A model for the relative biological effectiveness of protons: The tissue specific parameter α/β of photons is a predictor for the sensitivity to LET changes

Abstract

Background. The biological effects of particles are often expressed in relation to that of photons through the concept of relative biological effectiveness, RBE. In proton radiotherapy, a constant RBE of 1.1 is usually assumed. However, there is experimental evidence that RBE depends on various factors. The aim of this study is to develop a model to predict the RBE based on linear energy transfer (LET), dose, and the tissue specific parameter α/β of the linear-quadratic model for the reference radiation. Moreover, the model should capture the basic features of the RBE using a minimum of assumptions, each supported by experimental data. Material and methods. The α and β parameters for protons were studied with respect to their dependence on LET. An RBE model was proposed where the dependence of LET is affected by the (α/β)_phot ratio of photons. Published cell survival data with a range of well-defined LETs and cell types were selected for model evaluation rendering a total of 10 cell lines and 24 RBE values. Results and Conclusion. A statistically significant relation was found between α for protons and LET. Moreover, the strength of that relation varied significantly with (α/β)_phot. In contrast, no significant relation between β and LET was found. On the whole, the resulting RBE model provided a significantly improved fit (p-value < 0.01) to the experimental data compared to the standard constant RBE. By accounting for the α/β ratio of photons, clearer trends between RBE and LET of protons were found, and our results suggest that late responding tissues are more sensitive to LET changes than early responding tissues and most tumors. An advantage with the proposed RBE model in optimization and evaluation of treatment plans is that it only requires dose, LET, and (α/β)_phot as input parameters. Hence, no proton specific biological parameters are needed.

Acknowledgements

The authors thank Dr. Nina Tilly for an initial literature review of the experimental studies, and Dr. Johanna Kempe for the pre-study. We also thank Assoc. Prof. Iuliana Toma-Daşu for her constructive and insightful comments, and her careful reading of the manuscript. The research was supported by the Swedish Research Council (VR).

Declaration of interest: The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the paper.