Empirical model variability: developing a new global optimisation approach to populate compression and compaction mixture rules

This study systematically evaluated the predictive accuracy of common empirical models for pharmaceutical powder compaction. A dataset of nine placebo and twelve active pharmaceutical ingredient (API) loaded blend formulations (four APIs at three drug loadings) was fitted to the widely used empirical tablet compression (Gurnham, Heckel, and Kawakita) and compaction (Ryshkewitch-Duckworth and Leuenberger) models. At low API loadings (<20w/w%), all models achieved R2 above 90 % and RRMSE (relative root mean squared error) below 0.1. However, as API loads increased, overall model performance decreased, notably in the Heckel model. A parameter variability analysis identified multiple parameter pairs achieving acceptable fits. Consequently, a novel global optimization approach was developed populating arithmetic, geometric, and harmonic mixture rules for empirical tuning parameters. This method outperformed the traditional line of best fit approach. A cross validation study revealed that this method is capable of predicting tuning parameters which achieve an acceptable Goodness of Fit for new blends. Finally, with the restriction of maintaining consistent parameters for the placebo blend, the proposed method could substantially reduce the experimental requirements and API consumption for the exploration of new blends.