Mathematical model for the electrochemical impedance response of a continuous glucose monitor

A mathematical model is developed for the impedance response of immobilized glucose oxidase electrochemical biosensors. The coupling between the homogeneous reactions and heterogeneous reactions considered in the model included anomerization between α-d-glucose and β-d-glucose and four reversible enzymatic catalytic reactions transforming β-d-glucose and oxygen into gluconic acid and hydrogen peroxide. The electroactive hydrogen peroxide was considered to be reversibly oxidized or reduced at the electrode. The electrochemical system was modeled mathematically as a one-dimensional boundary-value problem and solved by use of Newman's BAND algorithm. The corresponding impedance was calculated for each specified frequency. The resulted limiting current, reaction profiles, and impedance response provide insights into the influence of system parameters such as interstitial glucose concentration and enzymatic rate constants. This model has a potential application in predicting sensor design and diagnosing sensor failure mechanisms.