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Beam tracking as a mitigation technique for treatment of intra-fractionally moving organs requires prediction to overcome latencies in the adaptation process. We implemented and experimentally tested a prediction method for scanned carbon beam tracking. Beam tracking parameters, i.e. the shift of the Bragg peak position in 3D, are determined prior to treatment in 4D treatment planning and applied during treatment delivery in dependence on the motion state of the target as well as on the scanning spot in the target. Hence, prediction is required for the organ motion trajectory as well as the scanning progress to achieve maximal performance. Prediction algorithms to determine beam displacements that overcome these latencies were implemented. Prediction times of 25 ms for target spot prediction were required for ~6 mm water-equivalent longitudinal beam shifts. The experimental tests proved feasibility of the implemented prediction algorithm.

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Previous calculations of the water-to-air stopping power ratio (s(w,)(air)) for carbon ion beams did not involve tracking of delta ray electrons, even though previous calculations with protons predict an effect up to 1%. We investigate the effect of the delta ray production threshold in s(w,)(air) calculations and propose an empirical expression which takes into account the effect of the delta ray threshold as well as the uncertainty in the mean ionization potentials (I-values) of air and water. The formula is derived from the results of Monte Carlo calculations using the most up-to-date experimental data for I-values and a delta ray production threshold of 10 keV. It allows us to reduce the standard uncertainty in s(w,)(air) below 0.8%, instead of the current 2% given in international protocols, which results in a reduction of the overall uncertainty for absolute dosimetry based on air-filled ionization chambers.

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Reference dosimetry with ionization chambers requires a number of chamber-specific and beam-specific calibration factors. For carbon ion beams, IAEA report TRS-398 yields a total uncertainty of 3% in the determination of the absorbed dose to water, for which the biggest contribution arises from the water-to-air stopping power ratio (s(w, air)), with an uncertainty of 2%. The variation of (s(w, air)) along the treatment field has been studied in several Monte Carlo works presented over the last few years. Their results were, in all cases, strongly dependent on the choice of mean ionization potentials (I-values) for air and water. A smaller dependence of (s(w, air)) with penetration depth was observed. Since a consensus on I(w, air) and I(air) has not yet been reached, the validity of such studies for clinical use cannot be assessed independently. Our approach is based on a direct experimental measurement of water-equivalent thicknesses of different air gaps at different beam energies. A theoretical expression describing the variation of the stopping power ratio with kinetic energy, s(w,air)(E), was derived from the Bethe-Bloch formula and fit to the measured data, yielding a coherent pair of I(w) and I(air) values with I(air)/I(w) = 1.157 ± 0.023. Additionally, the data from five different beam energies were combined in an average value of s(w,air) = 1.132 ± 0.003 (statistical) ± 0.003 (variation over energy range), valid for monoenergetic carbon ion beams at the plateau area of the depth dose distribution. A detailed uncertainty analysis was performed on the data, in order to assess the limitations of the method, yielding an overall standard uncertainty below 1% in s(w,air)(E). Therefore, when properly combined with the appropriate models for the fragment spectra, our experimental work can contribute to narrow the uncertainty margins currently in use in absorbed dose to water determination for dosimetry of carbon ion beam radiotherapy.

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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.

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A dynamic phantom has been developed to allow for measurement of 3D cell survival distributions and the corresponding distributions of the RBE-weighted dose (RBED) in the presence of motion. The phantom consists of two 96-microwell plates holding Chinese hamster ovary cells inside a container filled with culture medium and is placed on a movable stage. Basic biological properties of the phantom were investigated without irradiation and after irradiation with a carbon ion beam, using both a stationary (reference) exposure and exposure during motion of the phantom perpendicular to the beam with beam tracking. There was no statistically significant difference between plating efficiency measured in the microwells with and without motion (0.75) and values reported in the literature. Mean differences between measured and calculated cell survival for these two irradiation modes were within +/-5% of the target dose of 6 Gy (RBE).

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Heavy-ion radiotherapy exploits the high biological effectiveness of localized energy deposition delivered by so-called Bragg-peak particles. Recent publications have challenged the established procedures to calculate biological effective dose distributions in treatment planning. They emphasize the importance of very low energy (<500 keV amu(-1)) ions, either as primary particles or originating from molecular and nuclear fragmentations. We show, however, that slow heavy ions with energies below 500 keV amu(-1) only play a negligible role in cancer treatments for several reasons. Their residual range is very small compared to the relevant length scale of treatment planning. Moreover, their relative frequency and also their relative dose distribution are insignificant, since energy loss and range straggling in ion slowing down processes as well as the necessary superposition of Bragg peaks wash out small-scale special effects. Additionally, we show that even a 1000 times larger biological damage of such slow ions would not result in a clinically relevant increase of the photon-equivalent dose. Therefore, neither a more precise physical description of ions in the very distal part of the Bragg peak nor the consideration of radiation damage induced by hyperthermal ions would result in a meaningful improvement of current models for heavy-ion treatment planning.

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We describe a method to irradiate arbitrarily shaped target volumes with simultaneously optimized multiple fields of fast carbon ions, explicitly taking into account sparing of organs at risk. The method was developed with realistic technical boundary conditions in mind, so that irradiations can be executed with devices like the GSI raster scanner or its successors at the upcoming dedicated ion-beam radiotherapy facilities. By virtue of the local effect model (LEM) biological effects are fully taken into account. Several minimization algorithms were investigated, and plain gradient search was found to be more effective than methods based on conjugate gradients or Newton's root finding algorithm. Two sets of cell survival experiments for the experimental verification of patient-like treatment plans were performed. Chinese hamster cells were used for quasi two-dimensional biological dosimetry. The plans combine a very good target conformation with an excellent sparing of organs-at-risk which was verified by the measurements. The results are compared to predictions of the local effect model in its original formulation and a modified version taking additional effects of clustered DNA damage into account. The new method is implemented in GSI's TRiP98 treatment planning system. It has already been applied clinically for planning and irradiating selected patients within the GSI pilot project.

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