Probabilistic relation between temperature, time, and local specific absorption rate (SAR) for regional hyperthermia

A probabilistic relation is proposed for the fraction of hyperthermia sessions that achieve a temperature elevation, T, within a time, t. The overall likelihood, P, of achieving temperature elevation T within time t and the fractional likelihood, p = P/(lim t→∞, P), are proposed to be functions of T, t, and the local specific absorption rate (SAR). These probabilities are based on the assumption that the dissipation of heat due to blood flow can be described probabilistically, with the likelihood of local dissipation, w, given by R(w). It is proven that, in both the limits p → 0 and p → 1, the asymptotic behavior of the fractional likelihood, p, is determined only by the range of likely values of dissipation and is otherwise independent of details of the blood flow distribution R(w). In particular, a simple step function distribution (R(w) = 0 for w > w(c), with R(w) = 1/w(c) for w ≤ w(c)) will give a good fit to p, even if the actual distribution, R, is more elaborate. With this model, simple closed expressions for p and P are proposed. To test this prediction, clinical data were prospectively gathered. The clinical material for this study consists of regional hyperthermia data obtained with the BSD-2000 system on 23 consecutive patients. The eligible data consisted of a total of 142 temperature courses vs time courses, 111 for tumor sensors and 31 for normal tissue sensors. The clinical data for both tumor and normal tissue for three different temperature elevations were compared with the theoretical predictions. The clinically obtained data confirm the feasibility of a probabilistic description in which the only variables are time, temperature, and local SAR. Moreover, the data support the proposed theoretical model. One application of this model would be in interpreting computer-generated predictions of relative SAR distribution. The results of this work also suggest that deep hyperthermia has the best chance of being effective if sufficient power can be applied to achieve an initial rate of temperature rise in tumor of about 0.8°C/min and if normal tissue SAR can be kept at less than 35% to 40% of tumor SAR.