## 3 Materials and Methods
### Volatile Profile
#### 3.4.3 Identification and Quantification of Volatiles from IWG by HS-SPME-GC/MS  
The determination of the volatile compounds was carried out using an Agilent 6890 gas chromatograph equipped with a PAL RSI 120 autosampler and coupled to an Agilent 5973 single-quadrupole detector (Agilent Technologies, Palo Alto, CA, USA). A DB-5 ms Ultra Inert column (30 m \(\times\) 250 \(\upmu\)m \(\times\) 0.25 \(\upmu\)m) was used. The inlet was set at 280 \({}^{\circ}\)C and in spitless mode. Helium at 1.2 mL/min was used as carrier gas. The oven temperature began at 40 \({}^{\circ}\)C followed by a ramp to 220 \({}^{\circ}\)C at 4 \({}^{\circ}\)C/min, which was held for 5 min, totaling 50 min of chromatography. The quadrupole, MS ion source, and transfer line were set at 150, 230, and 250 \({}^{\circ}\)C, respectively. Electron impact mass spectra were recorded at 70 eV ionization energy in scan mode (\(m/z\) 40-400). Volatile compound identification was conducted utilizing mass spectrometry (MS) with Agilent MassHunter Unknown software and the NIST 17 MS library. Only compounds exhibiting a signal-to-noise ratio greater than 3 and a match score higher than 80 were considered. To confirm the identity of the compounds, the Van den Dool and [PERSON] programmed temperature retention indexes (RIs) were calculated by injecting a solution of n-alkanes (C7-C20) (Supelco, Alltech, PA, USA) into the GC-MS under the same conditions. Only compounds with a maximum RI variation of 30 units were considered. When available, positive identification was performed by comparing the retention time of the compound of interest with that of authentic standards. The quantification of the compounds was performed by MHE. The MHE allows for the quantification of compounds by SPME by converting an equilibrium technique to an exhaustive technique by carrying out several extractions of the same sample. The sum of the instrumental response from each step of HS extraction corresponds to the total area (AT) of the compound, and can be obtained by Equation (1):  
\[\mathrm{A_{T}}=\sum_{i=1}^{i\to\infty}\mathrm{A_{i}}=\frac{\mathrm{A_{1}}}{1 {-}\mathrm{e^{-q}}}=\frac{\mathrm{A_{1}}}{1{-}\beta} \tag{1}\]  
where \(\mathrm{A_{T}}\) is the total peak area, \(\mathrm{A_{1}}\) is the peak area of the first extraction, and q is a constant describing the exponential decay associated with \(\beta\)[20]. The constant \(\beta\) is determined by the slope of the regression curve plotted using the logarithm of the areas of the individual peaks and the number of extractions, as described by Equation (2):  
\[\mathrm{ln}\,\mathrm{A_{i}}=\mathrm{ln}\,\mathrm{A_{1}}{+}(\mathrm{i-1}){ \cdot}\mathrm{ln}\,\beta \tag{2}\]  
where \(\mathrm{A_{i}}\) is the area obtained in the ith extraction. This linear equation is represented as y = ax + b, where ln \(\mathrm{A_{1}}\) is the y-axis intercept and ln\(\beta\) is the slope. Afterward, external calibration curves can be used for accurate quantitation of the compound in the sample, using only the analyte response after the first extraction step (\(\mathrm{A_{1}}\)) [13; 20]. For MHE, the amount of sample and number of extractions should be carefully evaluated. Sample size in MHE is crucial since small samples can lose significant mass between extractions and do not show exponential decay while large samples can cause HS saturation, \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Variables**} & \multicolumn{5}{c}{**Levels**} \\ \cline{2-6}  & \(-\)**1.41** & \(-\)**1** & **0** & **1** & **1.41** \\ \hline Temperature (\({}^{\circ}\)C) (X1) & 35.00 & 39.40 & 50.00 & 60.60 & 65.00 \\ Time (min) (X2) & 30.00 & 34.36 & 45.00 & 55.64 & 60.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Factors and levels applied to optimize the extraction conditions of volatiles from IWG samples by HS-SPME. which also affects quantification [39].