## 3 Results and Discussion
### Examination of the SI-HLIME Parameters Using 2-Level FFD  
Initially, a fractional factorial design (FFD) was constructed to find the significant parameters affecting the extraction efficiency. Five experimental parameters were investigated including the sample pH, the sample volume (\(V_{\mathrm{S}}\)), the acetonitrile volume (\(V_{\mathrm{ACN}}\)), the centrifugation time and the volume (\(V_{\mathrm{salt}}\)) of the salt solution. In order to ensure phase separation at each experimental run of the domain, a concentration of 2.5 mol L\({}^{-1}\) sodium sulfate was used. Table 1 summarizes the evaluated parameters, their respective levels and the experimental sequence. A random order of the experiments was used to reduce potential errors. During the screening of the SI-HLIME parameters, the extraction recoveries (ER%) of the analytes were calculated. The calculation of the ER% values is described in the Supplementary Material. Figure 1 shows the effects of the examined parameters after multivariate regression analysis (Pareto ranking plots).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Standard Run** & \(V_{\mathrm{ACN}}\) (\(\mu\)L) & \(V_{\mathrm{S}}\) (\(\mu\)L) & **Sample pH** & **Centrifugation Time** & \(V_{\mathrm{salt}}\) (\(\mu\)L)** \\ \hline
14 & 700 & 400 & 6 & 10 & 300 \\
10 & 700 & 400 & 3 & 10 & 500 \\
3 & 450 & 700 & 3 & 1 & 300 \\
5 & 450 & 400 & 6 & 1 & 300 \\
15 & 450 & 700 & 6 & 10 & 300 \\
2 & 700 & 400 & 3 & 1 & 300 \\
11 & 450 & 700 & 3 & 10 & 500 \\
8 & 700 & 700 & 6 & 1 & 300 \\
6 & 700 & 400 & 6 & 1 & 500 \\
7 & 450 & 700 & 6 & 1 & 500 \\
13 & 450 & 400 & 6 & 10 & 500 \\
1 & 450 & 400 & 3 & 1 & 500 \\
12 & 700 & 700 & 3 & 10 & 300 \\
16 & 700 & 700 & 6 & 10 & 500 \\
4 & 700 & 700 & 3 & 1 & 500 \\
9 & 450 & 400 & 3 & 10 & 300 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Plans of experiments generated by 2-level FFD for the screening of SI-HLIME procedure.  
In these charts, the bar length is proportional to the absolute value of the estimated standardized effects and the black line (vertical line) is used for the judgment of the statistical significance at a confidence level of 95%. As shown in Figure 1, the volume of the sample (\(V_{\rm S}\)) was found to be statistically significant (\(p<0.05\)), exhibiting negative effects on the ER% of both analytes. This mean that the increase in \(V_{\rm S}\) led to a decrease in the extraction recoveries. Oppositely, the volume of acetonitrile (\(V_{\rm ACN}\)) had a positive effect on the ER% of meloxicam, meaning that the extraction efficiency improved at elevated acetonitrile volumes. In both cases, the interactions of factors A, B and E were statistically significant, and these parameters were further investigated using response surface methodology (RSM). The sample pH and the centrifugation time were found to be non-significant (\(p>0.05\)) within the studied ranges. In order to avoid the pH adjustment of the urine samples before the extraction, the pH value of 6 was finally chosen. The centrifugation time was set to 1 min to accelerate the sample throughput.  
Figure 1: Pareto charts regarding the main effects of the SI-HLIME parameters for (**A**) piroxicam and (**B**) meloxicam using 2-level FFD. Orange and blue bars indicate the positive and negative effects, respectively.