Thermal Therapy in Urologic Systems: A Comparison of Arrhenius and Thermal Isoeffective Dose Models in Predicting Hyperthermic Injury

The Arrhenius and thermal isoeffective dose (TID) models are the two most commonly used models for predicting hyperthermic injury. The TID model is essentially derived from the Arrhenius model, but due to a variety of assumptions and simplifications now leads to different predictions, particularly at temperatures higher than $50°C$⁠. In the present study, the two models are compared and their appropriateness tested for predicting hyperthermic injury in both the traditional hyperthermia (usually, $43–50°C$⁠) and thermal surgery (or thermal therapy/thermal ablation, usually, $>50°C$⁠) regime. The kinetic parameters of thermal injury in both models were obtained from the literature (or literature data), tabulated, and analyzed for various prostate and kidney systems. It was found that the kinetic parameters vary widely, and were particularly dependent on the cell or tissue type, injury assay used, and the time when the injury assessment was performed. In order to compare the capability of the two models for thermal injury prediction, thermal thresholds for complete killing (i.e., 99% cell or tissue injury) were predicted using the models in two important urologic systems, viz., the benign prostatic hyperplasia tissue and the normal porcine kidney tissue. The predictions of the two models matched well at temperatures below $50°C$⁠. At higher temperatures, however, the thermal thresholds predicted using the TID model with a constant $R$ value of 0.5, the value commonly used in the traditional hyperthermia literature, are much lower than those predicted using the Arrhenius model. This suggests that traditional use of the TID model (i.e., $R=0.5$⁠) is inappropriate for predicting hyperthermic injury in the thermal surgery regime $(>50°C)$⁠. Finally, the time-temperature relationships for complete killing (i.e., 99% injury) were calculated and analyzed using the Arrhenius model for the various prostate and kidney systems.