## 4 Conclusions  
We applied THz-TDS and ML methods to study the blood serum of mice in the dynamics of experimental U87 glioblastoma development. Larger tumor growth was observed from 14 to 21 days after injection of U87 cells into the subcortical brain structure.  
The ML pipeline included THz spectra smoothing using the Savitsky-Golay filter, outlier removing using IF, subtraction of the mean and normalizing data to the standard deviation, informative feature extraction, and dimensionality reduction by PCA. The predictive data model was created using SVM with a linear kernel. The proposed ML pipeline provided over 90% sensitivity, specificity, and accuracy of glioblastoma detection.  
The relationship between tumor size and THz spectral profile of blood serum was studied by LASSO regression. We established that serum THz absorption decreased when tumor size increased. The informative THz frequencies providing the best classification were close to 0.19 and 1.9 THz, the latter spectral region making the largest contribution. The presented results demonstrate that the ML-based blood-serum THz spectra predictive data model can allow researchers to distinguish between cancer and healthy groups, and to differentiate glioma stages. The average performance of the SVM classifiers was shown to increase after outliers were removed. The achieved efficiency of the predictive data model can be improved further by increasing the dataset volume.  
Conceptualization, O.C. and Y.K.; methodology, Y.K. and D.V.; software, D.V.; validation, D.V.; formal analysis, D.V., A.K., O.S., I.R. and E.Z.; investigation, A.K., O.S., I.R., and E.Z.; writing--original draft preparation, O.C., D.V. and A.K.; writing--review and editing, O.C., Y.K., M.K., O.S., E.Z. and A.S.; visualization, D.V. and A.K.; supervision, A.S.; project administration, O.C. and Y.K.; funding acquisition, O.C. All authors have read and agreed to the published version of the manuscript.  
The study was funded by Russian Foundation for Basic Research and National Natural Science Foundation of China according to the research project No. 19-52-55004 using the equipment of the Center for Genetic Resources of Laboratory Animals, Institute of Cytology and Genetics, Siberian Branch of the Russian Academy of Sciences, supported by the Ministry of Science and Higher Education of the Russian Federation (unique identifier of the project: RFMEF62119X0023). This work was supported by the Ministry of Science and Higher Education of the Russian Federation within the State assignment FSRC \"Crystallography and Photonics\" of the Russian Academy of Sciences, within the State assignment Institute of Laser Physics, Siberian Branch of the Russian Academy of Sciences. This work was supported by the Interdisciplinary Scientific and Educational School of Moscow University \"Photonic and Quantum Technologies, Digital Medicine\". The analysis  
Figure 11: Informative frequencies for THz spectra obtained from the LASSO method.  
of THz data by D.V., A.K. and Y.K. was supported by the Ministry of Science and Higher Education of the Russian Federation (V.E. Zuev Institute of Atmospheric Optics of Siberian Branch of the Russian Academy of Sciences). The work of Y.K. was supported by the Tomsk State University Development Program (Priority-2030).  
The study was conducted according to the guidelines of the Declaration of Helsinki, and approved by the Inter-Institutional Commission on Biological Ethics at the Institute of Cytology and Genetics, Siberian Branch of the Russian Academy of Sciences (Permission #78, 16 April 2021).  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.