Efficiency function: improvement of classical bioheat approach

In view of the complex vascular architecture and the intricate physical heat transfer processes in the human body, convective heat transfer via the blood is generally described by simple substitutional processes ("non-vascular models"). The classical "bioheat" approach of Pennes (J. Appl. Physiol. 1: 93-122, 1948), defining the heat flow to or from the tissue as being proportional to the product of perfusion rate and the difference of arterial and tissue temperature, has been seriously questioned after having been used for > 40 yr in many applications. In our laboratory, we have at our disposal a complex three-dimensional vascular model for the special case of tissue in a human extremity. This was used to test the performance of simple nonvascular models. It turned out that the Pennes approach may deliver acceptable results if the body is in the thermoneutral zone or if heat stress acts uniformly on the whole body. However, when cold stress or local hyperthermia is present, unreliable results must be expected. As the vascular model is not generally practicable because of its extreme complexity, we offer the efficiency function concept as a simple way of correcting the classical bioheat approach by factor multiplication. Efficiency function is determined as a function of perfusion rate and tissue depth in a way that compensates for the deficiencies of the Pennes bioheat term. The results are reasonable compared with those of the vascular model and experimental results.