Modeling Blood Glucose for the Detection of Type 2 Diabetes

Undergraduate #87
Discipline: Mathematics and Statistics
Subcategory: Mathematics and Statistics
Session: 1
Room: Tyler

Matthew Clark - Fisk University
Co-Author(s): Giana Gray, Fisk University, Nashville, TN Sanjukta Hota, Fisk University, Nashville TN

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Diabetes mellitus refers to a category of metabolic disorders characterized by elevated blood glucose levels. Normally, after ingesting a meal, blood glucose levels increase before being reduced to homeostatic levels by hormones such as insulin. In diabetic patients, there is some failing that prevents normal regulation. For type 2 diabetics, this failing usually occurs because of adult-onset metabolic disorder resulting in insulin resistance or relative insulin deficiency. In this project, glucose regulation is considered as a forced spring-mass differential equation with glucose input as the forcing function. Three different input equations are considered for glucose, each one corresponding to a different type of glucose tolerance test. By applying the Laplace transform, explicit solutions for glucose are derived, each one corresponding to a particular form of external glucose input. This leads to the development of characterizing factors for type 2 diabetes. The model with Dirac-delta function as the forcing function for oral glucose tolerance tests proved particularly interesting and was found to agree closely with clinical data for a patient with type 2 diabetes.

Funder Acknowledgement(s): I'd like to acknowledge the NSF Targeted Infusion Project for funding the project, as well as Dr. Nelms, Dr. Qian, and Dr. Hota for allowing the project to take place at Fisk.

Faculty Advisor: Sanjukta Hota, sanjuktahota@gmail.com

Role: I did the majority of the work actually designing and deriving the equations used throughout the project.