A Mathematical Kinetic Model and Network Analysis for Multicomponent Dissolution Relationships during the Extraction of Natural Products

Abstract

Traditional Chinese Medicine (TCM) has a long history and typical ethnic traits. Astragalus and Angelica are used in a natural product called a buyang huanwu decoctionand are considered to function as both food and medicine; such products are called a “homology of medicine and food”. In this study, we examined the complex extraction kinetics that occur during the preparation of the natural product BYHWD. Mathematical tools, including the Laplace transformation and Fick’s law, were used to set up kinetic equations for different components in a model of the decoction. We selected the five most important bioactive ingredients of the BYHWD to find the most important speed control component. The intensity and capacity process parameters of the model were determined. A kinetic model was used to quantitatively analyze the dissolution restriction mechanism among the major components. Further, a component–effect network relationship was established to study the interactions of different components during extraction, considering the integrative effect of TCM compositions. Finally, using network pharmacology, certain network parameters were determined through topological analysis. The results indicate that Astragaloside IV exerts the strongest control over the dissolution rates of other components. The BYHWD has a short average path and a high clustering coefficient. The theoretical and experimental results can be used to quantitatively simulate and optimize TCM extraction processes.