Statistical methodology for scale-up of an anti-solvent crystallization process in the pharmaceutical industry

The scale-up of crystallization processes is a challenging step in production of active pharmaceutical ingredients (APIs). When moving from lab to industrial scale, the mixing conditions tend to modify due to the different geometry and agitation performance, which is particularly important in anti-solvent crystallizations where the size of the crystals depends on the mixing and incorporation of the anti-solvent in the solution. In this work, the results obtained in anti-solvent lab-scale crystallization experiments were used to develop multivariate statistical models predicting Particle Size Distribution (PSD) parameters (Dv10, Dv50 and Dv90) in function of predictors such as percentage of volume, power per volume and tip speed. Firstly, the collinearity among the predictors was assessed by Variance Inflation Factor (VIF) diagnosis. Subsequently, least squares method was employed to find correlations among the predictors and output variables. The optimization of the models was executed by testing quadratic, logarithmic and square root terms of the predictors and removing the least statistically significant regression coefficient. The quality of the fitting was evaluated in terms of adjusted R² (R²_adj). The modelled Dv10, Dv50 and Dv90 values presented a good fitting to the experimental data, with R²_adj higher than 0.79, either when using power per volume or tip speed along the percentage of volume as predictors. Afterwards, the particle size distribution parameters of industrial scale production were predicted using the previously developed models. The deviations between predicted and experimental values were lower than 17%. This demonstrates that multivariate statistical models developed in lab-scale conditions can be successfully used to predict particle size distribution in industrial-size vessels.