A. Michrafy

Modelling the compaction behaviour of powders: application to pharmaceutical powders

Abstract Stress and density changes in axi-symmetric compaction of pharmaceutical powders are analysed numerically. Data measured in a compression cycle are used with a calibration procedure to assess the mechanical behaviour of powders in compaction based on a Drucker–Prager Cap model. This model is based on the elastic–plastic theory and takes into account the macroscopic characteristics of powders such as cohesion and global friction between particles. Moreover, a yield function is used to limit the admissible stresses in a tablet during a compaction cycle. This yield function depends on the first and second invariants of the stress tensor: pressure and stress deviation. To represent the plastic compaction mechanisms, a strain hardening function is used to expand the yield function with increasing volumetric strain. A finite element method coupled to the finite strain plasticity theory is used to calculate stress and strain changes in a tablet during compression and decompression. The die wall friction is estimated from the transmission effort to the lower punch with the modified equation of Shaxby and Evans. This model and the calibration procedure are applied to lactose powder. Mechanical properties calculated are compared to the experimental data measurements with a Jenike shear cell. The relative density distribution at the end of compaction and after the unloading is analysed. The normal pressure on the die is numerically estimated and analysed in terms of load transferred from powder to die during compaction and load restitution to tablet during decompression.

WALL FRICTION AND ITS EFFECTS ON THE DENSITY DISTRIBUTION IN THE COMPACTION OF PHARMACEUTICAL EXCIPIENTS

The effect of powder-die wall friction during the compaction of pharmaceutical excipients has been investigated for three modes of lubrication: lubricated die, non-lubricated die and with the lubricant mixed with the powder. Coulomb friction is assumed and the wall friction coefficient was evaluated from the transmission ratio (applied pressure/transmitted pressure), the transfer ratio (radial pressure/axial pressure) and the aspect ratio (height/diameter of tablet). The friction coefficient of three pharmaceutical excipients was measured with respect to the relative density of the tablet by means of an instrumented press. It was found that the behaviour of the friction depends on the powder and the lubrication mode. Mixing the powder with a lubricant reduces the friction with respect to that of the lubricated die, but the evolution of the friction coefficient with the densification is different. The effect of the wall friction on the axial density distribution in the tablet was investigated by experiment and by modelling. The model was based on Janssen-Walker analysis coupled with the Heckel equation. For comparison, only the single action compaction in a non-lubricated die was considered. It was found that the measured and predicted axial density decrease from the top to the bottom of the tablet. Moreover, the predicted and measured density had the same tendency, but different values. However, the analysis should not be applied to the compaction of the powder mixed with lubricant because no physical parameter for this mode of lubrication is taken into account in the model.

Computational intelligence models to predict porosity of tablets using minimum features

The effects of different formulations and manufacturing process conditions on the physical properties of a solid dosage form are of importance to the pharmaceutical industry. It is vital to have in-depth understanding of the material properties and governing parameters of its processes in response to different formulations. Understanding the mentioned aspects will allow tighter control of the process, leading to implementation of quality-by-design (QbD) practices. Computational intelligence (CI) offers an opportunity to create empirical models that can be used to describe the system and predict future outcomes in silico. CI models can help explore the behavior of input parameters, unlocking deeper understanding of the system. This research endeavor presents CI models to predict the porosity of tablets created by roll-compacted binary mixtures, which were milled and compacted under systematically varying conditions. CI models were created using tree-based methods, artificial neural networks (ANNs), and symbolic regression trained on an experimental data set and screened using root-mean-square error (RMSE) scores. The experimental data were composed of proportion of microcrystalline cellulose (MCC) (in percentage), granule size fraction (in micrometers), and die compaction force (in kilonewtons) as inputs and porosity as an output. The resulting models show impressive generalization ability, with ANNs (normalized root-mean-square error [NRMSE] =1%) and symbolic regression (NRMSE =4%) as the best-performing methods, also exhibiting reliable predictive behavior when presented with a challenging external validation data set (best achieved symbolic regression: NRMSE =3%). Symbolic regression demonstrates the transition from the black box modeling paradigm to more transparent predictive models. Predictive performance and feature selection behavior of CI models hints at the most important variables within this factor space.