Hybrid models to support development of fluid bed granulation processes

The hybrid modeling strategy which is based on the integration of mechanistic and data-driven models is proposed and applied on fluidized bed granulation processes. The tight combination of empirical process knowledge by means of a mechanistic model and the multivariate data from PAT sensors allowed to gain benefits from both components. The hybrid strategy avoids any discrepancies between model and real process, increases transferability and general applicability of the model, as well as allows a smooth integration of Quality-by-Design principles for oral solid dosage forms.

In this contribution, two illustrative application examples for fluidized bed spray agglomeration and fluidized bed layering or coating processes are presented. It was shown that the proposed strategy can be successfully applied to support process development on different scales. It results in better process understanding, creation of regime maps and might end with the generation of a digital twin.

Highlights

• The simultaneous application of mechanistic and data-driven models was used to support process development.
• Aggregation rate factor (ARF) and accumulated process parameter (APP) were introduced as scale-independent parameters.
• Process regime maps for characterization of growth kinetics on different equipment scales were developed.
• The final model architecture was determined by the type of solved problem and the availability of experimental data.

Introduction

The numerous benefits of the fluidized bed spray granulation (FBG) technology for tailored manufacturing of high-quality particulate products, have resulted in its extensive use in various areas. Especially in the pharmaceutical industry FBG is considered as a robust process that is widely used for manufacturing of solid dosage oral forms [1,2]. As a result, over the past decades, intensive research was focused on the analysis and optimization of this process [3]. Starting with the theoretical and experimentally-based investigations of the basics of fluidization behavior and growth phenomena [[4], [5], [6]], the focus was shifted to the application of more advanced modeling techniques in various areas such as the pharmaceutical industry [7]. Here the integration of the Quality-by-Design (QbD) paradigm plays a key role in process development as described in ICH Q8 and other linked ICH-Q guidances.

Consequently, nowadays various simulation approaches and models for the description of fluid bed process on different time and length scales can be found. Some of these models and phenomena described within them can be classified according to the complexity level, as it is schematically shown in Fig. 1. The mass or heat balances in the entire plant, apparatus, or some of its compartments can be efficiently described with ordinary differential equations (ODE) or partial differential equations (PDE) [[8], [9], [10], [11], [12]]. In contrast, more advanced methods are required for the description of particle growth. For example, growth kinetics are often described with one- or multi-dimensional population balance models [[13], [14], [15], [16], [17]]. At the same time, the three-dimensional profile of the fluidized bed can be modeled with methods of computational fluid dynamics (CFD) coupled with the discrete element method (DEM) [[18], [19], [20]]. For the macroscale modeling of entire plants, flowsheet simulations are applied [15,21,22]. To predict microscale product morphology, Monte-Carlo based techniques can be used [23]. It should be noted, that in addition to the methods mentioned above, several other techniques and coupled approaches exist [[24], [25], [26], [27], [28]].

Compared to the relatively simple models which are based on mass balance considerations, the application of more advanced approaches like PBM, DEM-CFD, etc. significantly increases the level of model complexity and computational effort. To compensate this effect, the usage of high-performance computing (HPC) resources and advanced numerical techniques allows to minimize the problem of high computational effort. However, a more important challenge that limits the usage of these models, is the increased number of unknown model parameters needed to describe the kinetics of the investigated processes (s. Fig. 1). In the case of PBM, for example, the a-priori estimation of parameters for aggregation or breakage kernel is an almost unfeasible task. To solve that, the model parameters are usually adjusted based on experimental results obtained for a strictly limited domain of critical process parameters (CPP). Unfortunately, this significantly reduces the predictivity and general applicability of such models. Furthermore, even when applying most detailed mechanistic models, not all relevant effects can be properly considered. This often leads to large discrepancies between a mathematical model and real processes.

To perform predictive modeling of processes and to enhance the parameter space of model applicability, hybrid (also known as gray-box) modeling strategies can be applied [7,[28], [29], [30], [31], [32]]. In hybrid models, some knowledge-driven phenomenological (mechanistic) submodels are coupled with data-driven (black-box) components. Firstly, this allows to implicitly consider various not yet fully parametrized phenomena occurring in the process. Secondly, the inclusion of the mechanistic part extends the applicability and transferability of the final model. One of the main challenges related to the application of such models is the efficient decomposition of a modeled problem. Some parts of the considered process are described by a data-driven submodel and some parts by a mechanistic submodel. Another challenge is to ensure sound connectivity of such submodels. The model decomposition and selection of appropriate components strongly depend on the amount of available data obtained from experimental measurements or microscale simulations [28], as well as on the level of mechanistic knowledge and the resulting predictivity of mechanistic parts.

In this contribution, the above-described hybrid modeling strategy was used to build predictive models for fluidized bed (FB) agglomeration and coating processes used in the manufacturing of oral solid dosage forms. Two different models have been developed, each describing two different tasks during process development; both will be described in this work. The granulation processes addressed in this study were selected to highlight the necessity for a hybrid modeling strategy, as an efficient way to merge process data with a phenomenological description. Furthermore, through selected problems, we demonstrated that the material properties, process conditions, and the availability of experimental data may strongly influence the architecture of the final model. All data was obtained during the process development of NCEs. As a result, the direct applicability of the models in an appropriate and usable parameter space could be demonstrated.

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Materials

For both processes investigated in this study, the top-spray fluidized bed apparatuses from the company Glatt GmbH were used. Experiments were performed in the batch operation mode on three different scales using Glatt GPCG10, GPCG30 and GPCG60.

Maksym Dosta, Ragna Hoffmann, Peter Schneider, Martin Maus, Hybrid models to support development of fluid bed granulation processes, Powder Technology, Volume 444, 2024, 120005, ISSN 0032-5910, https://doi.org/10.1016/j.powtec.2024.120005.

Read also our introduction article on Orally Disintegrating Tablets (ODTs) here: