## 2 Materials and Methods
### Methods
#### 2.2.6 Individual Determination of Carotenoids  
Carotenoids, including zeaxanthin, cantaxanthin, trans-beta-apo-8\({}^{\prime}\)-carotenal, astaxanthin, alpha-carotene, beta-carotene, lutein, and lycopene were analyzed in our extract using a high-performance liquid chromatograph (LC-40B X3 SHIMADZU, Kyoto, Japan) equipped with a diode array detector. Separation was conducted on a CT99S05-2546 WT column with dimensions of 150 mm length and 4.6 mm diameter particles with 5 \(\upmu\)m separation. Elution was performed using a solvent system consisting of solvent A (methanol/MTBE*/water in a ratio of 81/15/4) and solvent B (methanol/MTBE*/water in a ratio of 86/90/4), at a flow rate of 1 mL/min. The gradient was 0-100%B (0-90 min). The compounds were detected at 450 nm. Figure 1 illustrates an HPLC-DAD chromatogram at 450 nm for the standards (100 mg/L). Figure 1: HPLC-DAD chromatogram at 450 nm for standard (100 mg/L); for sample (**A**) (extracted with ethanol/acetone for 10 h at 50 \({}^{\circ}\)C, 0.3g of pomace): trans-beta-apo-8\({}^{\prime}\)-carotenal, (18.282 min), astaxanthin (23.374 min), alpha-carotene (32.193 min), beta-carotene (39.918 min), lutein (43.265 min), and lycopene (73.649 min); and for sample (**B**) (extracted with ethyl acetate): zexaxanthin (13.025 min), trans beta apo 8 carotenoid (22.907 min), astaxanthin (27.608 min), alpha-carotene (33.105 min), beta-carotene (37.599 min), lutein (40.505 min), and lycopene (78.372 min). 2.2.7. Assessment of the Quality of Tomato Pomace, Tomato Seed Oil, and Extractions through FT-IR Spectroscopy  
Fourier-transform infrared spectroscopy (FT-IR) analysis was conducted using a Nicolet i-20 spectrophotometer (ThermoScientific, Waltham, MA, USA). Spectra were recorded in transmission mode utilizing the ATR system across the wave number range of 4000-400 cm\({}^{-1}\) at a resolution of 4 cm\({}^{-1}\). SpectraGryph spectroscopy software (Version 1.2.11) was employed to visualize the spectra. The samples (tomato pomace, tomato seed oil, and extractions) were positioned on the ATR crystal, and the spectra were recorded in triplicate [24]. Advanced optical FT-IR spectrometry with superior signal-to-noise ratio facilitates the identification of individual components and subtle variations in composition within complex samples in this study, Fourier-transform infrared spectroscopy (FT-IR) was employed to analyze the lipids extracted from the tomato pomace and the tomato pomace itself. 2.2.8. Design of Experiments and Statistical Analysis  
A Box-Behnken experimental design with three factors and three levels was utilized, tailored accordingly. This study aimed to explore and optimize the impacts of independent variables--solid/liquid ratio, temperature, and time--on the concentrations of lycopene, DPPH, total phenolic content (TPC), and total flavonoid content (TFC). The coded levels of the variables are outlined in Table 1. Graphs and calculations were conducted using the statistical software Design Expert 11. The Box-Behnken design relied on the second-order (quadratic) polynomial response surface model using the following equation:  
\[\mathrm{y}=\mathrm{b}_{0}+\sum\
olimits_{i=1}^{n}(b_{i}x_{i})+\sum\
olimits_{ i=1}^{n}\left(b_{ii}x_{ii}^{2}\right)+\sum\
olimits_{i=1}^{n}\left(b_{ij}x_{i}x_{j}\right) \tag{3}\]  
where \(y\) stands for the predicted response (lycopene, DPPH, TPC, TFC), \(x_{i}\) represents the coded levels of the design variable (ratio, temperature, and time), \(b_{0}\) is a constant, \(b_{i}\) represents the linear effects, \(b_{ii}\) denotes the quadratic effects, and \(b_{ij}\) represents the interaction effects. The results were submitted to analysis of variance (ANOVA) using XLSTAT Statistical Software 2022 trial version (Lumivero, Denver, CO, USA). [PERSON]'s least significant difference (LSD) procedure was used at the 95% confidence level. 3.1.