Mathematical Models for the Impedance Response of Subcutaneous Glucose Sensors

Abstract

Since 1974, the artificial pancreas has been acknowledged by the greater scientific community to be a possible way to manage type 1 diabetes [1]. In 2008, a case study showed that a subcutaneous continuous glucose monitor sensor could be implanted for 28 days in a patient with type 1 diabetes [2]. However, commercially available subcutaneous continuous glucose monitors are generally changed every seven days to avoid unreliable results. The object of this work is to explore the potential of impedance spectroscopy to monitor the state of health of subcutaneous continuous glucose monitor sensors. A mathematical model has been developed for the impedance response of a glucose oxidase enzyme-based electrochemical biosensor. The model accounts for a glucose limiting membrane GLM, which controls the amount of glucose participating in the enzymatic reaction. The glucose oxidase was assumed to be immobilized within a thin film adjacent to the electrode. In the glucose oxidase layer, a process of enzymatic catalysis transforms the glucose into peroxide, which can be detected electrochemically. This system may be considered to be a special case of the coupled homogeneous and heterogeneous reactions addressed by Levich [3]. The model development required two steps. The nonlinear coupled differential equations governing this system were solved under the assumption of a steady state. The steady-state concentrations resulting from the steady-state simulation were used in the solution of the linearized set of differential equations describing the sinusoidal steady state. The enzymatic catalysis was treated in terms of two homogeneous reactions, one consuming the glucose oxidase and forming gluconic acid, and the other regenerating the glucose oxidase and forming the peroxide. References A. M. Albisser, B. S. Leibel, T. G. Ewart, Z. Davidovac, C. K. Botz, and W. Zingg, Diabetes 23 (1974), 389–396. J. J. Chamberlain and D. Small, Clin. Diabetes, 26 (2008), 138–139. V. G. Levich, Physicochemical Hydrodynamics, Prentice Hall, Englewood Cliffs, NJ, (1962), p. 345-357.