(318d) Mathematical Modeling Of The Impact Of Raw Material Variabilities On Granule Particle Size Distribution During Fluidized Bed Granulation | AIChE

# (318d) Mathematical Modeling Of The Impact Of Raw Material Variabilities On Granule Particle Size Distribution During Fluidized Bed Granulation

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Merck &Co.
Merck & Co, Inc.

The desired state for pharmaceutical manufacturing is envisioned as a maximally efficient, agile, flexible sector that produces high-quality drug products without extensive regulatory oversight [1]. The initiative, called Quality by Design (QbD), is regarded as a framework along with Quality Risk Management and Quality Systems initiatives to attain that state. As described in [1,2], determination of a design space for raw material attributes and process parameters is at the crux of Quality by Design framework, which can be accomplished by using a combination of tools: first-principles (theory and modeling) approach, statistically designed experiments (DOEs), and scale-up correlations. In practice, a heavy reliance on DOEs in pharmaceutical solid-dosage form development and manufacturing is apparent historically (see e.g. [3,4]), while first-principles approach has attracted much less attention although it could be much more effective if successfully developed.

An important aspect of QbD framework is to develop a full understanding of how material attributes and process parameters affect critical product attributes, which in turn determine product performance. In this paper, we attempt to explore and demonstrate the use of mechanism-based mathematical modeling (first principles approach) in developing a fundamental understanding of the effects of raw material variabilities on granule quality. Specifically, fluid bed granulation of two active pharmaceutical ingredients (APIs) is considered. Granule size distribution is one of the most important attributes of the granulation that impacts tablet quality attributes. The granule size distribution is a function of both raw material attributes and process parameters. Here, we focus on the effects of the former.

Temporal growth profile of the granule size distribution under a given set of fluidized bed conditions was fit successfully using a population balance model. The model has a remarkably simple mathematical structure: one fitting parameter (agglomeration rate constant) in a size-dependent agglomeration kernel. Then, either the initial particle size of one of the major API or the process parameters were varied, and the impact on the granulation size was simulated using the same fitting parameter. Although the model has not been advanced to the level for quantitative validation, the simulations agree with experimental observation that the higher the mean size of the API is, the larger the resultant granule mean size will be. More importantly, the simulations suggest that the impact of variability in API particle size is less than that of variation of the process parameters in pilot batches, where the API size was not varied. With further refinement, the model could be validated via a minimal number of experiments, and is expected to be capable of defining the boundaries of a design space for API particle size. As the model is based on first principles, it is possible to extrapolate the validated model outside the experimentally studied domain. It is our hope that this paper will stimulate more interest in the use of theory/modeling within the QbD framework for developing and manufacturing pharmaceutical solid dosage forms.

References 1. M. Nasr, Quality by Design (QbD)? A Modern System Approach to Pharmaceutical Development and Manufacturing ? FDA Perspective, FDA Quality Initiatives Workshop, North Bethesda, MD, Feb. 2007. 2. M. Nasr, FDA's Pharmaceutical Quality Initiatives, IFPAC-2007, Baltimore, MD, Jan. 2007. 3. M. Yelvigi, Design Space and Control Space Application Strategy, IFPAC-2007, Baltimore, MD, Jan. 2007. 4. P. Dickinson, Science and Risk-Based Product Development: An Example from the FDA Pilot Program, IFPAC-2007, Baltimore, MD, Jan. 2007.