Enhancing quality-by-design through weighted goal programming: a case study on formulation of ultradeformable liposomes.

Abstract

Introduction: Optimization of pharmaceutical formulations requires advanced tools to ensure quality, safety, and efficacy. quality-by-design (QbD), introduced by the FDA, emphasizes understanding and controlling processes early in development. Advanced optimization methods, such as desirability, have surpassed traditional single-objective techniques. Others, such as weighted goal programming (WGP) offers unique advantages by integrating decision-maker preferences, enabling balanced solutions for complex drug delivery systems. This study applies WGP to optimize timolol (TM)-loaded nanoliposomes aligning with QbD principles.

Methods: The optimization process followed six steps: identifying factors and responses, developing a Design of Experiments (DoE) plan, defining ideal and anti-ideal points, setting aspiration levels, assigning relative weights, and applying WGP compared to desirability function. Minimized and balanced deviations from aspiration levels served as criteria for selecting the most robust optimization results. Six responses were analyzed: vesicle size $\left(z_1\right)$, polydispersity index $\left(z_2\right)$, zeta potential $\left(z_3\right)$, deformability index $\left(z_4\right)$, phosphorus content $\left(z_5\right)$, and drug entrapment efficiency $\left(z_6\right)$.

Results: WGP produced a more balanced formulation that simultaneously optimized multiple responses. By incorporating the importance of each response, the WGP approach improved control over size, colloidal stability, and drug entrapment, based on its mathematical formulation. Comparative analysis with the desirability function confirmed that WGP effectively addressed potential tradeoffs without oversimplifying conflicting objectives.

Conclusions: This case-study demonstrates WGP potential as an advanced multi-objective optimization tool for pharmaceutical applications, improving upon traditional methods in complex formulations. Its ability to harmonize multiple critical attributes in line with QbD highlights its value in developing high-quality pharmaceutical products.