Three-dimensional desirability spaces for quality-by-design-based HPLC development

In this study, three-dimensional desirability spaces were introduced as a graphical representation method of design space. This was illustrated in the context of application of quality-by-design concepts on development of a stability indicating gradient reversed-phase high-performance liquid chromatography method for the determination of vinpocetine and α-tocopheryl acetate in a capsule dosage form. A mechanistic retention model to optimize gradient time, initial organic solvent concentration and ternary solvent ratio was constructed for each compound from six experimental runs. Then, desirability function of each optimized criterion and subsequently the global desirability function were calculated throughout the knowledge space. The three-dimensional desirability spaces were plotted as zones exceeding a threshold value of desirability index in space defined by the three optimized method parameters. Probabilistic mapping of desirability index aided selection of design space within the potential desirability subspaces. Three-dimensional desirability spaces offered better visualization and potential design spaces for the method as a function of three method parameters with ability to assign priorities to this critical quality as compared with the corresponding resolution spaces.