Analytical Expressions for Steady-State Concentrations of Substrate and Oxidized and Reduced Mediator in an Amperometric Biosensor

A mathematical model of modified enzyme-membrane electrode for steady-state condition is discussed. This model contains a nonlinear term related to enzyme kinetics reaction mechanism. The thickness dependence of an amperometric biosensor is presented both analytically and numerically where the biological layer is immobilized between a solid substrate and permeable electrode. The analytical expressions pertaining to the concentration of species and normalized current are obtained using the Adomian decomposition method (ADM). Simple and approximate polynomial expressions of concentrations of an oxidized mediator, substrate, and reduced mediator are derived for all possible values of parameters (Thiele modulus), (normalized surface concentration of oxidized mediator), and (normalized surface concentration of substrate). A comparison of the analytical approximation and numerical simulation is also presented. A good agreement between theoretical predictions and numerical results is observed.