## 4 Discussion  
To study glioblastoma development and find adequate therapeutic approaches, various experimental models of glioblastoma have been developed [60, 69]. In the most popular models, tumor cells are injected into the brain of an animal [61]. However, the injection procedure is itself a factor of TBI [63, 64, 70]. A needle insertion into brain structures and the injection of different substances lead to the development of neuro inflammation within the first 24 h after such manipulations [63, 70, 71]. MRS in vivo measurements showed decreases in tNAA (the sum of N-acetylaspartate and N-acetylaspartate acid) and tCho (the sum of glycerophosphocholine and phosphocholine) levels on the 7 th day after CMI [64], indicating possible neuronal death and axonal damage associated with TBI [72]. The level of gamma aminobutyric acid also decreased, which is consistent with the dynamics of the level of this metabolite after TBI [73]. The major goal of this work was to discover the informative features in blood serum THz spectra, which differentiate TBI and glioblastoma. It should be noted that the blood serum samples analyzed here were from the same mice, which were analyzed in vivo by MRS (these data were presented in Ref. [64]). According to the presented results, the mean THz spectrum of the blood serum samples from CMI group 1 (day 7 after the injection) had lower intensities compared to similar spectra of CMI groups 2 and 3 (see Figure 3b). The results of the PCA and t-SNE processing of the CMI groups' THz spectra showed that CMI group 1 was separated from CMI groups 2 and 3 (see Figure 6). This is consistent with the data regarding the temporal development of TBI [63, 64, 70, 71]. Therefore, CMI group 1 was concluded to correspond to the TBI state. Figure 9: ROC-AUC analysis of SVM classifier (**a**) of the TBI group vs. the GBM group and the corresponding informative features (**b**). The development of neuro inflammation after CMI has a limited temporal period. After day 14 of the experiment, the histological analysis did not demonstrate a significant difference in the brains after CMI and healthy brains [70]. The aforementioned neuro metabolites' return to the levels of healthy mice was observed by day 21 after the CMI, which confirms the restoration of neurons and their viability [64]. Therefore, CMI group 3 can be used as a group of animals that no longer show clear signs of neuro inflammation and TBI. The mice in this group can be considered conditionally healthy. This was also confirmed by the fact that the mean THz intensity of CMI group 3 was higher compared to that of CMI groups 1 and 2 (see Figure 3b), growing closer to the amplitude of the THz spectrum of water [58]. As mentioned above, changes in the relative proportions of free and bound water and in relaxation times for either of these states can all be observed by THz spectroscopy [34; 46; 65]. Changes in blood composition at diabetes mellitus [74], liver cancer [75], and thyroid cancer [38], as well as GBM [65], were shown by us to be detected in the blood THz absorption spectra. The development of neuro inflammation [63; 64; 71] in experimental models of glioblastoma [61; 64] and the subsequent development of the tumor lead to the release of inflammatory and oncological molecular markers into the blood [14]. Molecular markers' discovery using THz spectroscopy is a complex and currently unsolved problem. ML methods allow for building predictive data models and finding informative frequencies in the THz spectral range associated with similar molecular markers [76; 77; 78]. A THz spectra analysis of blood serum from the CMI and GBM groups of mice to estimate the THz spectral regions responsible for the differentiation of glioblastoma from TBI was conducted. Two dimensionality reduction algorithms (PCA and t-SNE) were used for data visualization. Three supervised machine learning algorithms--SVM, RF, and Catboost--were used for classification and informative feature selection.