Multivariate spline interpolation as a novel method to optimize pharmaceutical formulations. 
One of the difficulties in the quantitative approach for formulation design is the difficulty in understanding the actual relationship between causal factors and individual pharmaceutical responses.  In this regard, several techniques were applied to determine the relationship between causal factors and the pharmaceutical responses.  The generation of response surfaces using multivariate spline interpolation (MSI) has provided rapid and detailed information.  Nevertheless, no application of MSI in the pharmaceutical field has been reported to date, even though it promises potential applications.  To overcome the shortcomings of the classical response surface method, we newly developed a multi-objective simultaneous optimization method, in which MSI had been incorporated.  The method was applied to the optimization problem of a transdermal hydrogel formulation for ketoprofen containing several chemical enhancers.  Results suggested a superior function of the MSI approach.