## 3 Results  
Figure 2 displays the SFs of HSGc-C5 cells for different LETs (reported in [15]), as well as the survival curves calculated according to the MK model and using Equations (1) and (3) with determined MK model parameters for HSGc-C5 cells (\(\alpha_{0}\) = 0.07 Gy\({}^{-1}\), \(\beta\) = 0.0474 Gy\({}^{-2}\), \(R_{n}\) = 6.6 \(\mu\)m, \(r_{d}\) = 0.43 \(\mu\)m, and \(y_{0}\) = 255 keV/\(\mu\)m) and \(y^{*}\) as described in Section 2.4. Figure 3a-d show the measured microdosimetric spectra across the SOBP of the ion beams at various depths in PMMA phantoms. Figure 4 shows the measured dose and the calculated \(\overline{y_{D}}\) and \(y^{*}\) from the microdosimetric spectra along the SOBP of the ion beams measured in Figure 3.  
Figure 3: _Cont_. Figure 2: In vitro survival fraction (markers) for HSGc-C5 cells for different LETs of pristine (**a**) \({}^{4}\)He-, (**b**) \({}^{12}\)C-, (**c**) \({}^{16}\)O-, and (**d**) \({}^{20}\)Ne-ion beams (reported in [15]) and the survival curves (solid lines) predicted by the measured dose and \(y^{*}\) with the MK model parameters: \(a_{0}=0.07\) Gy\({}^{-1}\), \(\beta=0.0474\) Gy\({}^{-2}\), \(R_{n}=6.6\)\(\upmu\)m, \(r_{d}=0.43\)\(\upmu\)m, and \(y_{0}=255\) keV/\(\upmu\)m. The survival curves of HSGc-C5 cells from the 200 kVp X-ray exposure (reported by [15]) calculated by the LQ model (\(\alpha_{X}=0.252\) Gy\({}^{-1}\), \(\beta_{X}=0.0474\) Gy\({}^{-2}\)) are indicated by broken lines, respectively. The smallest values of the variance for \({}^{4}\)He-, \({}^{12}\)C-, \({}^{16}\)O-, and \({}^{20}\)Ne-ion beams calculated using Equation (7) are 0.16, 0.18, 0.05, and 0.16, respectively. The black square markers in Figure 5 show the predicted SF for the HSGe-C5 cells, which were irradiated at various depth levels in PMMA phantoms across the SOBP of the ion beams. The SF values were calculated using the measured dose and \(y^{*}\) presented in Figure 4. Apart from the plateau region and the distal part of the target region of \({}^{4}\)He ions, the SFs predicted by the measured doses and the microdosimetric lineal energy spectra were consistent with the SFs predicted by the TPS. The averaged SFs over the SOBP region were 10.4 \(\pm\) 1.4, 10.3 \(\pm\) 1.4, 10.4 \(\pm\) 0.8, and 10.5 \(\pm\) 0.5% for the \({}^{4}\)He-, \({}^{12}\)C-, \({}^{16}\)O-, and \({}^{20}\)Ne-ion beams, respectively. The blue markers in Figure 5 indicate the predicted RBE at the same  
Figure 4: Physical dose, \(D\), measured using the IC, and \(\overline{y_{D}}\) and \(y^{*}\) calculated based on the microdosimetric lineal energy spectra displayed in Figure 3 at several depth levels in the PMMA phantoms along the SOBP of the (**a**) \({}^{4}\)He-, (**b**) \({}^{12}\)C-, (**c**) \({}^{16}\)O-, and (**d**) \({}^{20}\)Ne-ion beams. The physical dose was measured twice \(D_{IC.1 st\ and\ 2 nd}\). The black solid lines are the physical doses planned by the TPS. Each error bar corresponds to the uncertainties of the linear energies evaluated using error propagation from the measured spectrum. Figure 3: Typical microdosimetric lineal energy spectra measured utilizing the SOI MicroPlus-mushroom microdosimeter at several depth levels in the PMMA phantoms of the SOBP of the (**a**) \({}^{4}\)He-, (**b**) \({}^{12}\)C-, (**c**) \({}^{16}\)O-, and (**d**) \({}^{20}\)Ne-ion beams (the \(y\) on the horizontal axis in each figure is the value in the tissue calculated using the conversion factor of 0.58 between the tissue and silicon [22,29]). depth levels of the SOBP. The RBEs estimated at the middle of the target region (at 120 mm) were 0.98, 1.39, 1.58, and 1.71 for these ion beams, respectively. Except for the tail regions, the RBEs were very well aligned with the values planned by the TPS. Figure 6 shows the RBE-weighted dose planned by the TPS and the predicted biological dose from the measurements utilizing the SOI MicroPlus-mushroom microdosimeter toward these ion beams.