Transient Response of a Continuous Glucose Monitor

Abstract

Blood glucose is indirectly measured with a subcutaneous continuous glucose monitor (CGM). Glucose within the interstitial space is converted into hydrogen peroxide via an enzymatic reaction with glucose oxidase. Electrochemical oxidation of the hydrogen peroxide produces a faradaic current proportional to the hydrogen peroxide concentration. In vitro CGM experiments during transient operation demonstrate a range of time constants in the current response. A transient model adaptation of the steady model from Gao et al. was prepared. [1] The transient responses to potential and glucose steps were investigated experimentally and numerically.The transient current response of an electrochemical system with coupled homogeneous and heterogeneous reactions yields time constants dependent on the charging of the electrode, rates of homogeneous reactions, and mass transfer of the participating species. For nonlinear homogeneous reactions involving species of varying diffusion coefficients, analytic expression of these time constants is nontrivial and more readily obtained numerically.A transient model was discretized in space and time with finite differences and the Crank-Nicolson method. Numerical solutions of the model were obtained with Newman’s BAND algorithm. [2] The model demonstrates the charging current, faradaic current, and concentration profile responses within the sensor. When the model is perturbed with a potential step, the initial response is characterized by a charging current; whereas, larger time constants are due to both the mass transfer to the electrode through diffusion and homogeneous reactions.Steady, transient, and impedance responses of the CGM were experimentally obtained. Steady-state current was measured as a function of glucose concentration which provided an estimate for the permeability of glucose in the sensor. Current response to a glucose step was obtained, and the short-time behavior was fit with a single time constant. An equivalent circuit, fabricated based on the impedance spectra, demonstrated a potential step response similar to the sensor. The influence of dissolved oxygen concentration on the transient response was also investigated.The model was fit to the experimental current responses by adjusting diffusion and partition coefficients, rate and equilibrium constants, and electrolyte resistance and capacitance. The numerical model shows the short time constant is due to charging of the sensor, and the larger time constants are due to diffusion and enzymatic reactions. The large time constants of the current response are significantly larger than those predicted by a simple Gerischer model.[3,4] The presence of both diffusing and non-diffusing species involved in the homogeneous reactions may give rise to current instabilities and time constants.References Gao, M., Harding, M., Kong, R., & Orazem, M. (2018). Mathematical Model for the Electrochemical Impedance Response of a Continuous Glucose Monitor. Electrochimica Acta, 275. 119-132.Newman, J., & Thomas-Alyea, E. (2004). Electrochemical Systems (3rd ed.). NJ: John Wiley & Sons, Hoboken.Gerischer, H. (1951). Wechselstrompolarisation Von Elektroden Mit Einem Potentialbestimenden Schritt Beim Gleichgewichtspotential. Zeitschrift fur Physikalische Chemie, 198. 286-313.Orazem, M., & Tribollet, B. (2017). Electrochemical Impedance Spectroscopy. Hoboken, NJ: John Wiley & Sons. AcknowledgementThe support of Medtronic Diabetes (Northridge, CA), Mike Miller, program monitor, is gratefully acknowledged.