Experimental study of the water-to-air stopping power ratio of monoenergetic carbon ion beams for particle therapy

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 (sw,air), with an uncertainty of 2%. The variation of (sw,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 (sw,air) with penetration depth was observed. Since a consensus on Iw,air and Iair 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, sw,air(E), was derived from the Bethe–Bloch formula and fit to the measured data, yielding a coherent pair of Iw and Iair values with Iair/Iw = 1.157 ± 0.023. Additionally, the data from five different beam energies were combined in an average value of sw,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 sw,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. (paper)