SU-F-T-125: Radial Dose Distributions From Carbon Ions of Therapeutic Energies Calculated with Geant4-DNA.

PURPOSE: Radial dose distribution D(r) is the dose as a function of lateral distance from the path of a heavy charged particle. Its main application is in modelling of biological effects of heavy ions, including applications to hadron therapy. It is the main physical parameter of a broad group of radiobiological models known as the amorphous track models. Our purpose was to calculate D(r) with Monte Carlo for carbon ions of therapeutic energies, find a simple formula for D(r) and fit it to the Monte Carlo data.

METHODS: All calculations were performed with Geant4-DNA code, for carbon ion energies from 10 to 400 MeV/u (ranges in water: ∼ 0.4 mm to 27 cm). The spatial resolution of dose distribution in the lateral direction was 1 nm. Electron tracking cut off energy was 11 eV (ionization threshold). The maximum lateral distance considered was 10 µm. Over this distance, D(r) decreases with distance by eight orders of magnitude.

RESULTS: All calculated radial dose distributions had a similar shape dominated by the well-known inverse square dependence on the distance. Deviations from the inverse square law were observed close to the beam path (r<10 nm) and at large distances (r >1 µm). At small and large distances D(r) decreased, respectively, slower and faster than the inverse square of distance. A formula for D(r) consistent with this behavior was found and fitted to the Monte Carlo data. The accuracy of the fit was better than 10% for all distances considered.

CONCLUSION: We have generated a set of radial dose distributions for carbon ions that covers the entire range of therapeutic energies, for distances from the ion path of up to 10 µm. The latter distance is sufficient for most applications because dose beyond 10 µm is extremely low.