chapter  8
34 Pages

Glucose–Insulin Dynamics Modeling

WithDhanjoo N. Ghista, Dittakavi Sarma

CONTENTS 8.1 Background................................................................................................ 220

8.1.1 History and Prevalence of Diabetes .......................................... 220 8.1.2 Blood Glucose Regulation ........................................................... 220 8.1.3 Classification of Diabetes ............................................................ 222 8.1.4 Objective ......................................................................................... 223

8.2 Introduction to Glucose-Regulatory Modeling.................................... 223 8.3 Modeling of Glucose-Insulin Regulation ............................................. 224

8.3.1 Differential-Equation Model of the Glucose-Insulin System....224 8.3.2 Differential-Equation Model in Glucose

Concentration [y], for Insulin Infusion Rate [p¼ 0], and Glucose Inflow Rate [q] ................................. 227

8.3.3 Differential-Equation Model in Insulin Concentration (x), for p¼ 0 and q Input..................................................................... 229

8.3.4 Laplace Transform Representation of Governing Equations 8.3 and 8.4 ................................................................... 229

8.4 Block Diagrams of Blood Glucose Control System............................. 231 8.4.1 Blood Glucose-Insulin Regulatory Control System

(BGCS) Model................................................................................ 231 8.4.2 Control-System Derivation and Representation

of Equations 8.1 and 8.2 to Obtain Equations 8.5a and 8.8 ... 232 8.5 Analyses of Glucose and Insulin Responses to Clinically

Representative Glucose-Input Functions ............................................. 234 8.5.1 Glucose Response Characterization to Different Forms

of Input Functions q(t) into the Blood Pool.............................. 234 8.5.2 Insulin x(t) Responses of the System: x(t) Output

to Glucose q(t) Input..................................................................... 240 8.6 Model Characteristics and Physiological Significance ....................... 243

8.6.1 Model Characteristics................................................................... 243 8.6.2 Explanation of the Glucose-and Insulin-Simulated

Response Curves in Terms of the Model Characteristics ...... 245

8.6.3 Physiological Significance of the Model Simulation............... 246 Appendix A: Tutorial on Laplace Transform Methodology

to Solve DEQ(S) ......................................................................... 247 References ........................................................................................................... 251

8.1.1 History and Prevalence of Diabetes

Albert Einstein once said, ‘‘The most incomprehensible thing about the universe is that it is comprehensible.’’ Human or more specifically the human body is a part of this still largely incomprehensible universe. There has been and will always be constant effort to unravel the mystery of the human body. Diseases are part of this mystery. How do they happen? How do we cure

them? Why some diseases are more prevalent in one ethnic group than the others? Can we use the power of science and technology to know more about them? Diabetes is one of the diseases that has been around for a very long time and yet has not been fully understood amid progress in many fields of science and technology. There was a prescription for frequent urination, the most common symp-

tom of diabetes, on an Egyptian papyrus dating back to 1500 BC. Much later in 100 AD, the Greek physician Aretaeus of Cappadocia first named the condition ‘‘diabetes,’’ which is Greek for ‘‘siphon,’’ since people with diabetes urinated often. In 1889, two European scientists discovered that removing pancreases from dogs caused diabetes. Until this century, the only way doctors had to treat diabetes was through diet. Then the first major progress happened in 1922, with the successful purification and subsequent injection of insulin taken from an animal into a boy with diabetes. It greatly improved his condition and life expectancy, very uncommon at that time. Diabetes is now one of the commonest noninfectious medical conditions

in the world and the numbers are rising. It currently affects about 151 million people worldwide and the number will double by 2010 according to professor Paul Zimmet of the World Health Organization. Diabetes is a leading cause of blindness, renal failure, and limb amputation all over the world. The need to detect diabetic risk factors and treat organ disorders and complications associated with diabetes has provided the motivation for the technology for more precise categorization of at-risk subjects, confirmed diabetics, and severely diabetics. To gain understanding about diabetes, let us now take a look at blood glucose regulation of the human body.