  \item[Purpose] A recent study revealed that polyethylene (PE) would cause
extra carbon-ion attenuation per range shift by 0.45\%/cm due to compositional
differences in nuclear interactions. The present study aims to assess the
influence of PE range compensators on tumor dose in carbon-ion radiotherapy.
\item[Methods] Carbon-ion radiation was modeled to be composed of primary
carbon ions and secondary particles, for each of which the dose and the
relative biological effectiveness (RBE) were estimated at a tumor depth in the
middle of spread-out Bragg peak. Assuming exponential behavior for attenuation
and yield of these components with depth, the PE effect on dose was calculated
for clinical carbon-ion beams and was partly tested by experiment. The
two-component model was integrated into a treatment-planning system and the PE
effect was estimated in two clinical cases. \item[Results] The attenuation per
range shift by PE was 0.1\%--0.3\%/cm in dose and 0.2\%--0.4\%/cm in
RBE-weighted dose, depending on energy and range-modulation width. This
translates into reduction of RBE-weighted dose by up to 3\% in extreme cases.
In the treatment-planning study, however, the effect on RBE-weighted dose to
tumor was typically within 1\% reduction. \item[Conclusions] The extra
attenuation of primary carbon ions in PE was partly compensated by increased
secondary particles for tumor dose. In practical situations, the PE range
compensators would normally cause only marginal errors as compared to intrinsic
uncertainties in treatment planning, patient setup, beam delivery, and clinical
response.
