Oscillatory dynamics of an intravenous glucose tolerance test model with delay interval
Abstract
We report that type 2 diabetes mellitus (T2DM) has become prevalent pandemic disease in view of the modern life style. Both diabetic population and health expenses grow rapidly according to American Diabetes Association. Detecting the potential onset of T2DM is an essential focal point in the research of diabetes mellitus. The intravenous glucose tolerance test (IVGTT) is an effective protocol to determine the insulin sensitivity, glucose effectiveness, and pancreatic β-cell functionality, through the analysis and parameter estimation of a proper differential equation model. Delay differential equations have been used to study the complex physiological phenomena including the glucose and insulin regulations. In this paper, we propose a novel approach to model the time delay in IVGTT modeling. This novel approach uses two parameters to simulate not only both discrete time delay and distributed time delay in the past interval, but also the time delay distributed in a past sub-interval. Normally, larger time delay, either a discrete or a distributed delay, will destabilize the system. However, we find that time delay over a sub-interval might not. We present analytically some basic model properties, which are desirable biologically and mathematically. We show that this relatively simple model provides good fit to fluctuatingmore »
- Authors:
-
- Xinyang Normal University, Henan (China)
- Arizona State Univ., Tempe, AZ (United States)
- Univ. of Portsmouth (United Kingdom)
- Univ. of Louisville, KY (United States)
- Publication Date:
- Research Org.:
- Univ. of Louisville, KY (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1511149
- Grant/Contract Number:
- EM0000197
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Chaos: An Interdisciplinary Journal of Nonlinear Science
- Additional Journal Information:
- Journal Volume: 27; Journal Issue: 11; Journal ID: ISSN 1054-1500
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 59 BASIC BIOLOGICAL SCIENCES; 60 APPLIED LIFE SCIENCES
Citation Formats
Shi, Xiangyun, Kuang, Yang, Makroglou, Athena, Mokshagundam, Sriprakash, and Li, Jiaxu. Oscillatory dynamics of an intravenous glucose tolerance test model with delay interval. United States: N. p., 2017.
Web. doi:10.1063/1.5008384.
Shi, Xiangyun, Kuang, Yang, Makroglou, Athena, Mokshagundam, Sriprakash, & Li, Jiaxu. Oscillatory dynamics of an intravenous glucose tolerance test model with delay interval. United States. https://doi.org/10.1063/1.5008384
Shi, Xiangyun, Kuang, Yang, Makroglou, Athena, Mokshagundam, Sriprakash, and Li, Jiaxu. Thu .
"Oscillatory dynamics of an intravenous glucose tolerance test model with delay interval". United States. https://doi.org/10.1063/1.5008384. https://www.osti.gov/servlets/purl/1511149.
@article{osti_1511149,
title = {Oscillatory dynamics of an intravenous glucose tolerance test model with delay interval},
author = {Shi, Xiangyun and Kuang, Yang and Makroglou, Athena and Mokshagundam, Sriprakash and Li, Jiaxu},
abstractNote = {We report that type 2 diabetes mellitus (T2DM) has become prevalent pandemic disease in view of the modern life style. Both diabetic population and health expenses grow rapidly according to American Diabetes Association. Detecting the potential onset of T2DM is an essential focal point in the research of diabetes mellitus. The intravenous glucose tolerance test (IVGTT) is an effective protocol to determine the insulin sensitivity, glucose effectiveness, and pancreatic β-cell functionality, through the analysis and parameter estimation of a proper differential equation model. Delay differential equations have been used to study the complex physiological phenomena including the glucose and insulin regulations. In this paper, we propose a novel approach to model the time delay in IVGTT modeling. This novel approach uses two parameters to simulate not only both discrete time delay and distributed time delay in the past interval, but also the time delay distributed in a past sub-interval. Normally, larger time delay, either a discrete or a distributed delay, will destabilize the system. However, we find that time delay over a sub-interval might not. We present analytically some basic model properties, which are desirable biologically and mathematically. We show that this relatively simple model provides good fit to fluctuating patient data sets and reveals some intriguing dynamics. Moreover, our numerical simulation results indicate that our model may remove the defect in well known Minimal Model, which often overestimates the glucose effectiveness index. Delay differential equations (DDEs) have been frequently used to study complex dynamics observed in nature. More recently, they are used to understand intriguing physiological phenomena such as those expressed by glucose and insulin interaction. We propose a simple set of delay differential equations to model an intravenous glucose tolerance test. This model uses two parameters to simulate not only both discrete time delay and distributed time delay in the past interval, but also the time delay distributed in a past sub-interval. We show that this relatively simple model provides good fit to fluctuating patient data sets and reveals some intriguing dynamics. Lastly and most importantly, our model may remove the defect in the well known Minimal Model (MM) which often overestimates the glucose effectiveness (GE) index.},
doi = {10.1063/1.5008384},
journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science},
number = 11,
volume = 27,
place = {United States},
year = {Thu Nov 09 00:00:00 EST 2017},
month = {Thu Nov 09 00:00:00 EST 2017}
}
Web of Science
Works referenced in this record:
Analysis of a Model of the Glucose‐Insulin Regulatory System with Two Delays
journal, January 2007
- Li, Jiaxu; Kuang, Yang
- SIAM Journal on Applied Mathematics, Vol. 67, Issue 3
The range of time delay and the global stability of the equilibrium for an IVGTT model
journal, February 2012
- Li, Jiaxu; Wang, Minghu; Gaetano, Andrea De
- Mathematical Biosciences, Vol. 235, Issue 2
Analysis of IVGTT glucose-insulin interaction models with time delay
journal, January 2001
- Li, Bingtuan; Kuang, Yang; Li, Jiaxu
- Discrete and Continuous Dynamical Systems - Series B, Vol. 1, Issue 1
Minimal Model: Perspective from 2005
journal, January 2005
- Bergman, Richard N.
- Hormone Research in Paediatrics, Vol. 64, Issue 3
Can Mathematical Models Predict the Outcomes of Prostate Cancer Patients Undergoing Intermittent Androgen Deprivation Therapy?
journal, June 2014
- Everett, R. A.; Packer, A. M.; Kuang, Y.
- Biophysical Reviews and Letters, Vol. 09, Issue 02
Pulsatile insulin secretion, impaired glucose tolerance and type 2 diabetes
journal, April 2015
- Satin, Leslie S.; Butler, Peter C.; Ha, Joon
- Molecular Aspects of Medicine, Vol. 42
Continuous Structured Population Models for Daphnia magna
journal, September 2017
- Rutter, Erica M.; Banks, H. T.; LeBlanc, Gerald A.
- Bulletin of Mathematical Biology, Vol. 79, Issue 11
Mathematical models and software tools for the glucose-insulin regulatory system and diabetes: an overview
journal, March 2006
- Makroglou, Athena; Li, Jiaxu; Kuang, Yang
- Applied Numerical Mathematics, Vol. 56, Issue 3-4
Pathophysiology and treatment of type 2 diabetes: perspectives on the past, present, and future
journal, March 2014
- Kahn, Steven E.; Cooper, Mark E.; Del Prato, Stefano
- The Lancet, Vol. 383, Issue 9922
Impaired Pulsatile Secretion of Insulin in Relatives of Patients with Non-Insulin-Dependent Diabetes
journal, May 1988
- O'Rahilly, Stephen; Turner, Robert C.; Matthews, David R.
- New England Journal of Medicine, Vol. 318, Issue 19
Contributions of -Cell Dysfunction and Insulin Resistance to the Pathogenesis of Impaired Glucose Tolerance and Impaired Fasting Glucose
journal, April 2006
- Abdul-Ghani, M. A.; Tripathy, D.; DeFronzo, R. A.
- Diabetes Care, Vol. 29, Issue 5
Brief, Irregular Oscillations of Basal Plasma Insulin and Glucose Concentrations in Diabetic Man
journal, May 1981
- Lang, D. A.; Matthews, D. R.; Burnett, M.
- Diabetes, Vol. 30, Issue 5
Glucose Effectiveness in Nondiabetic Relatives: Dysglycemia and β-Cell Function at 10 Years
journal, April 2014
- Egede, M. B.; Henriksen, J. -E.; Durck, T. T.
- The Journal of Clinical Endocrinology & Metabolism, Vol. 99, Issue 4
How to measure insulin sensitivity
journal, January 1998
- Ferrannini, Ele; Mari, Andrea
- Journal of Hypertension, Vol. 16, Issue 7
MINMOD Millennium: A Computer Program to Calculate Glucose Effectiveness and Insulin Sensitivity from the Frequently Sampled Intravenous Glucose Tolerance Test
journal, December 2003
- Boston, Ray C.; Stefanovski, Darko; Moate, Peter J.
- Diabetes Technology & Therapeutics, Vol. 5, Issue 6
Advantages of the single delay model for the assessment of insulin sensitivity from the intravenous glucose tolerance test
journal, March 2010
- Panunzi, Simona; De Gaetano, Andrea; Mingrone, Geltrude
- Theoretical Biology and Medical Modelling, Vol. 7, Issue 1
Modeling the glucose–insulin regulatory system and ultradian insulin secretory oscillations with two explicit time delays
journal, October 2006
- Li, Jiaxu; Kuang, Yang; Mason, Clinton C.
- Journal of Theoretical Biology, Vol. 242, Issue 3
Global stability in a model of the glucose-insulin interaction with time delay
journal, April 2004
- Bennett, D. L.; Gourley, S. A.
- European Journal of Applied Mathematics, Vol. 15, Issue 2
A discrete Single Delay Model for the Intra-Venous Glucose Tolerance Test
journal, September 2007
- Panunzi, Simona; Palumbo, Pasquale; De Gaetano, Andrea
- Theoretical Biology and Medical Modelling, Vol. 4, Issue 1
Current approaches for assessing insulin sensitivity and resistance in vivo: advantages, limitations, and appropriate usage
journal, January 2008
- Muniyappa, Ranganath; Lee, Sihoon; Chen, Hui
- American Journal of Physiology-Endocrinology and Metabolism, Vol. 294, Issue 1
Qualitative behavior of a family of delay-differential models of the Glucose-Insulin system
journal, December 2006
- Gaetano, Andrea; Panunzi, Simona; Palumbo, Pasquale
- Discrete and Continuous Dynamical Systems - Series B, Vol. 7, Issue 2
Mathematical modelling of the intravenous glucose tolerance test
journal, February 2000
- De Gaetano, Andrea; Arino, Ovide
- Journal of Mathematical Biology, Vol. 40, Issue 2
Works referencing / citing this record:
Amplitude and Frequency Variation in Nonlinear Glucose Dynamics with Multiple Delays via Periodic Perturbation
journal, February 2020
- Bridgewater, Adam; Huard, Benoit; Angelova, Maia
- Journal of Nonlinear Science, Vol. 30, Issue 3
Bifurcation analysis in a delay model of IVGTT glucose–insulin interaction
journal, July 2019
- Mohabati, Fateme; Molaei, MohammadReza
- Theory in Biosciences, Vol. 139, Issue 1
Stochastic resonance in a monostable system driven by time-delayed feedback
journal, January 2020
- Zhang, Gang; Zhou, Lin; Zhang, Tianqi
- Indian Journal of Physics
Introduction to Focus Issue: Time-delay dynamics
journal, November 2017
- Erneux, Thomas; Javaloyes, Julien; Wolfrum, Matthias
- Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 27, Issue 11