@misc{oai:repo.qst.go.jp:00066436,
 author = {Kanematsu, Nobuyuki and Inaniwa, Taku and 兼松 伸幸 and 稲庭 拓},
 month = {Sep},
 note = {In carbon-ion radiotherapy, single-beam delivery each day in alternate directions has been commonly practiced for efficient operation, taking advantage of the Bragg peak and the relative biological effectiveness (RBE) for uniform dose conformation to a tumor.
These treatments are generally fractionated and their plans are evaluated with total RBE-weighted dose, which is however deficient in relevance to the biological effect.
In this study, we reformulate the biologically effective dose (BED) to normalize the dose-fractionation and cell-repopulation effects as well as the RBE of treating radiation, based on the inactivation of a reference cell line by a reference carbon-ion radiation.
The BED distribution virtually represents the biological effect of a treatment regardless of radiation modality or fractionation scheme.
We applied the BED formulation to simplistic model treatments and to a preclinical survey for hypofractionation based on an actual prostate-cancer treatment with carbon ions. 
The proposed formulation was demonstrated to be practical and implicative.
For the prostate-cancer treatment in 12 fractions, the distributions of BED and of RBE-weighted dose were very similar. 
With hypofractionation, while the RBE-weighted-dose distribution varied significantly, the BED distribution was nearly invariant, implying that the carbon-ion radiotherapy would be virtually insensitive to fractionation.
However, treatment evaluation with such simplistic biological dose is intrinsically limited and must be complemented in practice by clinical experience and biology experiment., 第114回日本医学物理学会学術大会},
 title = {Biological dose representation for carbon-ion radiotherapy of unconventional fractionation},
 year = {2017}
}