A new equation for calculating temperatures in living tissues, the tissue convective energy balance equation (TCEBE), is derived using only a few assumptions. The resulting equation is basic, general and applicable to any tissue. The (unsolved) TCEBE is used: (a) to relate both Pennes’ BHTE perfusion-related parameter (W) and the effective thermal conductivity equation’s perfusion-related parameter (keff) to the true capillary perfusion P˙cap, and (b) to show that both W and keff are defined, nonphysiological variables, which are only related to P˙cap in a problem-dependent manner. Finally, the derivation of the relationship between W and P˙cap provides a complete derivation of Pennes’ BHTE, something that has not been previously done.

1.
Arkin
H.
,
Xu
L. X.
, and
Holmes
K. R.
,
1994
, “
Recent Developments in Modeling Heat Transfer in Blood Perfused Tissues
,”
IEEE Transactions on Biomedical Engineering
, Vol.
41
, No.
2
, pp.
97
107
.
2.
Charny, C. K., 1992, “Advances in Heat Transfer Bioengineering Heat Transfer,” Y. I. Cho, ed., Mathematical Models of Bioheat Transfer, Vol. 22, Academic Press, Inc., San Diego, pp. 19–155.
3.
Charny
C. K.
,
Weinbaum
S.
, and
Levin
R. L.
,
1990
a, “
An Evaluation of the Weinbaum-Jiji Bioheat Equation for Normal and Hyperthermia Conditions
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
112
, pp.
80
87
.
4.
Charny, C. K., Levin, R. L., and Weinbaum, S., 1990b, “Advances in Measuring and Computing Temperatures in Biomedicine: Thermal Tomography Techniques, Bio-Heat Transfer Models,” R. Roemer, J. Valvano, L. Hayes, and G. Anderson, eds., Simulations of Heat Transfer in an Axisymmetric Layer of Perfused Muscle Using a Modified Three-Equation Model, ASME HTD-Vol. 147, pp. 37–42.
5.
Chato, J. C., 1990, “Thermal Dosimetry and Treatment Planning,” M. Gautherie, ed., Fundamentals of Bioheat Transfer, Springer-Verlag, Berlin, pp. 1–56.
6.
Chen
M. M.
, and
Holmes
K. R.
,
1980
, “
Microvascular Contributions in Tissue Heat Transfer
,”
Annals of the New York Academy of Science
, Vol.
335
, pp.
137
150
.
7.
Diller, K. R., 1992, “Advances in Heat Transfer Bioengineering Heat Transfer,” Vol. 22, Y. L Cho, ed., Modeling of Bioheat Transfer Processes at High and Low Temperatures, Academic Press, San Diego, pp. 157–357.
8.
Gutierrez, G., and Roemer, R. B., 1998, “The Tissue Convective Energy Balance Equation: Part II. Observations and Solutions,” in preparation.
9.
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 JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
106
, pp.
331
341
.
10.
Kaviany, M., 1995, Principles of Heat Transfer in Porous Media, Springer, New York.
11.
Kays, W. M., and Crawford, M. E., 1980, Convective Heat and Mass Transfer, McGraw-Hill, New York.
12.
Pennes
H. H.
,
1948
, “
Analysis of Tissue and Arterial Blood Temperatures in the Resting Human Forearm
,”
Journal of Applied Physiology
, Vol.
1
, pp.
93
122
.
13.
Roach, P. J., 1982, Computational Fluid Dynamics, Hermosa Publishers, Albuquerque, NM.
14.
Roemer, R. B., 1990a, “Thermal Dosimetry and Treatment Planning,” M. Gautherie, ed., Thermal Dosimetry, Springer-Verlag, Berlin, pp. 119–214.
15.
Roemer, R. B., 1990b, “A Convective Coefficient Based Thermal Energy Transport Equation for Tissues,” presented at 10th Annual North American Hyperthermia Society, Apr. 7–12, New Orleans, LA.
16.
Roemer, R. B., 1996, “Inverse Techniques for Estimating Complete Temperature Distributions During Hyperthermia Cancer Therapy,” La Thermique de L—homme Et De Son Proche Environnement, F. Penot and J. B. Saulnier, eds., Actes du Congre`s annuel de la Socie´te´ Franc¸aise des Thermiciens, 17–19 May, 1995, LET/ENSMA, Poitiers, France, Elsevier, pp. 86–97.
17.
Roemer, R. B., 1998, “Equations for Predicting Tissue Temperature Distributions: A Review of Alternate Formulations, I: Classification of Equations and Derivational Bases,” accepted, Int. J. Hyperthermia.
18.
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 JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
106
, pp.
321
330
.
19.
Weinbaum
S.
, and
Jiji
L. M.
,
1985
, “
A New Simplified Bio-Heat Equation for the Effect of Blood Flow on Local Average Tissue Temperature
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
107
, pp.
131
139
.
20.
Weinbaum
S.
,
Xu
L. X.
,
Zhu
L.
, and
Ekpene
A.
,
1997
, “
A New Fundamental Bioheat Equation for Muscle Tissue Part I: Blood Perfusion Term
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
119
, pp.
278
288
.
21.
Wulff, W., 1974, “The Energy Conservation Equation for Tissue,” IEEE Transactions of Biomedical Engineering, BME-21, pp. 494–495.
22.
Wulff
W.
,
1980
, “
Discussion Paper: Alternatives to the Bio-Heat Transfer Equation
,”
Annals of the New York Academy of Science
, Vol.
335
, pp.
151
154
.
This content is only available via PDF.
You do not currently have access to this content.