## 1 Introduction
A common animal model for studying brain tumors is the orthotopic transplantation of glioblastoma cells into the mouse brain [60; 61]. After the injection of tumor cells into the subcortical brain structures, rapid glioma growth occurs, resulting in the destruction of neurons, compression of individual brain structures, and deep irreversible lesions [62]. It has recently been shown that the injection itself can be considered as a traumatic brain injury (TBI) [63]. It is necessary to differentiate metabolic disorders in the mouse brain caused by TBI and GBM. The dynamics of nine neuro-metabolites in the mouse brain after a culture medium injection with \({}^{1}\)H magnetic resonance spectroscopy (MRS) were studied in vivo. The levels of these neuro-metabolites in the first week after intracranial injection were analogous to brain trauma ones and returned to normal values by 21 days after injection [64]. The orthotopic xenotransplantation of U87 human glioblastoma cells (GBM groups) into immunodeficient mice was analyzed [58; 61; 65]. The dynamics of U87 glioblastoma development were assessed by the growth of the tumor, the size of which increased 34 times from the 7 th day to the 21 st day of the experiment and amounted to 89.6 mm\({}^{3}\)[58]. The experiment design included an analysis of serum samples collected on the 7 th day (the first group), on the 14 th day (the second group), and on the 21 st day (the third group) after the U87 cells' injection, and three respective control groups with a culture medium injection (CMI groups) were used. The CMI and GBM groups were compared for each week of the experiment. It was shown that GBM development in the mouse brain can be effectively studied via a blood serum spectral analysis by THz-TDS. Still, differences discovered between the informative frequencies for the separation of the first, second, and third groups (GBM versus CMI) were not properly explained. Our hypothesis is that the main reason for this was the inflammatory processes in brain tissues arising as TBI at the injection site after the culture medium or U87 cells' injection in the first week of the experiment. To verify this hypothesis, the following analysis of the experimental data was suggested in this paper. First, the homogeneity of the groups on the 7 th, the 14 th, and the 21 st days after CMI was checked. Second, if there was a difference between these groups, then the third CMI group would be considered as mice with a healthy brain, while the first and the second CMI groups corresponded to TBI. Their comparison with the third CMI group allowed for extracting the informative features of TBI. Then, the difference between traumatic brain injury and glioblastoma could be found by comparing the first CMI group (associated with TBI) and the third GBM group (the 21 st day after U87 human glioblastoma cells' injection). So, the main objective of this paper was differentiation between traumatic brain injury and glioblastoma through a blood serum analysis by THz-TDS and machine learning methods. An illustration of the idea of our study is shown in Figure 1a. A list of corresponding ML models is given in Figure 1b. Models 1-3 were used to verify the homogeneity of the CMI groups, and Model 4 was used to test the separation between the TBI and GBM groups. Contrary to our previous work, the homogeneity of the CMI groups was tested by the unsupervised ML methods to prove that effect of CMI is detectable by THz spectroscopy. Both pre-processing and ML hyperparameters were optimized to achieve robust models. The effects of PCA and t-SNE parameters on an exploratory analysis of the THz data were revealed. Finally, the informative THz sub-bands allowing for distinguishing the CMI and GBM groups were selected. Figure 1: The idea of the study (**a**): red area illustrates the CMI state, blue, the GBM state, and white area, the healthy state. Arrow means comparison of groups for TBI and GBM differentiation. List of ML binary models under study (**b**).