Modeling and Simulation of Insulin Pump Set Failures Based on the Power Flow Method

The insulin pump is a critical device for intensive insulin therapy in diabetic patients. Failures in insulin pump sets such as blockage and leakage can disrupt normal insulin delivery, potentially causing hyperglycemia or life-threatening diabetic ketoacidosis. Developing a mathematical model to accurately describe the failure mechanisms of insulin pump sets is essential for fault diagnosis and performance optimization. However, modeling these systems is challenging due to the interplay of rigid and elastic constraints (e.g., needles and hoses) and multi-domain interactions (e.g., fluid insulin and solid components). To address these challenges, this study establishes a mathematical model for insulin pump sets with blockage and leakage faults based on the power flow method. The model is used to investigate the effects of these faults on insulin fluid dynamics, with a focus on impacts of failures at various positions. Numerical results demonstrate a maximum relative error of 0.57% compared to simulation data. Findings reveal that leakage faults closer to the flow source significantly reduce the output flow rate and chamber pressure. Conversely, as blockage approach the flow source, the impact on reducing flow rate diminishes, while their influence on increasing chamber pressure becomes more pronounced. Notably, when the blockage thickness exceeds 0.6 mm, both flow rate and pressure are markedly affected, with the effects intensifying as the thickness increases.