Scale-Agnostic Models Based on Dimensionless Quality by Design as Pharmaceutical Development Accelerator

Abstract

This comprehensive review of the synergistic use of Quality by Design (QbD) and the Pi– Buckingham theorem explores an innovative approach to enhancing product development and process optimization within the pharmaceutical industry. QbD is a systematic, proactive methodology that integrates quality considerations throughout the product lifecycle to ensure that pharmaceutical products meet regulatory standards for safety and efficacy from the outset of development. The Pi–Buckingham theorem serves as a foundational principle in dimensional analysis, facilitating the simplification of complex models by transforming physical variables into dimensionless parameters. This synergy enables researchers to better understand and control the factors affecting critical quality attributes (CQAs), thereby improving manufacturing outcomes and minimizing variability. Keywords: Quality by Design; design space; Pi–Buckingham; dimensional analysis; design of experiments; pharmaceutical process development