Modelling the radiobiological effect of intraoperative X-ray brachytherapy for breast cancer using an air-filled spherical applicator

PURPOSE: We present a framework, in which we compare a conventional standard dose of 50 Gy in 25 fractions with accelerated partial breast irradiation (APBI) using electronic brachytherapy (eBT). We discuss how radiobiological modelling enables us to establish a framework, within which we can compare external beam radiotherapy (EBRT). This leads to a determination of the shell of isoeffect in breast tissue, at which very low kV eBT can be considered to be clinically equivalent to standard EBRT. MATERIAL AND METHODS: To estimate relative biological effectiveness (RBE) values as a function of dose and irradiation time, we used a modified linear quadratic (LQ) approach, taking into account the ability of this new device, to deliver 20 Gy at the surface of a 40 mm diameter rigid, hollow spherical applicator in less than 2 minutes. In this study, we considered the radiobiological effectiveness of the Papillon +™ X-ray brachytherapy device operating at 30 kV, 0.3 mA producing dose rates in excess of 14 Gy/min. RESULTS: Calculated clinical RBEs ranged from 1.154 at the surface of a 40 mm diameter applicator to 1.100 at 35 mm from the applicator surface for the Papillon+ device. The absolute physical dose D (abs) 30 kV ranged from 20.00 Gy at the applicator surface to 1.20 at 35 mm distant. The product of the isoeffective single dose of (60)Co reference radiation – (RBE)(60)Co, and the RBE corrected standard 2 Gy equivalent dose fractions (EQD(2)) doses, EQD(2)(30 kV) * (RBE)(60)Co ranged from 98.62 Gy at the applicator surface to 1.13 at 35 mm. The ‘shell of isoeffect’, the value on the X-axis where the EQD(2)(30 kV) * (RBE)(60)Co line crosses the 50 Gy mark on the Y-axis, was found to be approximately 3.5 mm beyond the applicator surface. CONCLUSIONS: The ‘shell of isoeffect’ can serve as a useful metric with which to compare the radiobiological effectiveness of low kV eBT with various regimes of conventional EBRT.