## 2 Results and Discussion
### Optimisation of HS-SPME for the Key-Markers in Aromatic Rice  
The variables that were likely to influence the extraction of key-marker compounds from aromatic rice were optimised. The factors considered were the amount of the sample (\(x_{1}\)), the volume of water (\(x_{2}\)), adsorption temperature (\(x_{3}\)), pre-incubation time (\(x_{4}\)), and adsorption time (\(x_{5}\)). Based on the experimental design generated by the \(2^{5-2}_{III}\) FFD with two centre points, 11 extraction processes were completed to extract the key-marker compounds from rice (Table 2). The response for each extraction in the experimental design generated by the \(2^{5-2}_{III}\) FFD was calculated and expressed as the value relative to the maximum yield obtained (%) for the individual level of key-marker aroma compounds in rice (i.e., pentanal (C1), pyridine (C3), hexanal (C6), 2-acetyl-1-pyrroline (C13), 1-octen-3-ol (C19), 2-pentylfuran (C22), (\(E\))-2-octenal (C28) and 2,4-nonadien (C43)). The responses were simultaneously optimized using MRO, wherein the optimization target for each response was considered equivalently important. The importance of the responses for computational analysis was indicated by the impact coefficient given to the responses in the MRO. By default, values of the impact coefficients were set to three (STATGRAPHICS Centurion XVI, Warrenton, VA, USA) with medium sensitivity. Prior to MRO, the response surface methodology (RSM) data were formerly analysed to generate a model for each response separately. The efficiency of the model was checked by ANOVA and the suitability of the model was judged by considering coefficient of determination (\(R^{2}\)). The values of the \(R^{2}\) statistic ranged from 68.05% (2 PF) to 95.96% (OCA). Henceforth, the RSM for each response was confirmed to provide a high degree of correlation between the experimental and predicted values. As the response surface equation constructed by the software for each response was plotted, the model provides the variable effects on the response over the studied range of the \(2^{5-2}_{III}\) FFD. Subsequently, the desirability function d(y) was then constructed based on the values obtained for each optimized response. The MRO approach assumes the response values equal to (y) can be modelled through the d(y), where the desirability ranges from di(yi) = 0 for an undesirable response and di(yi) = 1 represents a completely desirable value. The target optimization defined by MRO was to maximize the HS-SPME recovery (100% extraction yield) of each key-marker aroma compound simultaneously. To obtain these optimum values, the d(y) was plotted as a 3D contour plot, which illustrated the optimum point of the simultaneous optimization (Figure S2 Supplementary Material). The proposed ordinates and optimal conditions for HS-SPME by MRO were as follows: Amount of the sample (\(x_{1}\), \(-\)1.00, 0.5 g), volume of water (\(x_{2}\), 1.00, 5 mL), adsorption temperature (\(x_{3}\), 0.36, \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Factors** & \(\mathbf{-1}\) & \(\mathbf{0}\) & \(\mathbf{+1}\) & **Unit** \\ \hline \(x_{1}\), sample mass & 0.5 & 1.5 & 2.5 & g \\ \(x_{2}\), water volume & 0 & 2.5 & 5.0 & mL \\ \(x_{3}\), adsorption temperature & 40 & 70 & 100 & \({}^{\circ}\)C \\ \(x_{4}\), pre-incubation time & 5 & 10 & 15 & min \\ \(x_{5}\), adsorption time & 10 & 30 & 50 & min \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Selected factors and their levels. 80.73 \({}^{\circ}\)C), pre-incubation time (\(x_{4}\), \(-1.00\), 5 min), and adsorption time (\(x_{5}\), 1.00, 50 min). Because the value for adsorption time was in the corner of the studied range for this extraction variable, it was decided to study values above the highest assayed level. The results of extraction yields by different adsorption times are shown in Figure S3 in Supplementary Material. A single-factor ANOVA was used to evaluate the significance of adsorption time in the extraction yield.