title: Modelling the radiobiological effect of intraoperative X-ray brachytherapy for breast cancer using an air-filled spherical applicator.
abstract: OBJECTIVE
  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.
  
  
  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 (EQD2) doses, EQD2(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 EQD2(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.
authors.affiliation: Department of Radiotherapy Physics, Royal Derby Hospital, Derby Teaching Hospitals NHS Foundation Trust, Uttoxeter Road, Derby.
authors.forename: Kris
authors.initials: K
authors.lastname: Armoogum
authors.affiliation: Department of Radiotherapy Physics, Royal Derby Hospital, Derby Teaching Hospitals NHS Foundation Trust, Uttoxeter Road, Derby.
authors.forename: Simon
authors.initials: S
authors.lastname: Evans
authors.affiliation: Breast Services, Sherwood Forest Hospitals NHS Foundation Trust, Sutton-in-Ashfield, Nottingham, United Kingdom.
authors.forename: David
authors.initials: D
authors.lastname: Morgan
keywords: X-ray; brachytherapy; breast cancer; radiobiology