Biological effect of pulsed dose rate brachytherapy with stepping sources if short half-times of repair are present in tissues

Abstract

Purpose: To explore the possible increase of radiation effect in tissues irradiated by pulsed brachytherapy (PDR) for local tissue dose rates between those "averaged over the whole pulse" and the instantaneous high dose rates close to the dwell positions. Increased effect is more likely for tissues with short half-times of repair of the order of a few minutes, similar to pulse durations.

Methods and materials: Calculations were done assuming the linear quadratic formula for radiation damage, in which only the dose-squared term is subject to exponential repair. The situation with two components of T1,2 is addressed. A constant overall time of 140 h and a constant total dose of 70 Gy were assumed throughout, the continuous low dose rate of 0.5 Gy/h (CLDR) providing the unitary standard effects for each PDR condition. Effects of dose rates ranging from 4 Gy/h to 120 Gy/h (HDR at 2 Gy/min) were studied, covering the gap in an earlier publication. Four schedules were examined: doses per pulse of 0.5, 1, 1.5, and 2 Gy given at repetiton frequencies of 1, 2, 3, and 4 h, respectively, each with a range of assumed half-times of repair of 4 min to 1.5 h. Results are presented for late-responding tissues, the differences from CLDR being two or three times greater than for early-responding tissues and most tumors.

Results: Curves are presented relating the ratio of increased biological effect (proportional to log cell kill) calculated for PDR relative to CLDR. Ratios as high as 1.5 can be found for large doses per pulse (2 Gy) if the half-time of repair in tissues is as short as a few minutes. The major influences on effect are dose per pulse, half-time of repair in tissue, and--when T1/2 is short--the instantaneous dose rate. Maximum ratios of PDR/CLDR occur when the dose rate is such that pulse duration is approximately equal to T1/2. As dose rate in the pulse is increased, a plateau of effect is reached, for most T1/2s, above 10 to 20 Gy/h, which is therefore radiobiologically equivalent to the highest HDR. A stepping source of 1 curie carries a sphere of "HDR" of radius 20 mm with it in its track through tissue. High ratios of PDR/LDR effect can be avoided by keeping dose per pulse below 1 Gy.

Conclusions: Therefore, about 75% of the total dose is delivered at HDR in a PDR implant of moderate volume, reducing to 40% as the source decays from 1 to 0.3 curies. Even so, restricting the dose per pulse to 0.5 or 0.6 Gy should avoid ratios of increased effect larger than about 10%. It appears likely that PDR delivered by stepping source might behave more like HDR than LDR, especially for tissues with a substantial component of repair of very short T1/2.