Modeling and Optimization of Insulin Injection for Type-1 Diabetes Mellitus Management

Diabetes mellitus is a global health crisis characterized by poor blood sugar regulation, impacting millions of people worldwide and leading to severe complications and mortality. Although Type 1 Diabetes Mellitus (T1DM) has a lower number of cases compared to other forms of diabetes, it is often diagnosed at a young age and requires lifelong exogenous insulin administration. In this paper, we focus on understanding the interaction of insulin and glucose molecules within the subcutaneous layer, which is crucial for blood sugar control in T1DM patients. Specifically, we propose a comprehensive model to characterize the insulin-glucose system within the subcutaneous layer, incorporating a multicellular molecular communication system. We then divide the T1DM system into insulin and glucose subsystems and derive the end-to-end expression for insulin-glucose interaction in the subcutaneous layer. We further validate the insulin-glucose interaction analysis with an agent-based simulator. As effectively managing postprandial glucose levels is crucial for individuals with T1DM to safeguard their overall health and avert short-term and long-term complications, we also derive the optimal insulin administration time based on the derived glucose response via the Lagrange multiplier and gradient descent ascent method. This allows us to explore the impact of different types of insulin and dietary management on blood sugar levels. Simulation results confirm the correctness of our proposed model and the effectiveness of our optimized effective time window for injecting insulin in individuals with T1DM.