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13 Axial 1.5 6 87.5 333.9 0.408 30.6 14 Center 1.5 12 87.5 609.8 0.655 27.2 15 Factorial 1 6 75 240.1 0.287 17.9 16 Factorial 1 6 100 447.6 0.676 15.6 17 Center 1.5 12 87.5 609.8 0.655 27.2 18 Factorial 1 18 100 453.4 0.62 25.1 19 Factorial 2 18 75 492.8 0.537 20.9 20 Center 1.5 12 87.5 609.8 0.655 27.2

      MPS, mean particle size; PDI, polydispersity index; ZP, zeta potential.

      Each row indicates an experiment while the columns present the composition and the critical quality attributes (CQAs) of the non‐phospholipid‐based topical ophthalmic emulsions.

The search for design space and optimized emulsion formula was carried out by numerical and graphical techniques using the software. The interaction effect of the CPPs on the CQAs was visualized using the response surfaces and 3D contour plots of the fitted polynomial regression equation. Furthermore, the quantitative comparison between the theoretical prediction and obtained experimental values was used by plotting the predicted versus observed value curve to validate/verify the chosen face‐centered CCD model. The predicted error is the difference between the experimental value and the predicted value divided by predicted value.

TABLE 2.7. Low and High Levels of Critical Material Attributes (CMAs) and Critical Process Parameters (CPPs, also Called as Independent Variables) Along with the Goals of Critical Quality Attributes (CQAs, also Called as Dependent Variables) Used for Making Face‐Centered Central Composite Design (CCD) Throughout the Initial Pilot Screening Study to Prepare Topical Ophthalmic Emulsions

Screened CMAs and CPPs	Quantity	Levels
Low	High
X 1: Castor oil (ml)	1, 1.5, 2	1	2
X 2: Chitosan (mg)	6, 12, 18	6	18
X 3: Poloxamer (mg)	75, 87.5, 100	75	100
CsA (% w/w)	0.05 or 0.1
Glycerin (g)	2.25
Double distilled water (ml)	Upto 100
Selected CQAs		Goal
R 1 : Mean particle size		Minimize
R 2 : Polydispersity index		Minimize
R 3 : Zeta potential		Maximize

      Note: Italics numbers and texts indicate constant quantity of independent variables while the quantity of other independent variables were altered.

       2.5.1.5. Systematic Optimization Using Face‐Centered CCD

A Box–Wilson central composite design, commonly termed as CCD, is frequently utilized to build a second‐order polynomial for the response variables (CQAs) in RSM without using a complete full factorial design of experiments. There are two main varieties of CCD, namely, face‐centered CCD and rotatable CCD. Due to its simplicity, regions of interest, and operability, the face‐centered CCD was chosen in the present study. As per the face‐centered CCD, the optimal composition and the experimental conditions to prepare the topical ophthalmic emulsions were fixed (Table 2.7). Although the goal of ZP is fixed at maximum (Table 2.7) by considering the previous observation that a stable cationic nanosized emulsion should contain the ZP value that ranges from +25 to +45 mV (Tamilvanan et al. 2010), the stable stability of emulsion is not increasing with the increase of ZP's values. With the help of polynomial regression equation, the factor–response relationship was examined for the response function (Yi) using the generalized response surface model [as given in Eq. (2.2)]. In Eq. (2.2), the terms X₁, X₂, and X₃ indicate the three different factors (CPPs, independent variables) such as amounts of castor oil, chitosan, and poloxamer, respectively. While the term a₀ represents intercept (a constant), the linear (first‐order), quadratic (second‐order), and interactive polynomial coefficients are given as a₁,

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