## 3 Results and Discussion
### Experimental Design for Optimization of HS-SPME Procedure for Volatiles Extraction  
The optimization procedure was carried out to obtain the optimal levels of the four studied independent variables (A: sample weight, B: extraction temperature, C: extraction time; D: NaCl addition), their quadratic effects and interactions leading to the highest headspace concentrations of hexanal, trans-2-heptenal, octanal and trans-2-decenal. Numerical optimization was also carried out using the RSM to determine the exact optimum levels of the independent variables leading to a desirable response goal. The Pareto chart estimates the statistical significance of the factors and interactions between them that had the greatest effect on the response (Figure S1). Among the studied factors, five had a significant effect on the response. The extraction temperature (B) had the greatest influence on the studied response, showing a positive effect. Also, the extraction time (C) and the interaction temperature and time (BC) had a significant and positive effect, followed by the tomato sauce weight (A) factor and its quadratic interaction (AA) with a negative effect. The rest of the investigated parameters had no significant impact on the studied responses. These results could be explained because of the cooking processing on the raw cellular structure of the _sofrito_ ingredients. Higher extraction temperatures and time allow the disruption of vegetable cell walls and, consequently, the inner contents of the cells become more accessible, as for example to volatiles compounds [3]. On the other hand, the transport of analytes from the matrix into the coating begins as soon as the coated fibre has been placed in contact with the sample. However, if the diffusion coefficient of the target compounds is low, the analyte remained at the interface and adsorption of target compounds decreased. This fact explained the negative effect of the quadratic interaction of _sofrito_ weight since the formation of high analyte concentrations saturates the closed vial headspace, increasing the competition of target and interference compounds to be absorbed in the fibre coating and, consequently, their extraction [36]. By applying multiple regression analysis on the experimental data, the mathematical model representing the studied response as a function of the independent variables within the region under investigation were expressed by Equation (2). \[ \begin{split}& Y=2.09012\times 10^{-7}-3.49115\times 10^{-6} \times\text{A}+1.02543\times 10^{-7}\times\text{B}+9.37307\times 10^{-6} \times\text{C}\\ &-1.05587\times 10^{-6}\times\text{D}-4.58137\times 10^{-6} \times\text{A}^{2}-5.61886\times 10^{-6}\times\text{AB}-2.66642\times 10^{-6} \times\text{AC}\\ &-867317\times\text{AD}+1.34314\times 10^{-6}\times\text{B}^{2}+7.0 4733\times 10^{-6}\times\text{BC}-3.23108\times 10^{-6}\times\text{D}\\ &\qquad\qquad\qquad-2.61914\times 10^{-6}\times\text{C}^{2}-1.02 289\times 10^{-6}\times\text{CD}-1.3836\times 10^{-6}\times\text{D}^{2}\end{split}  \tag{2}\]  
The test was performed by comparing the variability of the current model residuals to the variability between observations at replicate settings of the factors. The R-squared statistic indicates that the model as fitted explains 87.29% of the variability in the response. This value indicated a relatively high degree of correlation between the actual data and predicted values, confirming that the model obtained could be used to predict the studied responses. In contrast with reported literature, this optimized HS-SPME procedure can reduce the sample weight required during the extraction from 3 g [8] and 1.5 g [20] to 0.5 g tomato sauce, whereas the extraction time (60 min) was similar to reported ones.