Session Item

Though a fixed value of 1.1 is used for the relative biological effectiveness (RBE) in proton therapy (PT), more and more clinical evidence of varying RBE has been reported. For carbon irradiation, variable RBE has been considered for decades in clinical research and patient treatment. This experience may be useful to boost RBE research in PT given an ion-independent RBE description. In contrast to the linear energy transfer (LET), on which multiple proton-specific models are based, the beam quality Q = Z²/E (Z = ion charge, E = energy) was proposed and believed to lead to a potential simple ion-independent RBE model. The particle irradiation data ensemble (PIDE) provides experimental in-vitro RBE data from 115 publications for various ions and, thus, the possibility to build and test potential ion-type-independent RBE models. This work compares Q and LET using a Wedenberg-model-like formula for a multi-ion situation. 

PIDE-recorded data fulfilling the following criteria were considered in this work: 1) LET or Q range as in clinical PT, 2) asynchronous cell cycle, 3) monoenergetic irradiation, 4) positive α_x/β_x value, 5) more than 5 data points for the same ion type.

The Wedenberg-model-like formulas for LET and Q,

RBE_max = 1 + k_LET LET / (α_x/β_x)

and

RBE_max = 1 + k_Q Q / (α_x/β_x),

were considered (called LET and Q model in the following, respectively) with RBE_max = α_i/α_x being the ratio of ion and photon α. Linear regression was applied between RBE_max and either LET/(α_x/β_x) or Q/(α_x/β_x) for the selected data, both for each ion type individually and for all data points (figure 1, A and B). The linear regressions for the individual ions were compared. The dependence on ion type of the LET and Q model was tested by conducting an ANOVA test for the residuals between the global fitting (all data points) and the data points of each individual ion. Finally, the capability to predict proton RBE was tested. Predictions of a Q model that was built on a training dataset excluding all proton data were compared for the testing dataset consisting of the experimental proton data.

The slopes of the linear regression for individual ions were clearly different for the LET model (max difference: 116%) while they were similar for the Q model (18%, Fig 1C). Residuals for different ions were significantly different for the LET model (p<0.00001) but not for the Q model (p=0.63). The Q model trained without proton data was able to predict the experimental data for protons (Fig 2). The mean and standard deviation of the difference between prediction and test data were 0.153 and 0.923, respectively (Fig 2B).

A simple Wedenberg-like Q model was observed to be ion-independent in a clinical proton irradiation range for a large in-vitro RBE dataset. This may support proton RBE modelling by adding (pre)clinical RBE knowledge from carbon ion therapy to reduce the current biological uncertainty in the treatment planning process in PT.