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Title: 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 » 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.« less

Authors:
 [1]; ORCiD logo [2];  [3];  [4];  [4]
  1. Xinyang Normal University, Henan (China)
  2. Arizona State Univ., Tempe, AZ (United States)
  3. Univ. of Portsmouth (United Kingdom)
  4. 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. doi: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. doi: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 = {2017},
month = {11}
}

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