(224d) Modeling Crystallization Systems: Population Balance Approaches for Structurally Similar Impurities with Kinetically Controlled Impurity Incorporation Mechanisms

Crystallization plays a key role in the manufacturing of a variety of products, especially in small-molecule pharmaceuticals.¹ The crystalline product’s critical quality attributes determine the product’s performance in bioavailability, stability, and downstream processing. The critical quality attributes may include crystal size and shape distributions, polymorphic form, and chemical purity.² Through a variety of pathways during upstream processes, impurities can be introduced to the system that can impact desired critical quality attributes. For example, crystal habit could be altered to produce needles that make filtration cumbersome and alter bioavailability. Furthermore, the presence of the impurities in the final drug product could have safety and efficacy implications.³ Without proper impurity incorporation identification and control, a reduction in the crystal quality, yield and therapeutic efficacy can occur.^2,4 These changes to crystal quality occur through thermodynamic and kinetic modification of the crystallization process.³ Impurity incorporation mechanisms can be identified or narrowed down through a combination of experimental and modeling techniques. Some of the possible mechanisms identified include agglomeration, liquid inclusions, adsorption of mother liquor on crystal surfaces, co-crystal formation, and solid solutions.⁵ The inclusion mechanisms influenced by kinetics like agglomeration, surface deposition, and surface absorption are challenging to model and are common pharmaceutical impurities; thus, kinetic incorporation is the focus of this study. The simulation of kinetic effects of impurities through mathematical models can allow for a dynamic understanding of the role impurities play in the evolution of the final crystalline product.^6,7

To address the gap in kinetic impurity models, our study investigates the impact of two structurally similar impurities, acetanilide and 4-acetamidobenzoic acid, on the paracetamol cooling crystallization behavior in ethanol. Experimental findings reveal that acetanilide primarily affects paracetamol crystal purity through surface adsorption. In contrast, 4-acetamidobenzoic acid has notable integration into the crystal lattice. From the comprehensive experimental study performed, a population balance model (PBM) was solved to describe the effect of varying levels of each impurity on the critical quality attributes, e.g., size and shape distribution. A one and two-dimensional PBM were fitted using high-resolution finite volume method to assess model capabilities at varying levels of detail. The parameters estimations were completed with experimental data from crystal size distribution, concentration of paracetamol in the mother liquor, and particle counts. To more accurately address the complex crystallization of kinetically controlled impurity inclusion mechanisms, a novel growth and nucleation inhibition modifying term was developed, based on mechanistic adsorption theories. Parameter estimation was performed simultaneously considering the novel growth and nucleation inhibition modifiers on primary and secondary nucleation and temperature dependent growth. Model parameter sensitivity was also performed to evaluate the estimability of the overall model. After sufficient model development, a design space was established that allowed for quantification of impurity concentrations, which do not affect crystal quality and identified the threshold at which further increases in impurity concentrations could no longer inhibit crystallization. The proposed model structure allowed for enhanced prediction capabilities, allowing for more robust control of overall product quality. This novel formulation of the PBM will be tested on a different commercial drug product/impurity system to validate the adaptability of the novel impurity growth and nucleation inhibition modifiers to describe kinetically controlled mechanisms.

References

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