Comparing predictions of proton relative biological effectiveness between LETd and lineal energy spectrum-based models
Introduction
The dose-averaged linear energy transfer (LETd) is the quantity most widely used to predict the relative biological effectiveness (RBE) of protons. However, LETd collapses the natural random spread in energy deposition among all protons down to a single value. An alternative to LETd is to use the spectrum of lineal energy, f(y), to represent energy deposition by protons. Work by Grun et al. (2019) indicates that predictions in RBE between LETd-based and lineal energy spectrum-based proton RBE models can differ by as much as 40%. However, the functional form of the relationship linking lineal energy to proton-RBE is not yet well established. The aim of our work was to investigate the functional relationship between lineal energy and proton RBE. Additionally, we sought to compare predictions of RBE made between LETd and lineal energy spectrum based models.
Methods
Survival data for H460 and H1437 non-small cell lung carcinoma cell lines were retrieved from Guan et al. (2015). Lineal energy spectra and LETd were calculated at the location of each cell line. The α parameter of the linear quadratic model was calculated by integration over the lineal energy spectrum multiplied by a response function. Analogously α was calculated by multiplication of LETd with a response function. Fifteen different candidate response functions were investigated. Optimization of the response functions was achieved by a simulated annealing based fitting approach. Predictions of RBE were made for each of the models in a hypothetical spread out Bragg Peak (SOBP) of 4.8 cm range and 3 cm width.
Results
Compared to the Wedenberg, McNamara, and Chen and Ahmad models, our best performing lineal energy spectrum and LETd based models were more capable of predicting proton-RBE of H460 and H1437 at high LETs. Despite being trained on the same data, predictions of RBE made by the various candidate functions of the lineal energy spectrum-based models differed widely when applied to an SOBP.
Conclusion
Compared to existing models of proton-RBE, new non-linear RBE models were better capable of predicting proton RBE at high LETs. Further biological studies are needed to determine the surviving fraction of cells in pristine Bragg peaks and in an SOBP for the same cell line. Only with repeated surviving fraction measurements for the same cell line in differing irradiation conditions can the functional form of RBE as a function of lineal energy be determined.