Response surface formulation

For the PS case, a three-variable Box-Behnken response surface methodology (RSM) design using formulation variables has been carried out. For the RF system, an eight-variable fractional-factorial screening study was done first to select significant factors, and this was followed by two RSM s which were similar in design to the one done for PS. The results have led directly to substantial improvements in both materials. 

The resulting data of the Box-Behnken design were used to formulate a statistically significant empirical model capable of relating the extent of sugar 3deld to the four factors. A commonly used empirical model for response surface analysis is a quadratic polynomial of the type... 

In order to understand the relationship between the mixture component, physical properties and consumer acceptance of the lipstick, various lipstick formulations have to be produced. The physical properties of each formulation should be studied. The consumer acceptance towards the product also should be investigated. However, only a part of this work will be discussed in this paper. Here, natural waxes, oils and solvent have been used to produce natural ingredient based lipstick formulations based on the formulation suggested by the statistical mixture design. Contour plot and response surface graph were formed in order to understand the relationship between the mixture component and physical characteristic of the lipstick. 

A. Abdullah, A.V.A Resurreccion and L.R. Beuchat, Formulation and evaluation of a peanut milk based whipped topping using response surface methodology. Lebensm. Wiss. Technol., 26 (1993) 162-166. 

One example of the application of response surface analysis is a study of critical formulation variables for 20 mg piroxicam capsules [100]. Piroxicam is a BCS Class II drug (low solubility and high permeability). This... 

Fig. 25 Response surfaces for the effect of formulation variables on percent of piroxicam dissolving from capsules in 10 minutes. (From Ref. 100.)...

Similar overlaying of other response surface plots led to conclusions regarding the formulation variables and their effects on the properties of the copolymers. In addition, another (proprietary) computer program was used, which allowed the combination of several regression equations (for the various responses) and the calculation of variable values needed to achieve any desired combination of response values (if the models permit). 

To motivate the response surface approach, suppose that there is some response of interest (for example, crushing strength in the tablet formulation example of Section 2.1.1), and a set of quantitative, continuous design variables that are of interest to the researcher (for example, the quantities of glidant, lactose, and disintegrant for the tablet formulation example). One possible objective for the researcher might be to understand and describe the relationship between the design variables and the response. This relationship can be described mathematically by... 

After experimentation and calculation of a model, a relation is established between each formulation property separately and the variables in the employed model. When a model adequately describes this relation, predictions of this property can be made by interpolation over the whole range of the boundary values of the used variables, which forms the response surface. In Figure 4.12 the relation between the crushing strength and mixtures of three components (where the factor space can be represented by a triangle) is presented by a contour plot. The composition that gives a desired criterion value can be read directly fi-om the figure. 

Belloto, R.J., Jr., Dean, A.M., Moustafa, M.A., Molokhia, A.M., Gouda, M.W, and Sokoloski, T.D. Statistical techniques applied to solubility predictions and pharmaceutical formulations an approach to problem solving using mixture response surface methodology). Pharm., 23, 195, 1985. 

Nazzal, S., Nutan, M., Palamakula, A., Shah, R., Zaghloul, A.A., and Khan, M.A. (2002) Optimization of a self-nanoemulsi ed tablet dosage form of Ubiquinone using response surface methodology effect of formulation ingredientslnt. J. Pharm., 240 103-114. 

Sastry, S. V., Reddy, I. K., and Khan, M. A. Atenolol gastrointestinal therapeutic system optimization of formulation variables using response surface methodology. J. Contr. Rel. 45(2) 121-130, 1997. 

Nonlinear response surface models have been introduced by Hewlett and Plackett (1959), when they formulated simple similar action for mixture components with dissimilar concentration-response curves (note this is later defined as CA). Since then several response surface modeling methods specifically designed for mixtures have emerged in the literature. Although the various formulations in the literature may look different, their rationale is the same and can be described as follows. 

In all formulations that have appeared in the literature thus far, a generalization of the CA reference concept was performed to statistically test for deviations from CA. This means that a function describing interaction is incorporated in the CA model such that if the interaction parameter is 0, the interaction function disappears from the function. This nested structure allows testing whether its appearance in the model improves the description of the data significantly by applying the likelihood ratio test. The various nonlinear response surface approaches do differ in the way this deviation function is formulated. 

Innovations in statistical tools such as multivariate analysis, artificial intelligence, and response surface methodology have enabled rational development of formulations, and such methods allow formulators to identify critical variables without having to test each combination. 

These contour maps (also called response surfaces) give some useful insights into the nature of the FOR 1272 2EC formulation being studied. They indicate that within the limits studied ... 

It can be seen from these two figures that the response surface is saddle-shaped and has slightly more tilt at the low AI concentration. Overall they re very similar and show that active Ingredient of the purity range studied should perform satisfactorily in this formulation. 

Figure 9 shows a response surface for a commercial Dylox 1.5 Oil flowable formulation. The dependent variable of interest here is viscosity. It is typically linear with respect to thickener concentration. 

Figure 10 shows a response for a commercial Matacil 180 Oil flowable formulation. Unexpectedly, we found the response surface to be non-linear with respect to thickener concentration. 

Figure 2 clearly indicates that a captan wettable powder containing approximately 55% captan, 33% clay, 11% dispersant, and 1% surfactant should be evaluated if maximum suspensibility is desired. In addition to indicating regions of optimal composition, response-surface maps are extremely useful in analyzing cost vs. performance. Questions such as, "What is the most economical formulation that has 60% suspensibility " may be answered objectively, without additional experimentation. 

The process of drug discovery amounts to the search for optimality in a hyper-dimensional, multi-response surface area, and thus is a complex process. As discussed earlier, log P and the other R05 parameters, together with other properties such as PSA, and the number of flexible bonds, are significant contributors to a large number of models for different ADME/T properties. The open question is whether the use of such models provides an added value, compared to the simple and easily interpretable R05 criteria or the recent trends for the drug-likeness formulated by Gleeson. But can these models provide added value ... 

Formulations almost invariably consist of mixtures of a drug substance and excipients. Their properties usually depend not so much on the quantity of each substance present as on their proportions. The total comes to 100%, so the number of independent variables is one less than the number of eomponents. This has the effect that the models and the designs have particular properties, and the designs described above (screening, factor studies, and response surfaces) normally cannot be used. The entire topic of mixture designs is fully described by Cornell. ... 

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