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Mathematical Biosciences and Engineering

2016, Volume 13, Issue 1: 83-99. doi: 10.3934/mbe.2016.13.83
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Mathematical analysis of a model for glucose regulation

  • 1.
    Mathematical Biosciences Institute, The Ohio State University, Columbus, OH 43210
  • 2.
    College of Public Health, The Ohio State University, Columbus, OH 43210
  • 3.
    Department of Medicine, The Ohio State University, Columbus, OH 43210
  • 4.
    Mathematical Biosciences Institute and College of Public Health, The Ohio State University, Columbus, OH 43210
  • Received: 01 April 2015 Accepted: 29 June 2018 Published: 01 October 2015

  • MSC : Primary: 92B; Secondary: 92C60.

  • Diabetes affects millions of Americans, and the correct identification of individuals afflicted with this disease, especially of those in early stages or in progression towards diabetes, remains an active area of research. The minimal model is a simplified mathematical construct for understanding glucose-insulin interactions. Developed by Bergman, Cobelli, and colleagues over three decades ago [7,8], this system of coupled ordinary differential equations prevails as an important tool for interpreting data collected during an intravenous glucose tolerance test (IVGTT). In this study we present an explicit solution to the minimal model which allows for separating the glucose and insulin dynamics of the minimal model and for identifying patient-specific parameters of glucose trajectories from IVGTT. As illustrated with patient data, our approach seems to have an edge over more complicated methods currently used. Additionally, we also present an application of our method to prediction of the time to baseline recovery and calculation of insulin sensitivity and glucose effectiveness, two quantities regarded as significant in diabetes diagnostics.

    Citation: Kimberly Fessel, Jeffrey B. Gaither, Julie K. Bower, Trudy Gaillard, Kwame Osei, Grzegorz A. Rempała. Mathematical analysis of a model for glucose regulation[J]. Mathematical Biosciences and Engineering, 2016, 13(1): 83-99. doi: 10.3934/mbe.2016.13.83

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  • Diabetes affects millions of Americans, and the correct identification of individuals afflicted with this disease, especially of those in early stages or in progression towards diabetes, remains an active area of research. The minimal model is a simplified mathematical construct for understanding glucose-insulin interactions. Developed by Bergman, Cobelli, and colleagues over three decades ago [7,8], this system of coupled ordinary differential equations prevails as an important tool for interpreting data collected during an intravenous glucose tolerance test (IVGTT). In this study we present an explicit solution to the minimal model which allows for separating the glucose and insulin dynamics of the minimal model and for identifying patient-specific parameters of glucose trajectories from IVGTT. As illustrated with patient data, our approach seems to have an edge over more complicated methods currently used. Additionally, we also present an application of our method to prediction of the time to baseline recovery and calculation of insulin sensitivity and glucose effectiveness, two quantities regarded as significant in diabetes diagnostics.


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    3. Jean Marie Ntaganda, Froduald Minani, Wellars Banzi, Lydie Mpinganzima, Japhet Niyobuhungiro, Vincent Dusabejambo, Immaculate Kambutse, Eric Rutaganda, Analysis of physical activity effects on plasma glucose–insulin system dynamics: A mathematical model, 2021, 43, 0142-3312, 3272, 10.1177/01423312211022867
    4. Weijie Wang, Shaoping Wang, Yixuan Geng, Yajing Qiao, Teresa Wu, An OGI model for personalized estimation of glucose and insulin concentration in plasma, 2021, 18, 1551-0018, 8499, 10.3934/mbe.2021420
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  • © 2016 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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