Design expert 6

All data were analysed in triplicate and reported as a mean±standard deviation. The statistical analysis was conducted using SPSS 11.0 (SPSS Inc., IBM Corp., IL, USA) using Duncan’s multiple range test (DMRT) with a significant level determined at a 95% confidence limit (p < 0.05). The regression analysis on RSM to indicate the optimized ratio of DGP and DWPP was appointed using Design Expert 6.0 (Stat Ease Inc., MN, USA).

In this study, a Box-Behnken experimental design with three levels of three factors and response surface methodology was used to estimate optimal levels of variables. The three factors with three levels for FOS production included ultrasonication time (X₁, 2.00–15.00 min), microbubble time (X₂, 5.00–30.00 min), and reaction time (X₃, 2.00–6.00 h). Design expert 6.0.10 (Stat-Ease, Inc., Minneapolis, MN, USA) was used for experimental design and modelling analysis resulting in a total of 17 experiments, which were conducted in triplicate (Table 1). The model predicting the optimal values was expressed as Equation (1) given below:
$Y={\beta }_0+{\displaystyle \sum }_{i=1}^k{\beta }_i{X}_i+{\displaystyle \sum }_{i=1}^k{\beta }_{ii}{X}_i^2+{\displaystyle \sum }_{i\ge j}^k{\displaystyle \sum }_{i=1}^k{\beta }_{ij}{X}_{ij}{X}_j$
where Y is the predicted response, β is the regression coefficient and X is the independent variable. The F-value determined the statistical significance of the equation. The accuracy of the polynomial model equation was expressed by the coefficient of determination (R²).

A three-factor, three-level Box-Behnken design was employed for the optimization process using the statistical software Design Expert 6.0.10 (Stat-Ease Inc., USA). The non-linear quadratic model generated by the design was: $$\mathrm{Yi}={\mathrm{b}}_0+{\mathrm{b}}_1{\mathrm{X}}_1+{\mathrm{b}}_2{\mathrm{X}}_2+{\mathrm{b}}_3{\mathrm{X}}_3+{\mathrm{b}}_{12}{\mathrm{X}}_1{\mathrm{X}}_2+{\mathrm{b}}_{13}{\mathrm{X}}_1{\mathrm{X}}_3+{\mathrm{b}}_{23}{\mathrm{X}}_2{\mathrm{X}}_3+{\mathrm{b}}_{11}{{\mathrm{X}}_1}^2+{\mathrm{b}}_{22}{{\mathrm{X}}_2}^2+{\mathrm{b}}_{33}{{\mathrm{X}}_3}^2$$
In which Y_i is the measured response of each dependent variable; b₀ is the intercept; b₁ to b₃₃ are the regression coefficients of the factors; and X₁, X₂, and X₃ are the coded levels of independent variables. The term X₁ X₂, X₁ X_3, X₂ X₃ and X_i² (i = 1, 2, or 3) exhibit the interaction and the quadratic terms respectively. A description of the independent and dependent variables is given in Table 1. The models were evaluated in terms of statistically significant p-value and CE.Table 1

Variables in Box Behnken design

Factor	Levels used
Independent variables	−1	0	1
X1 = Cysteine (%w/w)	25	37.5	50
X2 = Trehalose (%w/w)	60	105	150
X3 = Tween 20 (%w/w)	0	0.03	0.05
Dependent variables			Constraints
Y1 = Yield (%)			Maximize
Y2 = Beta- sheet content (%)			66 ≤Y2≤73
Y3 = Amount of aggregation immediately following spray drying (%)			Minimize
Y4 = Amount of aggregation following 2 month storage at 45 °C (%)			Minimize

The Design-Expert 6.0.3 software (StatEase Inc., Minneapolis, MN, USA) was applied to conduct RSM based on CCD experiments to optimize the FST–NP formulations. The chosen factors were the concentration of PVA (X₁) and PLGA amount (X₂), and responses included particle size (Y₁), size distribution expressed by the polydispersity index (Y₂), encapsulation efficiency (Y₃), and zeta potential (Y₄), as shown in Table 6. The goals for exploring the optimized FST–NP formulation included the minimized particle size (Y₁), maximized encapsulation efficiency (Y₂), zeta potential (Y₃) < −20 mV and minimized polydispersity index (Y₄).

The obtained data are expressed as mean ± standard deviation. ANOVA for RSM was performed using Design-Expert 6.0.3 software (StatEase Inc., Minneapolis, MN, USA). The effects of the different extraction methods on alkaloid yield were compared statistically using ANOVA followed by a post hoc Scheffe test using SPSS v14.0 (SPSS Inc., Chicago, IL, USA). A p-value of < 0.05 was considered to indicate a significant difference.