Cooling Limit Approach for Single-Pulse Thermal Therapies

Based upon the commonly used Sapareto-Dewey thermal dose formula, a thermal treatment is divided into four periods: 1) period-1 is from 37°C to 43°C, 2) period-2 is from 43°C to T_peak, 3) period-3 is from T_peak to 43°C, and 4) period-4 is 43°C to 38°C. A recent study derived a closed form thermal dose formula based on a combined term, the “effective cooling frequency,” revealed that one can determine the best performance of a thermal therapy by concentrating on the cooling periods: period-3 and period-4. As an extension, this study used a closed-form temperature solution to investigate the influences from both cooling terms (perfusion and thermal conduction) separately. The results determined the upper bound of the peak temperature for pulses with different focal sizes under different blood perfusion values. Under practical settings, no pulse should introduce peak temperature higher than 67°C to avoid overdosing when the desired thermal dose is 240CEM43°C. It also showed that pulses with focal size smaller than or equal to 4 mm benefit the perfusion independence for the following quantities: the upper bound on the peak temperature, the treatment size, and the time/temperature for which 90% thermal dose is accumulated. Thus the conduction dominates the cooling process for each single pulse heated by the highly focused SFUS applicators when the pulses are properly isolated temporally. Results from this study further provide an estimation of the closest distance between two pulses and the time/temperature to re-activate the consecutive pulses. Thus the results can guide the researchers to design more efficient treatment protocol for multiple-pulse thermal therapies.