Efficiency function: improvement of classical bioheat approach

Abstract

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.

Local heating of human skin by millimeter waves: Effect of blood flow

“…For skin a correction of perfusion term is not necessary [Brinck and Werner, 1994;Weinbaum et al, 1997]. Our data shows that the BHTE accurately predicts local hyperthermia only at low blood perfusion rates.…”

“…Applying different thermal models for prediction of heat transfer in perfused tissue, many authors suggested that the BHTE is valid for describing mean temperatures and hyperthermia in peripheral tissue such as an inner cutaneous layer [Dagan et al, 1986;Song et al, 1987Song et al, , 1988Baish, 1994;Brinck and Werner, 1994]. For skin a correction of perfusion term is not necessary [Brinck and Werner, 1994;Weinbaum et al, 1997].…”

Thermal Therapy, Part IV: Electromagnetic and Thermal Dosimetry

“…The fi rst limitation is that it considers that all the heat leaving the artery is absorbed by the local tissue and there is no venous rewarming. 132 Brinck and Werner 133 and Wissler 134 suggested a correction coeffi cient that is less than unity and accounts for venous rewarming that should multiply the perfusion term. A correction coeffi cient that is close to zero implies a signifi cant countercurrent rewarming of the paired vein and a coeffi cient of unity implies no rewarming.…”

Assessment of the temperature distribution during hyperthermia treatment by isolated extremity perfusion

“…The EF-approach in essence corrects the Pennes-term by an EF-function …0 µ EF µ 1 †, dependent on perfusion ! and the local coordinate of tissue depth z (mean value in muscle 0.72 18 ). With this approach, a substantial correction of the perfusion term takes place in the peripheral part of the muscles and in the whole tissue where low perfusion rates are present…”

“…In a whole limb simulation, however, it is impossible to take into account every single vessel, so many attempts have been made to develop models of substitutional processes which adequately describe the thermal eOE ect of perfusion. [15][16][17][18][19][20][21][22] A special form of hyperthermia treatment is the hyperthermic isolated extremity perfusion (® gure 1). [23][24][25][26][27][28] The extremity circulation is separated from the body circulation and perfused extracorporally by a heart-lung-machine.…”