# Rational Function-Based Approach for Integrating Tableting Reduced-Order Models with Upstream Unit Operations: Lubricants and Glidants Case Study

## TL;DR

This paper introduces a modeling approach to understand how lubricants and glidants affect tablet quality during pharmaceutical manufacturing.

## Contribution

A rational-function-based framework is developed to systematically quantify the impact of lubricants and glidants on tablet performance.

## Key findings

- The model captures effects of lubricants and glidants on four stages of powder compaction.
- Upstream material attributes and process parameters are linked mechanistically to tablet quality attributes.

## Abstract

Background/Objectives: Glidants and lubricants are commonly used pharmaceutical excipients that enhance powder flowability and reduce inter-particle friction, respectively, but they also negatively impact critical quality attributes such as tablet tensile strength and drug release rate. Quantifying these effects is essential as the pharmaceutical industry transitions from batch to continuous manufacturing. Methods: This study develops a rational-function-based modeling approach to capture the effects of lubricants and glidants on tableting. The framework automatically identifies upstream critical material attributes and process parameters, such as excipient concentration and mixing time, and describes their coupling to first and second orders. Reduced-order models were constructed to evaluate the influence of these variables on the four stages of powder compaction—die filling, compaction, unloading, and ejection—using formulations composed of 10% acetaminophen, microcrystalline cellulose, and varying small concentrations of magnesium stearate or colloidal silica. Tablets were fabricated across a wide range of relative densities by varying dosing position and turret speed. Results: The modeling approach successfully quantified the effects of lubricant and glidant mixing conditions on each compaction stage, providing mechanistic insight into how upstream conditions propagate through the tableting process and influence critical quality attributes. Conclusions: Overall, the rational-function-based framework offers a systematic approach to quantify and predict the impact of lubricants and glidants on tablet performance, thereby enhancing product and process understanding in continuous manufacturing.