Modeling the Response Time of an in Vivo Glucose Affinity Sensor

A mathematical model was developed to describe the dose-response relationship of an optical glucose sensor. The basis for glucose detection is the reversible competitive displacement of a ligand from a receptor protein with specific binding sites for certain carbohydrates. Detection of glucose is based on measurements of the change in fluorescent lifetime of the donor-labeled protein, as it binds to the acceptor-labeled ligand. The sensor was modeled as a hollow fiber membrane, permeable to glucose, which encapsulates a solution of the receptor protein and competing ligand. Model equations that describe the diffusion of glucose through the fiber membrane and the subsequent displacement reactions within the fiber lumen were solved numerically to predict the response time of the sensor following a step change in bulk glucose concentration. The incorporation of an external mass transfer boundary layer was found to increase the response time by a factor of 3.7 over the well-stirred case. On the basis of the results of a parametric study, the response time of the sensor was found to be most sensitive to the diffusion coefficient of glucose in the membrane. When compared to experimental response times for an intensity-based affinity sensor using Concanavalin A as the receptor protein and dextran as the competing ligand, the model predictions were found to be significantly shorter than those observed. The effect of the in vivo environment on the performance of the sensor was also investigated through the incorporation of a fibrotic capsule layer. The additional diffusional resistance offered by the capsular tissue resulted in a 5-fold increase in the response time of the sensor.