Estimation of plasma insulin concentration under glycemic variability using nonlinear filtering techniques

The ultimate goal of an artificial pancreas is finding the optimal insulin rates that can effectively reduce high blood glucose (BG) levels in type 1 diabetic patients. To achieve this, most closed-loop control strategies need to compute the optimal insulin action on the basis of precedent glucose and insulin levels. Unlike glucose levels which can be measured in real-time, unavailability of insulin sensors makes it essential the use of mathematical models to estimate plasma insulin concentrations. Between others, filtering techniques based on a generalization of the Kalman filter (KF) have been the most widely applied in the estimation of hidden states in nonlinear dynamic systems. Nevertheless, poor predictability of BG levels is a key issue since the glucose-insulin dynamics presents great inter- and intra-patient variability. Here, the question arises as to whether glycemic variability is not properly taken into account in models formulations and whether or it would compromise proper estimation of plasma insulin concentration. In order to tackle this point, a deterministic model describing glucose-insulin interaction plus a stochastic process to account for BG fluctuations were incorporated into the extended (EKF), cubature (CKF) and unscented (UKF) configurations of the Kalman filter to provide an estimate of the plasma insulin concentration. We found that for low glycemic variability, insulin state estimation can be attained with acceptable accuracy; however, as glycemic variability rises, Kalman filters rapidly degrade their performance as a consequence of large nonlinearities.