Self-Organizing Map Analysis Using Multivariate Data from Theophylline Powders Predicted by a Thin-Plate Spline Interpolation

The quality by design concept in pharmaceutical formulation development requires establishment of a science-based rationale and a design space. We integrated thin-plate spline (TPS) interpolation and Kohonen’s self-organizing map (SOM) to visualize the latent structure underlying causal factors and pharmaceutical responses. As a model pharmaceutical product, theophylline powders were prepared based on the standard formulation. The angle of repose, compressibility, cohesion, and dispersibility were measured as the response variables. These responses were predicted quantitatively on the basis of a nonlinear TPS. A large amount of data on these powders was generated and classified into several clusters using an SOM. The experimental values of the responses were predicted with high accuracy, and the data generated for the powders could be classified into several distinctive clusters. The SOM feature map allowed us to analyze the global and local correlations between causal factors and powder characteristics. For instance, the quantities of microcrystalline cellulose (MCC) and magnesium stearate (Mg-St) were classified distinctly into each cluster, indicating that the quantities of MCC and Mg-St were crucial for determining the powder characteristics. This technique provides a better understanding of the relationships between causal factors and pharmaceutical responses in theophylline powder formulations. © 2010 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 99:4535-4542, 2010