OPTIMIZATION TECHNIQUES 293 Table V Other Possible Dependent Variables Chemical Stability Sedimentation Rate, dv/dt Viscosity: One Point (Slope) -• Shear Rate vs. Shear Stress Yield Value Area of Hysteresis Loop Coacervation Dissolution Cost Penetrometer Reading (Creams, Ointments) Grittiness Synuresis Table VI Oral Suspension Experimental Design--Translation to Physical Units Formulation Factors 0 - 1.547 -- 1.0 EU + 1.0 + 1.547 EU EU (Base) EU EU x• = Veegum K (1 EU = 2.586 mg) 0 1.414 4.O 6.586 8.O x2 = Keltrol (1 EU = 0.323 mg) 0 0.177 0.5 0.823 1.0 x• = Water • (! EU = 0.09 g/Liter) 0 0.049 0.139 0.229 0.238 x4 = Citric Acid (1 EU = 0.646 mg) 0 0.354 1.0 1.646 2.0 x 5 = Mixing/Wetting Time (! EU = 60 Min.) 27.18 60.0 120.0 180.0 212.82 •Greater than 20%. Any change in water content from the base will be corrected with an adjustment in the sorbitol solution content. The next step requires analysis of the data to generate predictor equations. The technique applied is regression analysis and the predictions will only be as good as the fit of the data to the equations generated i.e. the index of determination (R-square value) should be greater than 90%. The type of equation used with the design shown previously is a second order polynomial of the form, Y = a o + a•xp.. + as x 5 -•- a•X•2... q-a55X52 -• a12XlX2... -• a45X4X5, where: ¾ = level of given response, ai = coefficients for second degree polynomial, x i = level of the independent variable.

294 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS One such equation is generated for each dependent variable e.g. one for sedimenta- tion rate, one for viscosity, one for resuspendability, etc., and the set of equations defines a response surface and, in fact, defines the system under study. Once the mathematical model has been generated, it can be treated in several ways to find the optimum formulation: Mathematical Methods: Such as the Lagrangian Method used by Fonner, Buck and Banker for a tablet formulation (8) and later by Buck, Peck, and Banker for a suspension formulation (9) Search Methods: Such as the system previously described, which is assisted by computer 00) or Graphical Methods: Used in all of the above, and the method of steepest descent was used mathematically by Dincer and Ozdur- mus for an enteric film coating Xl=X2=X3=X4=X5=O. GVEEGUMK (• z ss 4. z2 -b. 80 -b. 2' o: •8 o: so •: o• •: •( X(I} Figure 3. Computer generated plot of pH (dependent variable) as a function of suspending agent concentration (independent variable).