基于LNDM模型的碳离子束混合辐射场相同剂量平均LET下关键纳剂量学指标及RBE分析

纳剂量学量正在成为新的表征辐射品质的量，也是用于精确计算相对生物学效应(RBE)的基础数据。具有相同剂量平均传能线密度(LET)离子束混合辐射场导致的生物学效应也未必相同。为研究关键纳剂量学指标电离簇尺寸N_ICS$\geqslant 1 $的条件概率密度分布的一阶矩($M_1^{{C_1}}$)、N_ICS$\geqslant 2$的条件概率密度分布的一阶矩($M_1^{{C_2}}$)、N_ICS$\geqslant 2 $的累计概率($F_2^{{C_1}}$)和N_ICS$\geqslant 3 $的累计概率($F_3^{{C_2}}$)]以及RBE在相同剂量平均LET混合辐射场中的分布，在蒙特卡罗(Monte Carlo，MC)模拟的基础上，结合单能离子束关键纳剂量学指标数据集，计算得到了不同能量碳离子束在不同贯穿深度处相同剂量平均LET混合辐射场中的$M_1^{{C_1}}$、$M_1^{{C_2}}$、$F_2^{{C_1}}$、$F_3^{{C_2}}$及RBE值。计算结果显示:在相同剂量平均LET混合辐射场中，不同能量碳离子束的$F_3^{{C_2}}$没有发生显著变化，而$M_1^{{C_1}}$、$M_1^{{C_2}}$和$F_2^{{C_1}}$变化显著，且随能量的增大而减小，并且随剂量平均LET的增加，$M_1^{{C_1}}$、$M_1^{{C_2}}$和$F_2^{{C_1}}$变化差异逐渐变大。正是由于$M_1^{{C_1}}$、$M_1^{{C_2}}$、$F_2^{{C_1}}$和$F_3^{{C_2}}$的不同，在相同剂量平均LET混合辐射场中基于纳剂量学模型计算得到的RBE值也显著不同。这些结果表明，剂量平均LET并不能很好地用于描述离子束混合辐射场的品质，而关键纳剂量学指标则有望成为表征离子束混合辐射场品质的量。

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.