## 4 Rationale of Proton Beam Therapy
PCA has been proven to be especially effective for analyzing infrared spectra, too. It is based on a mathematical decomposition of the spectral data with the aim of reducing data set dimensions by using only some new principal components (PCs) or loadings that explain most data set variance and then are thought to carry the most important information of the spectra [50]. Spectral data can be inspected by using different combinations of PCs to obtain a new system of coordinates. PCA is based on the analysis of the correlation or covariance matrix. The number of components necessary to explain at least 80% of the total variance is usually considered. Recently, selected regions of Raman spectra have been separately analyzed by PCA to extract information hidden in those specific ranges. This kind of approach is called the interval-PCA (iPCA) method [51]. An example of the results that can be obtained by PCA in this framework is reported in Reference [46]. In this case, the second derivatives analysis reported in Figure 2B of Reference [46] indicated an intensity change of the O-P-O symmetric stretching mode at 1083 cm\({}^{-1}\). The decrease in intensity shows a dose-dependent behavior that can indicate the occurrence of strand cleavage and chromatin fragmentation [52; 53]. This last effect is due to the high number of DSBs. The small shift of the O-P-O asymmetric stretching band at approximately 1234 cm\({}^{-1}\) was probably caused by local conformational changes in the DNA. PCA was applied to different groups of infrared spectra collected from cells fixed immediately after irradiation. In the first case, four groups of cells were considered: (a) irradiated by 4000 protons; (b) irradiated by 200 and 400 protons; (c) irradiated by 50 protons; (d) the untreated ones. PCA showed that PC-1 (corresponding to 73% of the total variance) was positively correlated with features attributed to vibrations of DNA base-sugar bonds C-O-P tranrose-DNA backbone stretching vibrations and O-P-O symmetric and asymmetric stretching in DNA. In the second case, PCA was applied to two groups of spectra acquired from control cells and cells irradiated with 4000 protons per cell and fixed just after irradiation. In this case, a very good separation of controls versus irradiated cellson the PC1 versus PC2 scores plot was evidenced for the two groups (see Reference [46] and Figure 4a,b therein for further details). To study the cellular response and the repairing processes after exposure to ionizing radiation, the spectra acquired from cells fixed 24 h after irradiation were examined. In this case, lipid accumulation was evidenced by an increase in the lipid ester carbonyl mode and other CH lipid bands. These variations were discussed as related to an increase in lipid metabolism during apoptosis and the inclusion of lipid droplets involved in the formation of apoptotic bodies. The lipid peroxidation effect was considered as the cause of the observed decreased intensity of the CH\({}_{3}\) stretching mode and the increased intensity of the CH\({}_{2}\) stretching mode [46]. The same group of researchers also investigated prostate cancer cells derived from brain metastasis (DU-145 cell line) using two experimental setups for uFTIR spectroscopy. The former uses a Gobar source with a focal plane array (FPA) detector and the latter a synchrotron radiation source with a mercury-cadmium-telluride (MCT) detector [54]. The high brightness of the SR source allowed for the acquisition of spectra from individual cells and permitted them to study the contribution of DNA in the spectral region 1300-900 cm\({}^{-1}\), which is usually difficult for conventional uFTIR spectroscopy due to the high density of the nucleus. For proton irradiation, DU-145 cells were treated as previously described for the PC-3 cells. In this case, cells were irradiated using a 1 MeV focused proton microbeam from the [PERSON] accelerator, which available at the Institute of Nuclear Physics PAN, Krakow, Poland.