Closed-loop glucose control: Application to the Euglycemic Hyperinsulinemic Clamp

The Euglycemic Hyperinsulinemic Clamp (EHC) is considered the gold standard experiment for the determination of insulin sensitivity. It consists of a nontrivial perturbation experiment, during which large amounts of insulin are administered intra-venously to the subject, and exogenous glucose is administered, according to given protocols, in order to keep glycemia constant. This note proposes a closed-loop glucose control methodology for the EHC. A Delay Differential Equation (DDE) model of the EHC is considered to synthesize the control law. The use of an observer for nonlinear DDE systems allows the use of only glucose measurements in order to design the feedback (instead of insulin measurements, which are less accurate, more expensive and more cumbersome to obtain). The main result consists in the proof of convergence of the observer estimate error in case of a piecewise-constant control, which is what occurs in practice by intermittent manual regulation of the glucose infusion pump. Numerical results show the effectiveness of the proposed methodology.