## 3 Results and Discussion  
One of the aims of this work is the comparison of three methods to calculate the RBE in a clinical setting: microdosimetric-based, Monte Carlo and LEM II model. All of the proposed approaches were compared with experimental data. Radiation-induced cell death was measured by clonogenic assay and RBE values were calculated using the Linear-Quadratic model. The clonogenic survival curves of two specific cell lines were experimentally measured at 24 mm, the mid-position of the 62 MeV clinical proton SOBP. Additionally, at the SOBP entrance, the survival curves were also estimated from the experimental measurements of the microdosimetric spectra. The estimation of the survival curves with these three approaches permitted the estimation of the RBE values in the centre of the SOBP region. The radiobiological effects of protons were experimentally evaluated using the human 92.1 uveal melanoma cell line. In order to evaluate the damage induced by proton therapy in a typical tissue belonging to the same anatomical site, the human normal retinal pigment epithelial ARPE-19 cell line was also irradiated. The assessment of the detrimental effects in healthy tissues due to radiotherapy is pivotal, especially for the treatment of cancers affecting the eye since even slight impairment of the normal ocular tissue would lead to a loss of function of the entire organ [42]. The results of the clonogenic curves with the fitted parameters, for the two cell lines irradiated at the proton mid-SOBP and under a reference gamma beam, are summarised in Table 1. Table also report the corresponding derived values of RBEs. Two fundamental radiobiological parameters were contextually obtained, the alpha and beta values, together with their ratio. Within the LQ model context, the alpha and beta coefficients of the clonogenic survival curves represent the single-hit, lethal damage, generally not repairable, and the multiple-hit damage, associated with sub lethal damage, respectively. Sublethal damage is responsible for the shouldered part of the clonogenic curve and can be usually repaired [43]. The \(\alpha/\beta\) ratio is an useful indicator of radiosensitivity, hence, its calculation is of paramount importance to evaluate the cell response to the radiation therapy (RT) treatment [44; 45]. The clonogenic endpoint has, in fact, shown a lower radiosensitivity exhibited by the ocular cancer cells with respect to the normal cells as expected. In addition, for both cell lines, an increased RBE with proton beam irradiation was obtained. The capability of the two microdosimeters to describe not only the RBE but also the survival curve at the mid-SOBP was then investigated. Figure 2 shows the acquired microdosimetric spectra from which the RBEs values and the parameters of the corresponding clonogenic curves were derived. Distributions are presented as \(yd(y)\) versus \(y\) on a logarithmic \(x\)-axis to facilitate visual interpretation. In this representation, the area under the curve between two values of \(y\) is proportional to the fraction of physical absorbed dose due to the events in that interval. Specifically, in Figure 2 the two positions (entrance and mid of the SOBP) and the two detectors (mini-TEPC and MicroPlus Bridge) are considered. In the same figures, the Loncol's biological weighting function \(r(y)\) and the corresponding weighted-dose curves \(yr(y)d(y)\) are also reported. The observed increase of the area under the red curve (i.e., the \(yr(y)d(y)\) curve) for the spectra acquired at the cell position (bottom row of Figure 2), reflects an increase in the RBE. It can be observed, in fact, that at the entrance position the biologically weighted distributions overlap almost perfectly with the un-weighted distributions, because for \(y<10\) keV\(/\)\(\mu\)m the weighting function \(r(y)\) almost equals almost equals 1.