Discipline: Mathematics and Statistics
Subcategory: Mathematics and Statistics
Samantha Deal - Tennessee State University
The regulation of glucose in the human body is a complex and dynamic process. Mathematical models of this system are frequently used to analyze clinical data and predict future outcomes. Often these models are minimal models, which are later adapted to become more precise. One of the simplest, Bolie’s model, will be examined in this study, as well as the slightly more complex Bergman Minimal Model (BMM). Of the many models portraying the dynamics of glucose and insulin in the human body, these minimal models are foundational to this area of biomathematics. Based on these models, it is possible to characterize the outcomes of data from normal, diabetic, and insulin resistant subjects. The purpose of this study is to explore quantitatively both the Bolie and Bergman nonlinear differential models. The solution of the Bolie system was found using mathematical principles and stability analysis of the BMM was performed. Additionally, evaluating particular parameters of Bergman’s model with reduced values showed their individual impact on the system. Two of the most important clinical parameters, glucose effectiveness (SG), and insulin sensitivity (SI) were investigated to understand their influence on glucose-insulin regulation process under different physical conditions. Numerical simulations were performed using python, generating several plots to display the outcome using different parameter values. It is found that the minimal models, even if simple, establish the underlying mathematical principle of the complex mechanism of glucose and insulin interactions well.
Funder Acknowledgement(s): This research was funded by the NSF-TIP programs.
Faculty Advisor: Dr. Sanjukta Hota, firstname.lastname@example.org
Role: With oversight and guidance from my advisor, Dr. Hota, I performed the entirety of this research.