Comprehensive theoretical analysis of the solubility of two benzodiazepine drugs in supercritical solvent; thermodynamic and advanced machine learning approaches

The pharmaceutical industry is showing growing interest in exploring supercritical CO₂ techniques to develop advanced drug delivery systems. In this regard, assessing the solubility of drugs in supercritical CO₂ under different conditions is a vital parameter. In this study, the solubility of two benzodiazepine family drugs, diazepam and alprazolam, in supercritical CO₂ was theoretically assessed using two distinct thermodynamic approaches; the SRK model, which treats supercritical CO₂ as a gas, and the regular solution model, which considers supercritical CO₂ as a liquid and incorporates various expressions for the solubility parameter. Furthermore, machine learning models, including MLP with various training algorithm, GPR and KNN, were employed to predict the solubility of these drugs. The accuracy of the models for each medicine is validated by comparing their results with previously published experimental solubility data. It was demonstrated that both thermodynamic models successfully model the solubility of these drugs in supercritical CO₂. The SRK model yielded mean AARD values of 10.36 for diazepam and 3.15 for alprazolam, while the regular solution model, using a specific expression for the solubility parameter, provided the best fit to the experimental results, with mean AARD values of 4.69 for diazepam and 6.97 for alprazolam. Also, it was demonstrated that all intelligent models achieved the highest performance in predicting the solubility of diazepam and alprazolam in supercritical CO₂.