Biological dose representation for carbon-ion radiotherapy of unconventional fractionation

In carbon-ion radiotherapy, single-beam delivery each day in alternate directions has been common practice for efficient operation, taking advantage of the Bragg peak and the relative biological effectiveness (RBE) for uniform dose conformation to a tumor. Treatments are usually fractionated and treatment plans are evaluated with the total RBE-weighted dose; however, this is of limited 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 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 to give theoretical implications. For a 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 carbon-ion radiotherapy would be effectively insensitive to fractionation. However, treatment evaluation with such a simplistic biological dose is intrinsically limited and must be complemented in practice by clinical experience and biological experiments.