*2.6. Optimization Design*

A 3<sup>2</sup> full factorial design was used to assess the influence of independent variables on the dependent variables for the prepared clarithromycin SLNs. Based on the fractional factorial design data, the two factors of amount of lipid (mg) (X1) and sonication time (min) (X2) showed substantial effects on the particle size, drug entrapment efficiency, and drug loading, and hence were applied at 3 levels. In addition, the other three factors, namely homogenization speed, surfactant ratio, and surfactant concentration, were kept constant at 9000 rpm, 5:5, and 3%, respectively, during the experimental run of nine experiments. The dependent variables were Y1: particle size; Y2: percent entrapment efficiency; and Y3: percent drug loading. Table 3 shows coded and actual values of the independent variables of the 3<sup>2</sup> full factorial design.

**Table 3.** Coded and actual values of independent variables of 3<sup>2</sup> full factorial design.


The responses Y1, Y2, and Y<sup>3</sup> were evaluated using the equation Y = b<sup>0</sup> + b1X<sup>1</sup> + b2X<sup>2</sup> + b<sup>12</sup> X1X<sup>2</sup> + b11X<sup>11</sup> + b22X22. This equation represents the main factors (X<sup>1</sup> and X2), interaction factors (X1X2), and polynomial factors (X<sup>11</sup> and X22). The b<sup>0</sup> is the mathematic mean value of total runs, and b<sup>1</sup> and b<sup>2</sup> are the projected coefficients for the factors X<sup>1</sup> and X2, respectively. For validation of selected statistical design, polynomial equations were generated using Design Expert software, and one-way analysis of variance (ANOVA) was tested. With the help of response surface plots, the correlation between variables and response parameters was established. The method of preparation was the same as per the screening design batches. Table 4 shows the coded and actual values for 9 batches of the 3<sup>2</sup> full factorial design.


**Table 4.** Coded and actual values for 9 batches of the 3<sup>2</sup> full factorial design.
