A trichrome beam model for biological dose calculation in scanned carbon-ion radiotherapy treatment planning

In scanned carbon-ion (C-ion) radiotherapy, some primary C-ions undergo nuclear reactions before reaching the target and the resulting particles deliver doses to regions at a significant distance from the central axis of the beam. The effects of these particles on physical dose distribution are accounted for in treatment planning by representing the transverse profile of the scanned C-ion beam as the superposition of three Gaussian distributions. In the calculation of biological dose distribution, however, the radiation quality of the scanned C-ion beam has been assumed to be uniform over its cross-section, taking the average value over the plane at a given depth (monochrome model). Since these particles, which have relatively low radiation quality, spread widely compared to the primary C-ions, the radiation quality of the beam should vary with radial distance from the central beam axis. To represent its transverse distribution, we propose a trichrome beam model in which primary C-ions, heavy fragments with atomic number Z ≥ 3, and light fragments with Z ≤ 2 are assigned to the first, second, and third Gaussian components, respectively. Assuming a realistic beam-delivery system, we performed computer simulations using Geant4 Monte Carlo code for analytical beam modeling of the monochrome and trichrome models. The analytical beam models were integrated into a treatment planning system for scanned C-ion radiotherapy. A target volume of 20  ×  20  ×  40 mm(3) was defined within a water phantom. A uniform biological dose of 2.65 Gy (RBE) was planned for the target with the two beam models based on the microdosimetric kinetic model (MKM). The plans were recalculated with Geant4, and the recalculated biological dose distributions were compared with the planned distributions. The mean target dose of the recalculated distribution with the monochrome model was 2.72 Gy (RBE), while the dose with the trichrome model was 2.64 Gy (RBE). The monochrome model underestimated the RBE within the target due to the assumption of no radial variations in radiation quality. Conversely, the trichrome model accurately predicted the RBE even in a small target. Our results verify the applicability of the trichrome model for clinical use in C-ion radiotherapy treatment planning.