Abstract

Fredrik Kalholm^1,2, Niels Bassler^3,4,5,6, Iuliana Toma-Dasu^1,2

¹Stockholm University, Medical Physics, Stockholm, Sweden; ²Karolinska Institutet, Department of Oncology and Pathology, Medical Radiation Physics, Stockholm, Sweden; ³Stockholm Universiry, Medical Physics, Stockholm, Sweden; ⁴Aarhus University Hospital, Department of Experimental Clinical Oncology, Aarhus, Denmark; ⁵Aarhus University Hospital, Danish Centre for Particle Therapy, Aarhus, Denmark; ⁶Aarhus University, Department of Clinical Medicine, Aarhus, Denmark

For proton therapy, a relative biological effectiveness (RBE) of 1.1 has broadly been applied clinically. However, as unexpected toxicities have been observed by the end of the proton tracks, variable RBE models have been proposed. Typically, the dose averaged linear energy transfer (LETd) has been used as an input variable for these models but the way the LETd was defined, calculated or determined was not consistent, which may impact the corresponding RBE value. This study compares consistently calculated LETd with other quantities as input variables for a phenomenological RBE model and attempts to determine which quantity that can best predict the RBE value for protons.

Experimental set-ups of in vitro cell survival experiments for proton RBE determination are simulated using the SHIELD-HIT12A Monte Carlo particle transport code. In addition to LETd, several other beam quality quantities are determined, such as track averaged LET, z*²/β², Q and average energy. The averaging methods applied and which secondary particles are included were also varied for each included quantity. A phenomenological RBE model is finally applied to the in vitro data with the various beam quality quantities used as input variables and the goodness of fit is determined and compared.

Assuming a linear relationship between the beam quality quantities and the α/αₓ and β/βₓ-terms, track averaged Q (Qt) including only primary protons has the overall best fit, with a RMSE of 0.74 ± 0.11 and 1.14 ± 0.17, respectively. Also for a quadratic relationship, Qt, including only primary protons has the best fit with an RMSE of 0.70 ± 0.11 and 0.88 ± 0.14 for α/αₓ and β/βₓ, respectively. While these quantities yield slightly better average results than LETd, LETd with any variation of included secondary particles is still within one standard error from the quantity with the best fit (Figure 1 and Figure 2). This indicates that for protons, the choice of input parameters considered as alternatives to LETd in the RBE model has a smaller impact than the statistical uncertainties in the cell survival experiments.

No quantity could be identified as superior. More experimental data with smaller statistical uncertainties are needed to determine the best input parameter for phenomenological RBE models for protons. Alternatively, it might be the case that for protons, many of the various beam quality quantities might correlate to such a high degree that the corresponding RBE predictions become only marginally different, thereby making the choice of beam quality quantity almost inconsequential. This question will be resolved in the future when more RBE data are available.