Weinbaum-Jiji equation

The main limitations of the Weinbaum-Jiji equation are associated with the importance of the countercurrent heat exchange. It was derived to describe heat transfer in peripheral tissue only, where its fundamental assumptions are most applicable. In tissue area containing a big blood vessel (>200 /rm in diameter), the assumption that most of the heat leaving the artery is recaptured by its countercurrent vein could be violated, thus, it is not an accurate model to predict the temperature field. In addition, this theory was primarily developed for closely paired microvessels in muscle tissue, which may not always be the main vascular structure in other tissues, such as the renal cortex. Furthermore, unlike the Pennes equation, which requires only the value of blood perfusion, the estimation of the enhancement in thermal conductivity requires that detailed anatomical studies be performed to estimate the vessel number density, size, and artery-vein spacing for each vessel generation, as well as the blood perfusion rate (Zhu et al., 1995). These anatomic data are normally not available for most blood vessels in the thermally significant range. 

Weinbaum, S. and L.M. Jiji, The matching of thermal fields surrounding countercurrent microvessels and the closure approximation in the Weinbaum-Jiji equation. J. Biomech. Eng., 1989, 111 271-275. 

Weinbaum-Jiji Bioheat Equation. Since 1980, researchers (Chen and Holmes, 1980 Chato, 1980 Weinbaum et al., 1984) have begun to question the validity of the Pennes bioheat equation. Later, Weinbaum and Jiji (1985) developed a new equation for microvascular blood tissue heat transfer, based on the anatomic analysis (Weinbaum et 1984), that illustrated that the predominant mode of heat transfer in the tissue was the countercurrent heat exchange between a thermally significant artery and vein pair. The near-perfect countercurrent heat exchange mechanism implies that most of the heat leaving the artery is transferred to its countercurrent vein rather than released to the sur-... 

Chamy, C. K., Weinbaum, S and Levin, R. L 1990, An Evaluation of the Weinbaum-Jiji Bioheat Equation for Normal and Hyperthermic Conditions, ASME Journal cf Biomechanical Engineering, 112 80-87. 

Weinbaum, S., and Jiji, L. M., 1985, A New Simplified Bioheat Equation for the Effect of Blood Flow on Local Average Tissue Temperature, ASAfE 7. Biomech. Eng., 107 131-139. 

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