Analytical expressions for the steady-state concentrations of glucose, oxygen and gluconic acid in a composite membrane for closed-loop insulin delivery.

The mathematical model of Abdekhodaie and Wu (J Membr Sci 335:21-31, 2009) of glucose-responsive composite membranes for closed-loop insulin delivery is discussed. The glucose composite membrane contains nanoparticles of an anionic polymer, glucose oxidase and catalase embedded in a hydrophobic polymer. The model involves the system of nonlinear steady-state reaction-diffusion equations. Analytical expressions for the concentration of glucose, oxygen and gluconic acid are derived from these equations using the Adomian decomposition method. A comparison of the analytical approximation and numerical simulation is also presented. An agreement between analytical expressions and numerical results is observed.