Systematic evaluation and platform construction of kinetics modeling for herbal extraction in phytomedicine

Kinetic modeling for herbal extraction in phytomedicine is of great importance for understanding the underlying mechanisms and improving process control and extraction efficiency. This study provides a systematic, comprehensive analysis and rigorous derivation of commonly used kinetic models, including ordinary differential equation (ODE) models, partial differential equation (PDE) models, and empirical fitting models. Notably, the intrinsic logical relationships among these models are elucidated, highlighting that many differential equation models exhibit hierarchical or subordinate structures. This study further evaluates the performance of these models using experimental data reported in academic theses. A comprehensive assessment is conducted based on four criteria: the coefficient of determination (R²), Akaike information criterion (AIC), residual normality test (p_n), and mean value test (p_m). Model stability is also examined to ensure the robustness of the evaluation results. The results offer practical guidelines for selecting appropriate kinetic models and highlight the superior performance of the film theory model across most evaluation metrics. Additionally, when applied to ultrasound-assisted extraction data, the film theory model indicates that the rate constant k tends to increase with increasing ultrasonic power, whereas C_∞ and α show no consistent trends. These findings indicate a possible influence of ultrasonic power on mass transfer and extraction efficiency, which deserves further investigation. To facilitate model fitting and comparative analysis, this work develops an integrated modeling platform that enables researchers to easily use and evaluate various kinetic models.