Aspect Ratio Distribution and Chord Length Distribution Driven Modeling of Crystallization of Two-Dimensional Crystals for Real-Time Model-Based Applications

Abstract

Two dimensional crystals, for which the shape is described by two linear sizes are common in fine chemical and pharmaceutical industries. Since the crystal size and shape are directly related to the performance of active pharmaceutical ingredients (API), the simultaneous size and shape 2 distribution control is of paramount importance in pharmaceutical crystallization engineering. To efficiently achieve simultaneous size and shape control often requires model based control strategies, however the increased computational cost of the process simulation and the substantial differences between the simulated and measurable quantities make the implementation of model based control approaches challenging. This paper addresses the important problem of the real-time simulation of the most likely measurable chord length distribution (CLD) and aspect ratio distribution (ARD) as well as the concentration variations during the crystallization of 2D needleshape crystals. This enables the application of focused beam reflectance measurement (FBRM) and particle vision and microscopy (PVM), two routinely applied probes, as quantitative direct feedback control tools. Artificial neural network (ANN) based FBRM and PVM soft-sensors are developed, which enable the direct and fast transformation of 2D crystal size distribution (CSD) to CLD and ARD on arbitrary 2D grids. The training data for the ANN is generated by a first principle, geometrical model based simulation of FBRM and PVM for high aspect ratio crystals. Although, the ANN approach is applicable for any simulated or experimental training datasets. It is also demonstrated that the in-situ imaging based shape measurement underestimates the real aspect ratio (AR) of crystals, for which a simple correction is proposed. From the model-equation solution perspective, the soft-sensors require full PB solution. The 2D high resolution finite volume method (HR-FVM) is applied to simulate the full 2D CSD, which is an accurate, stable, but computationally expensive technique. The real time applicability is achieved through various implementation improvements including grid optimization and data-type optimized hybrid CPU-GPU calculations.

Application of PAT-Based Feedback Control Approaches in Pharmaceutical Crystallization

“…Artificial neural networks (ANN) are also used in the field of crystallization processes [25][26][27][28][29]. The ANN-based PVM and FBRM sensors were developed by Szilagyi et al [30] and can transform the two-dimensional crystal size distribution to chord length distribution and aspect ratio distribution on arbitrary two-dimensional grids. The software soft sensor based on ANN is used to simulate the most likely average value of the bivariate crystal size distribution (2D CSD), and guide the experiment to control the crystal size and shape [31].…”

Cross-Pharma Collaboration for the Development of a Simulation Tool for the Model-Based Digital Design of Pharmaceutical Crystallization Processes (CrySiV)

“…Due to their massively parallel hardware architecture, GPUs have been used for accelerating scientific calculations in the last decade. In CrySiV, CUDA C is employed to accelerate the parallelizable parts of codes, which is compliant with nVidia GPUs, and in certain cases can bring up to 2 orders of magnitude speedup over the serial C implementation. , Further gain can be achieved without accuracy loss by applying nonuniform grids, which is supported by CrySiV.…”

Application of Model-Free and Model-Based Quality-by-Control (QbC) for the Efficient Design of Pharmaceutical Crystallization Processes

“…FBRM has become a standard PAT tool in both industrial and academic crystallization systems. Even though the model-free design and control approach relies on FBRM data, only a few papers have been published with FBRM being involved in PBM-based applications, mainly because of the challenges associated with the CSD to chord length distribution (CLD) transformationsboth forward and backward. , It is broadly accepted that the FBRM count is proportional with the true number density. The correlation can be linear (e.g., dilute suspension of isotropic particles), concave (double counting of high aspect-ratio crystals/large crystals due to sharp edges), and convex (crystals overlapping)see Figure b.…”