The development of advanced mathematical models for continuous glucose sensors

Abstract

A series of mathematical models was developed to describe both the steady-state behavior and the electrochemical impedance response of continuous glucose sensors. The models may be considered advanced in following respects: 1) the models use ping-pong kinetics and the law of mass action to account for enzyme kinetics; 2) the chemistry considered includes enzymatic reactions, glucose anomerization, pH-dependent enzyme activity, and dissociation reactions for water, acids, and buffering systems, including phosphate buffered saline and bicarbonate buffers; 3) the physical properties of the sensor and the transport process are also considered, including the effective diffusion coefficients of the species within different films and associated partition coefficients; 4) diffusion into or from the surrounding tissue is considered explicitly; and 5) the model allows simulation of both steady-state and electrochemical impedance response. The models may be used to visualize the influence of the coupling between the homogeneous reactions, heterogeneous reactions, and transport processes. The models can be applied to predict performance of sensor designs and to diagnose sensor failure mechanisms.