Comparative Kinetic Modeling and Mathematical Analysis of Monoterpene Release from Nanocarrier Systems

In recent years, the application of nanotechnology has gained remarkable attention for addressing the formulation challenges of monoterpenes, which are limited by their volatility, low aqueous solubility, and chemical instability. Since release behavior determines their bioavailability and pharmacological efficacy, this study conducted a comparative kinetic analysis of monoterpene release from different nanocarriers to establish a generalized release model. Experimental data were fitted to eight kinetic models (zero-order, first-order, Higuchi, Hixson-Crowell, square root of mass, three-second-root of mass, Weibull, and Korsmeyer-Peppas), and the best-fitting models were selected based on correlation coefficient (R²), error percentage, and normalized error values. To overcome the limitations of single-metric model selection, a Unified Release Fit Index (URFI) was introduced, integrating correlation strength and multiple error-based criteria into a single composite score, thereby enabling robust and consistent comparison across heterogeneous release datasets. Overall, this study establishes a unified statistical framework for analyzing the release kinetics of monoterpenes from nanocarriers. The Weibull model demonstrated the highest predictive performance across the analyzed datasets, exhibiting superior fitting quality for lipid-based and polymeric nanocarriers. The Korsmeyer-Peppas and Higuchi models ranked second, particularly effective in describing diffusion-controlled release in systems with hydrophilic matrices such as chitosan and dextrin. These findings highlight the robustness and versatility of the Weibull model as a universal descriptor for heterogeneous release kinetics of monoterpenes, while the Korsmeyer-Peppas model remains valuable for mechanistic interpretation of diffusion-dominated systems.