Comparing the applicability of mixing rules to predict the tensile strength of compacted mixtures

Mechanical strength is a key determinant of the manufacturability of tablet formulations. Therefore, the prediction of the tablet strength of compacted pharmaceutical mixtures from the properties of the ingredients is of great practical interest. Many different mixing rules have been proposed in the literature. These range from simple averaging approaches, such as the arithmetic, geometric, harmonic, and Ryshkewitch-Duckworth equation-based rules, to more complex models, including the 4^th-order model, the compressibility-based geometric mixing rule, and the tabletability-power law model. The literature contains conflicting conclusions about their applicability and new models continue to be proposed. Given the lack of consensus, it is important to compare models under conditions where model selection makes the most difference in obtaining accurate tensile strength predictions. In this work, we demonstrate that different models work best with a different set of mixtures. Furthermore, we will show the conditions when these models yield the most similar and divergent predictions. Among the present models, the 4^th-order model was found to be most accurate in predicting the behavior of non-DCPA mixtures, whereas the compressibility-based geometric mixing rule provided the most accurate predictions for DCPA mixtures.