Design expert software

The process and composition of EPL-NCs were optimized by using Design-Expert software (version 12, Stat-Ease Inc., Minneapolis, MN). D-optimal combined mixture process design was applied to generate different runs of formulations. For this purpose, solvent (tertiary butyl alcohol) to antisolvent (water) ratio (total volume = 10 mL), cryoprotectant (mannitol) concentration, and freezing method (slow or rapid) were chosen as independent variables. On the other hand, NCs size and dissolution efficiency were selected as dependent variables. These variables along with their levels and constraints are presented in Table 1. EPL concentration was kept constant at 200 mg in all formulations. The software generated runs of formulations with different composition and process variables were practically prepared and their responses were measured in terms of NCs size and dissolution efficiency.
The measured responses of both dependent variables (NCs size and dissolution efficiency) were introduced in the response column of Design-Expert software (Stat-Ease Inc., Minneapolis, MN). These responses were fitted to empirical model which interpreted the behavior of independent variables. Statistical analysis of the experimental data was carried to check the adequacy of proposed model by applying ANOVA test with Design-Expert software (Stat-Ease Inc., Minneapolis, MN).

Formulation optimization was performed by the response surface optimal design using Design-Expert software (version 10.0, Stat-Ease Inc., Minneapolis, USA) according to our previous studies using the same methodology in the optimization process^{14 (link),55} . Four independent variables including (1) surfactant to lipid (S/L) ratio, (2) percentage of Brij 35, (3) percentage of Brij 72, and (4) percentage of Span 60 were considered in the optimization process. Response variables were particle size and entrapment efficiency (%EE). According to the defined independent variables, the software suggested 27 runs, as shown in Table 1. Finally, based on the optimization results, ART-loaded niosomes with average diameters of 100 and 300 nm and desired %EE values were targeted by Design-Expert® software (version 10.0.7, Stat-Ease Inc., Minneapolis, USA) for further characterization tests. The rationale for the selection of ART-loaded niosomes with particle sizes of 100 nm and 300 nm through the Design-Expert software was that according to the previous studies, nanoparticles with an average diameter of about 100–300 nm can efficiently enhance the skin permeation of the loaded drug^{25 (link),56 (link),57 (link)}, which was the main purpose of the current study for CL management.

The aloesin content was the dependent (or response) variable used to optimize the extraction processes involving the three alcohol–water binary systems. Fitting procedures, coefficient estimates, and statistical analysis were performed using Design-Expert software as previously described [24 (link),25 (link)]. Briefly, the variance analysis (ANOVA) was used to assess the significance of the generated polynomial model equations and of all the terms that make up these models, as well as the lack-of-fit. Only the statistically significant terms (p < 0.05) were considered in the development of the models (except those required to maintain hierarchy). The coefficient of determination (R²), the adjusted coefficient of determination (R²_adj) and the adequate precision were used to estimate the adequacy of the polynomial model equations to the response. A non-significant (p > 0.05) lack-of-fit is desired so that the model can adequately describe the functional relationship between the three independent variables and the aloesin content. Design-Expert software was also used to generate the response surface graphs.