A modified microdosimetric kinetic model for relative biological effectiveness calculation

In the heavy ion therapy, not only the distribution of physical absorbed dose, but also the relative biological effectiveness (RBE) weighted dose needs to be taken into account. The microdosimetric kinetic model (MKM) can predict the RBE value of heavy ions with saturation-corrected dose-mean specific energy, which has been used in clinical treatment planning at the National Institute of Radiological Sciences. In the theoretical assumption of the MKM, the yield of the primary lesion is independent of the radiation quality, while the experimental data shows that DNA double strand break (DSB) yield, considered as the main primary lesion, depends on the LET of the particle. Besides, the β parameter of the MKM is constant with LET resulting from this assumption, which also differs from the experimental conclusion. In this study, a modified MKM was developed, named MMKM. Based on the experimental DSB yield of mammalian cells under the irradiation of ions with different LETs, a RBEDSB (RBE for the induction of DSB)-LET curve was fitted as the correction factor to modify the primary lesion yield in the MKM, and the variation of the primary lesion yield with LET is considered in the MMKM. Compared with the present the MKM, not only the α parameter of the MMKM for mono-energetic ions agree with the experimental data, but also the β parameter varies with LET and the variation trend of the experimental result can be reproduced on the whole. Then a spread-out Bragg peaks (SOBP) distribution of physical dose was simulated with Geant4 Monte Carlo code, and the biological and clinical dose distributions were calculated, under the irradiation of carbon ions. The results show that the distribution of clinical dose calculated with the MMKM is closed to the distribution with the MKM in the SOBP, while the discrepancy before and after the SOBP are both within 10%. Moreover, the MKM might overestimate the clinical dose at the distal end of the SOBP more than 5% because of its constant β value, while a minimal value of β is calculated with the MMKM at this position. Besides, the discrepancy of the averaged cell survival fraction in the SOBP calculated with the two models is more than 15% at the high dose level. The MMKM may provide a reference for the accurate calculation of the RBE value in heavy ion therapy.