An Evaluation of the Weinbaum-Jiji Bioheat Equation for Normal and Hyperthermic Conditions

[+] Author and Article Information
C. K. Charny

Department of Chemical Engineering, The Cooper Union School of Engineering, New York, NY 10003

S. Weinbaum

Department of Mechanical Engineering, The City College of the City University of New York, New York, NY 10031

R. L. Levin

Biomedical Engineering and Instrumentation Branch, Division of Research Services, National Institutes of Health, Bethesda, MD 20892

J Biomech Eng 112(1), 80-87 (Feb 01, 1990) (8 pages) doi:10.1115/1.2891130 History: Received January 20, 1989; Revised September 30, 1989; Online March 17, 2008


The predictions of the simplified Weinbaum-Jiji (WJ) bioheat transfer equation in one dimension are compared to those of the complete one-dimensional three-equation model that represented the starting point for the derivation of the WJ equation, as well as results obtained using the traditional bioheat transfer equation of Pennes [6]. The WJ equation provides very good agreement with the three-equation model for vascular generations 2 to 9, which are located in the outer half of the muscle layer, where the paired vessel diameters are less than 500 μm, under basal blood flow conditions. At the same time, the Pennes equation yields a better description of heat transfer in the first generation, where the vessels’ diameters are greater than 500 μm and ε, the vessels’ normalized thermal equilibration length, is greater than 0.3. These results were obtained under both normothermic and hyperthermic conditions. A new conceptual view of the blood source term in the Pennes equation has emerged from these results. This source term, which was originally intended to represent an isotropic heat source in the capillaries, is shown to describe instead the heat transfer from the largest countercurrent microvessels to the tissue due to small vessel bleed-off. The WJ equation includes this effect, but significantly overestimates the second type of tissue heat transfer, countercurrent convective heat transfer, when ε > 0.3. Indications are that a “hybrid” model that applies the Pennes equation in the first generation (normothermic) and first two to three generations (after onset of hyperthermia) and the Weinbaum-Jiji equation in the subsequent generations would be most appropriate for simulations of bioheat transfer in perfused tissue.

Copyright © 1990 by The American Society of Mechanical Engineers
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