A Quantitative Method for Modeling Blend Composition Distributions in the Presence of Agglomerates

Abstract

Purpose This paper communicates a methodology that uses experimental data and a new statistical method that uses a simulation to reconstruct the composition distribution of a powder blend containing drug agglomerates. The reconstructed distribution can be used subsequently to optimize sampling protocols, compute operating characteristic curves, and estimate process capability for blends containing agglomerates. Methods A blend containing a cohesive API and an excipient is prepared in a blender. Although the API is sieved (mesh 100 μm) prior to its addition to the blender, API agglomerates are found in samples after blending. These agglomerates have either survived the mixing operation, or been created by the operation. The population of sample concentrations is used to estimate the parameters of a statistical model that combines multiple distribution functions to describe the binary mixture with the minor component partially agglomerated. The local concentration for the non-agglomerated portion of the minor component throughout the entire blend is estimated using a Gaussian distribution with parameters x (mode) and s (standard deviation) that are typically well established. The function and the parameters that describe the population of agglomerates of the minor component are estimated using (typically sparse) experimental data. The optimization of the parameters describing the agglomerate population is performed using a simulation of the powder bed in an iterative manner. The simulated blend, built using the statistical model, is extensively examined and a distribution of RSD estimates is obtained. The iterative process for seeking the parameters that describe the agglomerate population converges when the mode of the distribution of RSD estimates matches the experimental RSD value, which is the best available estimate of the blend homogeneity. Results This methodology is applied to populations of samples for different binary formulations prepared in different blenders. In all cases, after iterating to adjust the parameters of the model, there is an agreement between the experimental and the simulated population of samples with a confidence of, at least, 95%. Conclusions The methodology described here is an effective tool to create an accurate representation of agglomerated blends based on limited sampling results.