(545f) Morphological Population Balance Modeling of a Pharmaceutical Compound for Size and Shape Prediction for in-Silico Experimental Design

Crystallization is a particle formation and purification techniques in all chemical industries, having particularly important role in the pharmaceutical industry. After the crystallization step, numerous downstream processes are performed such as filtration, milling or granulation to obtain the desired product that meets the critical quality attributes (CQAs). The size and shape distribution of crystals are important CQAs, which may significantly affect the bioavailability, bulk density and manufacturability of the final drug product.¹ The prediction of the process behavior plays key role in the design of complex, nonlinear processes with tight CQA constraints. A predictive process model can be used for in silico design of experiments (DoE), optimizing design tasks, as well as in model-based control, which inherently decreases the time and effort put into laboratory work as well as reduces the active pharmaceutical ingredient (API) requirements to find the operating strategy required for the manufacturing of the desired product.

In this work, we present the development and validation of a two-dimensional morphological population balance model (2D-PBM) for the batch cooling crystallization of a commercial API (compound A), from Takeda Pharmaceuticals International Co., which forms needle-like crystals. It was observed that compound A shows significant growth rate dependency in the function of actual thermodynamic conditions in both width and length directions, leading to considerable dynamic changes in the aspect ratio distribution of the crystals, which cannot be accurately captured with a single characteristic dimension used in 1D-PBM. Therefore a morphological population balance model that described the dynamic variations of both the length and width distribution of particles was developed using a two-dimensional (2D-PBM) that involves secondary nucleation, growth and dissolution of particles. The model-equations are solved with a graphical processing unit (GPU) accelerated high resolution finite volume method.² The kinetic parameters are estimated based on batch crystallization experiments, by defining and solving a process optimization problem that minimizes the deviations between the measured concentration, as well as distributions of particle length, width and sphere-equivalent mean diameter. The calibrated process model was able to reproduce the crystallization behavior of compound A, both in terms of the dynamics of crystal size and shape distributions as well as the variation of concentration. For the identification of the model parameters, several experiments were performed with temperature cycling to promote the growth of the crystals for kinetic studies by using process analytical technology tools (PAT) for data acquisition and monitoring the system, including ParticleTrack G400 (Mettler-Toledo) for in-line chord length distribution (CLD), for detecting the crystallization events like nucleation and dissolution, as well as for the crystal count measurement, the Zeiss MCS621 ATR-UV/Vis spectrophotometer for concentration measurement, and the ParicleView v19 (Mettler Toledo) for in-situ microscope images. First, a model was developed using size independent growth kinetics, but experimental evidence and parameter estimation studies showed that both length and width exhibit apparent size dependent growth mechanisms. A new semi-empirical size dependent growth formulation was developed, which covers both the exponential growth behavior of the small crystals (< 10 µm) and the slower growing trend of the larger crystals. The new size-dependent growth (SDG) expression was compared to two common size-dependent growth expression from literature, by performing parameter identification and model validation for each of the SDG models.³ Sum of square error results from the validation and training experiments showed that the new SDG rate model proposed provides a better description of the growth behavior for this system and provides a more accurate predictive model for this system without over fitting the parameters. In addition, a novel parameter estimation formulation was proposed that incorporates the measured crystal count term in the objective function by correlating the crystal density to the crystal count from focused bean reflectance measurement (FBRM), as well as including additional mechanistic constraints to restrict growth rates within physical meaningful values during the parameter estimation. It was shown that the novel parameter estimation formulation enhances the convergence of the optimization process and provides kinetic parameters with smaller uncertainty bounds, hence a more reliable predictive model. The developed model with the highly efficient numerical PBM solution approach developed, can be used for in silico design of experiments, crystallization process design and optimization, and implementation of nonlinear model predictive control.⁴

References:

[1] Bag, P. P., Chen, M., Sun, C. C., & Reddy, C. M. (2012). Direct correlation among crystal structure, mechanical behaviour and tabletability in a trimorphic molecular compound. CrystEngComm, 14(11), 3865–3867.

[2] Szilágyi, B., & Nagy, Z. K. (2018). Aspect Ratio Distribution and Chord Length Distribution Driven Modeling of Crystallization of Two-Dimensional Crystals for Real-Time Model-Based Applications. Crystal Growth and Design, 18(9), 5311–5321.

[3] Mydlarz, J., & Jones, A. G. (1993). On the estimation of size-dependent crystal growth rate functions in MSMPR crystallizers. The Chemical Engineering Journal, 53, 125–135.

[4] Szilagyi, B., & Nagy, Z. K. (2019). Real-time feasible model-based crystal size and shape control of crystallization processes. Computer Aided Chemical Engineering (Vol. 46). Elsevier Masson SAS.