A comprehensive review of mathematical modeling in probiotic microencapsulation

Abstract

The field of probiotics has garnered significant attention due to their potential health benefits, such as enhancing gut health and immune response. The effective delivery of probiotics through microencapsulation is crucial due to the sensitivity of probiotics to environmental stresses. Mathematical modeling offers profound insights into the growth, survival, inactivation, and release dynamics of microencapsulated probiotics, providing a basis for optimizing formulation and predicting behavior under various conditions. Although some of these subjects are cross-sectionally imported from the field of drug delivery, there are no specific papers that comprehensively discuss the mathematical modeling of probiotic microencapsulation from production to delivery. Thus, this paper aims to review the current landscape of mathematical models utilized in the microencapsulation of probiotics in different timelines, including cell culturing, microencapsulation process, storage, and delivery in the gastrointestinal tracts. Predictive microbial models, empirical reaction models, and drug release models were highlighted in each activity. In addition to the principles and equations, recent studies on the application of kinetic models for probiotics and their microcapsules were summarized and discussed. The review emphasizes the necessity of a mathematical approach for the comprehensive understanding of microencapsulated probiotics, combined with insights into food chemistry, microbiology, and engineering, to innovate and advance the application of probiotics for health improvement.