Heat transfer inside the tissues with a supplying vessel for the case when metabolic heat generation and blood perfusion are temperature dependent

Abstract

The heat transfer within a perfused tissue in the presence of a supplying vessel is considered. Approximate analytical solutions are obtained for the case when the arterial temperature of the perfused blood in the bio-heat transfer equation varies along the direction of the vessel and is equal to the axially varying mixed mean temperature of the blood in the vessel. Smaller diameter vessels (arterioles) are found to be good heat exchanger whereas large arteries are found to be bad exchangers of heat with tissue. The equilibrium length in case of supplying vessel is found to be larger than that of traversing vessel. Equilibrium temperature of the blood for the large arteries is found to be greater than that of traversing vessel, for other smaller size vessels it is found to be almost equal. It is observed that as the blood perfusion increases, decrease in the tissue temperature starts from the reference surface and rapidly moves towards the vessel as we move along the downstream direction of the blood vessel. It is found that variable metabolic heat generation and variable blood perfusion instead of constant metabolic heat generation and constant blood perfusion in the Pennes equation give accurate description about the process of the heat transfer inside the tissue.