Mathematical Modeling and Simulation of Glucagon-Insulin Dynamics for Dual-Hormone Closed-Loop Systems in Type 1 Diabetes

Type 1 diabetes is a chronic disease that is becoming increasingly common worldwide, especially among children and young adults. Despite technological advances, maintaining stable blood glucose levels remains a major challenge, including preventing hypoglycemia. This thesis presents the development of a mathematical model of glucose dynamics, which was used to simulate and design a dual-hormone closed-loop control system for individuals with type 1 diabetes. Traditional insulin-only systems lack the ability to actively prevent hypoglycemia, making bi-hormonal approaches that combines insulin and glucagon a promising alternative. The aim of this work was to model the dynamic effects of insulin and glucagon on blood glucose regulation, and to use this model to develop and evaluate various dual-hormone control algorithms. A modified version of the glucose model by Herrero et al. was implemented in Python using the SUND toolbox. Key improvements included reducing the number of individual-specific parameters and removing time-window dependencies to enhance model robustness. The model was validated using clinical data and evaluated through uncertainty analysis. Multiple control systems were developed, including a derivative-based algorithm with meal bolus support, and a biologically inspired $\beta$-cell algorithm. Simulation results showed that the dual-hormone systems improved glucose stability and reduced hypoglycemic episodes compared to single-hormone approaches. The derivative-based controller with meal bolus resulted in the best performance compared to the other systems. These results demonstrate that mathematical modeling can be a powerful tool for designing and evaluating closed-loop glucose control systems, and that dual-hormone systems have strong potential to improve glucose stability and support safer and more autonomous diabetes management.