Latent Structure Analysis in Pharmaceutical Formulations Using Kohonen's Self-Organizing Map and a Bayesian Network

ABSTRACT A latent structure analysis of pharmaceutical formulations was performed using Kohonen's self-organizing map (SOM) and a Bayesian network. A hydrophilic matrix tablet containing diltiazem hydrochloride (DTZ), a highly water-soluble model drug, was used as a model formulation. Nonlinear relationship correlations among formulation factors (oppositely charged dextran derivatives and hydroxypropyl methylcellulose), latent variables (turbidity and viscosity of the polymer mixtures and binding affinity of DTZ to polymers), and release properties [50% dissolution times ( t 50s ) and similarity factor] were clearly visualized by self-organizing feature maps. The quantities of dextran derivatives forming polyion complexes were strongly related to the binding affinity of DTZ to polymers and t 50s . The latent variables were classified into five characteristic clusters with similar properties by SOM clustering. The probabilistic graphical model of the latent structure was successfully constructed using a Bayesian network. The causal relationships among the factors were quantitatively estimated by inferring conditional probability distributions. Moreover, these causal relationships estimated by the Bayesian network coincided well with estimations by SOM clustering, and the probabilistic graphical model was reflected in the characteristics of SOM clusters. These techniques provide a better understanding of the latent structure between formulation factors and responses in DTZ hydrophilic matrix tablet formulations.