Calculation and experimental verification of the RBE-weighted dose for scanned ion beams in the presence of target motion.

We present an algorithm suitable for the calculation of the RBE-weighted dose for moving targets with a scanned particle beam. For verification of the algorithm, we conducted a series of cell survival measurements that were compared to the calculations. Calculation of the relative biological effectiveness (RBE) with respect to tumor motion was included in the treatment planning procedure, in order to fully assess its impact on treatment delivery with a scanned ion beam. We implemented an algorithm into our treatment planning software TRiP4D which allows determination of the RBE including its dependence on target tissue, absorbed dose, energy and particle spectra in the presence of organ motion. The calculations are based on time resolved computed tomography (4D-CT) and the corresponding deformation maps. The principal of the algorithm is illustrated in in silico simulations that provide a detailed view of the different compositions of the energy and particle spectra at different target positions and their consequence on the resulting RBE. The calculations were experimentally verified with several cell survival measurements using a dynamic phantom and a scanned carbon ion beam. The basic functionality of the new dose calculation algorithm has been successfully tested in in silico simulations. The algorithm has been verified by comparing its predictions to cell survival measurements. Four experiments showed in total a mean difference (standard deviation) of -1.7% (6.3%) relative to the target dose of 9 Gy (RBE). The treatment planning software TRiP is now capable to calculate the patient relevant RBE-weighted dose in the presence of target motion and was verified against cell survival measurements.