## 3 Results and Discussion
Different behaviour can be observed at the mid-SOBP, where the weighting function augments the contribution of events above 10 keV\(/\)\(\mu\)m leading to an increase of the \(RBE_{\mu}\) (Equations (8)-(11)). The RBE calculated at the mid-SOBP with the mini-TEPC, (\(RBE_{\mu}\)-TECP = 1.18), resulted slightly higher than that calculated with the Microplus \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Irr. Type** & **\(\alpha\)(Gy\({}^{-1}\))** & **\(\beta\)(Gy\({}^{-2}\))** & **\(\alpha\)/\(\beta\)** & **Fit. Std. Err.** & \(RBE_{10}\) \\ \hline \multirow{2}{*}{92.1} & \(\gamma\)-rays & 0.20 \(\pm\) 0.03 & 0.076 \(\pm\) 0.004 & 2.68 & 0.02 & \multirow{2}{*}{1.4} \\ \cline{2-6}  & protons & 0.40 \(\pm\) 0.02 & 0.095 \(\pm\) 0.003 & 4.25 & 0.007 & \\ \hline \multirow{2}{*}{ARPE19} & \(\gamma\)-rays & 0.34 \(\pm\) 0.14 & 0.03 \(\pm\) 0.02 & 11.33 & 0.02 & \multirow{2}{*}{1.2} \\ \cline{2-6}  & protons & 0.43 \(\pm\) 0.01 & 0.041 \(\pm\) 0.003 & 10.49 & 0.04 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Survival curve parameters measured for proton and gamma irradiation of the 92.1 and ARPE-19 cell line. The statistical parameters of the double exponential fit function and the values of the derived RBEs are reported. Bridge (\(RBE_{\mu}\)-MicroPlus = 1.12). With respect to the entrance position, the \(RBE_{\mu}\)-TECP at the mid-SOBP increases by about 17%, and the \(RBE_{\mu}\)-MicroPlus increases by about 13%. The reason for this underestimation of the MicroPlus with respect to the TEPC is the larger simulated site size (about 17 \(\upmu\)m with respect to 1 \(\upmu\)m of the TEPC): low energy protons stop inside the silicon thickness, therefore the largest proton events (proton-edge) are at about 40 keV/\(\upmu\)m for the Microplus, while they are at about 140 keV/\(\upmu\)m for the mini-TEPC. The \(RBE_{\mu}\) values, corrected by a constant factor to have \(RBE_{\mu}=1.1\) at the entrance position of the SOBP, and the linear parameters \(\alpha_{\mu}\) of the linear-quadratic model, calculated using Equation (11), are reported in Table 2. The \(\beta_{\mu}\) was assumed to be equal to \(\beta_{\gamma}\) (see Section 2.4). Finally, the survival curves relative to the mid-SOBP position and derived from the microdosimetric data, experimentally measured from cell irradiation experiments and calculated with the described Monte Carlo and using the Survival software [37], are reported in Figure 3 (92.1 cell line) and Figure 4 (ARPE-19 cell line). Both figures also show the survival curve measured for the \({}^{60}Co\) gamma-ray irradiation. The survival experimental curves were fitted using the double exponential function (Equation (1)) and the \(\alpha\) and \(\beta\) derived from it were reported in Table 1. The survival fraction related to the experimental data and applyed approaches for the two investigated curves is reported in the Table 3 (92.1 cell line) and Table 4 ARPE-19 cell line). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Cell Type** & \(RBE_{\mu}\)**-TEPC** & \(RBE_{\mu}\)**-MicroPlus** & \(\alpha_{\mu}\)**TEPC** & \(\alpha_{\mu}\)**MicroPlus** \\ \hline
92.1 & 1.29 & 1.24 & 0.35 \(\pm\) 0.03 & 0.31 \(\pm\) 0.02 \\ \hline ARPE19 & 1.29 & 1.24 & 0.45 \(\pm\) 0.04 & 0.41 \(\pm\) 0.04 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: \(RBE_{\mu}\) calculated from microdosimetric spectra, and corrected by a constant factor to have \(RBE_{\mu}=1.1\) in entrance. The parameters \(\alpha_{\mu}\) TEPC and \(\alpha_{\mu}\) MicroPlus were calculated with Equations (8)–(11). Figure 2: The microdosimetric spectra \(yd(y)\) measured at the entrance (**top**) and at cell position (**bottom**) acquired with the mini-TEPC (**left**) and with the MicroPlus Bridge microdosimeter (**right**). The thick grey line represents the biological weighting function \(r(y)\) ([PERSON], 1994). The red curves are the weighted distributions \(yr(y)d(y)\). The black curves are the experimental microdosimetric spectra. See text for more details. Figure 4: Survival fractions for ARPE19.