Research progress on mathematical modeling in the extraction of active components from traditional Chinese medicine

Mathematical modeling of the extraction of active components from traditional Chinese medicine (TCM) is essential for process optimization and intelligent manufacturing. Therefore, this review sought to systematically compare the four major modeling approaches used in TCM extraction processes: mechanistic, empirical, data-driven, and hybrid modeling. We further aimed to provide practical guidance for model selection. A comprehensive literature review covering mechanistic models based on Fickian diffusion laws, empirical kinetic models, data-driven methods, and hybrid modeling strategies was conducted. The four approaches were compared across multiple dimensions: theoretical foundations, interpretability, data requirements, predictive performance, and application scenarios. This review reveals that the widely adopted first-order empirical model can be rigorously derived from Fickian diffusion theory through two distinct pathways: the external diffusion pathway via Fick’s first law with a steady-state film approximation and the internal diffusion pathway via the first-term approximation of Fick’s second law in spherical coordinates. Although empirical models offer simplicity and rapid fitting, they have limited extrapolation capability. Similarly, mechanistic models offer strong interpretability but limited adaptability, whereas data-driven models provide high predictive accuracy but require substantial amounts of data. In contrast, hybrid models achieve the best balance between interpretability and predictive performance. This review provides a comparative summary of the four modeling approaches and practical guidance for model selection. Hybrid modeling is the most promising approach because it combines mechanistic insights with data-driven adaptability. Future research should investigate next-generation artificial intelligence methods, adaptive self-optimization technologies, standardized hybrid modeling frameworks, and digital twin systems for TCM extraction processes. These approaches have the potential to advance the intelligent manufacturing of TCM products.