## 3 Results and Discussion  
### Concentrations of Organic Compounds in the Dissolved Plased  
One of the ways to assess the efficiency of pre-treatment processes is to analyze the concentrations of selected indicators in the dissolved phase of the organic substrate undergoing disintegration [28]. Analyses conducted in this case usually entail monitoring concentrations of organic compounds and less frequently concentrations of sugars and suspended solids, as well as measurements of turbidity and color, and concentrations of nutrients or genetic material [29]. In some cases, it is possible to develop reliable correlations and models to estimate AD efficiency based on the presence of organic compounds in the dissolved phase [30; 31]. For this reason, carrying out this type of assessment is useful from a practical point of view, as it reduces the need to conduct more advanced measurements in order to determine the efficiency of the applied pre-treatment methods [17]. In S0, where the H-LSPW was not subjected to thermal pre-treatment, the values of the analyzed indicators characterizing concentrations of organic compounds were as follows: 29,400 \(\pm\) 1950 mgO\({}_{2}\)/dm\({}^{3}\) (COD), 11,580 \(\pm\) 1020 mg/dm\({}^{3}\) (TOC), and 21,370 \(\pm\) 1330 mgO\({}_{2}\)/dm\({}^{3}\) (BOD\({}_{5}\)) (Table 3). The use of CTP in S1 (70 \({}^{\circ}\)C) and S2 (90 \({}^{\circ}\)C) caused a significant increase in the concentrations of dissolved organic compounds to the values noted in S0. In contrast, no significant differences were found that would be dependent on CTP temperature (Figure 1). The COD values reached 32,890 \(\pm\) 1070 mgO\({}_{2}\)/dm\({}^{3}\) in S1 and 33,920 \(\pm\) 2130 mgO\({}_{2}\)/dm\({}^{3}\) in S2. In the respective experimental stages, the TOC values were 12,410 \(\pm\) 980 mg/dm\({}^{3}\) (an increase by 7.2 \(\pm\) 0.79%) and 12,960 \(\pm\) 1270 mg/dm\({}^{3}\) (an increase by 11.9 \(\pm\) 0.98%), whereas the BOD\({}_{5}\) values reached 23,880 \(\pm\) 1580 mgO\({}_{2}\)/dm\({}^{3}\) (an increase by 11.7 \(\pm\) 0.66%) and 24,030 \(\pm\) 1720 mgO\({}_{2}\)/dm\({}^{3}\) (an increase by 12.4 \(\pm\) 0.72%) (Table 3). The use of the combined process of thermal pre-treatment and ultrasound disintegration (UTP) allowed for a significant increase in the organic matter content in the dissolved phase (Figure 1). The highest COD, TOC, and BOD\({}_{5}\) values, reaching 40,710 \(\pm\) 1420 mgO\({}_{2}\)/dm\({}^{3}\); 17,970 \(\pm\) 1090 mg/dm\({}^{3}\); and 31,460 \(\pm\) 1240 mgO\({}_{2}\)/dm\({}^{3}\), respectively, were determined in S4. The achieved concentrations were due to the 38.5 \(\pm\) 0.35% increase in COD, 55.2 \(\pm\) 0.61% increase in TOC, and 47.2 \(\pm\) 0.39% increase in BOD\({}_{5}\) (Table 3). In the case of C3 waste, like the analyzed H-LSPW, the thermal pre-treatment is not an intended deliberate procedure but results from regulations in force advising the hygiization of this type of organic substrate [32]. Regardless of this fact, an expected technological outcome of the required thermal pre-treatment is the increased efficiency of methane fermentation. Undoubtedly, the disintegration of complex macromolecules of the biomass followed by the efficient transfer of organic compounds to the dissolved phase increases substrate availability to anaerobic bacteria [33]. The present study demonstrated a strong linear correlation between the thermal pre-treatment method and the efficiency of organic matter transfer to the dissolved phase. In the case of COD, the fit of the correlation reached R\({}^{2}\) = 0.9650, whereas in the case of TOC and BOD\({}_{5}\), the R\({}^{2}\) values were only slightly lower and reached R\({}^{2}\) = 0.8959 and R\({}^{2}\) = 0.8932, respectively. It was found that organic matter transfer to the dissolved phase was affected to a greater extent by the heating method than by the heating temperatures in the analyzed range (Figure 1). The results of a study conducted by [PERSON] et al.