## 2 Results and Discussion
### Optimization of the Extraction Procedure
#### 2.1.2 Central Composite Design  
After selecting the most important factors using a screening design, those selected parameters were optimized by a central composite design (CCD). Considering that five out of the seven factors were relevant (ionic strength, extraction and desorption time, and extraction and desorption temperature), a total of 26 experimental runs were performed, including six assays in the center of the cubic domain (pattern 00000), resulting in a total of 32 experiments. The CCD factor values and experiments are summarized in Supplementary Tables S1 and S2. The experimental data were fitted to a second-order polynomial equation and the model coefficients were determined based on a least-square regression analysis. The equations and the model suitability were assessed using the ANOVA approach and the main results are presented in Supplementary Table S3 (only the factors that significantly affect the response are shown). The R\({}^{2}\) values ranged from 0.80 to 0.97, which indicates a reasonable relationship between the experimental data and the fitted model. Models for most compounds show a F-probability below 0.1, indicating that variations in the response are associated with the models, rather than with the experimental error. However, M4Q and L5 show a higher F-probability, indicating a strong influence of experimental errors, possibly due to some problems related to competition within the fiber pores. Supplementary Table S4 presents the relevant variables and interactions identified by the Student's \(t\)-test, where the values in bold indicate the variables that present significant effect. Figure 2 presents the results from the Student's \(t\)-test for the main and quadratic effects. The main factors (\(X1\) to \(X5\)) are the same defined in the screening design. None of the interactions presented Prob \(>|t|\) lower than 0.05. As can be observed, the \"extraction  
Figure 1: F-probability obtained with screening design. time\" (X2) and \"extraction temperature\" (X4) are the variables that significantly affect a larger number of responses, as defined by the low Student's _t_-test values. Due to the high number of responses, the desirability function was applied to obtain the best compromise value for all variables, maximizing the response areas (Supplementary Figure S1). The optimal conditions were: 19.5% NaCl, 39 min extraction time, 10 min desorption time, 33 \({}^{\circ}\)C extraction temperature and 240 \({}^{\circ}\)C desorption temperature (D = 0.71). The optimization indicates that the addition of NaCl favors the transfer of analytes to the headspace and, consequently, to the fiber, due to the decrease of VMSs solubility in water (although it may also favor the co-extraction of interferets). Extraction time affects the amount of analyte extracted in the fiber coating, and this extraction is maximal when equilibrium is reached, achieving the highest sensitivity. However, in equilibrium extraction, competition might occur at higher concentrations. In this study, the optimal extraction temperature was set at 33 \({}^{\circ}\)C. Although the adsorption of fewer volatile compounds is favored by the increase in temperature (due to the improved mass transfer process of VMSs from sample to headspace), the partition coefficient between the coating and the sample decreases with increasing temperature, negatively affecting the adsorption of more volatile analytes. The desorption temperature of 240 \({}^{\circ}\)C is in the temperature range supported by the fiber and is high enough to properly desorb previously extracted molecules without damaging the fiber. Figure 3 presents an example of three-dimensional response surface plot for \(D6\). Figure 3A presents the relationship between ionic strength and extraction time, Figure 3B the relationship between extraction time and desorption time, and Figure 3C the relationship between ionic strength and extraction temperature.