Discrete Element Modeling of Solid Dosage Manufacturing Processes
Solid dosage manufacturing primarily involves powder process operations, such as mixing, granulation, and compaction. A model-based approach can be used to develop a better scientific understanding of these processes and implement Quality by Design. These
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Introduction In order to implement Quality by Design (QbD) in solid dosage manufacturing, a model-based approach can be taken, relating process parameters and material properties to the critical quality attributes (CQAs) of the product. These mathematical models establish the process understanding required to facilitate the definition of the design space. Pharmaceutical process modeling often employs process-scale models, such as population balance modeling (PBM) and residence time distribution (RTD) models. These models are typically empirical and have limited ability to predict particle-scale behavior. Experimental calibration and validation are needed to estimate unknown parameters, resulting in models that are only valid within the experimental design space. While DEM also requires calibration, its basis on first-principles and particle-scale phenomena results in predictive capabilities beyond those of PBM or RTD models.
Marianthi G. Ierapetritou and Rohit Ramachandran (eds.), Process Simulation and Data Modeling in Solid Oral Drug Development and Manufacture, Methods in Pharmacology and Toxicology, DOI 10.1007/978-1-4939-2996-2_4, © Springer Science+Business Media New York 2016
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Dana Barrasso and Rohit Ramachandran
In contrast, discrete element modeling (DEM) tracks individual particles or granules as they move through space and collide. DEM is a particle scale model that is mechanistic in nature, able to capture velocity profiles and the effects of equipment geometry, particle size and shape distributions, and material properties. While the framework is computationally intensive, it produces detailed results that can be used to build a multi-scale process model. Due to current computational limitations, DEM is often applied to large particles ( > 1 mm in diameter) or granules but in theory can be used to model particles of any size. Ketterhagen et al. [1] reviewed the applications of DEM in the pharmaceutical industry. However, since then the usage of DEM in process modeling of solid dosage manufacturing has expanded greatly. This chapter will discuss the applications of DEM in pharmaceutical operations, emphasizing recent advances in process modeling, multi-scale modeling, and experimental validation.
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DEM Theory and Background Fundamentally, DEM uses Newton’s laws of motion to solve force balances on granular elements and compute any movement. Each particle is assigned a size and density along with position and velocity vectors. The net external force acting on each particle is calculated to account for any gravitational, electrostatic, fluid, and impact forces, among others when applicable. From Newton’s second law of motion, the acceleration of each particle is calculated, resulting in a set of ordinary differential equations for each parcel. Explicit integration is typically used to determine position and velocity vectors at each point in time, while time is incremented in discrete steps. Despite this simple formulation, detecting contacts and evaluating their forces is not trivial, an
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