*2.2. Methods*

2.2.1. Optimization of Fluconazole-Sesame Oil Nanotransfersomes Using the Box–Behnken Statistical Design

A response surface Box–Behnken statistical design was adopted for our current investigation using Design-Expert® software version 12.0.6.0 (2019, Stat-Ease, Inc., Minneapolis, MN, USA). Three factors at three levels were incorporated to optimize the fluconazole nanotransfersome formulations. Based on data in the literature, higher and lower levels of the independent variables, such as the lecithin concentration and amounts of fluconazole and sesame oil, were selected for the identification of the optimized FS-NTF formulation [10,13]. The software generated 19 batches with various combinations of the three independent variables at their low (−1), medium (0), and high (+1) levels. The batches were developed and analyzed for the four dependent variables, which were the globule size of the prepared FS-NTF (Y1), entrapment efficiency (EE%) of fluconazole within the prepared FS-NTF (Y2), zone of inhibition against *C. albicans* (Y3), and ulcer index score (Y4) (Table 1). Experimental data for the four dependent variables were included in the software. The interactions of the independent variables at their different levels with the dependent variables were analyzed to gain insight into the composition of the optimized formulation. The significance of the data was statistically analyzed using the analysis of variance (ANOVA). The effect of the three independent variables at their different levels was assessed by the generated perturbation plot, contour plots, and three-dimensional surface plot [14,15]. The best fitting model was used based on data on the adequate precision ratio and the predicted and adjusted determination coefficients for the dependent variables.

The software generated a polynomial equation consisting of three factors, and the responses are depicted in the following Equation (1):

$$\mathbf{Y} = \mathbf{b}\mathbf{0} + \mathbf{b}1\mathbf{A} + \mathbf{b}2\mathbf{B} + \mathbf{b}3\mathbf{C} + \mathbf{b}12\mathbf{A}\mathbf{B} + \mathbf{b}13\mathbf{A}\mathbf{C} + \mathbf{b}23\mathbf{B}\mathbf{C} + \mathbf{b}11\mathbf{A}2 + \mathbf{b}22\mathbf{B}\mathbf{B} + \mathbf{b}33\mathbf{C}\mathbf{C} \tag{1}$$

where Y was the measured response associated with each factor level combination, b0 was the intercept, b1 to b3 were the regression coefficients [16], and A, B, and C were the coded levels of the independent variables.

*Pharmaceutics* **2020**, *13*, 27



FS-NTF; Y3 = zone of inhibition against *Candida albicans*; Y4 = ulcer index score.
