## 3 Results
### The Characterization of Muiprocin-Loaded NE Formulations  
#### 3.2.1 The Effect of Selected Factors on Y\({}_{1}\)  
The particle size of the developed formulations is a very significant factor to be assessed. Referring to Table 1, the particle sizes of all developed NEs along with their corresponding PDI values are displayed. The particle sizes of all NE formulations seemed to range from (\(97\pm 2.0\) to \(375\pm 4.5\)) nm. It was observable that using a higher concentration of tea tree oil would provide a formula with a larger particle size due to an increase in the dispersed phase [41]. On the contrary, a higher concentration of surfactant (B) would provide a smaller particle size while using the same oil concentration. This result was \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Source**} & \multicolumn{2}{c}{**Y\({}_{1}\)**} & \multicolumn{2}{c}{**Y\({}_{2}\)**} \\ \cline{2-5}  & **F-Value** & **_p-Value_** & **_F-Value_** & **_p-Value_** \\ \hline
**Model** & 639.74 & \textless{}0.0001 * & 403.40 & \textless{}0.0001 * \\ A & 5245.74 & \textless{}0.0001 * & 1126.16 & \textless{}0.0001 * \\ B & 339.32 & \textless{}0.0001 * & 61.19 & \textless{}0.0001 * \\ C & 72.07 & \textless{}0.0001 * & 22.84 & 0.0004 * \\ AB & 37.14 & 0.0005 * & & \\ AC & 12.21 & 0.0101 * & & \\ BC & 4.81 & 0.0643 & & \\ A\({}^{2}\) & 31.41 & 0.0008 * & & \\ B\({}^{2}\) & 0.0157 & 0.9040 & & \\ C\({}^{2}\) & 3.60 & 0.0994 & & \\ Lack of fit & 3.78 & 0.2221 & 0.8965 & 0.6378 \\ \hline R\({}^{2}\) analysis & & & & \\ \hline R\({}^{2}\) & 0.9988 & & 0.9894 & \\ Adjusted R\({}^{2}\) & 0.9972 & & 0.9869 & \\ Predicted R\({}^{2}\) & 0.9911 & & 0.9820 & \\ Adequate & 85.9518 & & 62.9684 & \\ precision & & & & \\ \hline Model & Quadratic & Linear & \\ \hline Remark & Suggested & Suggested & \\ \hline \hline \end{tabular}  
* A: Oil concentration; B: Tween 80 concentration; C: PEG 400; Y\({}_{1}\): particle size; and Y\({}_{2}\): in vitro release.  
\end{table} 
Table 2: Statistical analysis of responses. ascribed to the relation between surfactant and interfacial tension since adding more surfactant would reduce the interfacial tension at the formula's interface and subsequently prevent the coalescence of particles and the formation of aggregates, keeping the particle size small [42]. On the same track, using a higher concentration of factor C, related to PEG 400, would lower the particle size upon using the same oil and surfactant concentration. Likewise, this finding could be attributed to the same fact concerning how surfactants and co-surfactants have a role in lowering interfacial tension, which would accordingly drop the particle size of the formulation [43]. In order to confirm the obtained results, the following mathematical equation was generated using the design approach, showing that particle size (Y\({}_{1}\)) was directly proportional to factor A, which was confirmed by the positive sign. On the other hand, the negative sign in front of factors B and C indicated an inverse relation between them and response Y\({}_{1}\). \[ \begin{array}{l}\text{Y}_{1}=214.449+85.2714\;\text{*}\;\text{A}-21.6873\; \text{*}\;\text{B}-9.99492\;\text{*}\;\text{C}-9.375\;\text{*}\;\text{AB}-5.375 \;\text{*}\\ \text{AC}+3.375\;\text{*}\;\text{BC}+7.2625\;\text{*}\;\text{A}^{2}-0.162123\; \text{*}\;\text{B}^{2}-2.46022\;\text{*}\;\text{C}2\end{array} \]  
To further emphasize the attained data, several graphs were created using a CCD approach, which demonstrated the relation between all the selected factors and the observed particle size response Y\({}_{1}\). The substantial positive effect of factor (A) in addition to the negative effect of both factors B and C on the particle size response (Y\({}_{1}\)) is demonstrated clearly by the 3D-response surface plot as exhibited in Figure 1a-c. Moreover, the one-factor graph as plotted in Figure 2a-c explains the influence of each factor against the particle size response.