.
, 1988, “A Combined Macro and Microvascular Model for Whole Limb Heat Transfer
,” ASME J. Biomech. Eng.
0148-0731, 110
(4
), pp. 259
–268
.104.
Abramson
, D. I.
, 1967, Circulation in the Extremities
, Academic
, New York
.105.
Chato
, J. C.
, 1980, “Heat Transfer to Blood Vessels
,” ASME J. Biomech. Eng.
0148-0731, 102
(2
), pp. 110
–118
.106.
Weinbaum
, S.
, Jiji
, L. M.
, and Lemons
, D. E.
, 1984, “Theory and Experiment for the Effect of Vascular Microstructure on Surface Tissue Heat Transfer-Part I: Anatomical Foundation and Model Conceptualization
,” ASME J. Biomech. Eng.
0148-0731, 106
(4
), pp. 321
–330
.107.
Lemons
, D. E.
, Chien
, S.
, Crawshaw
, L. I.
, Weinbaum
, S.
, and Jiji
, L. M.
, 1987, “Significance of Vessel Size and Type in Vascular Heat Transfer
,” Am. J. Physiol.
0002-9513, 253
(1
), pp. R128
–135
.108.
Mescon
, H.
, Hurley
, H. J.
, and Moretti
, G.
, 1956, “The Anatomy and Histochemistry of the Arteriovenous Anastomoses in Human Digital Skin
,” J. Invest. Dermatol.
0022-202X, 27
, pp. 133
–145
.109.
Sherman
, J. L.
, 1963, “Normal Arteriovenous Anastomoses
,” Medicine (Baltimore)
0025-7974, 42
, pp. 247
–267
.110.
Braverman
, I. M.
, and Yen
, A.
, 1977, “Ultrastructure of the Human Dermal Microcirculation. II. The Capillary Loops of the Dermal Papillae
,” J. Invest. Dermatol.
0022-202X, 68
(1
), pp. 44
–52
.111.
Chen
, M. M.
, and Holmes
, K. R.
, 1980, “Microvascular Contributions in Tissue Heat Transfer
,” Ann. N.Y. Acad. Sci.
0077-8923, 335
, pp. 137
–150
.112.
Lagendijk
, J. J.
, Schellekens
, M.
, Schipper
, J.
, and van der Linden
, P. M.
, 1984, “A Three-Dimensional Description of Heating Patterns in Vascularised Tissues During Hyperthermic Treatment
,” Phys. Med. Biol.
0031-9155, 29
(5
), pp. 495
–507
.113.
Baish
, J. W.
, Ayyaswamy
, P. S.
, and Foster
, K. R.
, 1986, “Heat Transport Mechanisms in Vascular Tissues: A Model Comparison
,” ASME J. Biomech. Eng.
0148-0731, 108
(4
), pp. 324
–331
.114.
Mooibroek
, J.
, and Lagendijk
, J. J.
, 1991, “A Fast and Simple Algorithm for the Calculation of Convective Heat Transfer by Large Vessels in Three-Dimensional Inhomogenous Tissues
,” IEEE Trans. Biomed. Eng.
0018-9294, 38
, pp. 490
–501
.115.
Crezee
, J.
, and Lagendijk
, J. J.
, 1992, “Temperature Uniformity During Hyperthermia: The Impact of Large Vessels
,” Phys. Med. Biol.
0031-9155, 37
, pp. 1321
–1337
.116.
Li
, H.
, Zhang
, X.
, and Liu
, J.
, 2002, “Heat Transfer Analysis on Laser-Tissue Thermal Interaction Using Heterogeneous Model
,” Chin. J. Lasers
0258-7025, A29
(5
), pp. 465
–470
.117.
Hand
, J. W.
, Ledda
, J. L.
, and Evans
, N. T.
, 1982, “Considerations of Radiofrequency Induction Heating for Localised Hyperthermia
,” Phys. Med. Biol.
0031-9155, 27
(1
), pp. 1
–16
.118.
Sanyal
, D. C.
, and Maji
, N. K.
, 2001, “Thermoregulation Through Skin Under Variable Atmospheric and Physiological Conditions
,” J. Theor. Biol.
0022-5193, 208
, pp. 451
–456
.119.
Gowrishankar
, T. R.
, Stewart
, D. A.
, Martin
, G. T.
, and Weaver
, J. C.
, 2004, “Transport Lattice Models of Heat Transport in Skin With Spatially Heterogeneous, Temperature-Dependent Perfusion
,” Biomed. Eng. Online
1475-925X, 3
(1/42
), pp. 1
–17
.120.
Erdmann
, B.
, Lang
, J.
, and Seebass
, M.
, 1998, “Optimization of Temperature Distributions for Regional Hyperthermia Based on a Nonlinear Heat Transfer Model
,” Ann. N.Y. Acad. Sci.
0077-8923, 858
, pp. 36
–46
.121.
Davies
, C. R.
, Saidel
, G. M.
, and Harasaki
, H.
, 1997, “Sensitivity Analysis of One-Dimensional Heat Transfer in Tissue With Temperature-Dependent Perfusion
,” ASME J. Biomech. Eng.
0148-0731, 119
(1
), pp. 77
–80
.122.
Utoh
, J.
, and Harasaki
, H.
, 1992, “Prolonged Heat Effects on Human Erythrocytes
,” Clin. Sci.
0323-5084, 12
, pp. 707
–714
.123.
Song
, C. W.
, 1984, “Effect of Local Hyperthermia on Blood Flow and Microenvironment: A Review
,” Cancer Res.
0008-5472, 44
, pp. 4721S
–4730S
.124.
Sekins
, K. M.
, Lehmann
, J. F.
, Esselmann
, P.
, Dundore
, D.
, Emery
, A. F.
, de Lateur
, B. J.
, and Nelp
, W. B.
, 1984, “Local Muscle Blood Flow and Temperature Responses to 915 MHz Diathermy as Simultaneously Measured and Numerically Predicted
,” Arch. Phys. Med. Rehabil.
0003-9993, 65
, pp. 1
–7
.125.
Rai
, K. N.
, and Rai
, S. K.
, 1999, “Heat Transfer Inside the Tissues With a Supplying Vessel for the Case When Metabolic Heat Generation and Blood Perfusion are Temperature Dependent
,” Heat Mass Transfer
0947-7411, 35
(4
), pp. 345
–350
.126.
London
, R. A.
, Glinsky
, M. E.
, Zimmerman
, G. B.
, Bailey
, D. S.
, Eder
, D. C.
, and Jacques
, S. L.
, 1997, “Laser-Tissue Interaction Modeling With LATIS
,” Appl. Opt.
0003-6935, 36
(34
), pp. 9068
–9074
.127.
Ma
, N.
, Gao
, X.
, and Zhang
, X. X.
, 2004, “Two-Layer Simulation Model of Laser-Induced Interstitial Thermo-Therapy
,” Lasers Med. Sci.
0268-8921, 18
, pp. 184
–189
.128.
Patterson
, A. M.
, 1976, An Analytical Model of Steady-State Heat Flow Through the Superficial Tissues of the Forearm
, University of the Witwatersrand
, Johannesburg
.129.
Hodson
, D. A.
, Eason
, G.
, and Barbenel
, J. C.
, 1986, “Modeling Transient Heat Transfer Through the Skin and Superficial Tissues—1: Surface Insulation
,” ASME J. Biomech. Eng.
0148-0731, 108
(2
), pp. 183
–188
.130.
Wilson
, S. B.
, and Spence
, V. A.
, 1988, “A Tissue Heat Transfer Model for Relating Dynamic Skin Temperature Changes to Physiological Parameters
,” Phys. Med. Biol.
0031-9155, 33
(8
), pp. 895
–912
.131.
Deng
, Z. S.
, and Liu
, J.
, 2004, “Mathematical Modeling of Temperature Mapping Over Skin Surface and Its Implementation in Thermal Disease Diagnostics
,” Comput. Biol. Med.
0010-4825, 34
(6
), pp. 495
–521
.132.
Guyton
, A. C.
, 1976, Medical Physiology
, Saunders
, London
.133.
Mahanty
, S. D.
, and Roemer
, R. B.
, 1979, “The Effect of Pressure on Skin Temperature Measurements for a Disc Sensor
,” ASME J. Biomech. Eng.
0148-0731, 101
, pp. 261
–266
.134.
Mahanty
, S. D.
, and Roemer
, R. B.
, 1980, “Thermal and Circulatory Response to Localized Pressure Application: A Mathematical Model
,” Arch. Phys. Med. Rehabil.
0003-9993, 61
, pp. 335
–340
.135.
Timoshenko
, D. A.
, Timoshenko
, D. D.
, and Golovushkin
, A. A.
, 2002, “Mathematical Simulation of Heat-Induced Effects on Human Skin Surface
,” Biomed. Eng. Online
1475-925X, 36
(1
), pp. 19
–22
.136.
Vendrik
, A. J. H.
, and Vos
, J. J.
, 1957, “A Method for the Measurement of the Thermal Conductivity of Human Skin
,” J. Appl. Physiol.
8750-7587, 11
, pp. 211
–215
.137.
Shen
, G.
, and Xie
, S.
, 2002, “Theoretical Analysis and Numerical Simulation of Temperature Distribution for Laser-Irradiated Skin Tissue
,” Journal of Fujian Teachers University (Natural Science)
, 18
(4
), pp. 26
–29
.138.
Shen
, W.
, Zhang
, J.
, and Yang
, F.
, 2005, “Three-Dimensional Model on Thermal Response of Skin Subject to Laser Heating
,” Comput. Methods Biomech. Biomed. Eng.
1025-5842, 8
(2
), pp. 115
–125
.139.
Özen
, S.
, Çerezci
, O.
, Çömlekçi
, S.
, and Demir
, Z.
, 2002, “Heat Effect Analysis of Microwave Exposed Skin by Using a Multilayer Human Skin Model
,” Bioeffects of EMFS, Second International Workshop
, Rhobes, Greece.140.
Panescu
, D.
, Webster
, J. G.
, and Stratbucker
, R. A.
, 1994, “A Nonlinear Finite Element Model of the Electrode-Electrolyte-Skin System
,” IEEE Trans. Biomed. Eng.
0018-9294, 41
(7
), pp. 681
–687
.141.
van Gemert
, M. J.
, Jacques
, S. L.
, Sterenborg
, H. J.
, and Star
, W. M.
, 1989, “Skin Optics
,” IEEE Trans. Biomed. Eng.
0018-9294, 36
(12
), pp. 1146
–1154
.142.
Welch
, A. J.
, Pearce
, J. A.
, Diller
, K. R.
, Yoon
, G.
, and Cheong
, W. F.
, 1989, “Heat Generation in Laser Irradiated Tissue
,” ASME J. Biomech. Eng.
0148-0731, 111
(1
), pp. 62
–68
.143.
El-dabe
, N. T. M.
, Mohamed
, M. A. A.
, and El-Sayed
, A. F.
, 2003, “Effects of Microwave Heating on the Thermal States of Biological Tissues
,” Afr. J. Biotechnol.
, 2
(11
), pp. 453
–459
. 1684-5315144.
Trembly
, B. S.
, 1985, “The Effects of Driving Frequency and Antenna Length on Power Deposition Within a Microwave Antenna Array Used for Hyperthermia
,” IEEE Trans. Biomed. Eng.
0018-9294, BME-32
(2
), pp. 152
–157
.145.
Balanis
, C. A.
, 1989, Advanced Engineering Electromagnetics
, Wiley
, New York
.146.
Torell
, L. M.
, and Nilsson
, S. K.
, 1980, “Calculation of Skin Temperature Increase Caused by Subcutaneous Veins Perpendicular to the Skin Surface
,” Phys. Med. Biol.
0031-9155, 25
(1
), pp. 85
–91
.147.
Pal
, D. S.
, and Pal
, S.
, 1990, “Prediction of Temperature Profiles in the Human Skin and Subcutaneous Tissues
,” J. Math. Biol.
0303-6812, 28
(3
), pp. 355
–364
.148.
Deng
, Z. S.
, and Liu
, J.
, 2002, “Analytical Study on Bioheat Transfer Problems With Spatial or Transient Heating on Skin Surface or Inside Biological Bodies
,” ASME J. Biomech. Eng.
0148-0731, 124
(6
), pp. 638
–649
.149.
Ng
, E. Y. K.
, and Ng
, W. K.
, 2006, “Parametric Optimisation of the Biopotential Equation for Breast Tumour Idendification Using ANOVA and Taguchi Method
,” Med. Biol. Eng. Comput.
0140-0118, 44
(1-2
), pp. 131
–139
.150.
Sudharsan
, N. M.
, and Ng
, E. Y. K.
, 2000, “Parametric Optimisation for Tumour Identification: Bioheat Equation Using ANOVA & Taguchi Method
,” Proc. Inst. Mech. Eng., Part H: J. Eng. Med.
0954-4119, 214
(5
), pp. 505
–512
.151.
Cai
, R.
, 1995, “Analytical Solution of Unsteady One-Dimensional Bioheat Transfer Equation
,” Chin. Sci. Bull.
1001-6538, 40
(19
), p. 1663
.152.
Steketee
, J.
, and Van Der Hoek
, M. J.
, 1979, “Thermal Recovery of the Skin After Cooling
,” Phys. Med. Biol.
0031-9155, 24
(3
), pp. 583
–592
.153.
Nyborg
, W. L.
, 1988, “Solutions of the Bio-Heat Transfer Equation
,” Phys. Med. Biol.
0031-9155, 33
(7
), pp. 785
–792
.154.
Durkee
, J. W.
, Jr., Antich
, P. P.
, and Lee
, C. E.
, 1990, “Exact Solutions to the Multiregion Time-Dependent Bioheat Equation. II: Numerical Evaluation of the Solutions
,” Phys. Med. Biol.
0031-9155, 35
(7
), pp. 869
–889
.155.
Durkee
, J. W.
, Jr., Antich
, P. P.
, and Lee
, C. E.
, 1990, “Exact Solutions to the Multiregion Time-Dependent Bioheat Equation. I: Solution Development
,” Phys. Med. Biol.
0031-9155, 35
(7
), pp. 847
–867
.156.
Durkee
, J. W.
, Jr., and Antich
, P. P.
, 1991, “Characterization of Bioheat Transport Using Exact Solution to the Cylindrical Geometry, Multiregion, Time-Dependent Bioheat Equation
,” Phys. Med. Biol.
0031-9155, 36
, pp. 1377
–1406
.157.
Ozisik
, M. N.
, 1993, Heat Conduction
, Wiley
, New York
.158.
Gordon
, R. G.
, Roemer
, R. B.
, and Howath
, S. M.
, 1976, “A Mathematical Model of the Human Temperature Regulatory System—Transient Cold Exposure Responses
,” IEEE Trans. Biomed. Eng.
0018-9294, BME-23
(6
), pp. 434
–444
.159.
Aschoff
, J.
, and Wever
, R.
, 1959, “Anisotropy of the Skin for Heat Transfer
,” Pfluegers Arch. Gesamte Physiol. Menschen Tiere
0365-267X, 269
, pp. 130
–134
.160.
Vermey
, G. F.
, 1975, “The Simulation of Skin Temperature Distributions by Means of a Relaxation Method
,” Phys. Med. Biol.
0031-9155, 20
(3
), pp. 384
–394
.161.
Jiji
, L. M.
, Weinbaum
, S.
, and Lemons
, D. E.
, 1984, “Theory and Experiment for the Effect of Vascular Microstructure on Surface Tissue Heat Transfer—Part II: Model Formulation and Solution
,” ASME J. Biomech. Eng.
0148-0731, 106
(4
), pp. 331
–341
.162.
Weinbaum
, S.
, and Jiji
, L. M.
, 1984, A New Simplified Bioheat Equation for the Effect of Blood Flow on Local Average Tissue Temperature
, ASME
, New York
, p. 8
.163.
Xie
, S.
, Yang
, H.
, and Li
, B.
, 2001, “Optical-Thermal Interaction of Laser-Irradiated Layered Skin Tissue and Its Heat Transfer Model
,” J. Optoelectron., Laser
1005-0086, 12
(7
), pp. 746
–750
.164.
Dai
, T.
, Pikkula
, B. M.
, Wang
, L. V.
, and Anvari
, B.
, 2004, A Theoretical Investigation of Human Skin Thermal Response to Near-Infrared Laser Irradiation
, International Society for Optical Engineering
, Bellingham, WA
, pp. 7
–12
.165.
Saxena
, V. P.
, 1983, “Temperature Distribution in Human Skin and Subdermal Tissues
,” J. Theor. Biol.
0022-5193, 102
(2
), pp. 277
–286
.166.
Diller
, K. R.
, and Hayes
, L. J.
, 1983, “A Finite Element Model of Burn Injury in Blood-Perfused Skin
,” ASME J. Biomech. Eng.
0148-0731, 105
(3
), pp. 300
–307
.167.
Cui
, Z. F.
, and Barbenel
, J. C.
, 1990, “The Influence of Model Parameter Values on the Prediction of Skin Surface Temperature: I. Resting and Surface Insulation
,” Phys. Med. Biol.
0031-9155, 35
(12
), pp. 1683
–1697
.168.
Diller
, K. R.
, and Hayes
, L. J.
, 1991, “Analysis of Tissue Injury by Burning. Comparison of In Situ and Skin Flap Models
,” Int. J. Heat Mass Transfer
0017-9310, 34
(6
), pp. 1393
–1406
.169.
Torvi
, D. A.
, and Dale
, J. D.
, 1994, “A Finite Element Model of Skin Subjected to a Flash Fire
,” ASME J. Biomech. Eng.
0148-0731, 116
(3
), pp. 250
–255
.170.
Liu
, J.
, and Wang
, C.
, 1997, Bioheat Transfer
, Science
, Beijing
.171.
Enalejev
, R. S.
, and Kachalkin
, W. A.
, 1998, “Mathematical Simulation of Heat Transfer Process in Skin Cover at Burn Injury
,” Burn Injury
, 858
, pp. 30
–35
.172.
Liu
, J.
, 2000, “Preliminary Survey on the Mechanisms of the Wave-Like Behaviors of Heat Transfer in Living Tissues
,” Forsch. Ingenieurwes.
0015-7899, 66
(1
), pp. 1
–10
.173.
Liu
, J.
, Chen
, X.
, and Xu
, L. X.
, 1999, “New Thermal Wave Aspects on Burn Evaluation of Skin Subjected to Instantaneous Heating
,” IEEE Trans. Biomed. Eng.
0018-9294, 46
(4
), pp. 420
–428
.174.
Ng
, E. Y. K.
, and Chua
, L. T.
, 2000, “Mesh-Independent Prediction of Skin Burns Injury
,” J. Med. Eng. Technol.
0309-1902, 24
(6
), pp. 255
–261
.175.
Ng
, E. Y. K.
, and Chua
, L. T.
, 2002, “Prediction of Skin Burn Injury. Part 2: Parametric and Sensitivity Analysis
,” Proc. Inst. Mech. Eng., Part H: J. Eng. Med.
0954-4119, 216
(3
), pp. 171
–183
.176.
Ng
, E. Y. K.
, and Chua
, L. T.
, 2002, “Prediction of Skin Burn Injury. Part 1: Numerical Modelling
,” Proc. Inst. Mech. Eng., Part H: J. Eng. Med.
0954-4119, 216
(3
), pp. 157
–170
.177.
Ng
, E. Y. K.
, and Chua
, L. T.
, 2002, “Comparison of One- and Two-Dimensional Programmes for Predicting the State of Skin Burns
,” Burns
0305-4179, 28
(1
), pp. 27
–34
.178.
Majchrzak
, E.
, and Jasinski
, M.
, 2001, “Sensitivity of Burn Prediction to Variations in Thermophysical Properties of Skin
,” Joint Meeting of International Association for Boundary Element Methods and International Conference on Boundary Element Techniques
, New Brunswick, NJ.179.
Dai
, W.
, Nassar
, R.
, and Zhang
, J.
, 2002, A Three Level Finite Difference Scheme for Solving the Pennes’s Bioheat Transfer in a Triple-Layered Skin Structure
, University of Kentucky
, Lexington, KY
.180.
Jiang
, S.
, Ma
, N.
, Li
, X.
, and Zhang
, X. X.
, 2002, “Effects of Thermal Properties and Geometrical Dimensions on Skin Burn Injuries
,” Burns
0305-4179, 28
, pp. 713
–717
.181.
Jiang
, S.
, Ma
, N.
, Wang
, S.
, and Zhang
, X.
, 2003, “Analysis of Heat Transfer and Prediction of Skin Burn Subjected to a Hot Water Film
,” Space Med. Med. Eng. (Beijing)
, 16
(6
), pp. 400
–404
. 1002-0837182.
Jiang
, S. C.
, Li
, H. J.
, Ma
, N.
, and Zhang
, X. X.
, 2003, “Analysis of Heat Transfer in Skin Tissues Subjected to Hot Water
,” Space Med. Med. Eng. (Beijing)
, 16
(1
), pp. 44
–47
.183.
Ma
, N.
, Jiang
, S.
, Li
, H.
, and Zhang
, X.
, 2003, “Analysis of Non-Flourier Effect and Laser-Induced Thermal Damage of Laser-Irradiated Layered Human Skin Tissue
,” Space Med. Med. Eng. (Beijing)
, 16
(2
), pp. 133
–137
. 1002-0837184.
Andersen
, T. N.
, Jessen
, N. -C.
, and Arendt-Nielsen
, L.
, 2000, “Determination of the Temperature Distribution in Skin Using a Finite Element Model
,” Laser-Tissue Interaction XI: Photochemical, Photothermal, and Photomechanical
, SPIE
, San Jose, CA
, pp. 54
–65
.185.
Gustrau
, F.
, and Bahr
, A.
, 2002, “W-Band Investigation of Material Parameters, SAR Distribution, and Thermal Response in Human Tissue
,” IEEE Trans. Microwave Theory Tech.
0018-9480, 50
(10
), pp. 2393
–2400
.186.
Saxena
, V. P.
, and Arya
, D.
, 1981, “Steady-State Heat Distribution in Epidermis, Dermis and Subdermal Tissues
,” J. Theor. Biol.
0022-5193, 89
(3
), pp. 423
–432
.187.
Diller
, K. R.
, Hayes
, L. J.
, and Baxter
, C. R.
, 1983, “A Mathematical Model for the Thermal Efficiency of Cooling Therapy for Burns
,” J. Burn Care Rehabil.
0273-8481, 4
, pp. 81
–89
.188.
Ng
, E. Y. K.
, Ooi
, E. H.
, Xu
, F.
, Tan
, H. M.
, and Lu
, T. J.
, 2009, “Prediction and Parametric Analysis of Thermal Profiles Within Heated Human Skin Using Boundary Element Method
,” in press.189.
Keller
, K. H.
, and Seiler
, L.
, 1971, “An Analysis of Peripheral Heat Transfer in Man
,” J. Appl. Physiol.
8750-7587, 30
, pp. 779
–786
.190.
Geng
, Q.
, Holmer
, I.
, and Coldsurf Research Group
, 2001, “Change in Contact Temperature of Finger Touching on Cold Surfaces
,” Int. J. Ind. Ergonom.
0169-8141, 27
, pp. 387
–391
.191.
Peshkov
, V.
, 1944, “Second Sound in Helium II
,” J. Phys. (Moscow)
0368-3400, 8
, pp. 381
–383
.192.
Ackerman
, C. C.
, Bertman
, B.
, Fairbank
, H. A.
, and Guyer
, R. A.
, 1966, “Second Sound in Solid Helium
,” Phys. Rev. Lett.
0031-9007, 16
(18
), pp. 789
.193.
Von Gutfeld
, R. J.
, and Nethercot
, A. H.
, 1966, “Temperature Dependence of Heat-Pulse Propagation in Sapphire
,” Phys. Rev. Lett.
0031-9007, 17
, pp. 868
–871
.194.
Von Gutfeld
, R. J.
, 1968, Physical Acoustic
, Academic
, New York
.195.
Brown
, J. B.
, Chung
, D. Y.
, and Matthews
, P. W.
, 1966, “Heat Pulses at Low Temperatures
,” Phys. Lett.
0370-2693, 21
, pp. 241
–242
.196.
Ackerman
, C. C.
, and Guyer
, R. A.
, 1968, “Temperature Pulses in Dielectric Solids
,” Ann. Phys.
0003-3804, 50
, pp. 128
–185
.197.
McNelly
, T. F.
, Rogers
, S. J.
, Channin
, D. J.
, Rollefson
, R. J.
, Goubau
, W. M.
, Schmidt
, G. E.
, Krumhansl
, J. A.
, and Pohl
, R. O.
, 1970, “Heat Pulses in NaF: Onset of Second Sound
,” Phys. Rev. Lett.
0031-9007, 24
, pp. 100
–102
.198.
Jackson
, H. E.
, Walker
, C. T.
, and McNelly
, T. F.
, 1970, “Second Sound in NaF
,” Phys. Rev. Lett.
0031-9007, 25
, pp. 26
–28
.199.
Jackson
, H. E.
, and Walker
, C. T.
, 1971, “Thermal Conductivity, Second Sound and Phonon-Phonon Interactions in NaF
,” Phys. Rev. B
0556-2805, 3
, pp. 1428
–1439
.200.
Rogers
, S.
, 1971, “Transport of Heat and Approach to Second Sound in Some Isotropically Pure Alkalishalide Crystals
,” Phys. Rev. B
0556-2805, 3
, pp. 1440
–1457
.201.
Glass
, D. E.
, Ozisik
, M. N.
, and Vick
, B.
, 1985, “Hyperbolic Heat Conduction With Surface Radiation
,” Int. J. Heat Mass Transfer
0017-9310, 28
(10
), pp. 1823
–1830
.202.
Brorson
, S. D.
, Fujimoto
, J. G.
, and Ippen
, E. P.
, 1987, “Femtosecond Electronic Heat Transfer Dynamics in Thin Gold Film
,” Phys. Rev. Lett.
0031-9007, 59
, pp. 1962
–1965
.203.
Yang
, H. Q.
, 1991, “Non-Fourier Effect on Heat Conduction During Welding
,” Int. J. Heat Mass Transfer
0017-9310, 34
(11
), pp. 2921
–2924
.204.
Li
, J. D.
, 1992, Reduction of Core Loss in Silicon Steel Sheets by Laser Processing
, Tsinghua University
, China
.205.
Qiu
, T. Q.
, and Tien
, C. L.
, 1992, “Short-Pulse Laser Heating on Metals
,” Int. J. Heat Mass Transfer
0017-9310, 35
(3
), pp. 719
–726
.206.
Qiu
, T. Q.
, and Tien
, C. L.
, 1993, “Heat Transfer Mechanisms During Short-Pulse Laser Heating of Metals
,” ASME J. Heat Transfer
0022-1481, 115
(4
), pp. 835
–841
.207.
Banerjee
, A.
, Ogale
, A. A.
, Das
, C.
, Mitra
, K.
, and Subramanian
, C.
, 2005, “Temperature Distribution in Different Materials Due to Short Pulse Laser Irradiation
,” Heat Transfer Eng.
0145-7632, 26
(8
), pp. 41
–49
.208.
Kaminski
, W.
, 1990, “Hyperbolic Heat Conduction Equation for Materials With a Nonhomogeneous Inner Structure
,” ASME J. Heat Transfer
0022-1481, 112
(3
), pp. 555
–560
.209.
Richardson
, A. W.
, Imig
, C. G.
, Feucht
, B. L.
, and Hines
, H. M.
, 1950, “Relationship Between Deep Tissue Temperature and Blood Flow During Electromagnetic Irradiation
,” Arch. Phys. Med. Rehabil.
0003-9993, 31
, pp. 19
–25
.210.
Roemer
, R. B.
, Oleson
, J. R.
, and Cetas
, T. C.
, 1985, “Oscillatory Temperature Response to Constant Power Applied to Canine Muscle
,” Am. J. Physiol.
0002-9513, 249
(2
), pp. R153
–R158
.211.
Mitra
, K.
, Kumar
, S.
, Vedavarz
, A.
, and Moallemi
, M. K.
, 1995, “Experimental Evidence of Hyperbolic Heat Conduction in Processed Meat
,” ASME J. Heat Transfer
0022-1481, 117
(3
), pp. 568
–573
.212.
Graßmann
, A.
, and Peters
, F.
, 1999, “Experimental Investigation of Heat Conduction in Wet Sand
,” Heat Mass Transfer
0947-7411, 35
(4
), pp. 289
–294
.213.
Herwig
, H.
, and Beckert
, K.
, 2000, “Experimental Evidence About the Controversy Concerning Fourier or Non-Fourier Heat Conduction in Materials With a Nonhomogeneous Inner Structure
,” Heat Mass Transfer
0947-7411, 36
(5
), pp. 387
–392
.214.
Herwig
, H.
, and Beckert
, K.
, 2000, “Fourier Versus Non-Fourier Heat Conduction in Materials With a Nonhomogeneous Inner Structure
,” ASME J. Heat Transfer
0022-1481, 122
(2
), pp. 363
–365
.215.
Roetzel
, W.
, Putra
, N.
, and Das
, S. K.
, 2003, “Experiment and Analysis for Non-Fourier Conduction in Materials With Non-Homogeneous Inner Structure
,” Int. J. Therm. Sci.
1290-0729, 42
(6
), pp. 541
–552
.216.
Davydov
, E. V.
, Lubashevsky
, I. A.
, Milyaev
, V. A.
, and Musin
, R. F.
, 2001, “Nondiffusive Heat Transfer in Muscle Tissue. Preliminary Results
,” e-print arXiv:cond-mat/0102006.217.
Liu
, J.
, Ren
, Z. P.
, and Wang
, C. C.
, 1996, “Simulating Experimental Study on the Mechanisms of Temperature Oscillation in Living Tissue
,” Journal of Basic Science and Engineering
, 4
(2
), pp. 173
–182
.218.
Liu
, J.
, Wang
, C. C.
, and Ren
, Z. P.
, 1997, “Theory and Experiments on Temperature Oscillations Effects in Living Tissue
,” Journal of Tsinghua University (Sci & Tech)
, 2
, pp. 91
–95
.219.
Tilahun
, M.
, Scott
, E. P.
, and Vick
, B.
, 1999, The Question of Thermal Waves in Heterogeneous and Biological Materials
, ASME
, New York, BED-Vol. 44
, pp. 145
–152
.220.
Antaki
, P. J.
, 2005, “New Interpretation of Non-Fourier Heat Conduction in Processed Meat
,” ASME J. Heat Transfer
0022-1481, 127
(2
), pp. 189
–193
.221.
Xu
, L. X.
, and Liu
, J.
, 1998, “Discussion of Non-Equilibrium Heat Transfer in Biological Systems
,” Advances in Heat and Mass Transfer in Biotechnology
, Proceedings of the 1998 ASME International Mechanical Engineering Congress and Exposition
, ASME
, New York
, pp. 13
–17
.222.
Sekins
, K. M.
, Lehmann
, J. F.
, Esselman
, P.
, Dundore
, D.
, Emery
, A. F.
, Delateur
, B. J.
, and Nelp
, W. B.
, 1984, “Local Muscle Blood Flow and Temperature Responses to 915 MHz Diathermy as Simultaneously Measured and Numerically Predicted
,” Arch. Phys. Med. Rehabil.
0003-9993, 65
, pp. 1
–7
.223.
Song
, C. W.
, Lokshina
, A.
, Rhee
, J. G.
, Patten
, M.
, and Levitt
, S. H.
, 1984, “Implication of Blood Flow in Hyperthermic Treatment of Tumors
,” IEEE Trans. Biomed. Eng.
0018-9294, BME-31
, pp. 9
–16
.224.
Akyurekli
, D.
, Gerig
, L. H.
, and Raaphorst
, G. P.
, 1997, “Changes in Muscle Blood Flow Distribution During Hyperthermia
,” Int. J. Hyperthermia
0265-6736, 13
, pp. 481
–496
.225.
Xu
, L. X.
, Zhu
, L.
, and Holmes
, K. R.
, 1998, “Thermoregulation in the Canine Prostate During Transurethral Microwave Hyperthermia, Part I: Temperature Response
,” Int. J. Hyperthermia
0265-6736, 14
, pp. 29
–37
.226.
Xu
, L. X.
, Zhu
, L.
, and Holmes
, K. R.
, 1998, “Thermoregulation in the Canine Prostate During Transurethral Microwave Hyperthermia, Part II: Blood Flow Response
,” Int. J. Hyperthermia
0265-6736, 14
, pp. 65
–73
.227.
Xu
, L. X.
, Zhu
, L.
, and Holmes
, K. R.
, 1998, “Blood Perfusion Measurements in the Canine Prostate During Transurethral Hyperthermia
,” Ann. N.Y. Acad. Sci.
0077-8923, 858
, pp. 21
–29
.228.
Zaerr
, J.
, Roemer
, R. B.
, and Hynynen
, K.
, 1990, “Computer Controlled Dynamic Phantom for Ultrasound Hyperthermia Studies
,” IEEE Trans. Biomed. Eng.
0018-9294, 37
, pp. 1115
–1120
.229.
Chen
, C.
, and Xu
, L. X.
, 2002, “Tissue Temperature Oscillations in an Isolated Pig Kidney During Surface Heating
,” Ann. Biomed. Eng.
0090-6964, 30
, pp. 1162
–1171
.230.
Tharp
, H. S.
, and Zhang
, W.
, 1993, “Analytical Study of Temperature Oscillations in Living Tissue
,” IEEE Trans. Biomed. Eng.
0018-9294, 40
(1
), pp. 108
–110
.231.
Deng
, Z. S.
, and Liu
, J.
, 2001, “Blood Perfusion-Based Model for Characterizing the Temperature Fluctuations in Living Tissue
,” Phys. A Stat Mech, Applicat.
, 300
(3-4
), pp. 521
–530
.232.
Chen
, C.
, and Roemer
, R. B.
, 2005, “A Thermo-Pharmacokinetic Model of Tissue Temperature Oscillations During Localized Heating
,” Int. J. Hyperthermia
0265-6736, 21
(2
), pp. 107
–124
.233.
Losev
, E. S.
, 1993, “Mathematical Simulation of Thermoregulation in Local Hyperthermia
,” Biofizika
0006-3029, 38
(5
), pp. 843
–848
.234.
Shih
, T. -C.
, Kou
, H. -S.
, Liauh
, C. -T.
, and Lin
, W. -L.
, 2005, “The Impact of Thermal Wave Characteristics on Thermal Dose Distribution During Thermal Therapy: A Numerical Study
,” Med. Phys.
0094-2405, 32
(9
), pp. 3029
–3036
.235.
Herivel
, J.
, 1980, Joseph Fourier: face aux objections contre sa theorie de la chaleur
, Bibliotheque Nationale
, Paris
.236.
Ozisik
, M. N.
, and Tzou
, D. Y.
, 1992, On the Wave Theory in Heat Conduction
, ASME
, New York
, pp. 13
–27
.237.
Vedavarz
, A.
, Kumar
, S.
, and Moallemi
, M. K.
, 1994, “Significance of Non-Fourier Heat Waves in Conduction
,” ASME J. Heat Transfer
0022-1481, 116
(1
), pp. 221
–224
.238.
Antaki
, P. J.
, 1998, “Importance of nonFourier Heat Conduction in Solid-Phase Reactions
,” Combust. Flame
0010-2180, 112
(3
), pp. 329
–341
.239.
Liu
, J.
, and Lu
, W. Q.
, 1997, “Dual Reciprocity Boundary Element Method for Solving Thermal Wave Model of Bioheat Transfer
,” Space Med. Med. Eng. (Beijing)
, 10
(6
), pp. 391
–395
. 1002-0837240.
Lu
, W. -Q.
, Liu
, J.
, and Zeng
, Y.
, 1998, “Simulation of the Thermal Wave Propagation in Biological Tissues by the Dual Reciprocity Boundary Element Method
,” Eng. Anal. Boundary Elem.
0955-7997, 22
(3
), pp. 167
–174
.241.
Lu
, W. -Q.
, Liu
, J.
, and Zeng
, Y.
, 1998, “Extension of the Dual Reciprocity Boundary Element Method to Simulate Thermal Wave Propagation in Biological Tissue
,” Journal of Engineering Thermophysics
, 19
(6
), pp. 728
–731
.242.
Morse
, P. M.
, and Feshbach
, H.
, 1953, Methods of Theoretical Physics
, McGraw-Hill
, New York
.243.
Cattaneo
, C.
, 1958, “A Form of Heat Conduction Equation Which Eliminates the Paradox of Instantaneous Propagation
,” Compt. Rend.
0001-4036, 247
, pp. 431
–433
.244.
Vernotte
, P.
, 1958, “Les paradoxes de la theorie continue de l’equation de la chaleur
,” Compt. Rend.
0001-4036, 246
, pp. 3154
–3155
.245.
Tzou
, D. Y.
, 1997, Macro- to Micro-Scale Heat Transfer: The Lagging Behavior
, Taylor & Francis
, Washington, DC
.246.
247.
Yu Tzou
, D.
, 1993, “An Engineering Assessment to the Relaxation Time in Thermal Wave Propagation
,” Int. J. Heat Mass Transfer
0017-9310, 36
(7
), pp. 1845
–1851
.248.
Ozisik
, M. N.
, and Tzou
, D. Y.
, 1994, “On the Wave Theory in Heat Conduction
,” ASME J. Heat Transfer
0022-1481, 116
, pp. 526
–535
.249.
Tzou
, D. Y.
, 1993, “An Engineering Assessment to the Relaxation Time in Thermal Wave Propagation
,” Int. J. Heat Mass Transfer
0017-9310, 36
(7
), pp. 1845
–1851
.250.
Tzou
, D. Y.
, 1992, “Thermal Shock Phenomena Under High-Rate Response in Solids
,” Annual Review of Heat Transfer
, C. L.
Tien
, ed., Hemisphere
, Washington, DC
, pp. 111
–185
.251.
Sieniutycz
, S.
, 1977, “The Variational Principles of Classical Type for Non-Coupled Non-Stationary Irreversible Transport Processes With Convective Motion and Relaxation
,” Int. J. Heat Mass Transfer
0017-9310, 20
(11
), pp. 1221
–1231
.252.
Taitel
, Y.
, 1972, “On the Parabolic, Hyperbolic and Discrete Formulation of the Heat Conduction Equation
,” Int. J. Heat Mass Transfer
0017-9310, 15
(2
), pp. 369
–371
.253.
Antonishyn
, N. V.
, Geller
, M. A.
, and Parnas
, A. L.
, 1974, “Hyperbolic Heat Conduction Equation for Disperse System
,” Inzh.-Fiz. Zh.
0021-0285, 26
(3
), pp. 503
–508
.254.
Raspopov
, B. M.
, 1967, “Control of Some Transfer Processes
,” Inzh.-Fiz. Zh.
0021-0285, 12
, pp. 444
–450
.255.
Brazhnikov
, A. M.
, Karpychev
, V. A.
, and Luikova
, A. V.
, 1975, “One Engineering Method of Calculating Heat Conduction Processes
,” Inzh.-Fiz. Zh.
0021-0285, 28
(4
), pp. 677
–680
.256.
Michalowski
, S.
, Mitura
, E.
, and Kaminski
, W.
, 1982, “The Application of Mathematical Method to Describe the Kinetics of Drying
,” Hung. J. Ind. Chem.
0133-0276, 10
, pp. 387
–394
.257.
Mitura
, E.
, Michalowski
, S.
, and Karnlnski
, W.
, 1988, “A Mathematical Model of Convection Drying in Falling Drying Rate Period
,” Drying Technol.
0737-3937, 6
, pp. 113
–137
.258.
Luikov
, A. V.
, 1966, “Application of Irreversible Thermodynamics Methods to Investigation of Heat and Mass Transfer
,” Int. J. Heat Mass Transfer
0017-9310, 9
(2
), pp. 139
–152
.259.
Stratigos
, A. J.
, and Dover
, J. S.
, 2000, “Overview of Lasers and Their Properties
,” Dermatologic Therapy
, 13
(1
), pp. 2
–16
.260.
Tang
, D. W.
, and Araki
, N.
, 1996, “The Wave Characteristics of Thermal Conduction in Metallic Films Irradiated by Ultra-Short Laser Pulses
,” J. Phys. D: Appl. Phys.
0022-3727, 29
(10
), pp. 2527
–2533
.261.
Baumeister
, K. J.
, and Hamill
, T. D.
, 1969, “Hyperbolic Heat Conduction Equation—A Solution for the Semi-Infinite Body Problem
,” ASME J. Heat Transfer
0022-1481, 91
, pp. 543
–548
.262.
Todos
, O. M.
, Antonishyn
, N. V.
, Sumchenko
, L. E.
, and Lushchikov
, V. V.
, 1970, “Possibility of Description of the Process of Unsteady-State Heat Conduction of Dense Disperse Systems by Differential Equations Allowing the Peculiarities of Phase Interaction
,” Inzh.-Fiz. Zh.
0021-0285, 5
, pp. 815
–822
.263.
Wiggert
, D. C.
, 1977, “Analysis of Early-Time Transient Heat Conduction by Method of Characteristics
,” ASME J. Heat Transfer
0022-1481, 19
, pp. 245
–248
.264.
Vick
, B.
, and Ozisik
, M. N.
, 1983, “Growth and Decay of a Thermal Pulse Predicted by the Hyperbolic Heat Conduction Equation
,” ASME J. Heat Transfer
0022-1481, 105
, pp. 902
–907
.265.
Ozisik
, M. N.
, and Vick
, B.
, 1984, “Propagation and Reflection of Thermal Waves in a Finite Medium
,” Int. J. Heat Mass Transfer
0017-9310, 27
(10
), pp. 1845
–1854
.266.
Frankel
, S. I.
, Vick
, B.
, and Ozisik
, M. N.
, 1985, “Flux Formulation of Hyperbolic Heat Conduction
,” J. Appl. Phys.
0021-8979, 58
(9
), pp. 3340
–3345
.267.
Liu
, J.
, Zhang
, X. X.
, Wang
, C. C.
, and Lu
, W. Q.
, 1997, “Engineering Investigation on Medical Application Approaches for the Thermal Wave Effects in Living Tissue
,” Space Med. Med. Eng. (Beijing)
, 10
(2
), pp. 135
–139
. 1002-0837268.
Liu
, J.
, Zhang
, X. X.
, Lu
, W. Q.
, and Wang
, C. C.
, 1999, “The Thermal Pulse Decay Method for Invasive Measurement of Blood Perfusion of Tissue In Vivo
,” Prog. Nat. Sci.
1002-0071, 9
(2
), pp. 179
–184
.269.
Zhu
, T. C.
, and Feng
, X. Z.
, 2001, “Numerical Analysis of the Relationship Between Blood Flow Coefficient and Living Tissue Thermal Behavior
,” Chin. J. Hemorh
, 11
(3
), pp. 182
–183
.270.
Deng
, Z. S.
, and Liu
, J.
, 2003, “Non-Fourier Heat Conduction Effect on Prediction of Temperature Transients and Thermal Stress in Skin Cryopreservation
,” J. Therm. Stresses
0149-5739, 26
(8
), pp. 779
–798
.271.
Chato
, J. C.
, and Lee
, R. C.
, 1998, “The Future of Biothermal Engineering
,” Ann. N.Y. Acad. Sci.
0077-8923, 858
, pp. 1
–17
.272.
Bayazitoglu
, Y.
, and Peterson
, G. P.
, 1992, Fundamental Issues in Hyperbolic Heat Conduction
, ASME
, New York
, p. 227
.273.
Tzou
, D. Y.
, Ozisik
, M. N.
, and Chiffelle
, R. J.
, 1994, “The Lattice Temperature in the Microscopic Two-Step Model
,” ASME J. Heat Transfer
0022-1481, 116
, pp. 1034
–1038
.274.
Körner
, C.
, and Bergmann
, H. W.
, 1998, “Physical Defects of the Hyperbolic Heat Conduction Equation
,” Appl. Phys. A: Mater. Sci. Process.
0947-8396, 67
(4
), pp. 397
–401
.275.
Godoy
, S.
, and García-Colín
, L. S.
, 1997, “Nonvalidity of the Telegrapher’s Diffusion Equation in Two and Three Dimensions for Crystalline Solids
,” Phys. Rev. E
1063-651X, 55
, pp. 2127
–2131
.276.
Tzou
, D. Y.
, 1995, “A Unified Field Approach for Heat Conduction From Macro- to Micro-Scales
,” ASME J. Heat Transfer
0022-1481, 117
(1
), pp. 8
–16
.277.
Tzou
, D. Y.
, 1995, “Experimental Support for the Lagging Behavior in Heat Propagation
,” J. Thermophys. Heat Transfer
0887-8722, 9
, pp. 686
–693
.278.
Quintanilla
, R.
, and Racke
, R.
, 2006, “A Note on Stability in Dual-Phase-Lag Heat Conduction
,” Int. J. Heat Mass Transfer
0017-9310, 49
(7-8
), pp. 1209
–1213
.279.
Tzou
, D. Y.
, and Chiu
, K. S.
, 2001, “Temperature-Dependent Thermal Lagging in Ultrafast Laser Heating
,” Int. J. Heat Mass Transfer
0017-9310, 44
(9
), pp. 1725
–1734
.280.
Wakaki
, M.
, 1979, “Thermal Effect of the CO2 Laser and Our Technique in Dealing With It
,” Laser Surgery
, I.
Kaplan
, ed., Academic
, Jerusalem
, pp. 27
–42
.281.
Anvari
, B.
, Milner
, T. E.
, Tanenbaum
, B. S.
, Kimel
, S.
, Svaasand
, L. O.
, and Nelson
, J. S.
, 1995, “Selective Cooling of Biological Tissues: Application for Thermally Mediated Therapeutic Procedures
,” Phys. Med. Biol.
0031-9155, 40
(2
), pp. 241
–252
.282.
Anvari
, B.
, Milner
, T. E.
, Tanenbaum
, B. S.
, and Nelson
, J. S.
, 1998, “Comparative Study of Human Skin Thermal Response to Sapphire Contact and Cryogen Spray Cooling
,” IEEE Trans. Biomed. Eng.
0018-9294, 45
(7
), pp. 934
–941
.283.
Anvari
, B.
, Tanenbaum
, B. S.
, Milner
, T. E.
, Hoffman
, W.
, Said
, S.
, Chang
, C. -J.
, Liaw
, L. -H. L.
, Kimel
, S.
, and Nelson
, J. S. M. D.
, 1996, “Cryogen Spray Cooling for Spatially Selective Photocoagulation: A Feasibility Study With Potential Application for Treatment of Hemangiomas
,” Proc. SPIE
0277-786X, 2922
, pp. 29
–37
.284.
Anvari
, B.
, Tanenbaum
, B. S.
, Milner
, T. E.
, Kimel
, S.
, Svaasand
, L. O.
, and Nelson
, J. S.
, 1996, “Theoretical Study of the Thermal Response of Skin to Cryogen Spray Cooling and Pulsed Laser Irradiation: Implications for Treatment of Port Wine Stain Birthmarks
,” Phys. Med. Biol.
0031-9155, 41
(7
), pp. 1245
–1253
.285.
Anvari
, B.
, Ver Steeg
, B. J.
, Milner
, T. E.
, Tanenbaum
, B. S.
, Klein
, T. J.
, Gerstner
, E.
, Kimel
, S.
, and Nelson
, J. S.
, 1997, Cryogen Spray Cooling of Human Skin: Effects of Ambient Humidity Level, Spraying Distance, and Cryogen Boiling Point
, The International Society for Optical Engineering
, San Remo, Italy
, pp. 106
–110
.286.
Nelson
, J. S.
, Milner
, T. E.
, Anvari
, B.
, Tanenbaum
, B. S.
, Svaasand
, L. O.
, and Kimel
, S.
, 1996, “Dynamic Epidermal Cooling in Conjunction With Laser-Induced Photothermolysis of Port Wine Stain Blood Vessels
,” Lasers Surg. Med.
0196-8092, 19
(2
), pp. 224
–229
.287.
Nelson
, J. S. M. D.
, Anvari
, B.
, Tanenbaum
, B. S.
, Milner
, T. E.
, Kimel
, S.
, and Svaasand
, L. O.
, 1996, Epidermal Cooling During Pulsed Laser Treatment of Selected Dermatoses
, Society of Photo-Optical Instrumentation Engineers
, Bellingham, WA
, pp. 32
–39
.288.
Fiskerstrand
, E. J.
, Norvang
, L. T.
, and Svaasand
, L. O.
, 1996, “Laser Treatment of Port-Wine Stains: Reduced Pain and Shorter Duration of Purpura by Epidermal Cooling
,” Proc. SPIE
0277-786X, 2922
, pp. 20
–28
.289.
Ross
, E. V.
, and Paithankar
, D.
, 2000, “Comparison of Cryogen Spray and Surface Contact Cooling Through Heat Transfer Modeling
,” Laser News.Net, LLC.290.
Ross
, E. V.
, Sajben
, F. P.
, Hsia
, J.
, Barnette
, D.
, Miller
, C. H.
, and McKinlay
, J. R.
, 2000, “Nonablative Skin Remodeling: Selective Dermal Heating With a Mid-Infrared Laser and Contact Cooling Combination
,” Lasers Surg. Med.
0196-8092, 26
(2
), pp. 186
–195
.291.
Armon
, E.
, and Laufer
, G.
, 1987, “New Techniques for Reducing the Thermochemical Damage in the Course of Laser Surgery
,” Lasers Surg. Med.
0196-8092, 7
(2
), pp. 162
–168
.292.
Fiskerstran
, E. J.
, Ryggen
, K.
, Norvang
, L. T.
, and Svaasand
, L. O.
, 1997, “Clinical Effects of Dynamic Cooling During Pulsed Laser Treatment of Port-Wine Stains
,” Lasers Med. Sci.
0268-8921, 12
, pp. 320
–327
.293.
Sturesson
, C.
, and Andersson-Engels
, S.
, 1996, “Mathematical Modelling of Dynamic Cooling and Pre-Heating, Used to Increase the Depth of Selective Damage to Blood Vessels in Laser Treatment of Port Wine Stains
,” Hamburg, Germany, p. 311
.294.
Tunnell
, J. W.
, Nelson
, J. S.
, Torres
, J. H.
, and Anvari
, B.
, 2000, “Epidermal Protection With Cryogen Spray Cooling During High Fluence Pulsed Dye Laser Irradiation: An Ex Vivo Study
,” Lasers Surg. Med.
0196-8092, 27
(4
), pp. 373
–383
.295.
Aguilar
, G.
, Diaz
, S. H.
, Lavernia
, E. J.
, and Nelson
, J. S.
, 2002, “Cryogen Spray Cooling Efficiency: Improvement of Port Wine Stain Laser Therapy Through Multiple-Intermittent Cryogen Spurts and Laser Pulses
,” Lasers Surg. Med.
0196-8092, 31
(1
), pp. 27
–35
.296.
Kelly
, K. M.
, Nanda
, V. S.
, and Nelson
, J. S.
, 2002, “Treatment of Port-Wine Stain Birthmarks Using the 1.5-msec Pulsed Dye Laser at High Fluences in Conjunction With Cryogen Spray Cooling
,” Dermatol. Surg.
1076-0512, 28
(4
), pp. 309
–313
.297.
Buscher
, B. A.
, McMeekin
, T. O.
, and Goodwin
, D.
, 2000, “Treatment of Leg Telangiectasia by Using a Long-Pulse Dye Laser at 595 nm With and Without Dynamic Cooling Device
,” Lasers Surg. Med.
0196-8092, 27
(2
), pp. 171
–175
.298.
Weiss
, R. A.
, and Sadick
, N. S.
, 2000, “Epidermal Cooling Crystal Collar Device for Improved Results and Reduced Side Effects on Leg Telangiectasias Using Intense Pulsed Light
,” Dermatol. Surg.
1076-0512, 26
(11
), pp. 1015
–1018
.299.
Choi
, B.
, Aguilar
, G.
, Vargas
, G.
, Welch
, A. J.
, and Stuart Nelson
, J.
, 2002, Dynamic Measurements of Laser Light Attenuation by Cryogen Film and Frost Formation
, The International Society for Optical Engineering
, San Jose, CA
, pp. 57
–66
.300.
Pikkula
, B. M.
, Domankevitz
, Y.
, Tunnell
, J. W.
, and Anvari
, B.
, 2002, Cryogen Spray Cooling: Effects of Cryogen Film on Heat Removal and Light Transmission
, The International Society for Optical Engineering
, San Jose, CA
, pp. 50
–56
.301.
Edris
, A.
, Choi
, B.
, Aguilar
, G.
, and Nelson
, J. S.
, 2003, “Measurements of Laser Light Attenuation Following Cryogen Spray Cooling Spurt Termination
,” Lasers Surg. Med.
0196-8092, 32
(2
), pp. 143
–147
.302.
Ramirez-San-Juan
, J. C.
, Choi
, B.
, Franco
, W.
, Nelson
, J. S.
, and Aguilar
, G.
, 2006, “Effect of Ambient Humidity on Light Transmittance Through Skin Phantoms During Cryogen Spray Cooling
,” Phys. Med. Biol.
0031-9155, 51
(1
), pp. 113
–120
.303.
Zenzie
, H. H.
, Altshuler
, G. B.
, Smirnov
, M. Z.
, and Anderson
, R. R.
, 2000, “Evaluation of Cooling Methods for Laser Dermatology
,” Lasers Surg. Med.
0196-8092, 26
(2
), pp. 130
–144
.304.
Majaron
, B.
, Kimel
, S.
, Verkruysse
, W.
, Aguilar
, G.
, Pope
, K.
, Svaasand
, L. O.
, Lavernia
, E. J.
, and Nelson
, J. S.
, 2001, “Cryogen Spray Cooling in Laser Dermatology: Effects of Ambient Humidity and Frost Formation
,” Lasers Surg. Med.
0196-8092, 28
(5
), pp. 469
–476
.305.
Tunnell
, J. W.
, Chang
, D. W.
, Johnston
, C.
, Torres
, J. H.
, Patrick
, C. W.
, Jr., Miller
, M. J.
, Thomsen
, S. L.
, and Anvari
, B.
, 2002, In-Vivo Study of Epidermal Protection by Cryogen Spray Cooling During Pulsed Laser Irradiation at High Radiant Exposures
, The International Society for Optical Engineering
, San Jose, CA
, pp. 67
–74
.306.
Kao
, B.
, Kelly
, K. M.
, Aguilar
, G.
, Hosaka
, Y.
, Barr
, R. J.
, and Nelson
, J. S.
, 2004, “Evaluation of Cryogen Spray Cooling Exposure on In Vitro Model Human Skin
,” Lasers Surg. Med.
0196-8092, 34
(2
), pp. 146
–154
.307.
Ramirez-San-Juan
, J. C.
, Choi
, B.
, Franco
, W.
, Nelson
, J. S.
, and Aguilar
, G.
, 2005, Effects of Relative Humidity on Laser Light Transmittance During Cryogen Spray Cooling of In Vitro Skin Phantoms
, International Society for Optical Engineering
, Bellingham, WA
, pp. 154
–158
.308.
Tuqan
, A. T.
, Kelly
, K. M.
, Aguilar
, G.
, Ramirez-San-Juan
, J. C.
, Sun
, C. H.
, Cassarino
, D.
, Derienzo
, D.
, Barr
, R. J.
, and Nelson
, J. S.
, 2005, “Evaluation of Single Versus Multiple Cryogen Spray Cooling Spurts on In Vitro Model Human Skin
,” Lasers Med. Sci.
0268-8921, 20
(2
), pp. 80
–86
.309.
Spector
, N.
, Spector
, J.
, Ellis
, D. L.
, and Reinisch
, L.
, 2003, “Reduction in Lateral Thermal Damage Using Heat-Conducting Templates: A Comparison of Continuous Wave and Pulsed CO2 Lasers
,” Lasers Surg. Med.
0196-8092, 32
(2
), pp. 94
–100
.310.
Fried
, N. M.
, and Walsh
, J. T.
, Jr., 2000, “Cryogen Spray Cooling During Laser Tissue Welding
,” Phys. Med. Biol.
0031-9155, 45
(3
), pp. 753
–763
.311.
Grossman
, M. C.
, Dierickx
, C.
, Farinelli
, W.
, Flotte
, T.
, and Anderson
, R. R.
, 1996, “Damage of Hair Follicles by Normal-Mode Ruby Laser Pulses
,” J. Am. Acad. Dermatol.
0190-9622, 35
, pp. 889
–894
.312.
Chess
, C.
, 1998, “Does Simultaneous Contact Cooling Reduce Intravascular Temperature During Laser Irradiation and Impinge on Selective Vascular Destruction?
” Dermatol. Surg.
1076-0512, 24
(3
), pp. 404
–405
.313.
Chess
, C.
, 2000, “Regarding the Use of Contact Cooling Devices During Laser Treatment of Spider Leg Veins
,” Dermatol. Surg.
1076-0512, 26
(1
), pp. 92
–93
.314.
Mordon
, S.
, Capon
, A.
, Creusy
, C.
, Fleurisse
, L.
, Buys
, B.
, Faucheux
, M.
, and Servell
, P.
, 2000, “In Vivo Experimental Evaluation of Skin Remodeling by Using an Er:Glass Laser With Contact Cooling
,” Lasers Surg. Med.
0196-8092, 27
(1
), pp. 1
–9
.315.
Levy
, J. L.
, Besson
, R.
, and Mordon
, S.
, 2002, “Determination of Optimal Parameters for Laser for Nonablative Remodeling With a 1.54 micron Er:Glass Laser: A Dose-Response Study
,” Dermatol. Surg.
1076-0512, 28
(5
), pp. 405
–409
.316.
Woo
, W. K.
, Jasim
, Z. F.
, and Handley
, J. M.
, 2003, “532-nm Nd:YAG and 595-nm Pulsed Dye Laser Treatment of Leg Telangiectasia Using Ultralong Pulse Duration
,” Dermatol. Surg.
1076-0512, 29
(12
), pp. 1176
–1180
.317.
Ramli
, R.
, Chung
, C. C.
, Fried
, N. M.
, Franco
, N.
, and Hayman
, M. H.
, 2004, “Subsurface Tissue Lesions Created Using an Nd:YAG Laser and a Sapphire Contact Cooling Probe
,” Lasers Surg. Med.
0196-8092, 35
(5
), pp. 392
–396
.318.
Acikel
, C.
, Kenkel
, J. M.
, Ozturk
, S.
, Nojima
, K.
, Hoopman
, J. E.
, Gokaslan
, S. T.
, and Brown
, S. A.
, 2005, “Nonsurgical Delay of Dorsal Rat Cutaneous Flap Using a Long-Pulsed 1064-nm Nd:YAG Laser With a Contact Cooling Device
,” Plast. Reconstr. Surg.
0032-1052, 116
(5
), pp. 1411
–1420
.319.
Wheeland
, R. C.
, 1997, “Laser-Assisted Hair Removal
,” Lasers in Dermatol.
, 15
(3
), pp. 469
–477
.320.
Spector
, N.
, Reinisch
, L.
, Spector
, J.
, and Ellis
, D. L.
, 2002, “Free-Electron Laser and Heat-Conducting Templates: A Study of Reducing Cutaneous Lateral Thermal Damage
,” Lasers Surg. Med.
0196-8092, 30
(2
), pp. 117
–122
.321.
Chess
, C.
, and Chess
, Q.
, 1993, “Cool Laser Optics Treatment of Large Telangiectasia of the Lower Extremities
,” J. Dermatol. Surg. Oncol.
0148-0812, 19
(1
), pp. 74
–80
.322.
Lahaye
, C. T.
, and van Gemert
, M. J.
, 1985, “Optimal Laser Parameters for Port Wine Stain Therapy: A Theoretical Approach
,” Phys. Med. Biol.
0031-9155, 30
(6
), pp. 573
–587
.323.
Laufer
, G.
, Joachims
, H. Z.
, Mordechovitz
, D.
, and Armon
, E.
, 1987, “Tissue Precooling for Thermochemical Damage Reduction During Laser Surgery
,” Lasers Surg. Med.
0196-8092, 7
, pp. 160
–161
.324.
Dreno
, B.
, Patrice
, T.
, Litoux
, P.
, and Barriere
, H.
, 1985, “The Benefit of Chilling in Argon-Laser Treatment of Port Wine Stains
,” Plast. Reconstr. Surg.
0032-1052, 75
, pp. 42
–45
.325.
Raulin
, C.
, Greve
, B.
, and Hammes
, S.
, 2000, “Cold Air in Laser Therapy: First Experiences With a New Cooling System
,” Lasers Surg. Med.
0196-8092, 27
(5
), pp. 404
–410
.326.
Chess
, C.
, 2001, “Cold Air in Laser Therapy
,” Lasers Surg. Med.
0196-8092, 29
(2
), p. 107
.327.
Chang
, C. W.
, Reinisch
, L.
, and Biesman
, B. S.
, 2003, “Analysis of Epidermal Protection Using Cold Air Versus Chilled Sapphire Window With Water or Gel During 810 nm Diode Laser Application
,” Lasers Surg. Med.
0196-8092, 32
(2
), pp. 129
–136
.328.
Greve
, B.
, and Raulin
, C.
, 2004, “Prospective Study of Port Wine Stain Treatment With Dye Laser: Comparison of Two Wavelengths (585 nm vs. 595 nm) and Two Pulse Durations (0.5 milliseconds vs. 20 milliseconds)
,” Lasers Surg. Med.
0196-8092, 34
(2
), pp. 168
–173
.329.
Hammes
, S.
, and Raulin
, C.
, 2005, “Evaluation of Different Temperatures in Cold Air Cooling With Pulsed-Dye Laser Treatment of Facial Telangiectasia
,” Lasers Surg. Med.
0196-8092, 36
(2
), pp. 136
–140
.330.
Torres
, J. H.
, Tunnell
, J. W.
, Pikkula
, B. M.
, and Anvari
, B.
, 2001, “An Analysis of Heat Removal During Cryogen Spray Cooling and Effects Of Simultaneous Airflow Application
,” Lasers Surg. Med.
0196-8092, 28
(5
), pp. 477
–486
.331.
Svaasand
, L. O.
, Randeberg
, L. L.
, Aguilar
, G.
, Majaron
, B.
, Kimel
, S.
, Lavernia
, E. J.
, and Nelson
, J. S.
, 2003, “Cooling Efficiency of Cryogen Spray During Laser Therapy of Skin
,” Lasers Surg. Med.
0196-8092, 32
(2
), pp. 137
–142
.332.
Majaron
, B.
, Aguilar
, G.
, Basinger
, B.
, Randeberg
, L. L.
, Svaasand
, L. O.
, Lavernia
, E. J.
, and Nelson
, J. S.
, 2001, Sequential Cryogen Spraying for Heat Flux Control at the Skin Surface
, Society of Photo-Optical Instrumentation Engineers
, San Jose, CA
, pp. 74
–81
.333.
Pikkula
, B. M.
, Torres
, J. H.
, Tunnell
, J. W.
, and Anvari
, B.
, 2001, “Cryogen Spray Cooling: Effects of Droplet Size and Spray Density on Heat Removal
,” Lasers Surg. Med.
0196-8092, 28
(2
), pp. 103
–112
.334.
Karapetian
, E.
, Aguilar
, G.
, Kimel
, S.
, Lavernia
, E. J.
, and Nelson
, J. S.
, 2003, “Effects of Mass Flow Rate and Droplet Velocity on Surface Heat Flux During Cryogen Spray Cooling
,” Phys. Med. Biol.
0031-9155, 48
(1
), pp. N1
–N6
.335.
Pikkula
, B. M.
, Tunnell
, J. W.
, Chang
, D. W.
, and Anvari
, B.
, 2004, “Effects of Droplet Velocity, Diameter, and Film Height on Heat Removal During Cryogen Spray Cooling
,” Ann. Biomed. Eng.
0090-6964, 32
(8
), pp. 1133
–1140
.336.
Karapetian
, E.
, Aguilar
, G.
, Lavernia
, E. J.
, and Nelson
, J. S.
, 2002, Influence of Cryogen Spray Cooling Parameters on the Heat Extraction Rate From a Sprayed Surface
, The International Society for Optical Engineering
, San Jose, CA
, pp. 83
–93
.337.
Aguilar
, G.
, Majaron
, B.
, Verkruysse
, W.
, Zhou
, Y.
, Nelson
, J. S.
, and Lavernia
, E. J.
, 2001, “Theoretical and Experimental Analysis of Droplet Diameter, Temperature, and Evaporation Rate Evolution in Cryogenic Sprays
,” Int. J. Heat Mass Transfer
0017-9310, 44
(17
), pp. 3201
–3211
.338.
Nelson
, J. S.
, Majaron
, B.
, and Kelly
, K. M.
, 2000, “Active Skin Cooling in Conjunction With Laser Dermatologic Surgery
,” Semin. Cutan. Med. Surg.
, 19
(4
), pp. 253
–266
. 1085-5629339.
Aguilar
, G.
, Majaron
, B.
, Pope
, K.
, Svaasand
, L. O.
, Lavernia
, E. J.
, and Nelson
, J. S.
, 2001, “Influence of Nozzle-to-Skin Distance in Cryogen Spray Cooling for Dermatologic Laser Surgery
,” Lasers Surg. Med.
0196-8092, 28
(2
), pp. 113
–120
.340.
Aguilar
, G.
, Majaron
, B.
, Verkruysse
, W.
, Nelson
, J. S.
, and Lavernia
, E. J.
, 2000, “Characterization of Cryogenic Spray Nozzles With Application to Skin Cooling
,” Proceedings of the International Mechanical Engineering Congress and Exposition
, ASME
, New York
, pp. 189
–197
.341.
Aguilar
, G.
, Verkruysse
, W.
, Majaron
, B.
, Svaasand
, L. O.
, Lavernia
, E. J.
, and Nelson
, J. S.
, 2001, “Measurement of Heat Flux and Heat Transfer Coefficient During Continuous Cryogen Spray Cooling for Laser Dermatologic Surgery
,” IEEE J. Sel. Top. Quantum Electron.
1077-260X, 7
(6
), pp. 1013
–1021
.342.
Pikkula
, B. M.
, Chang
, D. W.
, Dai
, T.
, and Anvari
, B.
, 2005, “Epidermal and Vascular Damage Analysis of In Vivo Human Skin in Response to 595 nm Pulsed Laser Irradiation
,” Lasers Surg. Med.
0196-8092, 37
(1
), pp. 19
–28
.343.
Aguilar
, G.
, Majaron
, B.
, Karapetian
, E.
, Lavernia
, E. J.
, and Nelson
, J. S.
, 2003, “Experimental Study of Cryogen Spray Properties for Application in Dermatologic Laser Surgery
,” IEEE Trans. Biomed. Eng.
0018-9294, 50
(7
), pp. 863
–869
.344.
Jia
, W.
, Aguilar
, G.
, Wang
, G. X.
, and Nelson
, J. S.
, 2004, “Heat-Transfer Dynamics During Cryogen Spray Cooling of Substrate at Different Initial Temperatures
,” Phys. Med. Biol.
0031-9155, 49
(23
), pp. 5295
–5308
.345.
Jia
, W.
, Aguilar
, G.
, Verkruysse
, W.
, Franco
, W.
, and Nelson
, J. S.
, 2006, “Improvement of Port Wine Stain Laser Therapy by Skin Preheating Prior to Cryogen Spray Cooling: A Numerical Simulation
,” Lasers Surg. Med.
0196-8092, 38
(2
), pp. 155
–162
.346.
Franco
, W.
, Liu
, J.
, Wang
, G. -X.
, Nelson
, J. S.
, and Aguilar
, G.
, 2005, “Radial and Temporal Variations in Surface Heat Transfer During Cryogen Spray Cooling
,” Phys. Med. Biol.
0031-9155, 50
(2
), pp. 387
–397
.347.
Basinger
, B.
, Aguilar
, G.
, and Nelson
, J. S.
, 2004, “Effect of Skin Indentation on Heat Transfer During Cryogen Spray Cooling
,” Lasers Surg. Med.
0196-8092, 34
(2
), pp. 155
–163
.348.
Wilson
, B. C.
, and Adam
, G.
, 1983, “A Monte Carlo Model for the Absorption and Flux Distributions of Light in Tissue
,” Med. Phys.
0094-2405, 10
(6
), pp. 824
–830
.349.
Wang
, L.
, and Jacques
, S.
, 1992, “Monte Carlo Modeling of Light Transport in Multilayered Tissues in Standard C
.”350.
Jacques
, S. L.
, and Prahl
, S. A.
, 1987, “Modeling Optical and Thermal Distributions in Tissue During Laser Irradiation
,” Lasers Surg. Med.
0196-8092, 6
(6
), pp. 494
–503
.351.
Gebremedhin
, K. G.
, and Wu
, B.
, 2001, “A Model of Evaporative Cooling of Wet Skin Surface and Fur Layer
,” J. Therm. Biol.
, 26
, pp. 537
–545
. 0306-4565352.
Arkin
, H.
, Kimmel
, E.
, Berman
, A.
, and Broday
, D.
, 1991, “Heat Transfer Properties of Dry and Wet Furs of Dairy Cows
,” Trans. ASAE
0001-2351, 34
(6
), pp. 2550
–2558
.353.
Bejan
, A.
, 1990, “Theory of Heat Transfer From a Surface Covered With Hair
,” ASME J. Heat Transfer
0022-1481, 112
, pp. 662
–667
.354.
Bejan
, A.
, 1990, “Optimum Hair Strand Diameter for Minimum Free-Convection Heat Transfer From a Surface Covered With Hair
,” Int. J. Heat Mass Transfer
0017-9310, 33
(1
), pp. 206
–209
.355.
Gebremedhin
, K. G.
, and Wu
, B.
, 2002, “Simulation of Sensible and Latent Heat Losses From Wet-Skin Surface and Fur Layer
,” J. Therm. Biol.
, 27
, pp. 291
–297
. 0306-4565356.
357.
Schwartz
, G. G.
, and Rosenblum
, L. A.
, 1981, “Allometry of Primate Hair Density and the Evolution of Human Hairlessness
,” Am. J. Phys. Anthropol.
0002-9483, 55
(1
), pp. 9
–12
.358.
Reay
, D. A.
, and Thiele
, F. A. J.
, 1977, “Heat Pipe Theory Applied to a Biological System Quantification of the Role of the Resting Eccrine Sweat Gland in Thermoregulation
,” J. Theor. Biol.
0022-5193, 64
, pp. 789
–803
.359.
360.
Benzinger
, T. H.
, 1961, “The Diminution of Thermoregulatory Sweating During Cold-Reception at the Skin
,” Proc. Natl. Acad. Sci. U.S.A.
0027-8424, 47
, pp. 1683
–1688
.361.
Benzinger
, T. H.
, 1964, “The Thermal Homeostasis of Man
,” Symp. Soc. Exp. Biol.
0081-1386, 18
, pp. 49
–80
.362.
He
, Q.
, Zhu
, L.
, and Weinbaum
, S.
, 2003, “Effect of Blood Flow on Thermal Equilibration and Venous Rewarming
,” Ann. Biomed. Eng.
0090-6964, 31
(6
), pp. 659
–666
.363.
Klug
, F.
, 1874, “Research on the Conduction of Heat in the Skin
,” Z. Biol.
0372-8366, 10
, p. 73
.364.
Putter
, A.
, 1921, Z. Biol.
0372-8366, 74
, p. 237
.365.
Lefevre
, J.
, 1929, Chaleur Animale et Bioenergetique
, Maison et Cie
, Paris
.366.
Lomholt
, S.
, 1930, Strahlentherapie
0039-2073, 35
, p. 324
.367.
Roeder
, F.
, 1934, “Die Messung der Warmeleitzahl der menschlichen Haut und ihre Veranderlichkeit
,” Z. Biol.
0372-8366, 95
, pp. 164
–168
.368.
Buttner
, R.
, 1936, “The Influence of Blood Circulation on the Transport of Heat in the Skin
,” Strahlentherapie
0039-2073, 55
, p. 333
.369.
Hardy
, J. D.
, and Oppel
, T. W.
, 1938, “Studies in Temperature Sensation
,” J. Clin. Invest.
0021-9738, 17
, pp. 771
–778
.370.
Lipkin
, M.
, and Hardy
, J. D.
, 1954, “Measurement of Some Thermal Properties of Human Tissues
,” J. Appl. Physiol.
8750-7587, 7
, pp. 212
–217
.371.
Henriques
, F. C.
, and Moritz
, A. R.
, 1947, “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.
0002-9440, 23
, pp. 531
–549
.372.
Norton
, M. J. T.
, Kadoph
, S. J.
, Hohnson
, R. F.
, and Jordan
, K. A.
, 1985, “Design, Construction, and Use of Minnesota Woman, A Thermally Instrumented Mannequin
,” Text. Res. J.
0040-5175, 55
, pp. 5
–12
.373.
Aschoff
, J.
, and Kaempffer
, F.
, 1947, “Warmedurchgang durch die Haut und seine Anderung bei Vasokonstriktion
,” Pfluegers. Arch. Ges. Physiol.
, 249
, pp. 112
–124
.374.
Buettner
, K.
, 1950, “Effects of Extreme Heat on Man; Protection of Man Against Conflagration Heat
,” J. Am. Med. Assoc.
0098-7484, 144
(9
), pp. 732
–738
.375.
Hensel
, H.
, 1950, “The Physiology of Thermoreception
,” Eng. Physiol.
, 47
, pp. 180
–182
.376.
Buettner
, K.
, 1951, “Effects of Extreme Heat and Cold on Human Skin. II. Surface Temperature, Pain and Heat Conductivity in Experiments With Radiant Heat
,” J. Appl. Physiol.
8750-7587, 3
(12
), pp. 703
–713
.377.
Buettner
, K.
, 1951, “Effects of Extreme Heat and Cold on Human Skin. I. Analysis of Temperature Changes Caused by Different Kinds of Heat Application
,” J. Appl. Physiol.
8750-7587, 3
(12
), pp. 691
–702
.378.
Hardy
, J. D.
, Goodell
, H.
, and Wolff
, H. G.
, 1951, “Influence of Skin Temperature Upon Pain Threshold Evoked by Thermal Irradiation
,” Sci. Total Environ.
0048-9697, 114
, pp. 149
–150
.379.
Hatfield
, H. S.
, and Puch
, L. G.
, 1951, “Thermal Conductivity of Human Fat and Muscle
,” Nature (London)
0028-0836, 168
(4282
), pp. 918
–919
.380.
Cook
, H.
, 1952, “A Comparison of the Dielectric Behaviour of Pure Water and Human Blood at Microwave Frequencies
,” Br. J. Appl. Phys.
0508-3443, 3
, pp. 249
–255
.381.
Hensel
, H.
, 1952, “The Physiology of Thermoreception
,” Ergeb Physiol.
0080-2042, 47
, pp. 180
–182
.382.
Reader
, S. R.
, 1952, “The Effective Thermal Conductivity of Normal and Rheumatic Tissues in Response to Cooling
,” Clin. Sci.
0323-5084, 11
, pp. 1
–12
.383.
Hensel
, H.
, and Bender
, F.
, 1956, “Fortlanfende bestimmang der hautdurchbutung am menschen mit einem elektrischen warmeleitmesser
,” Pfluegers. Arch. Ges. Physiol.
, 263
, pp. 603
–614
.384.
Dersken
, W. L.
, Martha
, T. D.
, and Monahan
, T. I.
, 1957, “Thermal Conductivity and Diathermancy of Human Skin for Sources of Intense Thermal Radiation Employed in Flash Burn Studies
,” J. Appl. Physiol.
8750-7587, 11
, pp. 205
–210
.385.
Hendler
, E.
, Crosbie
, R.
, and Hardy
, J. D.
, 1958, “Measurement of Heating of the Skin During Exposure to Infrared Radiation
,” J. Appl. Physiol.
8750-7587, 12
, pp. 177
–185
.386.
Stoll
, A. M.
, and Greene
, L. C.
, 1959, “Relationship Between Pain and Tissue Damage Due to Thermal Radiation
,” J. Appl. Phys.
0021-8979, 14
(3
), pp. 373
–382
.387.
388.
Poppendiek
, H. F.
, 1964, Technical Report No. AST1A AD.389.
Stoll
, A. M.
, 1967, “Heat Transfer in Biotechnology
,” Advances in Heat Transfer
, J. P.
Hartnett
and T. F.
Irvine
, eds., Academic Press
, New York
, pp. 65
–141
.390.
Stoll
, A. M.
, 1967, “The Role of Skin in Heat Transfer
,” Advances in Heat Transfer
, J. P.
Hartnett
and T. F.
Irvine
, eds., Academic
, New York
, pp. 115
–121
.391.
van de Staak
, W. J.
, Brakkee
, A. J.
, and Rijke-Herweijer
, H. E.
, 1968, “Measurements of the Thermal Conductivity of the Skin as an Indication of Skin Blood Flow
,” J. Invest. Dermatol.
0022-202X, 51
(3
), pp. 149
–154
.392.
Weaver
, J. A.
, and Stoll
, A. M.
, 1969, “Mathematical Model of Skin Exposed to Thermal Radiation
,” Aerosp. Med.
0001-9402, 40
(1
), pp. 24
–30
.393.
Umehara
, H.
, 1970, “On the Heat Diffusivity of the Human Hand
,” Rep. Toyoda. Phys. Chem. Res. Inst.
, 23
, pp. 47
–53
.394.
Tanasawa
, I.
, and Katsuda
, T.
, 1972, “Measurement of Thermophysical Properties of Biological System—Part 1
,” Seisan Kenkyu
, 24
, pp. 404
–406
.395.
Tanasawa
, I.
, and Katsuda
, T.
, 1972, “Measurement of Thermophysical Properties of Biological System—Part 2
,” Seisan Kenkyu
, 24
, pp. 440
–443
.396.
Kraning
, K. K.
, 1973, “Heat Conduction in Blackened Skin Accompanying Pulsatile Heating With a Xenon Flash Lamp
,” J. Appl. Physiol.
8750-7587, 35
, pp. 281
–287
.397.
Elkins
, W.
, and Thomson
, J. G.
, 1973, “Instrumented Thermal Manikin
,” Acurex Corporation, Aerotherm Division Report No. AD-781.398.
Holmes
, K. R.
, and Adams
, T.
, 1975, “Epidermal Thermal Conductivity and Stratum Corneum Hydration in Cat Footpad
,” Am. J. Physiol.
0002-9513, 228
(6
), pp. 1903
–1908
.399.
Drane
, C. R.
, 1981, “The Thermal Conductivity of the Skin of Crocodilians
,” Comp. Biochem. Physiol. A
0300-9629, 68
, pp. 107
–110
.400.
Bowman
, H. F.
, 1981, “Heat Transfer and Thermal Dosimetry
,” J. Microwave Power
0022-2739, 16
(2
), pp. 121
–133
.401.
Chato
, J. C.
, 1990, “Fundamentals of Bioheat Transfer
,” Thermal Dosimetry and Treatment Planning
, M.
Gautherie
, ed., Springer-Verlag
, New York
, p. 51
.402.
Werner
, U.
, Giese
, K.
, Sennhenn
, B.
, Plamann
, K.
, and Kolmel
, K.
, 1992, “Measurement of the Thermal Diffusivity of Human Epidermis by Studying Thermal Wave Propagation
,” Phys. Med. Biol.
0031-9155, 37
(1
), pp. 21
–35
.403.
Togawa
, T.
, and Saito
, H.
, 1994, “Non-Contact Imaging of Thermal Properties of the Skin
,” Physiol. Meas.
, 15
(3
), pp. 291
–298
. 0967-3334404.
Huang
, J.
, and Togawa
, T.
, 1995, “Improvement of Imaging of Skin Thermal Properties by Successive Thermographic Measurements at a Stepwise Change in Ambient Radiation Temperature
,” Physiol. Meas.
, 16
(4
), pp. 295
–301
. 0967-3334405.
Huang
, J.
, and Togawa
, T.
, 1995, “Measurement of the Thermal Inertia of the Skin Using Successive Thermograms Taken at a Stepwise Change in Ambient Radiation Temperature
,” Physiol. Meas.
, 16
(4
), pp. 213
–225
. 0967-3334406.
Hassan
, M.
, and Togawa
, T.
, 2001, “Observation of Skin Thermal Inertia Distribution During Reactive Hyperaemia Using a Single-Hood Measurement System
,” Physiol. Meas.
, 22
, pp. 187
–200
. 0967-3334407.
Telenkov
, S. A.
, Youn
, J. I.
, Goodman
, D. M.
, Welch
, A. J.
, and Milner
, T. E.
, 2001, “Non-Contact Measurement of Thermal Diffusivity in Tissue
,” Phys. Med. Biol.
0031-9155, 46
(2
), pp. 551
–558
.408.
Breuer
, H.
, 1924, “The Thermal Conductivity of Muscle and Fat
,” Pfluegers. Arch. Ges. Physiol.
, 204
, pp. 442
–447
.409.
Hardy
, J. D.
, and Soderstrom
, G. R.
, 1938, “Heat Loss and Peripheral Blood Flow
,” J. Nutr.
0022-3166, 16
, pp. 493
–510
.410.
Hatfield
, H. S.
, 1953, “An Apparatus for Measuring the Thermal Conductivity of Animal Tissue
,” J. Physiol. (London)
0022-3751, 120
(4
), pp. 35P
–36P
.411.
Lapshin
, A.
, 1954, “Thermal Conductivities of Fat
,” Myasnaya Ind. SSR
, 25
, pp. 55
–56
.412.
Cherneeva
, L. I.
, 1956, Rep. VNIKHI
, Gostorgisdat
, Moscow
.413.
Lehmann
, J. F.
, and Johnson
, E. W.
, 1958, “Some Factors Influencing the Temperature Distribution in Thighs Exposed to Ultrasound
,” Arehi. Php. Med. Rehobil. Ann. Congr.
, 35
, pp. 347
–356
.414.
Hensel
, H.
, and Doerr
, F. F.
, 1959, “Untersuchungen mit enem neuen haut-wärmeleitmesser
,” Pfluegers Arch.
0031-6768, 270
, p. 78
.415.
Daniels
, F.
, and Baker
, P. T.
, 1961, “Relationship Between Body Fat and Shivering in Air at 15°C
,” J. Appl. Physiol.
8750-7587, 16
, pp. 421
–425
.416.
Lentz
, C. P.
, 1961, “Thermal Conductivity of Meats, Fats, Gelatin Gels, and Ice
,” Food Technol.
, 15
, pp. 243
–247
. 0015-6639417.
Morley
, M. J.
, 1966, “Thermal Conductivities of Muscles, Fats, and Bones
,” J. Food Technol.
0022-1163, 1
, pp. 303
–331
.418.
Poppendiek
, H. F.
, Randell
, R.
, Breeden
, J. A.
, Chambers
, J. E.
, and Murphy
, J. R.
, 1967, “The Thermal Conductivity Measurements and Predictions for Biological Fluids and Tissues
,” Cryobiology
0011-2240, 3
, pp. 318
–327
.419.
Chato
, J. C.
, 1966, ASME Paper No. 66-WA/HT-37.420.
Chato
, J. C.
, 1969, Advanced Heat Transfer
, B. T.
Chao
, ed., University of Illinois Press
, Urbana, IL
, pp. 395
–408
.421.
Chato
, J. C.
, 1968, “A Method for the Measurement of Thermal Properties of Biologic Materials
,” Symposium on Thermal Problems in Biotechnology
, ASME
, New York
, pp. 16
–25
.422.
Chato
, J. C.
, 1968, Thermal Problems in Biotechnology
, ASME Symposium Series
, ASME
, New York
, pp. 16
–25
.423.
Chato
, J. C.
, 1968, 21st Proceedings of the Annual Conference on Engineering in Medicine and Biology
, pp. 51
–55
.424.
Robinson
, T. C.
, and Lele
, P. P.
, 1972, “An Analysis of Lesion Development in the Brain and in Plastics by High-Intensity Focused Ultrasound at Low-Megahertz Frequencies
,” J. Acoust. Soc. Am.
0001-4966, 51
, pp. 1333
–1351
.425.
Chen
, M. M.
, Holmes
, K. R.
, and Rupinskas
, V.
, 1981, “Pulse-Decay Method for Measuring the Thermal Conductivity of Living Tissues
,” ASME J. Biomech. Eng.
0148-0731, 103
(4
), pp. 253
–260
.426.
Valvano
, J. W.
, Cochran
, J. R.
, and Diller
, K. R.
, 1985, “Thermal Conductivity and Diffusivity of Biomaterials Measured With Self-Heated Thermistors
,” Int. J. Thermophys.
0195-928X, 6
, pp. 301
–311
.427.
Liang
, X. G.
, Ge
, X. S.
, Zhang
, Y. P.
, and Wang
, G. J.
, 1991, “A Convenient Method of Measuring the Thermal Conductivity of Biological Tissue
,” Phys. Med. Biol.
0031-9155, 36
(12
), pp. 1599
–1605
.428.
Kvadsheim
, P. H.
, Folkow
, L. P.
, and Blix
, A. S.
, 1994, “A New Device for Measurement of the Thermal Conductivity of Fur and Blubber
,” J. Therm. Biol.
, 19
, pp. 431
–435
. 0306-4565429.
Kvadsheim
, P. H.
, Folkow
, L. P.
, and Blix
, A. S.
, 1996, “Thermal Conductivity of Minke Whale Blubber
,” J. Therm. Biol.
, 21
, pp. 123
–128
. 0306-4565430.
Atzler
, E.
, and Richter
, F.
, 1920, Biochemistry
0006-2960, 7
, pp. 112
–310
.431.
Mendlowitz
, M.
, 1948, Sci. Total Environ.
0048-9697, 107
, pp. 97
–98
.432.
Spells
, K. E.
, 1960, “The Thermal Conductivities of Some Biological Fluids
,” Phys. Med. Biol.
0031-9155, 5
, pp. 139
–153
.433.
Ponder
, E.
, 1962, “The Coefficient of Thermal Conductivity of Blood and of Various Tissues
,” J. Gen. Physiol.
0022-1295, 45
, pp. 545
–551
.434.
Singh
, A.
, and Blackshear
, P. L.
, 1967, “The Thermal Conductivity of Stationary and Moving Blood
,” Proceedings of the Seventh International Conference on Medicine and Biology Engineering
, Stockholm, p. 400
.435.
Bowman
, H. F.
, Cravalho
, E. G.
, Woods
, M.
, Dmochowski
, J. R.
, and Hansen
, W. P.
, 1974, National Heart Lung Institute.436.
Balasubramaniam
, T. A.
, and Bowman
, H. F.
, 1977, “Thermal Conductivity and Thermal Diffusivity of Biomaterials: A Simultaneous Measurement Technique
,” ASME J. Biomech. Eng.
0148-0731, 99
, pp. 148
–154
.437.
Dumas
, A.
, and Barozzi
, G. S.
, 1984, “Laminar Heat Transfer to Blood Flowing in a Circular Duct
,” Int. J. Heat Mass Transfer
0017-9310, 27
, pp. 391
–398
.438.
Crezee
, J.
, and Lagendijk
, J. J.
, 1990, “Experimental Verification of Bioheat Transfer Theories: Measurement of Temperature Profiles Around Large Artificial Vessels in Perfused Tissue
,” Phys. Med. Biol.
0031-9155, 35
(7
), pp. 905
–923
.439.
Goldman
, M. P.
, and Fitzpatrick
, R. E.
, 1999, Cutaneous Laser Surgery: The Art and Science of Selective Photothermolysis
, Mosby
, London
.440.
Lanigan
, S. W.
, 2000, Lasers in Dermatology
, Springer
, London
.441.
Stratigos
, A. J.
, and Dover
, J. S.
, 2000, “Overview of Lasers and Their Properties
,” Dermatol. Ther.
, 13
, pp. 2
–16
. 1396-0296442.
Roetzel
, W.
, and Xuan
, Y.
, 1998, “Transient Response of the Human Limb to an External Stimulus
,” Int. J. Heat Mass Transfer
0017-9310, 41
(1
), pp. 229
–239
.443.
Sejrsen
, P.
, 1972, “Measurement of Cutaneous Blood Flow by Freely Diffusible Radioactive Isotopes
,” Dan. Med. Bull.
0907-8916, 18
, pp. 1
–38
.444.
Dahan
, S.
, Lagarde
, J. M.
, Turlier
, V.
, Courrech
, L.
, and Mordon
, S.
, 2004, “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.
1076-0512, 30
(6
), pp. 872
–879
.445.
Whitton
, J. T.
, and Everall
, J. D.
, 1973, “The Thickness of the Epidermis
,” Br. J. Dermatol.
0007-0963, 89
, pp. 467
–476
.446.
B.
Young
and J. W.
Heath
, eds., 2000, Wheater’s Functional Histology
, Churchill Livingstone
, Oxford, UK
.447.
Gawkrodger
, D. J.
, 1997, Dermatology: An Illustrated Colour Text
, Saunders
, New York
.448.
Zamanian
, A.
, and Hardiman
, C.
, 2005, Electromagnetic Radiation and Human Health: A Review of Sources and Effects
, High Frequency Electronics
, Bedford, NH
, pp. 16
–26
.449.
Eroschenko
, V. P.
, 2004, Di Fiores Atlas of Histology: With Functional Correlations
, Lippincott Williams and Wilkins
, Baltimore, MD
.Copyright © 2009
by American Society of Mechanical Engineers
You do not currently have access to this content.
