Mathematical analysis of a model for glucose regulation

Kimberly  Fessel; Jeffrey B.  Gaither; Julie K.  Bower; Trudy  Gaillard; Kwame  Osei; Grzegorz A.  Rempała

doi:10.3934/mbe.2016.13.83

Mathematical Biosciences and Engineering, 2016, 13(1): 83-99. doi: 10.3934/mbe.2016.13.83. Primary: 92B; Secondary: 92C60.

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Mathematical analysis of a model for glucose regulation

Kimberly Fessel, Jeffrey B. Gaither, Julie K. Bower, Trudy Gaillard, Kwame Osei, Grzegorz A. Rempała

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

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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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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

References:

1. CPT: Pharmacometrics & Systems Pharmacology, 2 (2013), 1-14.
2. Diabetes Care, 37 (2014), S14-S80.
3. Eur J Intern Med, 22 (2011), 8-12.
4. Diabetes, 38 (1989), 1512-1527.
5. in Mathematical Modeling in Nutrition and the Health Sciences (eds. J. A. Novotny, M. H. Green and R. C. Boston), Advances in Experimental Medicine and Biology, Kluwer Academic/Plenum, New York, 537 (2003), 1-19.
6. Horm Res, 64 (2005), 8-15.
7. Am J Physiol, 236 (1979), E667-E677.
8. J Clin Invest, 68 (1981), 1456-1467.
9. Diabetes Care, 15 (1992), 1313-1316.
10. J. Vet Intern Med., 11 (1997), 86-91.
11. Diabetes Care, 31 (2008), 1697-1703.
12. Diabetes Care, 34 (2011), S184-S190.
13. in Mathematical Modeling in Nutrition and the Health Sciences (eds. J. A. Novotny, M. H. Green and R. C. Boston), Advances in Experimental Medicine and Biology, Kluwer Academic/Plenum, New York, 2003, 21-42.
14. Diabetes technology & therapeutics, 5 (2003), 1003-1015.
15. BioMedical Engineering OnLine, 5 (2006), p43.
16. J Clin Endocrinol Metab, 85 (2000), 4396-4402.
17. information in diabetes and prediabetes in the United States, 2011.
18. J Pediatr, 138 (2001), 244-249.
19. Diabetes Care, 32 (2009), 2027-2032.
20. Diabetes Care, 34 (2011), 145-150.
21. J Math Bio, 40 (2000), 136-168.
22. Int J Clin Pract, 62 (2008), 642-648.
23. Diabetes, 57 (2008), 1638-1644.
24. Theor Biol Med Model, 8 (2011), p12.
25. Discrete and Continuous Dynamical Systems - Series B, 1 (2001), 103-124.
26. Diabetes Care, 35 (2012), 868-872.
27. Am J Physiol Endocrinol Metab, 294 (2008), E15-E26.
28. Diabetes Care, 30 (2007), 753-759.
29. BioMedical Engineering OnLine, 5 (2006), 44-57.
30. J Clin Endocrinol Metab, 79 (1994), 217-222.
31. Comput Meth Prog Bio, 23 (1986), 113-122.
32. in Data-driven Modeling for Diabetes (eds. V. Marmarelis and G. Mitsis), Lecture Notes in Bioengineering, Springer Berlin Heidelberg, 2014, 117-129.
33. Lancet, 365 (2005), 1333-1346.
34. BIOMIM & Control Systems, 1-21.
35. http://bmi.bmt.tue.nl/sysbio/parameter_estimation/gluc_mm_mle2012.m, 2012, Accessed: 2015-02-24.
36. Diabetes Care, 24 (2001), 1275-1279.

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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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Copyright Info: 2016, Kimberly Fessel, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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