Rational Function Framework to Integrate Tableting Reduced Order Models With Upstream Unit Operations

We present a systematic approach for integrating reduced-order models of tableting with upstream pharmaceutical unit operations. This method identifies critical material attributes (CMAs) and process parameters (CPPs) from upstream operations, describing their coupling to both first and second orders, while selecting the appropriate mathematical forms and estimating parameters. The coupling is modeled using normalized bivariate rational functions.

The approach is demonstrated for dry granulation, a process that enhances powder flowability but compromises tabletability by reducing particle porosity and increasing plastic work. Using a formulation of 10\% w/w acetaminophen and 90\% w/w microcrystalline cellulose, granules with varying densities and size distributions are produced, and tablets of different relative densities are fabricated. This work provides essential insights for end-to-end process integration, control, and optimization of dry granulation and tableting. It also identifies granule properties that predominantly influence the four stages of powder compaction: die filling, compaction, unloading, and ejection.

Furthermore, we examine the effects of excipients such as lubricants (magnesium stearate) and glidants (silica) on tablet critical quality attributes (CQAs) in continuous manufacturing. Lubricants were found to affect all compaction stages, with sensitivity to mixing time, while glidants influenced bulk density and tensile strength without significantly impacting tablet density or compaction force. Reduced-order models are developed to predict tablet weight, density, and tensile strength based on excipient concentration and mixing time. These models are integral to implementing real-time control under the quality-by-control paradigm.