Direct Comparison of Biologically Optimized Spread-out Bragg Peaks for Protons and Carbon Ions

Purpose: In radiotherapy with hadrons, it is anticipated that carbon ions are superior to protons, mainly because of their biological properties: the relative biological effectiveness (RBE) for carbon ions is supposedly higher in the target than in the surrounding normal tissue, leading to a therapeutic advantage over protons. The purpose of this report is to investigate this effect by using biological model calculations. Methods and Materials: We compared spread-out Bragg peaks for protons and carbon ions by using physical and biological optimization. The RBE for protons and carbon ions was calculated according to published biological models. These models predict increased RBE values in regions of high linear energy transfer (LET) and an inverse dependency of the RBE on dose. Results: For pure physical optimization, protons yield a better dose distribution along the central axis. In biologically optimized plans, RBE variations for protons were relatively small. For carbon ions, high RBE values were found in the high-LET target region, as well as in the low-dose region outside the target. This means that the LET dependency and dose dependency of the RBE can cancel each other. We show this for radioresistant tissues treated with two opposing beams, for which the predicted carbon RBE within the target volume was lower than outside. Conclusions: For tissue parameters used in this study, the model used does not predict a biologic advantage of carbon ions. More reliable model parameters and clinical trials are necessary to explore the true potential of radiotherapy with carbon ions.