This study aimed to develop a practical semi-mechanistic modeling framework to predict particle size evolution during wet bead milling of pharmaceutical nanosuspensions over a wide range of process conditions and milling scales. The model incorporates process parameters, formulation parameters, and equipment-specific parameters such as rotor speed, bead type, bead size, bead loading, active pharmaceutical ingredient (API) mass, temperature, API loading, maximum bead volume, blade diameter, distance between blade and wall, and an efficiency parameter. The characteristic particle size quantiles, i.e., x10, x50, and x90, were transformed to obtain a linear relationship with time, while the general functional form of the apparent breakage rate constant of this relationship was derived based on three models with different complexity levels. Model A, the most complex and general model, was derived directly from microhydrodynamics. Model B is a simpler model based on a power-law function of process parameters. Model C is the simplest model, which is the pre-calibrated version of Model B based on data collected from different mills across scales, formulations, and drug products. Being simple and computationally convenient, Model C is expected to reduce the amount of experimentation needed to develop and optimize the wet bead milling process and streamline scale-up and/or scale-out.
Keywords: microhydrodynamic model; milling; modeling; particle size prediction; process optimization; process scale-up; semi-mechanistic modeling; wet bead milling.