# Mathematical Analysis of Type 2 Diabetes Predisposition

Initial Publication Date: October 7, 2016 | Reviewed: November 15, 2018

## Summary

In this activity, students will examine the relationship between glucose and insulin in the human body using models based on the physiology of glucose metabolism and insulin secretion. We will view the body and its organs quantitatively, as dynamic systems, and the model will describe the dynamics of the system using ordinary differential equations. Students will use the model to simulate the glucose-insulin response after one or more meals, for normal human subjects and for human subjects with various kinds of insulin impairments. Students will examine disease factors such as insulin sensitivity and pancreas beta-cell function and their relationship to plasma glucose concentrations.

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## Learning Goals

This Bergmann Minimal model is revolved around insulin sensitivity and the pancreatic response parameters and how these parameters can help determine if a subject is at high-risk for pre-diabetes or is already at type 2 diabetic levels. The Bergman's Minimal model is coded and simulated using MATLAB and SimBiology. Users will plot functions and data, input ordinary differential equations, and use additional applications to simulate data. The exercise will be used with MS Excel to help organize the data collected from MATLAB after certain parameter scans. Disposition Index curves will also be created in Excel. Users will use high-order skills (e.g. critical thinking, computation, data analysis, synthesis of ideas and model development) in this activity.

## Context for Use

In the western world today, more than 25 million people suffer from Type 2 diabetes. Currently, diabetes is an incurable disease, where systems in the body may not properly control glucose and insulin concentrations in the blood. Glucose is a prime energy source for the brain and is also a source of energy for cells throughout the body. When consuming simple sugars, such as glucose, the bloodstream carries the glucose to body tissues for energy and stores the excess glucose as glycogen in the liver. The hormone insulin is key for the active uptake of insulin in body tissues. If the concentration of blood glucose is too high or too low, serious physiological issues can occur. The relationship between glucose and insulin in the human body will be examined using models based on the physiology of glucose metabolism and the disposition index. Diabetes is an incurable disease which is segmented into two different types. Here we examine diabetes mellitus Type 2, also known as adult-onset diabetes. Diabetics must adjust their dietary and exercise styles and often must take medicine. By managing diabetes, people with diabetes can reduce their risk for heart disease and stroke. This activity includes tools and approaches to understand composite effects of insulin secretion and insulin sensitivity based on the Intravenous Glucose Tolerance Test (IVGTT). This minimal model was created by Dr. Richard N. Bergman over 35 years ago and consists of 3 ordinary differential equations. Students will use the model to simulate the glucose-insulin response after one or more meals, for normal human subjects and for human subjects with various kinds of insulin impairments. Students will examine disease factors such as insulin sensitivity and pancreas beta-cell function and their relationship to plasma glucose concentrations.

## Description and Teaching Materials

Glucose is the molecule that the cells of the human body use as an energy source. Cells use glucose to make ATP, which is the primary energy provider in the cell. Maintaining a steady level of glucose in the blood is critical in the human body. If the amount of blood glucose is too much or too little, serious physical problems can occur. In people with diabetes, the body cannot properly control its glucose level. In this activity, students will examine the relationship between glucose and insulin in the human body using models based on the physiology of glucose metabolism and insulin secretion.When consuming simple sugars, such as glucose, the bloodstream carries the glucose to body tissues for energy and stores the excess glucose as glycogen in the liver. The hormone insulin is key for the active uptake of insulin in body tissues. If the concentration of blood glucose is too high or too low, serious physiological issues can occur. The relationship between glucose and insulin in the human body will be examined using models based on the physiology of glucose metabolism and the disposition index. Important organs will be viewed quantitatively, as dynamic systems, and the model will describe the dynamics of the system using ordinary differential equations. The model will also be used to simulate the glucose-insulin response after adjusting the numerical values of certain parameters (P3, P2, P4,P6). These key parameters are responsible for the prediction of the disposition index . By adjusting parameters, mathematically users will be able to determine values that quickened the glucose and insulin response in diabetic subjects. Additionally, users will find that p6 ,p3 and p2 are crucial parameters that can determine whether or not a person is a pre diabetic or a type 2 diabetic.
Teaching Activity Background Notes (Microsoft Word 2007 (.docx) 114kB Sep30 16)
Goals and Outcomes (Microsoft Word 2007 (.docx) 14kB Sep30 16)
Teaching Notes (Microsoft Word 2007 (.docx) 251kB Sep30 16)
BMI and Glucose Tolerance Graphs (Excel 2007 (.xlsx) 48kB Sep30 16)

## Teaching Notes and Tips

Background: Diabetes can be segmented into two categories Type 1 and Type 2. This activity is primarily focused on type 2 diabetes. Type 2 is a disease relating to the body's inability to use insulin. The human body requires the blood glucose concentration to be kept at a narrow range around 70-110 mg/dl (Makroglou, Li and Kuang). Risk factors such as weight, age and race ultimately determine if subjects will get diabetes. Weight, race and age are not the only determinants of diabetes as we have learned from research. There are a multitude of test that can determine whether or not a person has normal glucose tolerance or if they are a diabetic. The Oral Glucose tolerance test (OGTT) is the most common glucose tolerance test. The amount of glucose in the blood after the testing determines whether or not a person has diabetes. The IVGTT is a test that is widely used along with Bergman's Minimal model and can be used to estimate Insulin sensitivity (SI), glucose effectiveness (SG) and the pancreatic response parameters in a subject (Friis-Jensen 2007).

When consuming simple sugars, such as glucose, the bloodstream carries the glucose to body tissues for energy and stores the excess glucose as glycogen in the liver. The hormone insulin is key for the active uptake of insulin in body tissues. If the concentration of blood glucose is too high or too low, serious physiological issues can occur. The relationship between glucose and insulin in the human body will be examined using models based on the physiology of glucose metabolism and the disposition index. Important organs will be viewed quantitatively, as dynamic systems, and the model will describe the dynamics of the system using ordinary differential equations. Models will also be used to simulate the glucose-insulin response after adjusting the numerical values of certain parameters associated in insulin uptake and release (P3, P2, P4, and P6). These key parameters help predict risks associated with insulin resistance leading to type 2 diabetes. By adjusting parameters mathematically, users will be able to observe whether patients are at risk of becoming pre-diabetic or type 2 diabetic.

## Assessment

1. Students should be able to simulate glucose release into the bloodstream and the insulin secreting response of the pancreas and understand how the model is based on the physiology of glucose metabolism and insulin secretion.
2. Students should be able to evaluate the sensitivity of model parameters for predicting the pre-disposition of TYP2 diabetes.
3. Students should be able to construct scenarios and consequences when an individual is less sensitive to the insulin and apply understanding to the function of insulin responsive cells and their ability to respond to insulin

## References and Resources

Bergman R.N, L. S. (1981, December 1). Physiologic evaluation of factors controlling glucose
tolerance in man: measurement of insulin sensitivity and beta-cell glucose sensitivity from the response to intravenous glucose. The Journal of Clinical Investigation, pp. 1456-1467.

Chandler-Laney, P. (2010, November). Adiposity and β-cell function: relationships differ with
ethnicity. Obesity (Silver Spring), pp. 2086–2092.

Friis-Jensen, E. (2007). Modeling and Simulation of Glucose-Insulin Metabolism. Kongens Lyngby: Technical University of Denmark.

Kahn SE, Prigeon RL, McCulloch DK, Boyko EJ, Bergman RN, Schwartz MW, Neifing JL,
Ward WK, Beard JC, Palmer JP. (1993) Quantification of the relationship between insulin sensitivity and beta-cell function in human subjects. Evidence for a hyperbolic function. Diabetes 42: 1663–1672, 1993.

Makroglou, Athena, Jiaxu Li and Yang Kuang. "Mathematical models and software tools for the glucose-insulin." Elsevier (2006): 559-573.

Norman, James. "Normal Regulation of Blood Glucose." 27 May
2014. Endocrineweb. .

Pacini, B. A. (2004). Importance of quantifying insulin secretion in relation to insulin sensitivity
to accurately assess beta cell function in clinical studies. European Journal of Endocrinology, pp. 97–104.

Puckett, W.R. "Dynamic modeling of diabetes mellitus." 1992. The Global Diabetes Community. (2015). Retrieved from Diabetes.co.uk: http://www.diabetes.co.uk/body/beta-cells.html

Wisse, B. (2014, August 5). Glucose tolerance test. Retrieved from U.S. National Library of Medicine :http://www.nlm.nih.gov/medlineplus/ency/article/003466.htm