Design expert version 13

BBD and RSM were performed using Design–Expert version 13 (Stat-Ease, Inc., Minneapolis, MN, USA). All experiments were assayed in triplicate (n = 3) and presented as mean ± standard deviation (SD). The one-way analysis of variance (ANOVA) and Duncan’s multiple comparisons, Tukey’s multiple comparisons test, or an unpaired t-test (as indicated in the table legend) were performed using SPSS version 18 (Statistical Package for the Social Sciences, SPSS Inc., Chicago, IL, USA) to test the difference between samples. p ≤ 0.05 was considered a significant difference.

Design Expert^® Version 13 (Stat Ease, Inc., Minneapolis, MN) was involved in the investigation of the influence of altering various formulation aspects of EMLs on their responses. Eight experimental runs were attained from the manipulated design adopting 2³ experimental designs. Three factors were considered as the independent variables: lipid core amount (A), PC amount (B), and Brij52 amount (C), where EE% (Y1), PS (Y2), and ZP (Y3) were set as the dependent variables. The selection of the optimal 3b-loaded EML formulation was conducted based on the highest EE%, ZP, and lowest PS values. The consideration of the main effects and their relative significance were explored according to ANOVA statistical analyses. Furthermore, the optimal formulation with the highest desirability value was picked and involved in further assessments. Finally, the composition of the optimised formula was used in the preparation of the other compounds loaded emulsomal nanoparticles (EMLs) in order to investigate the effect of formulation of all compounds (3a–g) on their anti-SARS-CoV-2 activity which represent one of the prime targets of the study.

All experiments were determined in triplicate, and the data were shown as mean ± SD (n = 3). A one-way analysis of variance (ANOVA) was analyzed using Duncan’s multiple range test using SPSS version 18 (Statistical Package for the Social Sciences, SPSS Inc., Chicago, IL, USA). The data were considered to be significantly different at p < 0.05. The BBD and RSM were assigned using Design-Expert version 13 (Stat-Ease Inc., Minneapolis, MN, USA).

Central composite design (CCD) of response surface methodology (RSM) was carried out to optimize the conditions for luteolin recovery from PSs. CCD provides mathematical models by considering the interaction of variables. The model equation is converted into a quadratic function and the response value is estimated using the variable of the quadratic model. The variables and their ranges were as follows: temperature (X₁; 0–60 °C), time (X₂; 1–5 h) and MeOH concentration (X₃; 0–100%) (Table 9).
Analysis of variance (ANOVA) was carried out to prove the validity of the estimated model. The effects and interactions of variables on the response were determined using the following quadratic Equation (3): $$Y={\beta }_0+\sum _{i=1}^k{\beta }_i{X}_i+\sum _{i=1}^k{\beta }_{ii}{X}_i^2+\sum _{i=1}^k\sum _{j=i+1}^k{\beta }_{ij}{X}_i{X}_j,$$
where Y is the output response values (luteolin yield), β₀ is the offset term and β_i, β_ii and β_ij are regression model coefficients [41 (link)]. k indicates the number of variables (k = 3 in this study). X_i and X_j denote the input variables values (temperature, time and MeOH concentration). The ANOVA and numerical optimization were carried out using the software Design-Expert version 13 (Stat-Ease, Inc., Minneapolis, MN, USA). All experiments were performed in triplicate, and the results were calculated as an average.