## 2 Results and Discussion
### Optimization of the Extraction Procedure
#### 2.1.1 Screening Design  
Several parameters may influence the HS-SPME extraction. Therefore, a screening design considering seven main factors (\(X\)i) was implemented. Two levels (defined as \(-1\) and \(+1\) for the lower and upper limit, respectively) were set for each of the seven main factors, as presented in Table 1: \(X1\)--ionic strength (0-20%, \(w/v\)), \(X2\)--extraction time (5-45 min), \(X3\)--desorption time (1-10 min), \(X4\)--extraction temperature (25-80 \({}^{\circ}\)C), \(X5\)--desorption temperature (200-250 \({}^{\circ}\)C), \(X6\)--type of fibers (100 \(\upmu\) polydimethylsiloxane (PDMS), 65 \(\upmu\)m PDMS/Divinylbenzene (DVB)) and \(X7\)--sample volume (5-10 mL). A 2\({}^{\prime}\)-3 fractional factorial screening design was chosen (resolution IV), leading to a total of 16 experiments, which corresponds to one eighth of the full factorial design with 128 experiments (Table 2). All the extractions were tested using a concentration of 1 \(\upmu\)g/L for both VMSs and internal standard (M4Q). The main results are presented in Figure 1. The model was applied to all compounds and its suitability determined. All responses were adjusted to a quadratic model with a R\({}^{2}\) > 0.94. The main effects were determined by the F-probability, where F-probability \(\leq\) 0.05 represents a significant effect and if 0.05 < F-probability \(\leq\) 0.1, a relative effect may be considered. Since the main goal was to maximize the response areas for all compounds, a desirability function was applied in order to obtain the best compromise value for all variables. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(X1\) & **X2** & **X3** & **X4** & **X5** \\
**Run** & **Ionic** **Strength (\%** & **Extraction** & **Desorption** & **Extraction** & **Desorption** & **X6** & **X7** \\
**& **Strength (\%** & **Time (min)** & **Time (min)** & **Temperature (\({}^{\circ}\)C)** & **Temperature** & **Filter Type** & **Sample** \\  & _w/v_) & **Time (min)** & **Time (min)** & **Time (\({}^{\circ}\)C)** & **(\({}^{\circ}\)C)** & **Volume (mL)** \\ \hline
1 & 0 & 5 & 1 & 25 & 200 & PDMS & 5 \\
2 & 20 & 45 & 10 & 25 & 200 & PDMS & 5 \\
3 & 0 & 45 & 10 & 25 & 200 & PDMS/DVB & 10 \\
4 & 20 & 5 & 1 & 25 & 200 & PDMS/DVB & 10 \\
5 & 0 & 45 & 1 & 25 & 250 & PDMS & 10 \\
6 & 20 & 5 & 10 & 25 & 250 & PDMS & 10 \\
7 & 0 & 5 & 10 & 25 & 250 & PDMS/DVB & 5 \\
8 & 20 & 45 & 1 & 25 & 250 & PDMS/DVB & 5 \\
9 & 0 & 5 & 10 & 80 & 200 & PDMS & 10 \\
10 & 20 & 45 & 1 & 80 & 200 & PDMS & 10 \\
11 & 0 & 45 & 1 & 80 & 200 & PDMS/DVB & 5 \\
12 & 20 & 5 & 10 & 80 & 200 & PDMS/DVB & 5 \\
13 & 0 & 45 & 10 & 80 & 250 & PDMS & 5 \\
14 & 20 & 5 & 1 & 80 & 250 & PDMS & 5 \\
15 & 0 & 5 & 1 & 80 & 250 & PDMS/DVB & 10 \\
16 & 20 & 45 & 10 & 80 & 250 & PDMS/DVB & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Proposed screening design. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multirow{2}{*}{**Factor**} & \multicolumn{2}{c}{**Coded Values (\(x_{i}\))**} \\ \cline{3-4}  & & & **Low (\(-1\))** & **High (\(+1\))** \\ \hline
1 & Ionic strength (\% NaCl) & 0 & 20 \\
2 & Extraction time (min) & 5 & 45 \\
3 & Desorption time (min) & 1 & 10 \\
4 & Extraction temperature (\({}^{\circ}\)C) & 25 & 80 \\
5 & Desorption temperature (\({}^{\circ}\)C) & 200 & 250 \\
6 & Fiber type & PDMS & PDMS/DVB \\
7 & Sample volume (mL) & 5 & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimental factors and coded levels for the proposed screening approach. As presented in Figure 1, all main factors were significant for at least one compound and the extraction temperature (\(X4\)), fiber type (\(X6\)), and sample volume (\(X7\)) were the factors with stronger effects on the response (F-probability \(<0.0001\)). The fiber type is a discrete variable, and therefore to proceed with the model, it had to be defined in advance. A PDMS/DVB fiber was selected since it provided higher responses for all compounds.