## 4 Discussion
First, the sensitive volume of the SOI MicroPlus-mushroom microdosimeter (a thickness of 10 \(\upmu\)m and a diameter of 18 \(\upmu\)m) is approximately the size of cell nucleus (~10 \(\upmu\)m). The sensitive volume size of microdosimeter is higher than the domain size, which leads to different stochastic energy deposition spectra determined by the amorphous track structure model with an \(r_{d}\) of 0.34 \(\upmu\)m [37], but a less affecting difference in  
Figure 7: Markers show reported in vitro SF of HSGc-C5 cells for different LETs of pristine (**a**) \({}^{4}\)He-, (**b**) \({}^{12}\)C-, (**c**) \({}^{16}\)O-, and (**d**) \({}^{20}\)Ne-ion beams [15]. The lines represent the fitted survival curves based on the LQ model (solid lines: curves fitted with \(\alpha\) and \(\beta\) set as free parameters; broken lines: curves fitted with \(\alpha\) set as a free parameter and the constant \(\beta\) = 0.0474 Gy\({}^{-2}\)). as calculated by TPS and measured by SOI MicroPlus-mushroom microdosimeter, and the corresponding values of \(y^{*}\). Second, the model used in the TPS predicting biological response is the stochastic MK (SMK) model [13; 14; 15], which is an updated version of the MK model. The SMK model has been introduced because the MK model overestimates the biological effect at a high LET and a high dose. Although the biological effects at a relatively high LET or relatively high doses are not evaluated in this study (compared to Figure 3 in [13]), it can be seen that the MK model overestimates the biological effects at LET = 194.8 keV/\(\upmu\)m in \({}^{20}\)Ne ions in Figure 2d. Meanwhile, a solid-state detector that can measure the specific energy experimentally using the method of the SMK model has not yet been developed. The SMK model takes into account that a cell nucleus specific energy, \(\mathrm{z_{n}}\), can be stochastically different while the MK model considers that \(\mathrm{z_{n}}\) is the same. The SMK model might benefit from having solid state microdosimeters with many independent mushrooms and \(\sim\)0.5 \(\upmu\)m domains inside of each mushroom and measuring \(\mathrm{z_{n}}\) independently in both the domain and the mushroom [38]. We found that the RBE values predicted based on the measured dose and the microdosimetric lineal energy spectra are consistent with the values planned by the TPS except for the fragmentation tail regions (Figure 5). One of the probable reasons for the RBE inconsistency downstream of the SOBP is the setting of the low energy threshold value of the SOI detector used. The SOI MicroPlus-mushroom microdosimeter we used is suitable for measuring a lineal energy \(y\) higher than \(\sim\)1 keV/\(\upmu\)m for \({}^{4}\)He ions (using medium gain) and \(\sim\)2.2 keV/\(\upmu\)m for \({}^{12}\)C, \({}^{16}\)O, and \({}^{20}\)Ne ions (using low gain). In the fragmentation tail regions with many low LET particles below the energy threshold (see Figure 3), the measured \(y^{*}\) values could be higher than the actual values. To overcome the single gain measurements with the SOI-based microdosimeter, [PERSON] et al. [39] introduced an extrapolation approach that can lower the energy threshold by linearly extrapolating the measured spectrum up to \(\sim\)0.01 keV/\(\upmu\)m. This extrapolation approach could be one possible solution and may yield better results, but their approach was not adopted in this study. In our Monte Carlo simulation, the deposited energy of the entire electrons absorbed in the cylindrical volume used in the measurement was calculated to be approximately \(\sim\)20 keV (Si) (see Figure 10a). As mentioned in Section 2.2, since the LLD in our system is \(\sim\)50 keV (Si) at low gain and \(\sim\)15 keV (Si) at medium gain, the electron has no effect on the measurement result in \({}^{12}\)C, \({}^{16}\)O, and \({}^{20}\)Ne ions, but there may be little effect in \({}^{4}\)He ions. One of the drawbacks of this study is that this study did not evaluate the effect of the size of the sensitive volume of the SOI microdosimeter.