Consequences of dose heterogeneity on the biological efficiency of ¹⁰³Pd permanent breast seed implants

Brachytherapy is associated with highly heterogeneous spatial dose distributions. This heterogeneity is usually ignored when estimating the biological effective dose (BED). In addition, the heterogeneities of the medium including the tissue heterogeneity (TH) and the interseed attenuation (ISA) are also contributing to the heterogeneity of the dose distribution, but they are both ignored in Task Group 43 (TG43)-based protocols. This study investigates the effect of dose heterogeneity, TH and ISA on metrics that are commonly used to quantify biological efficiency in brachytherapy. The special case of 29 breast cancer patients treated with permanent (103)Pd seed implant is considered here. BED is compared to equivalent uniform BED (EUBED) capable of considering the spatial heterogeneity of the dose distribution. The effects of TH and ISA on biological efficiency of treatments are taken into account by comparing TG43 with Monte Carlo (MC) dose calculations for each patient. The effect of clonogenic repopulation is also considered. The analysis is performed for different sets of (α/β, α) ratios of (2, 0.3), (4, 0.27) and (10, 0.3) [Gy, Gy(-1)] covering the whole range of reported α/β values in the literature. BED is sometimes larger and sometimes smaller than EUBED(TG43) indicating that the effect of the dose heterogeneity is not similar among patients. The effect of the dose heterogeneity can be characterized by using the D(99) dose metric. For each set of the radiobiological parameters considered, a D(99) threshold is found over which dose heterogeneity will cause an overestimation of the biological efficiencies while the inverse happens for smaller D(99) values. EUBED(MC) is always larger than EUBED(TG43) indicating that by neglecting TH and ISA in TG43-based dosimetry algorithms, the biological efficiencies may be underestimated by about 10 Gy. Overall, by going from BED to the more accurate EUBED(MC) there is a gain of about 9.6 to 13 Gy on the biological efficiency. The efficiency gain is about 10.8 to 14 Gy when the repopulation is considered. Dose heterogeneity does not have a constant impact on the biological efficiencies and may under- or overestimate the efficacy in different patients. However, the combined effect of neglecting dose heterogeneity, TH and ISA results in underestimation of the biological efficiencies in permanent breast seed implants.