Multi-dimensional population balance model development using a breakage mode probability kernel for prediction of multiple granule attributes

Milling affects not only particle size distributions but also other important granule quality attributes, such as API content and porosity, which can have a significant impact on the quality of the final drug form. The ability to understand and predict the effects of milling conditions on these attributes is crucial. A hybrid population balance model (PBM) was developed to model the Comil, which was validated using experimental results with an R² of above 0.9. This presented model is dependent on the process conditions, material properties and equipment geometry, such as the classification screen size. In order to incorporate the effects of different quality attributes in the model physics, the dimensionality of the PBM was increased to account for changes in API content and porosity, which also produced predictions for these attributes in the results. Additionally, a breakage mode probability kernel was used to introduce dynamic breakage modes by predicting the probability of attrition and impact mode, which are dependent on the process conditions and feed properties at each timestep.