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We have developed a simple collimator model to improve the accuracy of penumbra behaviour in pencil-beam dose calculation for proton radiotherapy. In this model, transmission of particles through a three-dimensionally extended opening of a collimator is calculated in conjunction with phase-space distribution of the particles. Comparison of the dose distributions calculated using the new three-dimensional collimator model and the conventional twodimensional model to lateral dose profiles experimentally measured with collimated proton beams showed the superiority of the new model over the conventional one.

In this study, the survival fraction (SF) and relative biological effectiveness (RBE) of pancreatic cancer cells exposed to spread-out Bragg peak (SOBP) helium, carbon, oxygen, and neon ion beams are estimated from the measured microdosimetric spectra using a microdosimeter and the application of the microdosimetric kinetic (MK) model. To measure the microdosimetric spectra, a 3D mushroom silicon-on-insulator (SOI) microdosimeter connected to low noise readout electronics (MicroPlus probe) was used. The parameters of the MK model were determined for pancreatic cancer cells such that the calculated SFs reproduced previously reported in vitro SF data. For a cuboid target of 10×10×6 cm, treatment plans of helium, carbon, oxygen, and neon ion beams were designed using in-house treatment planning software (TPS) to achieve a 10% SF of pancreatic cancer cells throughout the target. The physical doses and microdosimetric spectra of the planned fields were measured at different depths in polymethyl methacrylate (PMMA) phantoms. The biological effects, such as SF, RBE, and RBE-weighted dose at different depths along the fields were predicted from the measurements. The predicted SFs at the target region were generally in good agreement with the planned SF from the TPS in most cases.

The pencil-beam algorithm is valid only when elementary Gaussian beams are small enough compared to lateral heterogeneity of a medium, which is not always true in actual radiotherapy with protons and ions. This work addresses a solution for the problem. We found approximate self-similarity of Gaussian distributions, with which Gaussian beams can split into narrower and deflecting daughter beams when their sizes have overreached lateral heterogeneity in beam-transport calculation. The effectiveness was assessed in an carbon-ion beam experiment in the presence of steep range compensation, where the splitting calculation reproduced the detour effect amounting up to about 10% in dose or as large as the lateral particle disequilibrium effect. The efficiency was analyzed in calculations for carbon-ion and proton radiations with a heterogeneous phantom model, where the beam splitting increased computing times by factors of 4.7 and 3.2. The present method generally improves accuracy of the pencil-beam algorithm without severe inefficiency. It will therefore be useful for treatment planning and potentially other demanding applications.