In 1948, Pennes  presented a mathematical model of heat transfer in human tissue. The effect of blood flow on heat transfer was modeled as heat sink or source whose magnitude is proportional to the volumetric perfusion rate and difference between arterial and venous temperature . Pennes assumed that thermal equilibrium occurs in the capillary beds, although Chen  showed that it occurs in bigger vessels before the blood enters the beds. Weinbaum et al.  and Zhu et al.  studied the thermal effect of vessels in the range of 50 to 1,000 μm on muscle tissue, and recognized the importance of countercurrent heat exchange. Hirata et al.  showed that the heat loss in the forearm is enhanced by the venous blood returning through the superficial veins and that arterious-venous anastomoses (AVAs) presented in the hands are important to thermoregulation.
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Modeling Heat Transfer in Human Arm and Forearm: Effect of Countercurrent Heat Exchange and Superficial Veins
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Ferreira, MS, & Yanagihara, JI. "Modeling Heat Transfer in Human Arm and Forearm: Effect of Countercurrent Heat Exchange and Superficial Veins." Proceedings of the ASME 2008 Summer Bioengineering Conference. ASME 2008 Summer Bioengineering Conference, Parts A and B. Marco Island, Florida, USA. June 25–29, 2008. pp. 393-394. ASME. https://doi.org/10.1115/SBC2008-192652
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