the homogenization speed was kept at a constant value of 15,000 rpm. For PDI and ZP, none of the formulation and process variables has shown significant influence (Fig. 2.5b, c) as they did not cross the t value limit in the Pareto chart. However, the premixing time deliberately omitted and considered as dummy factor since this variable involves in the initial dispersion/mixing of oil and water phases during the emulsion preparation step. The formulation and process variables such as premixing time, homogenization time, homogenization speed, and probe sonication time were decided to fix at constant values of 10 min, 15 min, 15,000 rpm, and 5 min, respectively, due to their insignificant influence on the selected three CQAs of the topical ophthalmic emulsions. By taking our previous experience in making of topical ophthalmic emulsions into consideration, the formulation and process variables such as the amounts of castor oil, chitosan, and poloxamer were, however, selected as critical formulation and process variables that were ultimately needed to be further optimized using the face‐centered CCD.
2.5.1.4. Formulation Optimization by QbD: Experimental Design
To identify the effect of (Taguchi design‐) screened CPPs (independent variables) such as castor oil concentration (1–2 ml, A), chitosan concentration (6–18 mg, B), and poloxamer concentration (75–100 mg, C) on the three CQAs (dependent or response variables) like MPS (R1), PDI (R2), and ZP (R3), a three‐factor face‐centered central composite design (CCD) was used. A total of 20 experiments, including 6 replications of central points (the leverage value of 0.1182 and α value of 1) together with 8 factorial points and 6 axial points (shown in Table 2.6), were run using Design‐Expert® software. While the leverage value indicates the potential for a design point (axial, central, or factorial) for influencing the model fit, the α value determines the geometry of the design region and for face‐centered CCD, it is equal to 1 defining a square design geometry. Table 2.7 summarizes the screened CPPs and their levels. The values of CQAs were fed into the software and second‐order mathematical model was used to study the factor–response (CPPs–CQAs) relationship. An appropriate polynomial model was chosen based on the significant terms (p < 0.005, ANOVA), the least significant lack of fit, coefficient of variance, the multiple correlation coefficient, and adjusted multiple correlation coefficient provided by Design‐Expert® software. The center point was repeated six times to determine the repeatability of the method.
Figure 2.5. Half‐normal and Pareto charts for screening of influential formulation and process variables as per Taguchi design using selected critical quality attributes (CQAs): (a) mean particle size, (b) polydispersity index, and (c) zeta potential.
TABLE 2.6. Independent and Dependent (Response) Variables: Face‐Centered Central Composite Design (CCD) Scheme
| Run | Type | Critical Process Parameters (CPPs, also Called as Independent Variables) | Critical Quality Attributes (CQAs, also Called as Dependent Variables) | ||||
|---|---|---|---|---|---|---|---|
| Castor Oil (ml) | Chitosan (mg) | Poloxamer (mg) | MPS (nm) | PDI | ZP (mV) | ||
| 1 | Axial | 2 | 12 | 87.5 | 676.4 | 0.655 | 27.6 |
| 2 | Center | 1.5 | 12 | 87.5 | 609.8 | 0.655 | 27.2 |
| 3 | Factorial | 1 | 18 | 75 | 247.6 | 0.376 | 24.6 |
| 4 | Axial | 1.5 | 12 | 75 | 396.4 | 0.275 | 35.5 |
| 5 | Axial | 1.5 | 18 | 87.5 | 449.4 | 0.661 | 29.1 |
| 6 | Center | 1.5 | 12 | 87.5 | 609.8 | 0.655 | 27.2 |
| 7 | Factorial | 2 | 6 | 100 | 417.1 | 0.62 | 17.1 |
| 8 | Factorial | 2 | 18 | 100 | 438.1 | 0.469 | 23.2 |
| 9 | Factorial | 2 | 6 | 75 | 390.5 | 0.438 | 28.5 |
| 10 | Center | 1.5 | 12 | 87.5 | 609.8 | 0.655 | 27.2 |
| 11 | Axial | 1.5 | 12 | 100 | 441.5 | 0.488 | 18.8 |
| 12 | Axial | 1 | 12 | 87.5 | 374.2 | 0.435 | 33.6 |