Mathematical Biosciences and Engineering, 2016, 13(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

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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Keywords parameter estimation; glucose tolerance test; insulin sensitivity.; Diabetes; minimal model

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

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This article has been cited by

  • 1. Mohammad Munir, Generalized sensitivity analysis of the minimal model of the intravenous glucose tolerance test, Mathematical Biosciences, 2018, 300, 14, 10.1016/j.mbs.2018.03.014

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