@misc{oai:repo.qst.go.jp:00069819,
 author = {Kanematsu, Nobuyuki and Komori, Masataka and Yonai, Shunsuke and Ishizaki, Azusa and 兼松 伸幸 and 小森 雅孝 and 米内 俊祐 and 石崎 梓},
 month = {Jul},
 note = {Purpose: To develop an algorithm to resolve intrinsic problems with dose calculations using pencil beams when particles involved in each beam are overreaching a lateral density interface or when they are detouring in a laterally heterogeneous medium. Method and Materials: A finding on a Gaussian distribution, such that it can be approximately decomposed into multiple narrower, shifted, and scaled ones, was applied to dynamic splitting of pencil beams implemented in a dose calculation algorithm for proton and ion beams. The method was tested in an experiment with a range-compensated carbon-ion beam. Its effectiveness and efficiency were evaluated for carbon-ion and proton beams in a heterogeneous phantom model. Results: The splitting dose calculation reproduced the detour effect observed in the experiment, which amounted to about 10% at a maximum or as large as the lateral particle-disequilibrium effect. The proton-beam dose generally showed large scattering effects including the overreach and detour effects. The overall computational times were 9 s and 45 s for non-splitting and splitting carbon-ion beams and 15 s and 66 s for non-splitting and splitting proton beams. Conclusions: The beam-splitting method was developed and verified to resolve the intrinsic size limitation of the Gaussian pencil-beam model in dose calculation algorithms. The computational speed slowed down by factor of 5, which would be tolerable for dose accuracy improvement at a maximum of 10%, in our test case., AAPM Annual Meeting 2009},
 title = {Dynamic splitting of Gaussian pencil beams in heterogeneity-correction algorithms for radiotherapy with heavy charged particles},
 year = {2009}
}