296 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS Once the computer has the predictor equations, appropriate programs can search for the optimum formulation based upon the constraints which the formulatot specifies as described in a previous publication (10). The formulation (combination of independent variables) is specified by the computer and the properties (dependent variables) are predicted. The formulation can then be prepared in the laboratory and tested. For one such case, which represented a tablet formulation, the predicted and experimental properties are shown in Table VII. These data show that the objective was accomplished i.e., to find the exact quantities of ingredients which give the best combination of properties which are all good at the same time. Table VII Optimum Formulation For Tablet System Response Experimental Predicted Disintegration Time (min.) 3.31 3.03 Hardness (kg.) 10.08 10.38 Dissolution (% in 30 min.) 89.85 • 98.02 Friability (%) 0.18 - 0.38 •Highest value in the 27 experimental trials was 78% (after Ref. 10). OPTIMIZATION OF BIOLOGICAL PARAMETERS The next logical step was to say that if the physical properties of a dosage form are controlled by the formulation and can be predicted, it should also be true of the biological properties. Therefore, a joint project was undertaken with the Massachu- setts College of Pharmacy (12). In this case, three independent variables were selected as shown in Table VIII. They were disintegrant level, lubricant level and compressional force. Table VIII Variables for Optimization Study of Biological Properties Independent Variable Dependent Variable x• Starch Level x2 Magnesium Stearate Level x 3 Compressional Force y• Absorption Rate y2 Lag Time Y3 Elimination Rate Y4 Time of Plasma Peak •In addition to the usual properties such as tablet hardness, etc. Fifteen formulations were prepared and the properties measured. This time, however, the study was continued, by administering the tablets to dogs and collecting appropriate blood samples, so that in addition to the usual physical properties of the tablets, we added the pharmacokinetic properties: Time of the peak plasma concentra- tion. (min.) Lag time. (min.) Absorption rate constant. (min.-•) and Elimination rate constant. (min.-•). The drug in this case was hydrochlorothiazide and the blood level curves were analyzed by assuming first order elimination, first order absorption and a one-compartment model. (It should be obvious that a medicated cream, a dandruff shampoo, or a lotion for a specific biological purpose could be studied in the same manner.)

OPTIMIZATION TECHNIQUES 297 x• X1ZX2•X3•O •CORN5TRRCH &MR•NE5IUM 5TERRRTE •?RE5$URE Figure 5. Computer generated plot of Elimination Rate Constant as a function of each independent variable. By graphical observation, the elimination rate constant was (correctly) not a function of the independent variables (Figure 5). It was indeed relatively constant. The other three were functions of the formulation factors, as illustrated by the composite plots in Figures 6-8. By our computer search methods, we asked the computer for the optimum formula- tion with a tablet hardness of about 6.5 kg and a peak plasma concentration time of less than 60 min. This formulation was prepared and tested. The predicted vs. experimental results are shown in Table IX, and the agreement is excellent. In addition we requested from the computer the worst formulation with respect to peak time, but one exhibiting equivalent tablet hardness. We called this the anti- optimum, and the predicted vs. experimental data are also shown in Table IX. The tablets from the two batches look alike. They have equivalent hardness values. They have exactly the same ingredients qualitatively, from the same batches of raw