Low-Order Nonlinear Animal Model of Glucose Dynamics for a Bihormonal Intraperitoneal Artificial Pancreas

The design of an Artificial Pancreas (AP) to regulate blood glucose levels requires reliable control methods. Model Predictive Control has emerged as a promising approach for glycemia control. However, model-based control methods require computationally simple and identifiable mathematical models that represent glucose dynamics accurately, which is challenging due to the complexity of glucose homeostasis.

In this work, a simple model is deduced to estimate blood glucose concentration in subjects with Type 1 Diabetes Mellitus (T1DM). Novel features in the model are power-law kinetics for intraperitoneal insulin absorption and a separate glucagon sensitivity state. Profile likelihood and a method based on singular value decomposition of the sensitivity matrix are carried out to assess parameter identifiability and guide a model reduction for improving the identification of parameters.

A reduced model with 10 parameters is obtained and calibrated, showing good fit to experimental data from pigs where insulin and glucagon boluses were delivered in the intraperitoneal cavity.

A simple model with power-law kinetics can accurately represent glucose dynamics submitted to intraperitoneal insulin and glucagon injections. The reduced model was found to exhibit local practical as well as structural identifiability.

The proposed model facilitates intraperitoneal bi-hormonal model-based closed-loop control in animal trials.