## 1 Introduction  
Brain tumors are fast-progressing and hard to detect at early stages [1]. Glioblastoma multiform (GBM) is a brain tumor with a poor prognosis owing to the absence of specific risk factors [2; 3]. GBM is an aggressive and undifferentiated type of malignant tissue, known as grade IV astrocytoma by the World Health Organization [4]. To diagnose GBM, medical imaging methods are usually used, such as Magnetic Resonance Imaging (MRI) [5; 6], computer tomography (CT) [7], and positron emission tomography (PET) [8]. However, these methods are expensive and time-consuming. This does not allow for using them for screening tests to provide early GBM detection. Sometimes, a procedure called a tissue biopsy is conducted before treatment begins [9; 10]. Tissue is cut through a small hole made in the skull using a thin needle. This procedure can cause traumatic brain injury (TBI), lead to inflammation, and accelerate tumor growth. Also, there is a suggestion that TBI may promote the development of GBM [11]. Therefore, differential and non-invasive diagnoses of glioblastoma and traumatic brain injury are of huge practical importance. Liquid biopsy based on analyses of body fluids is more preferable compared to tissue biopsy for early cancer diagnosis, including that of GBM [12]. Modern studies are aimed at tumor-associated molecular pathway investigations in body fluids [13; 14]. Liquid chromatography with mass spectrometry (LC-MS) [15; 16; 17] and nuclear magnetic resonance (NMR) [18; 19] methods are used to discover GBM molecular markers in liquid samples. GC-MS was used to measure the level of 2-hydroxyglutaric acid enantiomers in the blood serum, which are mutated isocitrate dehydrogenase proteins [16]. LC-MS combined with machine learning was used to study perturbations of the metabolic pathways of cell proliferation, regulation, survival, differentiation, and angiogenesis during glioma development [20]. NMR complements the methods mentioned above by studying the blood plasma and brain tissues [18; 19]. But these techniques have significant drawbacks, such as timely intraoperative analysis due to complex preparation procedures, along with a long test time. Optical spectroscopy methods are easier to use for biological fluid content analysis. Terahertz time-domain (THz-TDS) [21; 22], infrared (IR) [23; 24; 25; 26; 27; 28], and Raman spectroscopies [29; 30; 31; 32] were used for GBM early diagnostics through the discovery of specific spectral patterns in body fluids. THz-TDS is based on measurements of the electric field of femtosecond THz pulses transmitted through a sample. THz-TDS provides the possibility of measuring the medium refractive index n and absorption coefficient \(\alpha\), hence, determining the complex dielectric permittivity of the biological sample in a single spectral scan in a broad frequency range [33; 34; 35; 36]. THz spectra of body fluids and tissues do not contain resonance peaks, because many molecule absorption spectral peaks overlap in this spectral range [37; 35; 38]. Therefore, THz-TDS cannot provide detailed information about a sample's chemical content, but the total metabolic profiles of samples from healthy and ill people can be differentiated using a combination of THz-TDS and machine learning (ML) methods [22; 38]. One of the exceptions to this is the water component, because it has a rich THz absorption spectrum [39; 40] that opens up possibilities for the operative determination of malignant tumor boundaries due to the high water content there [41; 42; 43]. THz-TDS allows for distinguishing free and bound water, as the absorption of free water dominates by an order of magnitude over the absorption of bound water in the range of 0.1-1.0 THz [44; 45; 46]. Usually, in biomedical studies, spectral data dimensionality is essentially larger than the dataset volume [47]. In this case, data are highly correlated, which makes using standard methods of spectra decomposition like multivariate curve resolution inefficient.