Proton and carbon-ion minibeam therapy: from modeling to treatment

Arrays of minibeams of protons and $^{12}$C in tissue-like media were modeled with Geant4 toolkit. A set of beam energies was used in simulations to provide a Spead-out Bragg peak (SOBP) extended by 6 cm in depth for protons as well as for $^{12}$C. In both cases, beams of 0.3 mm or 0.5 mm FWHM were arranged at the entrance to a water phantom either on a rectangular or an hexagonal grid to compare two kinds of projectiles and different minibeam patterns. Differential and cumulative dose-volume histograms (DVH) were calculated and compared for protons and $^{12}$C as dose uniformity metrics. A uniform dose distribution was easily achieved with protons due to an enhanced lateral scattering of these projectiles in comparison to $^{12}$C. The cumulative DVHs calculated for 0.3 mm or 0.5 mm minibeams almost coincide in the target volume, but diverge for different grid patterns. In contrast, cumulative entry DVHs were found similar for both grid patterns, but different for 0.3 mm and 0.5 mm minibeams.