In this study, we try to estimate the relative biological effectiveness (RBE) of low-energy electrons released during the gadolinium neutron capture reaction (157GdNCR) using microdosimetric methods. It is assumed that the 157Gd is uniformly distributed throughout the cells and can be bound to DNAs. The microdosimetric parameters of Gd electrons along with those of carbon ions and protons were calculated using the Geant4-DNA and ROOT software. It was found that for a DNA target, the -ratio of carbon ions relative to reference radiation is proportional to the relevant RBE, independent of the radiation quality. Comparing the microdosimetric parameters of Gd electrons with those of carbon ions obtained in a 10-nm target, we evaluated the RBE of Gd electrons. In the case where 157Gd distributed inside of the DNA target, the RBE values of Gd electrons were obtained 2.36 and 2.21 using the modified microdosimetric kinetic model and biological weighting function with specific cell type and end-points, respectively. Although the amount of specific energy of Gd electrons in the DNA target is strongly dependent on the 157Gd distribution relative to the target, the RBE variations to the 157Gd distribution are low. The mean energy deposited of Gd electrons in the DNA target during one 157GdNCR with a value of 220.41 eV (equivalent to 207.73 kGy) is large enough for the induction of double-strand break of DNA. This microdosimetric estimation of the RBE of Gd electrons can be useful for assessing the biological dose of Gd electrons in neutron capture therapy. For other Gd compounds or Auger-electron emitters with heterogeneous distributions inside the cells, by comparing with the results obtained in this study, one can evaluate the RBE of their Auger electrons.

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