Robust insulin estimation under glycemic variability using Bayesian filtering and Gaussian process models

Abstract

The ultimate goal of an artificial pancreas (AP) is finding the optimal insulin rates that can effectively reduce high blood glucose (BG) levels in type 1 diabetic patients. To achieve this, most autonomous closed-loop strategies continuously compute the optimal insulin bolus to be administrated on the basis of the estimated plasma concentrations for glucose and insulin. Unlike subcutaneous glucose levels which can be measured in real-time, unavailability of insulin sensors makes it essential the use of mathematical models so as to fully estimate plasma insulin concentrations. For model-based estimation, GP-Bayesian filters have been recently proposed to incorporate probabilistic non-parametric Gaussian process (GP) models of dynamic systems into Kalman filtering techniques. As a result, model uncertainty can explicitly be incorporated into the prediction step and in the filtering processes, which is usually not the case for more traditional filtering strategies that resort to parametric models for state estimation. More specifically, the question arises as to whether glycemic variability is properly taken into account in model formulations and whether it would compromise proper estimation of plasma insulin concentration. To tackle this, a stochastic glycemic model including variability was incorporated into different parametric and nonparametric filtering techniques to provide an estimate of the plasma insulin levels. In particular, we compared density representation against using knowledge about the parameterization of the transition dynamics and the observation function. We found that, as glycemic variability increases, filtering techniques based on parametric models rapidly degrades their performance as a consequence of large nonlinearities. Results show that Bayes’ filtering techniques increase predictability of the patient state, and thus, boost safety and performance in the AP control and monitoring tasks.