Plasma insulin estimation using continuous-monitored plasma glucose

This thesis describes estimators of plasma insulin using measurement of plasma glucose. The estimators were based on Bergman's model of glucose-insulin metabolism which was chosen because it has relatively few parameters and it is widely used clinically. The Bergman model consists of two parts, the glucose disappearance and the insulin kinetics subsystems. Three direct integration methods (Euler, Step-Invariance, and Runge-Kutta) were employed to obtain six plasma insulin estimators based on the two subsystems. The insulin kinetics subsystem was found to be the better pathway on which to build the plasma insulin estimator. This argument was confirmed by using both computer simulations and human IVGTT (intravenous glucose tolerance test) data. Computer simulations also showed that the proposed estimators underestimate or overestimate plasma insulin profile when exogenous glucose input (glucose injection, infusion, food consumption, etc.) or exogenous insulin input (insulin injection, etc.) is presented to the system. Two modifications were made to the proposed estimators. First, Nomura's insulin secretion function was chosen from five candidates to replace the Bergman model's secretion function. The latter is an explicit function of time. Second, exogenous input estimators for both the glucose disappearance and insulin kinetics subsystems were proposed. Feedback linearization was applied to the model, and a linear input estimator was employed to obtain exogenous insulin input. Due to the relative degree constraint in the glucose-insulin system with exogenous glucose input, the exogenous glucose input estimator was obtained using direct integration. The combination of the insulin kinetics based estimator and the exogenous insulin input estimator was found to perform better than the combination of the glucose disappearance based estimator and the exogenous glucose input estimator. Simulation studies with a more complex model metabolism suggested that the estimator based on Bergman's model may not be complex enough to describe system responses to arbitrary inputs.