Model development and calibration of two-dimensional population balance model for twin-screw wet granulation based on particle size distribution and porosity

Population balance models (PBMs) have been widely studied for the simulation of continuous twin-screw wet granulation. Due to the limited data availability and computational efforts, one-dimensional PBM is the most popular application to the pharmaceutical industry. While multi-dimensional PBMs can predict multiple granule quality attributes, model development and calibration has been the big challenges. This paper presents a two-dimensional compartmental PBM which compute granule size and porosity. Granulation experiments were performed for two formulations and two process settings, followed by granule characterizations. In PBM development, consolidation was newly introduced, whereas the aggregation and breakage kernels were based on the previous model. Calibration results proved that the model can simulate granule size and porosity simultaneously for different formulations and process settings. Some cases show porosity increase that needs to be considered in the future. Further experiments and model development can increase the applicability of the two-dimensional PBM for the pharmaceutical industry.

Introduction

Twin-screw wet granulation (TSWG) has been recognized as a key unit operation of oral solid dosage manufacturing. While a direct compression method is preferred in terms of simplicity and energy efficiency, wet granulation needs to be performed if the flowability and compressibility of raw materials are poor. Among various granulation techniques, TSWG became a popular technique as an application for continuous manufacturing, which has merits of lower energy consumption and higher demand flexibility compared to the conventional batch production [1], [2], [3].

To understand the phenomena in TSWG, a large number of researchers from both academia and industry have performed experimental studies. Design of experiment (DoE) is the most popular approach to identify critical process parameters (CPPs), critical material attributes (CMAs), and the impact of screw configurations. Multiple studies have found that liquid-to-solid (L/S) ratio has the highest impact on granule critical quality attributes (CQAs), e.g., size, density, and porosity [4], [5]. L/S ratio was also identified as a key parameter for process response, e.g., torque [6] and start-up operation [7]. Experimental analyses were also performed for assessing the impact of material properties [8] and the screw configurations [9]. Sometimes, data-driven models were further developed to predict granule CQAs of different process settings [10] and formulations [11].

Acquired knowledge through experiments has been further used for mechanistic modeling. Population balance models (PBMs) have been widely used to track particle distributions within the barrel of TSWG. One-dimensional (1D) PBM with particle size is the most popular approach as an application to the pharmaceutical industry. This is because the particle size is a unique indicator whose distributions of inputs and outputs can be easily measured experimentally. Kumar et al. [12] developed a compartmental 1D-PBM to describe spatial heterogeneity. Compartmental 1D-PBMs were also used by other researchers to link PBM parameters with process settings and screw configuration [13], [14]. Van Hauwermeiren et al. [15] developed new kernels for a 1D-PBM, which can compute both mono- and bimodal granule size distributions (GSDs). This model was further updated by Barrera Jiménez et al. [16] to improve the applicability of the model with less number of calibration parameters. Whereas some 1D PBMs were validated through the experiments, difficulties in capturing specific phenomena, e.g., consolidation, were observed due to the lack of information on other attributes than size. In addition, predictions of GSDs are usually insufficient for the process design since other granule attributes also have high impacts on CQAs of the final products, e.g., tablet dissolution.

As a solution to these challenges, multi-dimensional PBMs have been extensively studied in academic research. Multi-dimensional PBMs can track volume distributions of multiple properties, e.g., solid, liquid, and gas, and in consequence predict multiple attributes, e.g., moisture content and porosity. Barrasso et al. [17] proposed a three-dimensional PBM that can compute distributions of granule size, liquid content, and porosity, where phenomena of aggregation, breakage, liquid addition, and consolidation were considered. McGuire et al. [18] developed a four-dimensional PBM, where the internal coordinates were solid, internal liquid, external liquid, and gas. Studies on multi-dimensional PBMs for TSWG can be also seen in kernel development [19], an extension of a solution technique [20], and a hybrid model with an artificial neural network [21].

Whereas the advancement in multi-dimensional PBMs allows researchers to describe complex phenomena mathematically, the biggest challenge exists in model calibration and validation and, hence, building a model with useful predictive power. Models with low predictive power are mere data-fitting exercises and are useless for decision-making or as digital twins. Distributions of other indicators than granule size, e.g., liquid content and porosity, are not easy to be measured in the experiments due to available measurement techniques. Furthermore, it is hardly possible to measure initial distributions of liquid content and porosity, which need to be used as inputs in PBMs, because granules are not generated at the beginning. For those reasons, most of the papers about multi-dimensional PBMs only show a comparison of GSDs between experiments and simulations. Ismail et al. [22] presented the first calibration case of a two-dimensional (2D) PBM by introducing an image processing technique for the measurement of liquid distribution. However, multi-dimensional PBMs have yet to be calibrated for the formulations containing active pharmaceutical ingredients (APIs), suggesting a huge gap between available models and industrial application.

This paper shows a new compartmental 2D-PBM for TSWG focusing on granule size and porosity. The proposed model was developed based on the reliable 1D-PBM that has been calibrated and validated for multiple formulations [16] for the sake of industrial application. From the original 1D-PBM, consolidation was also considered as a main phenomenon to simulate porosity changes. Both the solution technique (cell average technique, CAT) and objective function (energy distance) were extended to be applicable for the 2D-PBM. Calibrations were performed for two different formulations containing hydrophilic and hydrophobic APIs and L/S ratios, where the porosity of five granule size classes was measured at each compartment.

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Ana Alejandra Barrera Jiménez, Kensaku Matsunami, Michael Ghijs, Daan Van Hauwermeiren, Michiel Peeters, Fanny Stauffer, Thomas De Beer, Ingmar Nopens, Model development and calibration of two-dimensional population balance model for twin-screw wet granulation based on particle size distribution and porosity, Powder Technology, Volume 419, 2023, 118334, ISSN 0032-5910, https://doi.org/10.1016/j.powtec.2023.118334.