Range uncertainty in proton therapy due to variable biological effectiveness

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.