## 4 Discussion  
In this study, we demonstrated that the radiobiological effect of scanned \({}^{4}\)He-, \({}^{12}\)C-, \({}^{16}\)O-, and \({}^{20}\)Ne-ion beams in HSGc-C5 cells can be predicted based on the measured microdosimetric lineal energy spectra based on the MK model. The MK model parameters for HSG cells proposed by [PERSON] et al. [8], \(\alpha_{0}\) = 0.13 Gy\({}^{-1}\), \(\beta\) = 0.05 Gy\({}^{-2}\), and \(R_{n}\) = 4.1 \(\upmu\)m, have been known to estimate well the biological effects for HSG cells [20,21,33,34]. For the HSGc-C5 cells supplied from the same source, we obtained the MK parameters, which best predict the SF values for monoenergetic ion beams with different LETs. The \(R_{n}\) = 6.6 \(\upmu\)m we determined is quite plausible, because the radius distribution of 390 HSG cells measured using a fluoro-microscope showed a Gaussian distribution ranging from 4.6 to 8.6 \(\upmu\)m when cells were lightly sown [8]. However, the \(\alpha_{0}\) = 0.07 Gy\({}^{-1}\) we determined differs from \(\alpha_{0}\) = 0.13 Gy\({}^{-1}\) predicted by [PERSON] et al. [8]. [PERSON] et al. [15] mentioned that the radiosensitivity of HSGc-C5 cells might change from that of the HSG cells over time. That is, the \(\alpha_{x}\) for X-ray irradiation of HSG cells reported by [PERSON] et al. [35] was 0.331 Gy\({}^{-1}\), but the \(\alpha_{x}\) for X-ray irradiation reported by [PERSON] et al. [15] and used here was 0.252 Gy\({}^{-1}\), which reflected an increased radioresistance to the X-rays. For this reason, \(\alpha_{0}\) determined here is also considered to be smaller than \(\alpha_{0}\) as described by [8]. Figure 6: The blue markers show the biological dose along the SOBP of (**a**) \({}^{4}\)He-, (**b**) \({}^{12}\)C-, (**c**) \({}^{16}\)O-, and (**d**) \({}^{20}\)Ne-ion beams, calculated by means of multiplication of the physical doses and the RBE presented in Figure 5. The black square markers are the measured dose \(D_{IC}\) presented in Figure 4. The black and blue solid lines indicate the planned physical and biological doses calculated by the TPS. Each error bar corresponds to the uncertainties of the biological dose evaluated from the error of lineal energy using error propagation. The MK model utilizes a constant \(\beta\) value regardless of the LET of the ions. It is known that the \(\beta\) value typically converges to 0 as the LET increases to a certain level, which depends on the type of cell line investigated and the ions utilized [36]. At a high LET, even if the predicted \(\alpha\) value from the MK model agrees well with the fitted \(\alpha\) value from in vitro cell data based upon the LQ model, the constant \(\beta\) value derived from the MK model will be greater than the \(\beta\) value derived from the LQ model, such that the MK model may be underestimating the SF at high LET as the dose per fraction is increased. Our previous study showed how much the survival curve predicted by the MK model for late-responding cells differed from the survival curve (in vitro cell data) fitted with \(\alpha\) and \(\beta\) set as free parameters [22]. Meanwhile, HSGc-C5 cells used in this study have different radiation sensitivities, as they are early responding cells with a large \(\alpha\) and small \(\beta\) for X-rays [15]. In this case, the accuracy of SF prediction due to the constant \(\beta\) in the MK model will be higher than in the case of late-responding cells. In particular, up to the 10% survival level as shown in Figure 7, there was no significant difference between the survival curves from the constant \(\beta\) compared to the survival curve fitted with \(\alpha\) and \(\beta\) set as free parameters. [PERSON] et al. [8] mentioned that a change in \(\beta\) value might be required for higher doses when SF is less than 1%. It should be mentioned that MK model parameters for HSGc-C5 cells determined in this study are somewhat different from those of [PERSON] et al. [15] for two reasons.