@article{oai:repo.qst.go.jp:00047578,
 author = {Kanematsu, Nobuyuki and Komori, Masataka and Yonai, Shunsuke and Ishizaki, Azusa and Kanematsu, Nobuyuki and Komori, Masataka and Yonai, Shunsuke and Ishizaki, Azusa},
 issue = {7},
 journal = {Physics in Medicine and Biology},
 month = {Apr},
 note = {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.},
 pages = {2015--2027},
 title = {Dynamic splitting of Gaussian pencil beams in heterogeneity-correction algorithms for radiotherapy with heavy charged particles},
 volume = {54},
 year = {2009}
}