Abstract
A general analysis is presented for the thermal behavior of a biological tissue. Energy transport by the circulatory system is assumed to be represented by a modified Fick's law. General boundary conditions are assumed for the two-dimensional model and solutions are obtained for rectangular, cylindrical, and spherical geometries. The effects of blood perfusion rate, metabolic rate, arterial temperature and heat exchange with the environment are considered. Results indicate a region of almost constant temperature in the deeper layers of the tissue and reaffirm the important role which blood flow plays in maintaining homeostasis.
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Literature
Buchberg, H. and C. B. Harrah. 1968. “Conduction Cooling of the Human Body—A Biothermal Analysis.”Thermal Problems in Biothechnology, ASME Symposium Series, 82–95.
Chato, J. C. 1969. “Heat Transfer in Bioengineering.” InAdvanced Heat Transfer, B. T. Chao ed., pp. 345–414, University of Illinois Press.
Goldfarb, E. M. 1967. “Heat Engineering of Metallurgical Processes.” (In Russian),Metallurgizdat, Moscow.
Greenberg, G. A. 1948. “Selected Questions of the Mathematical Theory for Electrical and Magnetic Phenomena.” Edition of USSR Academy of Sciences.
Kleiner, M. K. 1966. “Temperature Field in Infinite Hollow Cylinders Heated Asymmetrically Around Their Perimeter Under General Nonuniform Boundary Conditions.”J. Engng. Phys.,11, 168–171.
Kleiner, M. K. 1967. “General Problem of Heat Conduction to Asymmetrical Heating of Non-limited Cylinders.” Symposium Research into Thermal Conductivity,Nauka i Tekhnika, Minsk, 343–351.
Kleiner, M. K. 1970. “Application of Approximate Methods to the Problem of Heating of Massive Bodies at a Constant and Variable Water Equivalent of Gases.”J. Engng. Phys.,18, 219–226.
Klinger, H. G. 1974. “Heat Transfer in Perfused Biological Tissue—I: General Theory.”Bull. Math. Biol.,34, 403–415.
Koshlyakov, N. S., M. M. Smirnov, and G. B. Gliner. 1964.Differential Equations of Mathematical Physics. Amsterdam: North-Holland Publishing Co.
Lin, S. H. 1972. “Analytical Solutions for Transient Thermal Behavior of Biological Systems.”Bull. Math. Biophys.,34, 413–418.
Nevins, R. G. and M. A. Darwish. 1971. “Heat Transfer Through Subcutaneous Tissue as Heat Generation Porous Material.” InPhysiological and Behavioral Temperature Regulation, J. D. Hardyet al. eds., pp. 281–301. Illinois: Charles C. Thomas.
Pennes, H. H. 1948. “Analysis of Tissue and Arterial Blood Temperatures in the Resting Human Forearm.”J. Appl. Physiol.,1, 93–122.
Shitzer, A. and J. C. Chato. 1971. “Analytical Solutions to the Problem of Transient Heat Transfer in Living Tissue.”ASME Paper, No. 71-WA/HT-36.
Shitzer, A. 1973. “A Model of Heat Transfer in a Biological Tissue Perfused by Blood of Arbitrary Temperature.”Israel J. Tech.,11, 169–177.
Shitzer, A. 1975. “Studies of Bio-Heat Transfer in Mammals.” InTopics in Transport Phenomena, C. Gutfinger ed., pp. 211–343. Scipta Book Co.
Stolwijk, J. A. J. 1971. “Mathematical Model of Thermoregulation.” InPhysiological and Behavioral Temperature Regulation, J. D. Hardyet al., pp. 703–721. Ilinois: Charles C. Thomas.
Trezek, G. J. and T. E. Cooper. 1968. “Analytical Determination of Cylindrical Source Temperature Fields and Their Relation to Thermal Diffusivity of Brain Tissue.”Thermal Problems in Biothechnology, ASME Symposium Series, 1–15.
Wissler, E. H. 1964. “A Mathematical Model of the Human Thermal System.”Bull. Math. Biophys.,4, 147–166.
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Shitzer, A., Kleiner, M.K. Thermal behavior of biological tissues—A general analysis. Bltn Mathcal Biology 38, 369–386 (1976). https://doi.org/10.1007/BF02462212
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DOI: https://doi.org/10.1007/BF02462212