Latent structure modeling underlying theophylline tablet formulations using a Bayesian network based on a self-organizing map clustering.

The "quality by design" concept in pharmaceutical formulation development requires the establishment of a science-based rationale and design space. In this article, we integrate thin-plate spline (TPS) interpolation, Kohonen's self-organizing map (SOM) and a Bayesian network (BN) to visualize the latent structure underlying causal factors and pharmaceutical responses. As a model pharmaceutical product, theophylline tablets were prepared using a standard formulation. We measured the tensile strength and disintegration time as response variables and the compressibility, cohesion and dispersibility of the pretableting blend as latent variables. We predicted these variables quantitatively using nonlinear TPS, generated a large amount of data on pretableting blends and tablets and clustered these data into several clusters using a SOM. Our results show that we are able to predict the experimental values of the latent and response variables with a high degree of accuracy and are able to classify the tablet data into several distinct clusters. In addition, to visualize the latent structure between the causal and latent factors and the response variables, we applied a BN method to the SOM clustering results. We found that despite having inserted latent variables between the causal factors and response variables, their relation is equivalent to the results for the SOM clustering, and thus we are able to explain the underlying latent structure. Consequently, this technique provides a better understanding of the relationships between causal factors and pharmaceutical responses in theophylline tablet formulation.

Self-organizing map analysis using multivariate data from theophylline tablets predicted by a thin-plate spline interpolation.

The "quality by design" concept in pharmaceutical formulation development requires the 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 tablets were prepared based on a standard formulation. The tensile strength, disintegration time, and stability of these variables were measured as response variables. These responses were predicted quantitatively based on nonlinear TPS. A large amount of data on these tablets 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 tablets were classified into several distinct clusters. The SOM feature map allowed us to analyze the global and local correlations between causal factors and tablet characteristics. The results of this study suggest that increasing the proportion of microcrystalline cellulose (MCC) improved the tensile strength and the stability of tensile strength of these theophylline tablets. In addition, the proportion of MCC has an optimum value for disintegration time and stability of disintegration. Increasing the proportion of magnesium stearate extended disintegration time. Increasing the compression force improved tensile strength, but degraded the stability of disintegration. This technique provides a better understanding of the relationships between causal factors and pharmaceutical responses in theophylline tablet formulations.

Determination of the optimal cell-penetrating peptide sequence for intestinal insulin delivery based on molecular orbital analysis with self-organizing maps.

Our recent work has shown that the intestinal absorption of insulin can be improved significantly by coadministration of cell-penetrating peptides (CPPs), especially penetratin. However, a relatively high dose of penetratin is required to adequately stimulate the intestinal absorption of insulin. Therefore, in this study, we sought to determine the CPP that most effectively enhanced intestinal insulin absorption. An in situ loop absorption study using 26 penetratin analogues suggested that the chain length, hydrophobicity, and amphipathicity of the CPPs, as well as their basicity, contribute to their absorption-enhancing efficiency. Moreover, a molecular orbital method with self-organizing maps (SOMs) classification suggested that multiple factors, including the molecular weight, basicity, the lowest unoccupied molecular orbital energy, absolute hardness, and chemical potential of CPPs, are associated with their effects on intestinal insulin absorption. Furthermore, the new CPPs proposed by SOM clustering had a marked capacity to interact with insulin, and their ability to enhance insulin absorption was much stronger than that of the original penetratin. Therefore, the peptide sequence that optimally enhances intestinal insulin absorption could be defined by SOM with the molecular orbital method, and our present work emphasizes the utility of such methodologies in the development of effective drug delivery systems.

Latent structure analysis in pharmaceutical formulations using Kohonen's self-organizing map and a Bayesian network.

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 (t50s) 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 t50s. 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.

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.

Role of individual test samples in optimal solutions in pharmaceuticals predicted using a nonlinear response surface method.

Establishing a method to evaluate the reliability of an optimal solution is an exciting challenge for the nonlinear response surface method. We reported previously that the bootstrap (BS) resampling technique and Kohonen's self-organizing map are promising tools for meeting this challenge. To understand the usefulness of these techniques further, we employed a formulation optimization study of photocrosslinked polyacrylic acid (PAA) hydrogel as a case study. In a series of experiments, a large number of optimal solutions were generated with BS resampling and they were classified into three distinct clusters with SOM clustering. Using analysis of Bayesian estimation, we clarified the mode of generating clusters; e.g., cluster 2 was distinguished by the difference in features between the BS optimal solutions and the original optimal solution, whereas cluster 3 was distinguished by the substantial change in the shape of the response surfaces. We concluded that cluster 1 represents the global optimal solution, and then estimated 95% confidence intervals of the optimal solutions using the BS optimal solutions. These findings prove that our method is a valid approach for evaluating nonlinear optimal solutions. This method has applications for establishing a science-based rationale for, and a design space in, pharmaceutical formulation development.