An analytical model of depth-dose distributions for carbon-ion beams

Abstract

Improving effective treatment plans in carbon ion therapy, especially for targeting radioresistant tumors located in deep seated regions while sparing normal tissues, depends on a precise and computationally efficient dose calculation model. Although dose calculations are mostly performed using Monte Carlo simulations, the large amount of computational effort required for these simulations hinders their use in clinical practice. To address this gap, we propose, for the first time in the literature, an analytical model for the depth dose distribution of carbon ion beams by adapting and extending Bortfeld proton dose model. The Bortfeld model was modified and expanded by introducing additional terms and parameters to account for the energy deposition and fragmentation effects characteristic of carbon ions. Our model was implemented in MATLAB software to calculate depth-dose distributions of carbon ion beams across the clinical energy range of 100-430 MeV/u. The calculated results for carbon ion energies of 280 MeV/u and 430 MeV/u were compared with Monte Carlo simulation results from TOPAS to assess the precision of our model. It is observed that the results of the proposed model are in good agreement with those of several analytical and experimental studies for clinical carbon ion beams within the therapeutic energy range of 100-400 MeV/u. At 280 MeV/u, the analytical model result exhibited strong consistency with the depth dose curve produced by TOPAS Monte Carlo simulations. However, noticeable discrepancies appeared at higher energies, such as 430 MeV/u, particularly in the Bragg peak height and the dose falloff. In the clinically useful energy range, our model could potentially be an effective tool in carbon ion therapy as an alternative to complex Monte Carlo simulations. It will enable fast dose assessment with accuracy and in real time, thus improving workflow efficiency.