A Novel Three-Compartmental Model for Artificial Pancreas: Development and Validation

Closed-loop insulin delivery system, also known as artificial pancreas (AP), provides the blood glucose control in diabetic patients, enabling the automatic blood-sugar management and reducing the risks and improving the lives of people with diabetes. A new three-compartmental model of glucose-insulin interaction for AP is presented and tested in this paper. The glucose and insulin "spaces" are split into a plasma compartment and interstitial fluids compartment, respectively. The model includes an additional subcutaneous compartment and provides three explicit delays and three parameters influencing the regulatory system and correlating with the physiopathology of the patients. Two delays are related with hepatic glucose production and insulin secretion; the third delay represents the lag time in the absorption of exogenous insulin in subcutaneous tissue. The parameters regulate the system dynamics acting on the glucose utilization and the insulin secretion. The clinical data (including information on food ingestion and exogenous insulin injection) from five case studies of Type 1 diabetics are presented and used to validate the mathematical model. After training the parameters for each case study, the model well simulates the glucose level during a 4-day test. The estimated values are physiologically meaningful and provide a further insight on the subject's dysfunctions and on the state of the disease. The results have been also compared with a parallel simulation carried out by implementing a previous two-compartmental model. The proposed algorithm produces a lower sum of the squared error between the simulated and the measured glucose concentrations over time.