Predictive compaction modelling of ternary direct compression formulations

Developing directly-compressed formulations remains a resource-intensive task, requiring substantial experimental effort to characterise the compressibility and compactability of a formulation space. This study extends a global optimisation of mixture rules to a ternary formulation space (API-brittle filler-elastic filler) and investigates the potential for reducing experimental burden whilst maintaining the predictive accuracy of empirical compression and compaction models. Three grades each of paracetamol and ibuprofen, combined with a consistent placebo base, were used to evaluate the approach. The global optimisation outperformed the traditional line of best fit approach, achieving strong predictive performance for the Kawakita model (R²>0.94; RMSE<0.01) and more variable fits for the Ryshkewitch-Duckworth model (R² = 0.93 - 0.95 and RMSE = 0.23 - 0.39 MPa for paracetamol; R² = 0.70 - 0.83 and RMSE = 0.31 - 0.37 MPa for ibuprofen). The optimisations performance was found to improve when the training dataset considered only drug-loaded blends. The exploration of reducing experimental burden considered a Model-Based Design of Experiments (MBDoE) which was benchmarked against random experiment selection. Integrating MBDoE with optimised mixture rules reduced API consumption by over 30% across all formulations, with median savings of 75%-95% under Acceptable and Good performance thresholds. Savings decreased with increasing threshold stringency, with the greatest variability observed in ibuprofen formulations. The Kawakita model supported reductions across all threshold levels, whilst the Ryshkewitch-Duckworth model showed limited capacity beyond the Acceptable threshold. The MBDoE did not outperform the random selection of experiments, however the optimisation framework for populating empirical compression and compaction models offers a resource-efficient approach to predicting tablet porosity and tensile strength of ternary API loaded blends.