Averaged linear energy transfer andother beam quality descriptors inrelation to relative biological effec-tiveness

Abstract: In radiotherapy with protons, a constant relative biological effectiveness (RBE) of 1.1 is traditionally applied, i.e. protons are assumed to be 10\% more effective than photons in killing cells. This constant RBE is however being questioned, as an abundance of in vitro studies indicate a variable RBE with particle energy, and as in vivo studies also show unexpected toxities near proton track ends, thereby indicating that a variable RBE might also be present clinically.Variable RBE is in turn typically described by a model. For protons, the vast majority of suggested models are based on the linear quadratic (LQ) model, where an expression for RBE is derived by comparing the dose from protons and a reference radiation (typically photons) to achieve a desired survival fraction. The parameters for the model are subsequently obtained by fitting parameters of the derived expression to in vitro data, where the survival fraction of cells has been determined as a function of dose and an averaging over the fluence spectrum of linear energy transfer (LET).While the beam quality parameter typically is the averaged LET, how the averaged LET value has been calculated or determined has often not been fully provided, possibly introducing a source of error in the estimated RBE value. This can vary with respect to the averaging method (typical dose- or track averaging), included particles (only primary, or also including secondaries) and other aspects. Furthermore, while LET is the most commonly used beam quality descriptor, other quantities exist such as Q and z'2/β2 , here renamed as Qeff. These alternative metrics have been shown to better correlate with RBE across different particle species compared to LET, and can possibly also perform better for a single particle species. However, this has so far not been systematically tested or verified.Paper I investigates which kind of averaged LET is provided in the scientific literature for the purpose of RBE determination, for both protons and other hadronic particles. It also attempts to quantify the corresponding impact to the calculated RBE values. Paper II investigates which beam quality descriptor is most suitable for predicting RBE by simulating the experimental setup of recently published high throughput in vitro cell survival studies for RBE determination by a Monte Carlo particle transport code, and fitting parameters to a phenomenological LQ-based model based on the cell survival data. Different variations of LET, Q and Qeff are included, to generate both linear and non linear variable RBE models.In paper I, it is shown that averaged LET for the purpose of RBE determination is, typically, not entirely well defined with a significant minority not mentioning which averaging method is used, and a majority not mentioning what particles are included when averaging. The corresponding impact to the RBE for protons is, in most cases, small, unless heavier secondary particles are included. In paper II it is shown that Q and especially Qeff are expected to better predict RBE compared to LET by a statistically significant margin, for both linear and non-linear models, suggesting they are likely to be more suitable beam quality descriptors to use in a LQ based phenomenological variable RBE model.