Proton RBE models: commonalities and differences

Stephen J Mcmahon

doi:10.1088/1361-6560/abda98

Abstract

Uncertainties in the relative biological effectiveness (RBE) of protons remains a major barrier to the biological optimisation of proton therapy. While a constant value of 1.1 is widely used in treatment planning, extensive preclinical in vitro and in vivo data suggests that proton RBE is variable, depending on proton energy, target tissue, and endpoint. A number of phenomenological models have been developed to try and explain this variation, but agreement between these models is often poor. This has been attributed to both the models’ underlying assumptions and the data to which they are fit. In this brief note, we investigate the underlying trends in these models by comparing their predictions as a function of relevant biological and physical parameters, to determine where models are in conceptual agreement or disagreement. By doing this, it can be seen that the primary differences between models arise from how they handle biological parameters (i.e. and from the linear–quadratic model for photon exposures). By contrast, when specifically explored for linear energy transfer-dependence, all models show extremely good correlation. These observations suggest that there is a pressing need for more systematic exploration of biological variation in RBE across different cells in well-controlled conditions to help distinguish between these different models and identify the true behaviour.

Highlights

Introduction cri ptProtons offer significant physical dosimetric advantages over photons for many cancers, with their finite range and Bragg peak enabling dose to be more accurately conformed to tumours
A given dose of proton therapy will lead to greater cell-killing than the same dose of photons. This is quantified in terms of their Relative Biological Effectiveness (RBE), which is the ratio of a reference photon dose to the dose of a radiation of interest which causes the same biological effect
The thirteen different LQ-based models characterised in Rørvik et al were considered in this work (Wilkens and Oelfke, 2004; Tilly et al, 2005; Carabe-Fernandez, Dale and Jones, 2007; Frese et al, 2011; Chen and Ahmad, 2012; Wedenberg, Lind and Hårdemark, 2013; Jones, 2015; McNamara, Schuemann and Paganetti, 2015; Peeler, 2016; Unkelbach et al, 2016; Mairani et al, 2017; Rørvik et al, 2017). As these RBE models are complex functions depending on multiple parameters, there is no single quantitative method to determine how well they agree

Summary

Introduction

Protons offer significant physical dosimetric advantages over photons for many cancers, with their finite range and Bragg peak enabling dose to be more accurately conformed to tumours. This has the potential to significantly reduce radiotherapy side-effects and has driven a dramatic expansion in the usage of proton therapy in recent years (Mohan and Grosshans, 2017). A given dose of proton therapy will (typically) lead to greater cell-killing than the same dose of photons This is quantified in terms of their Relative Biological Effectiveness (RBE), which is the ratio of a reference photon dose to the dose of a radiation of interest (such as protons, alpha particles, etc.) which causes the same biological effect. Unlike the well-understood physical characteristics of proton therapy, these biological effects remain poorly quantified and have not seen significant clinical exploitation (Underwood and Paganetti, 2016; Lühr et al, 2018)

Methods

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Discussion

Conclusion