A semi-analytical model of light ions' Bragg peaks is presented and used in conjunction with a detailed probabilistic radiobiological module to predict the biological effectiveness of light ion irradiation for hadrontherapy applications. The physical Bragg peak model is based on energy-loss calculations with the SRIM code and phenomenological formulae for the energy-loss straggling. Effects of nuclear reactions are accounted for on the level of reducing the number of primary particles only. Reaction products are not followed at all and their contribution to dose deposition is neglected. Beam widening due to multiple scattering and calculations of spread-out Bragg peaks are briefly discussed. With this simple physical model, integral depth-dose distributions are calculated for protons, carbon, oxygen and neon ions. A good agreement with published experimental data is observed for protons and lower energy ions (with ranges in water up to approximately 15 cm), while less satisfactory results are obtained for higher energy ions due to the increased role of nuclear reaction products, neglected in this model. A detailed probabilistic radiobiological module is used to complement the simple physical model and to estimate biological effectiveness along the penetration depth of Bragg peak irradiation. Excellent agreement is found between model predictions and experimental data for carbon beams, indicating potential applications of the present scheme in treatment planning in light ion hadrontherapy. Due to the semi-analytical character of the model, leading to high computational speed, applications are foreseen in particular in the fully biological optimization of multiple irradiation fields and intensity-modulated beams.

Institute of Physics Academy of Sciences of the Czech Republic Na Slovance 2 CZ 182 21 Praha 8 Czech Republic

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Condensed Matter Systems Exposed to Radiation: Multiscale Theory, Simulations, and Experiment