A phenomenological relative biological effectiveness (RBE) model for proton therapy based on all publishedin vitrocell survival data

Abstract

Purpose Proton therapy treatments are currently planned and delivered using the assumption that the proton relative biological effectiveness (RBE) relative to photons is 1.1. This assumption ignores strong experimental evidence that suggests the RBE varies along the treatment field, i.e. with linear energy transfer (LET) and with tissue type. A recent review study collected over 70 experimental reports on proton RBE, providing a comprehensive dataset for predicting RBE for cell survival. Using this dataset we developed a model to predict proton RBE based on dose, LET and the ratio of the linear-quadratic model parameters for the reference radiation (α/β)x, as the tissue specific parameter. Methods and Materials The relationship of the RBE on dose, dose average LET (LETd) and (α/β)x was explored using 287 experimental data points. A RBE model based on the linear quadratic model was derived from a nonlinear regression fitting to the data. Results The proposed model predicts that the RBE increases with increasing LETd and decreases with increasing (α/β)x. The model additionally predicts a decrease in RBE with increasing dose. Conclusions The proposed phenomenological RBE model is derived using the most comprehensive collection of proton RBE experimental data to date. The model agrees with previous theoretical predictions on the relationship between RBE, LETd and (α/β)x and also makes predictions on the relationship between RBE and dose. The proposed model shows a relationship between both α and β with LETd. Previously published phenomenological models, based on a limited data set, may have to be revised.

Proton Relative Biological Effectiveness – Uncertainties and Opportunities

“…Phenomenologic models based on measured in vitro cell survival data predict a more or less linear relationship between RBE and LET d (see Figure 2) [27]. The RBE also depends on the tissue (eg, the (α/β) x ) and models predict a steeper slope as (α/β) x decreases.…”

RBE Model-Based Biological Dose Optimization for Proton Radiobiology Studies

“…The phenomenologic McNamara model [14], which was recently developed on the basis of all in vitro proton datasets published through 2015, was used to calculate the RBE for protons in the current study. The RBE calculation formula in the McNamara model [14] is straightforward and requires only the α and β values from reference photons ( α x and β x ) for the specified cell line, as well as the dose and LET d from selected proton beams.…”

“…The RBE calculation formula in the McNamara model [14] is straightforward and requires only the α and β values from reference photons ( α x and β x ) for the specified cell line, as well as the dose and LET d from selected proton beams. The McNamara RBE calculation formula is expressed in Equation (1).…”

“…As in most other RBE models [6, 8], the McNamara model predicts that the proton RBE increases with increases in dose-averaged LET (LET d ) [14]. This prediction motivated us to investigate the feasibility of enhancing the target RBE by increasing the LET d therein.…”

“…Therefore, in the current study, we sought to develop a straightforward and fast method to generate a uniform biological dose SOBP that can be used to validate the accuracy of a selected RBE model. We invoked the McNamara [14] RBE calculation model in the biological dose optimization process to demonstrate the feasibility of our method. The involvement of other models in the biological dose optimization process will be reported in future work.…”