Solubility Prediction of Different Forms of Pharmaceuticals in Single and Mixed Solvents Using Symmetric Electrolyte Nonrandom Two-Liquid Segment Activity Coefficient Model

An improved framework has been developed for solubility prediction of different forms of a medium-sized antibiotic (i.e., nonelectrolyte, electrolyte, and solvate) in single and mixed solvents using a symmetrically reformulated electrolyte nonrandom two-liquid segment activity coefficient (eNRTL-SAC) model.

The methodology incorporates key features of the symmetric eNRTL-SAC model structure to reduce the number of parameters and uses a hybrid of global search algorithms for parameter estimation. Moreover, a design of experiments is included in the methodology to generate and use experimental data appropriately for model parameter regression and model validation.

Because of the semipredictive nature of the symmetric eNRTL-SAC model, the segment parameter regression is a critical step for solubility prediction accuracy. A particle swarm optimization algorithm is incorporated to preregress conceptual segment parameters of solutes. The preregressed segment parameters were used as initial guesses for further segment parameter estimation.

In this way, consistent segment parameters that reflect the characteristics of solutes in solution were estimated. The methodology application is demonstrated by predicting the solubility of fusidic acid, sodium fusidate, and fusidic acid acetone solvate in single and mixed solvents as well as at different temperature.

The solubility predictions of fusidic acid, fusidic acid acetone solvate, and sodium fusidate in various single solvents show good agreement with experimental solubility with average squared relative errors of 0.055, 0.079, and 0.084 in logarithmic mole fraction scale, respectively. The model moreover predicts solubilities in binary solvent mixture and as a function of temperature in satisfactory agreement with experimental solubility.