Mathematical Modelling and Analytical Expressions for Steady-state Concentrations of Non-linear Glucose-responsive Composite Membranes for Closed-loop Insulin Delivery: Akbari-Ganji and Differential Transform Methods

The dynamic mechanism comprising an enzymatic reaction and the diffusion of reactants and products inside a glucose-sensitive composite membrane is described using a mathematical model created by Abdekhodaie and Wu. A set of non-linear steady-state reaction-diffusion equations is presented in this theoretical model. These equations have been meticulously and accurately solved analytically, considering the concentrations of glucose, oxygen, and gluconic acid, using a novel approach of Akbari Ganji and differential transform methods. The high level of agreement between these analytical results and the numerical results for steady-state conditions is a testament to the model's precision. A numerical simulation was produced via the precise and widely used MATLAB software. A comprehensive graphic representation of the model's various kinetic parameters' effects has also been provided. Additionally, a theoretical analysis of the kinetic parameters, such as the maximal reaction velocity (V<sub>max</sub>) and the Michaelis-Menten constants (Kg and Kox) for oxygen and glucose, pH profiles with membranes is presented. This expressed model is incredibly helpful when creating glucose-responsive composite membranes for closed-loop insulin delivery.