Session Item

Variable relative biological effectiveness (RBE) models based on the linear-quadratic model for cell survival depend on the tissue-specific α/β value, fraction dose and the dependence on the dose-weighted average linear energy transfer (LET_d). The relation between RBE-LET_d is often proposed to be nonlinear, but linearity is often implied in normal tissue complication probability (NTCP) modelling and LET_d optimization. In this study we aim to investigate the linearity of the RBE-LET relation using two commonly used variable RBE models.

This study was conducted in  three sets of 20 consecutive head & neck, breast and brain cancer patients resulting in a total sample of 60 patients. The RBE weighted dose (D_RBE) was calculated for the Wedenberg (WED) and McNamara (MCN) RBE models using an α/β value between 1 and 10 Gy. A linear fit was made for each RBE model based on the average D_RBE and LET_d to the target and all relevant organs-at-risk (OARs). The D_RBE for clinically relevant dosimetric parameters was then calculated and compared using the WED and MCN models as well as the linear fits of the RBE models.

The average D_RBE parameters models plotted against the D⋅LETd are shown in figure 1 for selected α/β values. For the average D_RBE of OARs, the coefficient of determination (R²) was between 0.94 and 1.00  and between 0.87 and 0.99 for the MCN and WED models respectively, with lower R² values occurring for low α/β values (figure 2). The R2 for an α/β of 2 Gy or higher was higher than 0.92 for both models. For clinically relevant dosimetric parameters, the mean absolute error (MAE) between the WED and MCN model decreased with increasing α/β. The MAE between the MCN model with an α/β of 2 Gy and its linear estimate was 1.57, 0.44 and 0.64 Gy for HNC, breast and brain patients, respectively. The MAE between the MCN and WED model with an α/β of 2 Gy was 0.73, 0.22 and 0.32 Gy for HNC, breast and brain patients respectively. The MAE between an RBE model and its linear fit was of a similar order of magnitude as the MAE between two RBE models.

Both considered RBE models are more linear for high α/β values which are typically observed for acutely responding tissues and the MCN model was more linear than the WED model. The  linear fits to estimate mean D_RBE parameter generated good fits with high (>0.90) R² values for α/β of 2 Gy and very high (>0.95) for α/β of 3 Gy or higher. Using a linear RBE-LET_d relation does not clinically meaningfully contribute to the uncertainty of the D_RBE when considering clinically relevant dosimetric parameters.