Analysis on the Key Nanodosimetric Indexes and RBE in Mixed Carbon Ion-beam Irradiation Fields with the Same Dose-averaged LET Value on LNDM Model

Nanodosimetric quantities are becoming new measures to characterize radiation quality, which provide basic data for calculating Relative Biological Effectiveness(RBE). The biological effects under mixed ion-beam irradiation fields with the same dose-averaged Linear Energy Transfer(LET) value may not be the same. To study the distributions of key nanodosimetric indexes the first moment of the conditional cluster size distribution with ionization cluster size (N_ICS)\geqslant 1 ( M_1^C_1 ), the first moment of the conditional cluster size distribution with N_ICS\geqslant 2 (M_1^C_2), the conditional cumulative probabilities with N_ICS\geqslant 2 (F_2^C_1)and the conditional cumulative probabilities with N_ICS\geqslant 3 (F_3^C_2) and RBE values in mixed ion-beam irradiation fields with the same dose-averaged LET value, a pre-calculated key nanodosimetric indexes database combined with Monte Carlo(MC) simulation was introduced to accurately calculate M_1^C_1, M_1^C_2, F_2^C_1, F_3^C_2 and RBE in mixed irradiation fields with the same dose-averaged LET value for carbon ion beams at different penetration depths. The results showed that F_3^C_2 for different energy carbon ion beams did not change significantly, while M_1^C_1, M_1^C_2 and F_2^C_1 varied remarkably, and decreased with the increase of energy. Moreover, with the increase of dose-averaged LET value, the difference between M_1^C_1, M_1^C_2 and F_2^C_1 increased gradually. Due to the difference of M_1^C_1, M_1^C_2, F_2^C_1 and F_3^C_2 exactly, the calculated RBE values based on the Logistic NanoDosimetry model in mixed irradiation fields with the same dose-averaged LET value for carbon ion beams were also significantly different. These results indicated that the dose-averaged LET is not a good measure to describe the quality of the mixed irradiation fields of an ion beam, and the key nanodosimetric indexes are expected to be the candidates to characterize the quality of the mixed ion-beam irradiation fields.