Digital Design of the Crystallization of an Active Pharmaceutical Ingredient Using a Population Balance Model with a Novel Size Dependent Growth Rate Expression. From Development of a Digital Twin to In Silico Optimization and Experimental Validation

Abstract

Prediction and control of the product properties in crystallization processes are practical challenges in the pharmaceutical industry. Effective crystallization process design and operation techniques are needed to meet the critical quality attributes (CQAs) and minimize batch-to-batch variation. Mathematical modeling can enhance process understanding and save a considerable amount of time, effort and raw material when used in process development following the guidelines of the Quality-by-Design (QbD) framework. When the mathematical model of the process is fitted and validated with experimental data, it provides a digital twin of the process that enables execution of in silico design of experiments (DoEs), which is particularly beneficial when the number of factors increases or if the material is expensive or sparingly available, e.g., during early stage development. This work presents the benefits of crystallization process modeling by studying an active pharmaceutical ingredient (API) from Takeda Pharmaceuticals International Co., referred hereafter as Compound A. A framework for crystallization model construction, parameter estimation and validation are demonstrated through the case study of Compound A by using the population balance modeling (PBM) approach. Secondary nucleation, size dependent growth (SDG), and size dependent dissolution mechanisms are considered. Size dependency is introduced with a new formulation capturing the considerably slower growth of small crystals (D 90 < 10 μm) while having size dependency for the larger crystal size domain (D 90 > 200 μm) similar to the models from the literature. To make the model parameter estimation more industrially relevant, a novel method developed recently by the authors is applied to use the focused beam reflectance measurement (FBRM) data directly in the parameter estimation without further transformations. The kinetic parameters are estimated by minimizing the difference between measured and simulated concentrations, crystal size distributions (CSDs) and maximizing the correlation between the simulated crystal number density and measured FBRM counts. The paper also illustrates that the novel SDG rate expression can capture the CSD dynamics considerably better than the standard SDG rate models. The digital twin is used for in silico DoE and process optimization, and the simulation results are validated experimentally, demonstrating the benefits of model-based digital design for crystallization process development.

Modeling and Predictive Control of Cooling Crystallization of Potassium Sulfate by Dynamic Image Analysis: Exploring Phenomenological and Machine Learning Approaches

“…Usually, PBM’s numerical solution allows the simulation of the process, , which can be followed by estimating model parameters based on experimental data. Many works in the literature used PBMs to obtain the kinetic model parameters for the phenomena involved in the process, especially examining the kinetics of primary nucleation, secondary nucleation, and particle growth. − A sequential approach to estimate the kinetic model parameters is presented in Pérez-Calvo et al The solute concentration is the most common and necessary measured variable, usually obtained from in situ spectroscopic techniques or from measuring another property such as conductivity or solution density . Offline measurements of the crystal size distribution traditionally characterize the solid phase. ,, …”

Experimental Design for the Efficient Determination of the Crystallization Kinetics of a Polymorphic System in Combined Cooling and Antisolvent Crystallization

“…Szilágyi et al. created a digital design of a slow-growing API cooling crystallization process and used in silico DoE and optimization to minimize the span and maximize the size …”

“…Population balance models (PBMs) have been used to study and control polymorphic transformations. − Typically, seeded isothermal crystallization experiments are performed to estimate the growth and nucleation kinetics of the stable form and the growth and dissolution kinetics of the metastable form that are used in the population balance equation. Simone et al studied model-based active polymorphic control of ortho -aminobenzoic acid (OABA) by determining the kinetic parameters through an experimental design that minimizes correlation between parameters .…”

Direct Crystal Growth Control: Controlling Crystallization Processes by Tracking an Analogue Twin

“…Various methods for concentration measurement during crystallization are summarized by Zhang et al Attenuated total reflection-Fourier transform infrared (ATR-FTIR) spectroscopy is often applied. ,, There are other methods, such as ATR spectroscopy with ultraviolet and visible light (ATR-UV/vis) − impedance spectroscopy, , or refractometry. , However, all of these methods need calibration. This may be challenging, especially for complex mixtures in which potentially unknown impurities affect calibration.…”

“…In summary, determining supersaturation alone is not an easy task. For model-based process design and control schemes, kinetic parameters such as growth rates , and nucleation rates ,− need to be additionally determined.…”