Several closed form analytical solutions to the bioheat transfer problems with space or transient heating on skin surface or inside biological bodies were obtained using Green’s function method. The solutions were applied to study several selected typical bioheat transfer processes, which are often encountered in cancer hyperthermia, laser surgery, thermal comfort analysis, and tissue thermal parameter estimation. Thus a straightforward way to quantitatively interpret the temperature behavior of living tissues subject to constant, sinusoidal, step, point or stochastic heatings etc. both in volume and on boundary were established. Further solution to the three-dimensional bioheat transfer problems was also given to illustrate the versatility of the present method. Implementations of this study to the practical problems were addressed.

1.
Diller
,
K. R.
,
1992
, “
Modeling of Bioheat Transfer Processes at High and Low Temperatures
,”
Adv. Heat Transfer
,
22
, pp.
157
357
.
2.
Field
,
S. B.
, and
Bleehen
,
N. M.
,
1979
, “
Hyperthermia in the Treatment of Cancer
,”
Cancer Treat Rev.
,
6
, pp.
63
69
.
3.
Chen
,
Z. P.
, and
Roemer
,
R. B.
,
1992
, “
The Effect of Large Blood Vessels on Temperature Distributions During Simulated Hyperthermia
,”
ASME J. Biomech. Eng.
,
114
, pp.
473
481
.
4.
Clegg
,
S. T.
, and
Roemer
,
R. B.
,
1993
, “
Reconstruction of Experimental Hyperthermia Temperature Distributions: Application of State and Parameter Estimation
,”
ASME J. Biomech. Eng.
,
115
, pp.
380
388
.
5.
Liu
,
J.
,
Zhu
,
L.
, and
Xu
,
L. X.
,
2000
, “
Studies on the Three-Dimensional Temperature Transients in the Canine Prostate During Transurethral Microwave Thermal Therapy
,”
ASME J. Biomech. Eng.
,
122
, pp.
372
379
.
6.
Magin
,
R.
, and
Peterson
,
A.
,
1989
, “
Noninvasive Microwave Phased Arrays for Local Hyperthermia: A Review
,”
Int. J. Hyperthermia
,
5
, pp.
467
484
.
7.
Seip
,
R.
, and
Ebbini
,
E. S.
,
1995
, “
Noninvasive Estimation of Tissue Temperature Response to Heating Fields Using Diagnostic Ultrasound
,”
IEEE Trans. BioMed. Eng.
,
42
, pp.
828
839
.
8.
Fibich, G., 1995, “Time Dispersive Effects in Ultrashort Laser-Tissue Interactions,” ASME Heat Transfer Division, HTD 322, pp. 27–31.
9.
Whelan, W. M., and Wyman, D. R., 1995, “Temperature Reconstruction by Estimating the Thermophysical and Optical Properties of Tissue During Interstitial Laser Heating,” ASME Heat Transfer Division, HTD 322, pp. 17–26.
10.
Rastegar, S., Chard, A. M., and Azeemi, A., 1993, “Analysis of the Kinetics of Single-Rate and Multi-Rate Thermal Damage in Laser Irradiation of Biological Tissue,” ASME Heat Transfer Division, HTD 268, pp. 137–140.
11.
Yilbas
,
Z.
,
Sami
,
M.
, and
Patiroglu
,
T.
,
1998
, “
Study into Penetration Speed During Laser Cutting of Brain Tissues
,”
J. Med. Eng. Technol.
,
22
, pp.
274
279
.
12.
Valderrama
,
G. L.
,
Fredin
,
L. G.
,
Berry
,
M. J.
,
Dempsey
,
B. P.
, and
Harpole
,
G. M.
,
1991
, “
Temperature Distributions in Laser-Irradiated Tissues
,”
Proc. SPIE
,
1427
, pp.
200
213
.
13.
Pustovalov
,
V. K.
,
1993
, “
Thermal Processes under the Action of Laser Radiation Pulse on Absorbing Granules in Heterogeneous Biotissues
,”
Int. J. Heat Mass Transf.
,
36
, pp.
391
399
.
14.
Liu
,
J.
, and
Xu
,
L. X.
,
2000
, “
Boundary Information Based Diagnostics on the Thermal States of Biological Bodies
,”
Int. J. Heat Mass Transf.
,
43
, pp.
2827
2839
.
15.
Markee
,
N. L.
,
Hatch
,
K. L.
,
Maibach
,
H. I.
,
Barker
,
R. L.
,
Radhakrishnaiah
,
P.
, and
Woo
,
S. S.
,
1990
, “
In Vivo Cutaneous and Perceived Comfort Response to Fabric. Part IV. Perceived Sensations to Three Experimental Garments Worn by Subjects Exercising in a Hot, Humid Environment
,”
Textile Research Journal
,
60
, pp.
561
568
.
16.
Burch, S. D., Ramadhyani, S., and Pearson, J. T., 1991, “Analysis of Passenger Thermal Comfort in an Automobile under Severe Winter Conditions,” ASHRAE Trans., pt. 1, ASHRAE Winter Meeting, Atlanta, pp. 247–257.
17.
Arens
,
E.
, and
Bosselmann
,
P.
,
1989
, “
Wind, Sun and Temperature. Predicting the Thermal Comfort of People in Outdoor Spaces
,”
Building and Environ.
,
24
, pp.
315
320
.
18.
Chato
,
J. C.
,
1980
, “
Measurement of Thermal Properties of Growing Tumors
,”
Ann. N.Y. Acad. Sci.
,
335
, pp.
67
85
.
19.
Balasubramaniam
,
T. A.
, and
Bowman
,
H. F.
,
1974
, “
Temperature Field due to a Time Dependent Heat Source of Spherical Geometry in an Infinite Medium
,”
ASME J. Biomech. Eng.
,
93
, pp.
296
299
.
20.
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.
,
103
, pp.
253
260
.
21.
Bowman, H. F., 1985, “Estimation of Tissue Blood Flow,” Heat Transfer in Medicine and Biology, A. Shitzer, and R. C. Eberhart, eds., Plenum, New York, 1, pp. 193–230.
22.
Valvano
,
J. W.
,
Allen
,
J. T.
, and
Bowman
,
H. F.
,
1984
, “
The Simultaneous Measurement of Thermal Conductivity, Thermal Diffusivity, and Perfusion in Small Volumes of Tissue
,”
ASME J. Biomech. Eng.
,
106
, pp.
192
197
.
23.
Patel
,
P. A.
,
Valvano
,
J. W.
,
Pearce
,
J. A.
,
Prahl
,
S. A.
, and
Denham
,
C. R.
,
1987
, “
A Self-Heated Thermistor Technique to Measure Effective Thermal Properties from the Tissue Surface
,”
ASME J. Biomech. Eng.
,
109
, pp.
300
315
.
24.
Valvano, J. W., and Badeau, A. F., 1987, “In Vivo Measurement of Intrinsic and Effective Thermal Conductivity Using Sinusoidally Heated Thermistors,” in Proc. 6th Southern Biomedical Engineering Conf., pp. 1–4.
25.
Valvano, J. W., Badeau, A. F., and Pearce, J. A., 1987, “Simultaneous Measurement of Intrinsic and Effective Thermal Conductivity,” in Proc. ASME Winter Annual Meeting, Thermodynamics, Heat and Mass Transfer in Biotechnology, Boston, MA, pp. 1–5.
26.
Anderson
,
G. T.
,
Valvano
,
J. W.
, and
Santos
,
R. R.
,
1992
, “
Self-heated Thermistor Measurements of Perfusion
,”
IEEE Trans. Biomed. Eng.
,
39
, pp.
877
885
.
27.
Patera, A. T., Mikic, B. B., Eden, G., and Bowman, H. F., 1979, “Prediction of Tissue Perfusion from Measurement of the Phase Shift Between Heat Flux and Temperature,” Winter Annual Meeting of ASME, Advances in Bioengineering, pp. 187–191.
28.
Anderson, G. T., and Burnside, G., 1990, “A Noninvasive Technique to Measure Perfusion Using a Focused Ultrasound Heating Sources and a Tissue Surface Temperature Measurement,” in Proc. Advance in Measuring and Computing Temperatures in Biomedicine, 147, pp. 31–35.
29.
Liu
,
J.
, and
Xu
,
L. X.
,
1999
, “
Estimation of Blood Perfusion Using Phase Shift in Temperature Response to Sinusoidal Heating at the Skin Surface
,”
IEEE Trans. Biomed. Eng.
,
46
, pp.
1037
1043
.
30.
Torvi
,
D. A.
, and
Dale
,
J. D.
,
1994
, “
A Finite Element Model of Skin Subjected to a Flash Fire
,”
ASME J. Biomech. Eng.
,
116
, pp.
250
255
.
31.
Vyas
,
R.
, and
Rustgi
,
M. L.
,
1992
, “
Green’s Function Solution to the Tissue Bioheat Equation
,”
Med. Phys.
,
19
, pp.
1319
1324
.
32.
Gao
,
B.
,
Langer
,
S.
, and
Corry
,
P. M.
,
1995
, “
Application of the Time-Dependent Green’s Function and Fourier Transforms to the Solution of the Bioheat Equation
,”
Int. J. Hyperthermia
,
11
, pp.
267
285
.
33.
Newman
,
W. H.
,
Lele
,
P. P.
, and
Bowman
,
H. F.
,
1990
, “
Limitations and Significance of Thermal Washout Data Obtained During Microwave and Ultrasound Hyperthermia
,”
Int. J. Hyperthermia
,
6
, pp.
771
784
.
34.
Zhu
,
L.
, and
Weinbaum
,
S.
,
1995
, “
Model for Heat Transfer from Embedded Blood Vessels in Two-Dimensional Tissue Preparations
,”
ASME J. Biomech. Eng.
,
117
, pp.
64
73
.
35.
Zhu
,
L.
,
Xu
,
L. X.
, and
Chencinski
,
N.
,
1998
, “
Quantification of the 3-D Electromagnetic Power Absorption Rate in Tissue During Transurethral Prostatic Microwave Thermotherapy Using Heat Transfer Model
,”
IEEE Trans. Biomed. Eng.
,
45
, pp.
1163
1172
.
36.
Durkee
,
J. W.
,
Antich
,
P. P.
, and
Lee
,
C. E.
,
1990
, “
Exact-Solutions to the Multiregion Time-Dependent Bioheat Equation. 1. Solution Development
,”
Phys. Med. Biol.
,
35
, pp.
847
867
.
37.
Durkee
,
J. W.
,
Antich
,
P. P.
, and
Lee
,
C. E.
,
1990
, “
Exact-Solutions to the Multiregion Time-Dependent Bioheat Equation. 2. Numerical Evaluation of the Solutions
,”
Phys. Med. Biol.
,
35
, pp.
869
889
.
38.
Durkee
,
J. W.
, and
Antich
,
P. P.
,
1991
, “
Exact-Solution to the Multiregion Time-Dependent Bioheat Equation with Transient Heat-Sources and Boundary-Conditions
,”
Phys. Med. Biol.
,
36
, pp.
345
368
.
39.
Durkee
,
J. W.
, and
Antich
,
P. P.
,
1991
, “
Characterization of Bioheat Transport Using Exact Solution to the Cylindrical Geometry, Multiregion, Time-Dependent Bioheat Equation
,”
Phys. Med. Biol.
,
36
, pp.
1377
1406
.
40.
Lagendijk
,
J. J. W.
,
2000
, “
Hyperthermia Treatment Planning
,”
Phys. Med. Biol.
,
45
, pp.
R61–R76
R61–R76
.
41.
Crezee
,
J.
,
Mooibroek
,
J.
,
Lagendijk
,
J. J. W.
, and
Vanleeuwen
,
G. M. J.
,
1994
, “
The Theoretical and Experimental Evaluation of the Heat-Balance in Perfused Tissue
,”
Phys. Med. Biol.
,
39
, pp.
813
832
.
42.
Pennes
,
H. H.
,
1948
, “
Analysis of Tissue and Arterial Blood Temperatures in the Resting Human Forearm
,”
J. Appl. Physiol.
,
1
, pp.
93
122
.
43.
Carslaw, H. S., and Jaeger, J. C., 1959, Conduction of Heat in Solids, Clarendon Press, London.
44.
Ozisik, M. N., 1993, Heat Conduction, John Wiley & Sons, Inc., New York, pp. 506–507.
45.
Holmes, K. R., 1997, Biological Structures and Heat Transfer, Allerton Workshop on the Future of Biothermal Engineering.
46.
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.
,
106
, pp.
321
330
.
47.
Li, J. H., and Liang, H., eds., 1989, Laser Medicine—Applications of Laser in Biology and Medicine (in Chinese), Science Press, Beijing.
48.
Refinetti, R., 1997, “Homeostasis and Circadian Rhythmicity in the Control of Body Temperature,” Tenth International Symposium on the Pharmacology of Thermoregulation, 813, pp. 63–70.
49.
Tharp
,
H. S.
, and
Roemer
,
R. B.
,
1992
, “
Optimal Power Deposition with Finite-Sized, Planar Hyperthermia Applicator Arrays
,”
IEEE Trans. Biomed. Eng.
,
39
, pp.
569
579
.
You do not currently have access to this content.