Effects of dose-delivery time structure on biological effectiveness for therapeutic carbon-ion beams evaluated with microdosimetric kinetic model.

Treatment plans of carbon-ion radiotherapy have been made on the assumption that the beams are delivered instantaneously irrespective to the dose delivery time as well as the interruption time. The advanced therapeutic techniques such as a hypofractionation and a respiratory gating usually require more time to deliver a fractioned dose than conventional techniques. The purpose of this study was to investigate the effects of dose-delivery time structure on biological effectiveness in carbon-ion radiotherapy. The rate equations defined in the microdosimetric kinetic model (MKM) for primary lesions caused in the DNA were reanalyzed and applied to continuous or interrupted irradiation with therapeutic carbon-ion beams. The rate constants characterizing the time of the primary nonlethal lesions to repair or to convert to lethal lesion were experimentally determined for human salivary gland (HSG) tumor cells. Treatment plans were made for a patient case on the assumption that the beam is delivered instantaneously. The RBE weighted absorbed doses of 2.65, 3.45 and 6.86 Gy (RBE) was prescribed to the target. These plans were recalculated by varying the dose delivery time and the interruption time ranging from 1-60 min based on the MKM with the determined parameters. The sum of rate constants for nonlethal lesion to repair a and to convert to lethal lesion c, (a + c), is 2.19 ± 0.40 h⁻¹. The biological effectiveness in the target decreases with the dose delivery time T in continuous irradiation compared to the planned one due to the repair of nonlethal lesions during the irradiation. The biological effectiveness in terms of equivalent acute dose decreases to 99.7% and 96.4% for T = 3 and 60 min in 2.65 Gy (RBE), 99.5% and 94.3% in 4.35 Gy (RBE), and 99.4% and 91.7% in 6.86 Gy (RBE), respectively. For all the cases, the decrease of biological effectiveness is larger at the proximal side with low-LET than the distal side with high-LET. Similar reductions of biological effectiveness with comparable amounts are observed in the interrupted irradiations with prolonged interruption time τ. For the fraction time, i.e., T and/or τ, shorter than 3 min, the decrease of the biological effectiveness with respect to the planned one is less than 1.0%. However, if the fraction time prolongs to 30 min or longer, the biological effectiveness is significantly influenced in carbon-ion radiotherapy, especially with high-prescribed doses. These effects, if confirmed by clinical studies, should be considered in designing the carbon-ion treatment planning.