Mathematical Model for Estimating the Diffusion Coefficients of Protein Release from Bacterial Cellulose-based Hydrogel

To evaluate the oral protein delivery potential of pH-responsive bacterial cellulose-based hydrogels, a model protein drug was efficiently loaded into the hydrogels and the release profile was investigated in a simulated gastric fluid (SGF) and a simulated intestinal fluid (SIF). In this study, we will propose a mathematical approach to evaluating the performance of the hydrogels in the simulated gastrointestinal fluids. We start by using the power law to determine the type of the release in each fluid. Then, the swelling behaviour of the hydrogel will be studied and the least squares method will be developed to find a suitable mathematical function to represent the growth. Mathematical models for the release will be developed and solved to be used to find the concentration of the protein at a given time. The mathematical procedures for diffusion coefficient determination in SIF and SGF will be concluded in an algorithm at the end of this paper.