A multi-dimensional population balance model approach to continuous powder mixing processes

Leveraging Numerical Simulation Technology to Advance Drug Preparation: A Comprehensive Review of Application Scenarios and Cases

BACKGROUND/OBJECTIVES

Numerical simulation plays an important role in pharmaceutical preparation recently. Mechanistic models, as a type of numerical model, are widely used in the study of pharmaceutical preparations. Mechanistic models are based on a priori knowledge, i.e., laws of physics, chemistry, and biology. However, due to interdisciplinary reasons, pharmacy researchers have greater difficulties in using computer models.

METHODS

In this paper, we highlight the application scenarios and examples of mechanistic modelling in pharmacy research and provide a reference for drug researchers to get started.

RESULTS

By establishing a suitable model and inputting preparation parameters, researchers can analyze the drug preparation process. Therefore, mechanistic models are effective tools to optimize the preparation parameters and predict potential quality problems of the product. With product quality parameters as the ultimate goal, the experiment design is optimized by mechanistic models. This process emphasizes the concept of quality by design.

CONCLUSIONS

The use of numerical simulation saves experimental cost and time, and speeds up the experimental process. In pharmacy experiments, part of the physical information and the change processes are difficult to obtain, such as the mechanical phenomena during tablet compression and the airflow details in the nasal cavity. Therefore, it is necessary to predict the information and guide the formulation with the help of mechanistic models.

Process-Induced Crystal Surface Anisotropy and the Impact on the Powder Properties of Odanacatib

Crystalline active pharmaceutical ingredients with comparable size and surface area can demonstrate surface anisotropy induced during crystallization or downstream unit operations such as milling. To the extent that varying surface properties impacts bulk powder properties, the final drug product performance such as stability, dissolution rates, flowability, and dispersibility can be predicted by understanding surface properties such as surface chemistry, energetics, and wettability. Here, we investigate the surface properties of different batches of Odanacatib prepared through either jet milling or fast precipitation from various solvent systems, all of which meet the particle size specification established to ensure equivalent biopharmaceutical performance. This work highlights the use of orthogonal surface techniques such as Inverse Gas Chromatography (IGC), Brunauer-Emmett-Teller (BET) surface area, contact angle, and X-ray Photoelectron Spectroscopy (XPS) to demonstrate the effect of processing history on particle surface properties to explain differences in bulk powder properties.

Emerging Process Modeling Capabilities for Dry Powder Operations for Inhaled Formulations

Dry powder inhaler (DPI) products are commonly formulated as a mixture of micronized drug particles and large carrier particles, with or without additional fine particle excipients, followed by final powder filling into dose containment systems such as capsules, blisters, or reservoirs. DPI product manufacturing consists of a series of unit operations, including particle size reduction, blending, and filling. This review provides an overview of the relevant critical process parameters used for jet milling, high-shear blending, and dosator/drum capsule filling operations across commonly utilized instruments. Further, this review describes the recent achievements regarding the application of empirical and mechanistic models, especially discrete element method (DEM) simulation, in DPI process development. Although to date only limited modeling/simulation work has been accomplished, in the authors' perspective, process design and development are destined to be more modeling/simulation driven with the emphasis on evaluating the impact of material attributes/process parameters on process performance. The advancement of computational power is expected to enable modeling/simulation approaches to tackle more complex problems with better accuracy when dealing with real-world DPI process operations.

CFD-assisted modeling of the hydrodynamic cavitation reactors for wastewater treatment - A review

Hydrodynamic cavitation has been a promising method and technology in wastewater treatment, while the principles based on the design of cavitational reactors to optimize cavitation yield and performance remains lacking. Computational fluid dynamics (CFD), a supplementation of experimental optimization, has become an essential tool for this issue, owing to the merits of low investment and operating costs. Nevertheless, researchers with a non-engineering background or few CFD fundamentals used straightforward numerical strategies to treat cavitating flows, and this might result in many misinterpretations and consequently poor computations. This review paper presents the rationale behind hydrodynamic cavitation and application of cavitation modeling specific to the reactors in wastewater treatment. In particular, the mathematical models of multiphase flow simulation, including turbulence closures and cavitation models, are comprehensively described, whilst the advantages and shortcomings of each model are also identified and discussed. Examples and methods of the coupling of CFD technology, with experimental observations to investigate into the hydrodynamic behavior of cavitating devices that feature linear and swirling flows, are also critically summarized. Modeling issues, which remain unaddressed, i.e., the implementation strategies of numerical models, and the definition of cavitation numbers are identified and discussed. Finally, the advantages of CFD modeling are discussed and the future of CFD applications in this research area is also outlined. It is expected that the present paper would provide decision-making support for CFD beginners to efficiently perform CFD modeling and promote the advancement of cavitation simulation of reactors in the field of wastewater treatment.

An efficient multiscale bi-directional PBM-DEM coupling framework to simulate one-dimensional aggregation mechanisms

The mesoscale population balance modelling (PBM) technique is widely used in predicting aggregation processes. The accuracy and efficiency of PBM depend on the formulation of its kernels. A model of the volume- and time-dependent one-dimensional aggregation kernel is developed for predicting the temporal evolution of the considered particulate system. To make the developed model physically relevant, the PBM model needs three unknown parameters as input: volume-dependency in collisions, collision frequency per particle and aggregation probability. For this, the microscale discrete element model (DEM) is used. The system’s collision frequency is extracted periodically using a novel collision detection algorithm that detects and ignores duplicate collisions.

Finally, a multiscale bi-directional PBM–DEM coupling framework is presented to simulate the aggregation mechanism. PBM and DEM simulations take place periodically to update the particle size distribution (PSD) and extract the collision-frequency, respectively. The coupling framework successfully explains the dependence between the PSD and the collision frequency. Additionally, computational cost of the algorithm is optimized while maintaining the accuracy of the results. Lastly, the accuracy and efficiency of the developed framework are verified using two different test cases. In one of the examples, a simple aggregation is simulated directly inside the DEM for the first time.

Hybrid multi-zonal compartment modeling for continuous powder blending processes

To modernize drug manufacturing, the pharmaceutical industry has been moving towards implementing emerging technologies to enhance manufacturing robustness and process reliability for production of regulation compliant drug products. Although different science and risk based technologies, like Quality-by-Design, have been used to illustrate their potential, there still exist some underlying obstacles. Specifically, for the production of oral solid drug products, an in-depth process understanding, and predictive modeling of powder mixing in continuous powder blenders is one such major obstacle and originates from the current limitations of the experimental and modeling approaches. Though first principle based discrete element modeling (DEM) approach can address the above issues, it can get very computationally intensive which limits its applications for predictive modeling. In the proposed work, we aim to address this limitation using a multi-zonal compartment modeling approach, which is constructed from DEM. The approach provides a computationally efficient and mechanistically informed hybrid model. The application of the proposed approach is first demonstrated for a periodic section of the blender, followed by its extension for the entire continuous powder blender and the obtained model predictions are validated. The proposed approach provides an overall assessment of powder mixing along axial and radial directions, which is an important requirement for the quantification of blend uniformity. Given the low computational cost, the developed model can further be integrated within the predictive flowsheet model of the manufacturing line.

A Semi-Mechanistic Prediction of Residence Time Metrics in Twin Screw Granulation

This work is concerned with the semi-mechanistic prediction of residence time metrics using historical data from mono-component twin screw wet granulation processes. From the data, several key parameters such as powder throughput rate, shafts rotation speed, liquid binder feed ratio, number of kneading elements in the shafts and the stagger angle between the kneading elements were identified and physical factors were developed to translate those varying parameters into expressions affecting the key intermediate phenomena in the equipment, holdup, flow and mixing. The developed relations were then tested across datasets to evaluate the performance of the model, applying a k-fold optimization technique. The semi-mechanistic predictions were evaluated both qualitatively through the main effects plots and quantitatively through the parity plots and correlations between the tuning constants across datasets. The root mean square error (RMSE) was used as a metric to compare the degree of goodness of fit for different datasets using the developed semi-mechanistic relations. In summary this paper presents a new approach at estimating both the residence time metrics in twin screw wet granulation, mean residence time (MRT) and variance through semi-mechanistic relations, the validity of which have been tested for different datasets.

Characterization of Simultaneous Evolution of Size and Composition Distributions Using Generalized Aggregation Population Balance Equation

The application of multi-dimensional population balance equations (PBEs) for the simulation of granulation processes is recommended due to the multi-component system. Irrespective of the application area, numerical scheme selection for solving multi-dimensional PBEs is driven by the accuracy in (size) number density prediction alone. However, mixing the components, i.e., the particles (excipients and API) and the binding liquid, plays a crucial role in predicting the granule compositional distribution during the pharmaceutical granulation. A numerical scheme should, therefore, be able to predict this accurately. Here, we compare the cell average technique (CAT) and finite volume scheme (FVS) in terms of their accuracy and applicability in predicting the mixing state. To quantify the degree of mixing in the system, the sum-square χ2 parameter is studied to observe the deviation in the amount binder from its average. It has been illustrated that the accurate prediction of integral moments computed by the FVS leads to an inaccurate prediction of the χ2 parameter for a bicomponent population balance equation. Moreover, the cell average technique (CAT) predicts the moments with moderate accuracy; however, it computes the mixing of components χ2 parameter with higher precision than the finite volume scheme. The numerical testing is performed for some benchmarking kernels corresponding to which the analytical solutions are available in the literature. It will be also shown that both numerical methods equally well predict the average size of the particles formed in the system; however, the finite volume scheme takes less time to compute these results.

A machine learning framework for computationally expensive transient models

Transient simulations of dynamic systems, using physics-based scientific computing tools, are practically limited by availability of computational resources and power. While the promise of machine learning has been explored in a variety of scientific disciplines, its application in creation of a framework for computationally expensive transient models has not been fully explored. Here, we present an ensemble approach where one such computationally expensive tool, discrete element method, is combined with time-series forecasting via auto regressive integrated moving average and machine learning methods to simulate a complex pharmaceutical problem: development of an agitation protocol in an agitated filter dryer to ensure uniform solid bed mixing. This ensemble approach leads to a significant reduction in the computational burden, while retaining model accuracy and performance, practically rendering simulations possible. The developed machine-learning model shows good predictability and agreement with the literature, demonstrating its tremendous potential in scientific computing.

Robust state estimation of feeding-blending systems in continuous pharmaceutical manufacturing

State estimation is a fundamental part of monitoring, control, and real-time optimization in continuous pharmaceutical manufacturing. For nonlinear dynamic systems with hard constraints, moving horizon estimation (MHE) can estimate the current state by solving a well-defined optimization problem where process complexities are explicitly considered as constraints. Traditional MHE techniques assume random measurement noise governed by some normal distributions. However, state estimates can be unreliable if noise is not normally distributed or measurements are contaminated with gross or systematic errors. To improve the accuracy and robustness of state estimation, we incorporate robust estimators within the standard MHE skeleton, leading to an extended MHE framework. The proposed MHE approach is implemented on two pharmaceutical continuous feeding-blending system (FBS) configurations which include loss-in-weight (LIW) feeders and continuous blenders. Numerical results show that our MHE approach is robust to gross errors and can provide reliable state estimates when measurements are contaminated with outliers and drifts. Moreover, the efficient solution of the MHE realized in this work, suggests feasible application of on-line state estimation on more complex continuous pharmaceutical processes.

The Future of Pharmaceutical Manufacturing Sciences

The entire pharmaceutical sector is in an urgent need of both innovative technological solutions and fundamental scientific work, enabling the production of highly engineered drug products. Commercial-scale manufacturing of complex drug delivery systems (DDSs) using the existing technologies is challenging. This review covers important elements of manufacturing sciences, beginning with risk management strategies and design of experiments (DoE) techniques. Experimental techniques should, where possible, be supported by computational approaches. With that regard, state-of-art mechanistic process modeling techniques are described in detail. Implementation of materials science tools paves the way to molecular-based processing of future DDSs. A snapshot of some of the existing tools is presented. Additionally, general engineering principles are discussed covering process measurement and process control solutions. Last part of the review addresses future manufacturing solutions, covering continuous processing and, specifically, hot-melt processing and printing-based technologies. Finally, challenges related to implementing these technologies as a part of future health care systems are discussed.

Dynamic cross-flow filtration: enhanced continuous small-scale solid-liquid separation

In a previous study, a small-scale dynamic filtration device (SFD) was analyzed and the basic mechanisms governing the filtration process were characterized. The present work aims at improving the device's performance in terms of actual production. Various operation modes were tested in order to increase permeate flow and concentration factors (CF), while maintaining a fully continuous production mode. Both, a vacuum-enhanced and a pulsating operation mode, proved to be superior to the currently implemented open-operation mode. For example, for lactose, an increase of the CF could be achieved from 1.7 in open mode to 7.6 in pulsating operation mode. The investigated operation strategy enables process control systems to rapidly react to fluctuating feeds that may occur due to changes in upstream manufacturing steps. As a result, not only filtration performance in terms of permeate rate but also process flexibility can be significantly increased. Overall, vacuum-enhanced operation was shown to be most promising for integration into an industrial environment. The option to elevate achievable concentration factors, ease of flow monitoring as well as the ability to react to changes in the feed conditions allow for effective and efficient continuous small-scale filtration.

Quantifying Dry Milling in Pharmaceutical Processing: A Review on Experimental and Modeling Approaches

Particle size reduction by mechanical means is an important unit operation in the pharmaceutical industry, used to improve flow, solubility, and in amorphization of drugs. It is usually achieved by the fracturing of particles under the action of applied energy. Despite being pervasive in the pharmaceutical field, it is one of the least understood processes owing to the complexity of material and process variables involved during milling. To comprehend the process, efforts should be focused on techniques that measure the particle size as well as the control the process. With the ongoing initiative of US FDA to encourage design in quality, the review is focused on some process analytical tools to characterize particle size distribution as well as process modeling tools to simulate particle size reduction. Additionally, an overview of some fundamental aspects related to milling is provided. To this end, the review is limited, mainly concentrating on some of experimental and modeling approaches used to quantify and understand the physics behind the process of dry milling.

Mathematical Development and Comparison of a Hybrid PBM-DEM Description of a Continuous Powder Mixing Process

This paper describes the development of a multidimensional population balance model (PBM) which can account for the dynamics of a continuous powder mixing/blending process. The PBM can incorporate the important design and process conditions and determine their effects on the various critical quality attributes (CQAs) accordingly. The important parameters considered in this study are blender dimensions and presence of noise in the inlet streams. The blender dynamics have been captured in terms of composition of the ingredients, (relative standard deviation) RSD, and (residence time distribution) RTD. PBM interacts with discrete element modeling (DEM) via one-way coupling which forms a basic framework for hybrid modeling. The results thus obtained have been compared against a full DEM simulation which is a more fundamental particle-level model that elucidates the dynamics of the mixing process. Results show good qualitative agreement which lends credence to the use of coupled PBM as an effective tool in control and optimization of mixing process due to its relatively fewer computational requirements compared to DEM.