A hybrid system of mixture models for the prediction of particle size and shape, density, and flowability of pharmaceutical powder blends

This paper presents a system of hybrid models that combine both mechanistic and data-driven approaches to predict physical powder blend properties from their raw component properties. Mechanistic, probabilistic models were developed to predict the particle size and shape, represented by aspect ratio, distributions of pharmaceutical blends using those of the raw components. Additionally, the accuracy of existing mixture rules for predicting the blend's true density and bulk density was assessed. Two data-driven models were developed to estimate the mixture's tapped density and flowability (represented by the flow function coefficient, FFC) using data from 86 mixtures, which utilized the principal components of predicted particle size and shape distributions in combination with the true density, and bulk density as input data, saving time and material by removing the need for resource-intensive shear testing for raw components. A model-based uncertainty quantification technique was designed to analyse the precision of model-predicted FFCs. The proposed particle size and shape mixture models outperformed the existing approach (weighted average of distribution percentiles) in terms of prediction accuracy while providing insights into the full distribution of the mixture. The presented hybrid system of models accurately predicts the mixture properties of different formulations and components with often $R^2>0.8$, utilising raw material properties to reduce time and material resources on preparing and characterising blends.