Linear approximation of variable relative biological effectiveness models for proton therapy

Abstract

The McNamara (MCN) and Wedenberg (WED) RBE weighted dose (D_RBE), dose and dose-weighted average LET (LET_d) were calculated in twenty brain cancer patients. A linear approximation was made for each RBE model to give best agreement to clinically relevant dosimetric parameters. Additional evaluations were done on twenty head and neck and twenty breast cancer patients.The R² of the fits was ≥0.94 and ≥0.91 for MCN and WED respectively for α/β values ≥1.0 Gy. The graphs derived in this work can be used to convert RBE-LET slopes derived from clinical data to α/β values in the MCN or WED models.

Keywords: Linear Energy Transfer (LET); Proton therapy; Relative Biological Effectiveness (RBE).

Fig. 1

Slope of the RBE-LET_d relation and coefficient of determination (R²) as a function of α/β. R² calculated using the difference with physical dose (i.e. D_RBE – D_phys).

Fig. 2

Calibration curves of the McNamara, Wedenberg and linear models. Each datapoint represents a dosimetric parameter tied to a clinical goal. An α/β of 2.0 Gy was used. The figures illustrate the disagreement between McNamara and a linear fit (left), Wedenberg and a linear fit (middle) and between McNamara and Wedenberg. For perfect agreement between models all points are expected to lie on the dotted line. The linear fits were made based on parameters of brain patients (blue), but also head and neck (red) and breast (orange) patients are shown. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)