Mathematics Senior Capstone Papers

Document Type


Publication Date

Spring 5-17-2020


Type 1 diabetes is a condition characterized by a lack of insulin production. This lack of insulin causes glucose concentration in the blood to increase after meals. In order to maintain blood glucose levels, diabetics must inject insulin using needles or an insulin pump. Additionally, the lack of insulin can cause glucose levels to decrease overnight. This project uses a proportional integral derivative (PID) controller to modify the rate of insulin and glucagon infusion when glucose levels are increasing or decreasing, respectively. A system of 13 differential equations were used to anticipate changes in glucose concentration as insulin and glucagon were injected. The system was simulated for virtual patients over a 24-hour time span in order to test its feasibility in human patients. The PID controller uses the current, past, and anticipated future glucose levels, respectively, in order to better determine the best course of treatment for the virtual patient. One of the many difficulties in medical technology, however, is that everyone is different. These differences are a result of metabolism and other factors. To account for this fact the controller is designed to change the gain of the different controller components in order to better tailor the treatment to each patient.