The Simulation of Discrete Vessel Effects in Experimental Hyperthermia

Abstract

The ability of two simple thermal models to predict experimentally measured in vivo temperature profiles was compared. These comparisons were done both with and without the inclusion of separate, discrete blood vessels. The two tissue models were: 1) Pennes' Bio-Heat Transfer equation (BHTE), and 2) an effective thermal conductivity equation (ETCE). The experimental temperature data were measured (Moros, 1990; Moros et al., 1993) in the thighs of anesthetized greyhound dogs under hyperthermic conditions generated by scanned focused ultrasound. Blood vessels were added to the thermal models in counter-current pairs transiting the model domain. The blood vessels in both models were assumed to have a constant heat transfer coefficient, and an axially varying mixed mean temperature. The vessel locations were determined a posteriori, via inspection of the experimental temperature data. Least square error fits of the predicted model temperatures to the experimental temperature data were obtained by adjusting both (a) the mass flow rate within and (b) the position of each blood vessel, and (c) the value of either the perfusion parameter (W) in the BHTE or the effective thermal conductivity parameter (Keff) in the ETCE. When small numbers (3-4) of blood vessel pairs were included, both of the models showed significant improvement in their ability to predict the experimental temperatures. Although both models performed well in terms of predicting temperatures near large vessels, the BHTE had a statistically significant better ability to predict the complete set of measured temperatures at all locations.