Simple Methods to Predict Particle Size for Growth-Only Systems Undergoing One or More Temperature Cycles

Three simple methods are presented for predicting particle size distribution (PSD) percentiles when subjecting a pharmaceutical crystallization wet-milled slurry to a single temperature cycle for two of Biogen’s drug substances. The methods are (I) a mathematical manipulation of the wet-milled PSD based on particle death during dissolution; (II) a linear empirical model fit of product PSD percentiles as a function of the wet-milled PSD percentiles and the amount of material dissolved; and (III) a nonlinear model fit to the change in PSD as a function of the amount of material dissolved and the particle surface area/volume ratio. The three methods were verified on production scale batches. Method II’s approach was also used for particle size control during manufacture by implementing a temperature solved from the model using the batch’s wet-milled particle size percentiles and a final target size. Method III was found to be the most accurate at prediction because it models particle surface area to volume ratio influencing crystal dissolution and growth rates. Method II was found to be not as accurate as method III; however, it was easily implementable during process control at the production scale. Method I provided the quickest estimate of final particle size using only the initial PSD and a solubility expression. Method III was recommended for best particle size prediction.