Radiobiological evaluation of the stepping-source effect in single-fraction monotherapy high-dose-rate prostate brachytherapy

Abstract

Introduction: The continued reliance upon the traditional biologically effective dose (BEDT) formalism of BEDT=nd(1+d/(α/β)) may be one possible contributor to the poor clinical outcomes observed with single-fraction 19–20 Gy prescriptions in prostate high-dose-rate (HDR) brachytherapy because BEDT does not consider intrafraction sublethal damage repair (iSLDR). This, along with low α/β and repair half-times comparable to delivery time, could reduce the biological effect predicted using BEDT. Methods and Materials: BED was recalculated with a model accounting for iSLDR, using time-averaged uniform dose rate (BEDg1) patterns and time-variable dose rate (BEDgss) patterns inherent to stepping-source delivery. An assortment of two-pulse delivery sequences assuming 19 Gy in 972 s was analyzed. Calculations were repeated for 17470 and 61050 U to investigate source strength dependence. Results: BEDg1 and BEDgss was/were lower than BEDT by 16.9% and 11.1%–21.1%, respectively, for 40700 U. For 17470 U, BEDg1 and BEDgss was/were lower than BEDT by 32.5% and 21.5%–37.1%, respectively. For 61050 U, BEDg1 and BEDgss was/were lower than BEDT by 11.9% and 7.8%–15.3%, respectively. BEDgss was most dependent on pulse spacing with milder dependence on pulse onset time. BEDg1 served as a lower bound approximation of BEDgss for fast effective delivery time. Conclusions: Even for points with the same calculated dose, the biological dose was significantly reduced by iSLDR (as much as 37.1%). While BEDgss explicitly addressed the temporally-variable dose rate inherent to a stepping-source delivery, calculations were cumbersome. Under certain conditions, BEDg1 may serve as an approachable method to quickly assess “worst-case scenario” BED.