chapter  10
30 Pages

Modeling of OGTT Blood Glucose and Insulin Responses and Diagnostic Indices

WithDhanjoo N. Ghista, Kah Meng Loh, Meena Sankaranarayanan

CONTENTS 10.1 Oral Glucose Tolerance Test (OGTT) Protocol .................................. 276 10.2 Representing Glucose and Insulin Responses by Their

Concentration-Time Profiles................................................................. 277 10.3 Differential Equation Model of the Glucose-Insulin System.......... 279

10.3.1 Modeling of Glucose-Insulin Regulation of Oral Glucose Tolerance Test (OGTT) ............................................. 280

10.3.2 The Governing Differential Equations for Glucose and Insulin Systems ................................................................. 280

10.3.3 Laplace Transform Representation of the Governing Equations 10.3 and 10.4 ........................................................... 281

10.4 Solutions to the OGTT Model Governing Differential Equation, for Glucose Response (y) to Glucose Bolus Ingestion (in OGTT)... 283 10.4.1 Solution for Glucose Response y(t)........................................ 283 10.4.2 Solutions for Insulin Response x(t) to Glucose

Bolus Ingestion (OGTT) ........................................................... 284 10.5 Evaluating the Model Parameters (a, b, g, d) .................................... 285 10.6 Clinical Applications of the Model...................................................... 286

10.6.1 Underdamped Category for Patients Clinically Designated to be Normal (Table 10.1)................................... 286

10.6.2 Overdamped Category of Patients Clinically Designated as Diabetic (Table 10.2) ....................................... 288

10.6.3 Critically Damped Category of Patients (Table 10.3) ......... 288 10.7 Combined Nondimensional Index Representing Both Glucose

and Insulin Model Responses............................................................... 290 10.7.1 System Parameters Identification........................................... 291

10.8 Conclusion ............................................................................................... 296

Appendix A: Solution of Equation 10.13 ....................................................... 296 Appendix B: Solution of Equation 10.15........................................................ 297 Appendix C: Solution of Equation 10.17 ....................................................... 299 References ........................................................................................................... 300

In this chapter,we again provide thederivation of the basicmodel to represent blood glucose and insulin responses to glucose ingestion in the oral glucose tolerance test (OGTT). We then provide solutions, to the basic Blood glucoseinsulin regulatory system (BGIRS) model equations, for insulin response x(t) to glucose bolus injestion in OGTT. Finally, we develop a nondimensional index (NDI) based on the model parameters to facilitate characterization of subjects as normal or diabetic or at risk of becoming diabetic.