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ene een per ive h he p d bl 2011 Elsevier Ltd. All rights reserved. in livi enome ection d diffu eration apy an Pennes [1] bioheat equation is the most widely applied model for temperature distribution in the living biological tissues. The ef-fect of arterial blood on the heat transfer in a living tissue is taken into account by a blood perfusion term, which is proportional to the volumetric rate of blood perfusion and the difference between the average arterial blood and tissue temperatures. Pennes bioheat model is valid only if when the venous blood flows from the capil-lary bed to the main supply vein, its temperature remains the same veins and tissues, metabolic heat generation, convection and blood perfusion through the capillary beds and interaction with the envi-ronment in a complete model. In their series of papers, Weinbaum et al. [6–8] proposed a bioheat equation considering the variation of the number, density and size and flow velocity of the counter-current arterial-venous vessels. That model was applied for the sin-gle organ rather than the whole human body for thermoregulation. In Pennes bioheat equation, the heat conduction in biological tissue is modeled by using Fourier’s law; it assumes an infinite thermal energy propagation speed, i.e. any local temperature dis-turbance causes an instantaneous perturbation in the temperature ⇑ Corresponding author