Developing directly compressed oral solid doses typically requires extensive experimental characterisation of compressibility and compactability across formulation composition space. This study aimed to extend a previously described global optimisation of mixture rules into a ternary formulation domain consisting of an active pharmaceutical ingredient (API), a brittle filler, and an elastic filler. The objective was to determine whether optimised mixture rules combined with targeted experiment selection could reduce experimental burden while preserving predictive accuracy of empirical compression and compaction models.
The experimental evaluation used three grades each of paracetamol and ibuprofen. All API grades were combined with a consistent placebo base to create ternary direct-compression blends. The study explicitly compared performance across the two APIs and across grades to assess generalisability of the optimisation approach in practical formulation contexts.
Two empirical models were used to describe tablet behaviour. The Kawakita model was applied to describe compression behaviour (porosity/compressibility relationships). The Ryshkewitch–Duckworth model was used to characterise compactibility expressed as tensile strength as a function of porosity. These two models served as the endpoints for fitting mixture-rule-based predictive models over the ternary composition space.
The study extended a global optimisation strategy for mixture rules to the three-component space (API, brittle filler, elastic filler). The global optimisation approach was evaluated against a traditional line-of-best-fit mixture-rule method. The authors also examined how the content of the training dataset affected optimisation performance, specifically comparing results when the training dataset included placebo-only blends versus when it considered only drug-loaded blends.
Model fit and predictive performance were quantified using coefficient of determination (R2) and root mean square error (RMSE) for the respective models. Key findings reported in the source:
The global optimisation outperformed the traditional line-of-best-fit approach overall.
For the Kawakita model, the optimisation achieved very strong predictive performance with R2 > 0.94 and RMSE < 0.01 (units consistent with the Kawakita parameterisation used in the study).
For the Ryshkewitch–Duckworth model the fits were more variable by API:
The optimisation's performance improved when the training dataset excluded placebo-only blends and was restricted to drug-loaded mixtures, indicating the importance of representative training data for predictive accuracy.
To assess reductions in experimental workload and material consumption, the authors evaluated a Model-Based Design of Experiments (MBDoE) strategy. MBDoE selections were benchmarked against random selection of experiments. Performance of MBDoE-populated models was assessed against predefined Acceptable and Good performance thresholds (as applied to the Kawakita and Ryshkewitch–Duckworth endpoints), and material savings were quantified in terms of API consumption reduction relative to a full experimental campaign.
The combined MBDoE and optimised mixture-rule framework reduced API consumption by more than 30% across all formulations. Reported median API savings under Acceptable and Good performance thresholds were in the range of 75%–95%, demonstrating substantial material efficiency in many cases. Observations included:
Savings declined as the performance threshold became more stringent; tighter predictive criteria required more experiments and thus reduced material savings.
The Kawakita model supported reductions across all threshold levels tested, reflecting its consistently strong predictive performance under optimisation.
The Ryshkewitch–Duckworth model had limited capacity to support reductions beyond the Acceptable threshold; its greater variability—particularly for ibuprofen—reduced potential material savings at higher stringency.
The MBDoE approach did not consistently outperform random selection of experiments in this evaluation, indicating that experiment selection strategy alone did not guarantee better material efficiency under the tested conditions.
The optimisation framework for populating empirical compression and compaction mixture rules provides a material-sparing approach to predicting tablet porosity and tensile strength in ternary API-loaded blends. The method delivered robust predictions for compression behaviour (Kawakita) and mixed results for compactibility (Ryshkewitch–Duckworth), with paracetamol blends showing stronger compactibility prediction than ibuprofen in this dataset. Improvements in model performance when using drug-loaded training data highlight the importance of representative experimental design for predictive modelling.
Limitations noted by the source include variability in model fits across APIs and models, and the finding that MBDoE did not reliably beat random experiment selection in this instance. The abstract does not report additional experimental details such as exact blend ratios, number of experiments, or MBDoE algorithmic parameters; those details were not reported in the source abstract provided here.
Overall, the study indicates that global optimisation of mixture rules combined with targeted experiment strategies can reduce API usage substantially while maintaining acceptable predictive accuracy for many direct-compression endpoints, though performance depends on the chosen empirical model and the API under study.
The authors declared that Daniel Markl received financial support from GlaxoSmithKline Research & Development Limited and from the Scottish Funding Council. The remaining authors declared no known competing financial interests or personal relationships that could have influenced the reported work.