Extreme vertexes design in formulation development: solubility of butoconazole nitrate in a multicomponent system.

The extreme vertexes design was shown to be an efficient method for the study of mixture problems, for generating points in the factor space that define a region for response surface analysis. By using this method, the solubility of butoconazole nitrate, an imidazole antifungal agent, was studied as a function of four components, polyethylene glycol 400, glycerin, polysorbate 60, and water, whose levels were subject to given constraints. A fifth component, poloxamer 407, was held constant. The design was used to generate 14 points in the region defined by the constraints. The G efficiency of the design, with the assumption of a quadratic model for the response surface, was 79%. By using the solubilities determined at the 14 points and regression analysis, an equation was generated to characterize the response surface. Contour plots of the response surface illustrate the relationship of the solubility as a function of the components, and solubilities calculated at other points (in the region) agree well with the observed data.