3.2.3. Box–Behnken Statistical Designs: Optimization of Zone of Inhibition of Fluconazole-Sesame Oil Nanotransfersome Formulations

To assess the antifungal activity, we analyzed the interactions of the three independent variables of the zone of inhibition of the FS-NTF. During the optimization process, it was observed that the quadratic model was the best fit for the zone of inhibition of the formulation. The statistical outcome of the interactions of the amounts of lecithin, fluconazole, and sesame oil in the formulation's zone of inhibition of the FS-NTF is shown in Table 5. The model's F-value is 818.62, and the respective *p*-value of less than 0.05 represents the significance of the model. An F-value of 0.4747 for the lack of fit and respective *p*-value (>0.05) indicated the desirable lack of fit. The predicted R<sup>2</sup> value (0.9941) and adjusted R <sup>2</sup> value were in close agreement (0.9976). Close agreement was also observed for the predicted and actual zone of inhibition data in Table 1.

**Table 5.** Statistical outcome (ANOVA) of the interactions of three independent variables on the zone of inhibition of the FS-NTF.


All three model terms had a significant effect on the zone of inhibition as per the p-value in Table 5. Further, when the coefficient value of model terms A, B, and C in the quadratic equation (Equation (4)) indicated that a desirable signal-to-noise ratio was

higher than 4, the suggested model had a value of 79.149, indicating the adequate signal. Therefore, this model could be used to navigate the design space.

The generated quadratic equation on the interactions of the three independent variables on the zone of inhibition of the formulations is shown in Equation (7).

Y3 = +10.83 <sup>−</sup> 0.4081\*A + 6.10\*B + 1.31\*C + 0.0076\*A<sup>2</sup> <sup>−</sup> 0.0177\*A\*B <sup>−</sup> 0.1427\*A\*C <sup>−</sup> 0.8133\*B<sup>2</sup> + 0.3573\*B\*C + 0.5681\*C<sup>2</sup> (7)

> Model term B had the highest coefficient (+6.10) as was expected because as the fluconazole concentration increased the zone of inhibition also increased. Although model terms A and C exhibited a significant effect as per the *p*-value in Table 5, model term B had the maximum effect on the zone of inhibition. For the coefficient values, model term A exhibited an inverse effect whereas model term C exhibited a proportional relationship on the zone of inhibition. Similar findings on the effects of models A, B, and C are evident in the contour plot and three-dimensional surface plot (Figure 4a,b). In the contour plot and three-dimensional surface plot, no color changes were observed through the sesame oil axis.

**Figure 4.** (**a**) Contour plot showing the interactions of sesame oil and fluconazole on the zone of inhibition of the FS-NTF. (**b**) Three-dimensional surface plot showing the interactions of sesame oil and fluconazole on the zone of inhibition of the FS-NTF.

3.2.4. Box–Behnken Statistical Designs: Optimization of the Ulcer Index of the Fluconazole–Sesame Oil Nanotransfersome Formulations

During optimization of the interactions of the three independent variables on the ulcer index of the FS-NTF, the linear model was found to be the best fit. The statistical outcome of the suggested linear model for the ulcer index is seen in Table 6. The model was found to be significant. Close agreement was observed in the predicted and actual ulcer indexes in Table 1 and in the adjusted R<sup>2</sup> value (0.9771) and predicted R<sup>2</sup> value (0.9671).

**Table 6.** Statistical outcome (ANOVA) for the linear model showing the interactions between the three independent variables and the ulcer index of the FS-NTF.


It could be said that model terms B and C had a significant effect, whereas the effect of model term A was insignificant, as per the *p*-value in Table 6. The generated linear equation for the interactions of the three independent variables with the ulcer index of the formulations is shown in Equation (8).

$$\text{Y4} = +2.55 - 0.0166^{\circ} \text{A} - 0.6701^{\circ} \text{B} - 1.46^{\circ} \text{C} \tag{8}$$

The negative coefficient of significance for model terms B and C in Equation (8) represent a decrease in the ulcer index with an increasing amount of fluconazole and sesame oil, and this is in accordance with reported data [2,10]. Further, the maximum coefficient value of model term C represents a maximum effect of the sesame oil rather than the fluconazole, as per the contour plot and three-dimensional surface plot (Figure 5a,b), where the maximum effect of the sesame oil is reflected, followed by the amount of fluconazole.

**Figure 5.** (**a**) Contour plot showing the interactions of the sesame oil and fluconazole on the ulcer index of the FS-NTF. (**b**) Three-dimensional surface plot showing the interactions of the sesame oil and fluconazole on the ulcer index of the FS-NTF.
