## 3 Results and Discussion  
### HS-SPME Optimization by Experimental Design  
The flavour profile, alongside the sugar-acid balance, is among the most important parameters contributing to the overall quality of wine products [28; 29]. The qualitative determination of wine volatile compounds allows researchers to define an aromatic fin \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Variable**} & \multicolumn{3}{c}{**Coded Levels**} \\ \cline{2-4}  & **(\(-\)1.0)** & **(0.0)** & **(+1.0)** \\ \hline Extraction time (min) & 10 & 20 & 30 \\ \hline Extraction & 40 & 50 & 60 \\ temperature (\({}^{\circ}\)C) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Levels of the variables (extraction time and extraction temperature) explored in the face-centred composite experimental design experiments (DoE). gerprint. This is characteristic of a specific oenological product and is the result of several factors, including grape variety, fermentative and post-fermentative processes. The volatile fraction fingerprinting, performed by solid-phase microextraction, combined with direct analysis via gas chromatography coupled to mass spectrometry needs a preliminary optimization of the experimental parameters. A standard solution containing acetic acid, 1-butanol 3-methyl-acetate, 2-phenylethanol and nerolidol in EtOH/H2O was employed for HS-SPME optimization. Since the analytical standards used belonged to the main four classes of volatile compounds occurring in the wine, namely acids, esters, alcohols and terpen, they can be properly used as a model to mimic the effects of the studied matrix [30]. A 100 \(\upmu\)m PDMS fibre was used for the adsorption of a higher number of analytes for wine samples. The optimization of the extraction time and temperature was conducted by running experiments according to a face-centred composite design to select the best conditions of wine aroma compounds extraction with the lowest number of experiments. The extraction time was varied between 10 and 30 min, while the temperature ranged from 40 \({}^{\circ}\)C to 60 \({}^{\circ}\)C, as higher temperatures could change the composition of the wine sample by producing artifacts [15]. In total, 9 runs were carried out in triplicate to study the influence of the selected factors and their interactions on the HS-SPME. The results obtained for the responses, i.e., the total sum of peak areas of the standard mixture, are reported in Table 2.  
The quadratic equation obtained using coded values for the variables was given by:  
\[\text{R}=5.524\times 10^{9}+3.024\times 10^{9}\;\text{T}+1.026\times 10^{9}\; \text{t}+1.250\times 10^{9}\;\text{t}\times\text{T}+2.014\times 10^{9}\;\text{T}^{2}-4. 269\;\text{t}^{2}\]  
where R is the dependent response, i.e., the total sum of peaks areas of the standard mixture, T is the extraction temperature, t the extraction time, and T \(\times\) t the interaction between extraction temperature and time. All the coefficients were found to be statistically significant. A total of 95% of the total variance was explained by this model. To validate the model, three replicates in the central point were performed in order to estimate the experimental error and to detect any lack of fit. The response surface obtained by the use of DoE face-centred composite design is reported in Figure 1. The estimated optimum value range, obtained for the extraction temperature using a response surface methodology, was at around 60 \({}^{\circ}\)C (Figure 1). In general, in the SPME experiments, the temperature parameter decreases the partition coefficient between the analyte and the extraction polymer [31]. However, on the other hand, it acts on the extraction by increasing the diffusion of the compounds and therefore increasing the extraction rate. The extraction time was found to have a statistically important positive