title: Range uncertainty in proton therapy due to variable biological effectiveness.
abstract: Traditionally, dose in proton radiotherapy is prescribed as Gy(RBE) by scaling up the physical dose by 10%. The relative biological effectiveness (RBE) of protons is considered to vary with dose-averaged linear energy transfer (LET(d)), dose (d) and (α/β)(x). The increase of RBE with depth causes a shift of the falloff of the beam, i.e. a change of the beam range. The magnitude of this shift will depend on dose and (α/β)(x). The aim of this project was to quantify the dependence of the range shift on these parameters. Three double-scattered beams of different ranges incident on a computational phantom consisting of different regions of interest (ROIs) were used. Each ROI was assigned with (α/β)(x) values between 0.5 and 20 Gy. The distribution of LET(d) within each ROI was obtained from a Monte Carlo simulation. The LET(d) distribution depends on the beam energy and thus its nominal range. The RBE values within the ROIs were calculated for doses between 1 and 15 Gy using an in-house developed biophysical model. Dose-volume histograms of the RBE-weighted doses were extracted for each ROI for a 'fixed RBE' (RBE = 1.1) and a 'variable RBE' (RBE = f (d, α/β, LET(d))), and the percentage difference in range was obtained from the difference of the percentage volumes at the distal 80% of the dose. Range differences in normal tissue ((α/β)(x) = 3 Gy) of the order of 3-2 mm were obtained, respectively, for a shallow (physical range 4.8 cm) and a deep (physical range 12.8 cm) beam, when a dose of 1 Gy normalized to the mid-SOBP was delivered. As the dose increased to 15 Gy, the variable RBE decreases below 1.1 which induces ranges of about 1 mm shorter than those obtained with an RBE of 1.1. The shift in the range of an SOBP when comparing biological dose distributions obtained with a fixed or a variable RBE was quantified as a function of dose, (α/β)(x) and physical range (as a surrogate of the initial beam energy). The shift increases with the physical range but decreases with increasing dose or (α/β)(x). The results of our study allow a quantitative consideration of RBE-caused range uncertainties as a function of treatment site and dose in treatment planning.
authors.affiliation: Department of Radiation Oncology, Massachusetts General Hospital and Harvard Medical School, Boston, MA 02114, USA. a.carabe@uphs.upenn.edu
authors.forename: Alejandro
authors.initials: A
authors.lastname: Carabe
authors.forename: Maryam
authors.initials: M
authors.lastname: Moteabbed
authors.forename: Nicolas
authors.initials: N
authors.lastname: Depauw
authors.forename: Jan
authors.initials: J
authors.lastname: Schuemann
authors.forename: Harald
authors.initials: H
authors.lastname: Paganetti
mesh_terms: D001921:Brain / Q000473:pathology; D003198:Computer Simulation; D004307:Dose-Response Relationship, Radiation; D006801:Humans; D018499:Linear Energy Transfer; D015233:Models, Statistical; D009010:Monte Carlo Method; D019047:Phantoms, Imaging; D011522:Protons; D011878:Radiotherapy / Q000379:methods*; D011880:Radiotherapy Planning, Computer-Assisted / Q000379:methods*; D012062:Relative Biological Effectiveness; D035501:Uncertainty
chemical_list: D011522:Protons