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Mathematical analysis of a model for glucose regulation
1. | Mathematical Biosciences Institute, The Ohio State University, Columbus, OH 43210, United States, United States |
2. | College of Public Health, The Ohio State University, Columbus, OH 43210, United States |
3. | Department of Medicine, The Ohio State University, Columbus, OH 43210, United States, United States |
4. | Mathematical Biosciences Institute and College of Public Health, The Ohio State University, Columbus, OH 43210, United States |
References:
[1] |
I. Ajmera, M. Swat, C. Laibe, N. Le Novère and V. Chelliah, The impact of mathematical modeling on the understanding of diabetes and related complications, CPT: Pharmacometrics & Systems Pharmacology, 2 (2013), 1-14.
doi: 10.1038/psp.2013.30. |
[2] |
American Diabetes Association, Standards of medical care in diabetes-2014, Diabetes Care, 37 (2014), S14-S80. |
[3] |
E. Bartoli, G. P. Fra and G. P. Carnevale Schianca, The oral glucose tolerance test (OGTT) revisited, Eur J Intern Med, 22 (2011), 8-12.
doi: 10.1016/j.ejim.2010.07.008. |
[4] |
R. N. Bergman, Lilly lecture 1989. Toward physiological understanding of glucose tolerance. Minimal-model approach, Diabetes, 38 (1989), 1512-1527.
doi: 10.2337/diabetes.38.12.1512. |
[5] |
R. N. Bergman, The minimal model of glucose regulation: A biography, 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.
doi: 10.1007/978-1-4419-9019-8_1. |
[6] |
R. N. Bergman, Minimal model: Perspective from 2005, Horm Res, 64 (2005), 8-15.
doi: 10.1159/000089312. |
[7] |
R. N. Bergman, Y. Z. Ider, C. R. Bowden and C. Cobelli, Quantitative estimation of insulin sensitivity, Am J Physiol, 236 (1979), E667-E677. |
[8] |
R. N. Bergman, L. S. Phillips and C. Cobelli, Physiologic evaluation of factors controlling glucose tolerance in man: measurement of insulin sensitivity and $\beta$-cell glucose sensititivy from the response to intravenous glucose, J Clin Invest, 68 (1981), 1456-1467.
doi: 10.1172/JCI110398. |
[9] |
P. J. Bingley, P. Colman, G. S. Eisenbarth, R. A. Jackson, D. K. McCulloch, W. J. Riley and E. A. Gale, Standardization of IVGTT to predict IDDM, Diabetes Care, 15 (1992), 1313-1316.
doi: 10.2337/diacare.15.10.1313. |
[10] |
V. Biourge, R. W. Nelson, E. Feldman, N. H. Willits, J. G. Morris and Q. R. Roger, Effect of weight gain and subsequent weight loss on glucose tolerance and insulin response in healthy cats, J. Vet Intern Med., 11 (1997), 86-91.
doi: 10.1111/j.1939-1676.1997.tb00078.x. |
[11] |
Z. T. Bloomgarden, Approaches to treatment of type 2 diabetes, Diabetes Care, 31 (2008), 1697-1703.
doi: 10.2337/dc08-zb08. |
[12] |
E. Bonora and J. Tuomilehto, The pros and cons of diagnosing diabetes with A1C, Diabetes Care, 34 (2011), S184-S190.
doi: 10.2337/dc11-s216. |
[13] |
R. Boston, D. Stefanovski, P. Moate, O. Linares and P. Greif, Cornerstones to shape modeling for the 21st Century: Introducing the AKA-Glucose project, 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.
doi: 10.1007/978-1-4419-9019-8. |
[14] |
R. C. Boston, D. Stefanovski, P. J. Moate, A. E. Sumner, R. M. Watanabe and R. N. Bergman, MINMOD Millennium: A computer program to calculate glucose effectiveness and insulin sensitivity from the frequently sampled intravenous glucose tolerance test, Diabetes technology & therapeutics, 5 (2003), 1003-1015. |
[15] |
A. Boutayeb and A. Chetouani, A critical review of mathematical models and data used in diabetology, BioMedical Engineering OnLine, 5 (2006), p43.
doi: 10.1186/1475-925X-5-43. |
[16] |
A. Caumo, R. N. Bergman and C. Cobelli, Insulin sensitivity from meal tolerance tests in normal subjects: A minimal model index, J Clin Endocrinol Metab, 85 (2000), 4396-4402.
doi: 10.1210/jcem.85.11.6982. |
[17] |
Centers for Disease Control and Prevention, National diabetes fact sheet: National estimates and general, information in diabetes and prediabetes in the United States, 2011. |
[18] |
H. P. Chase, D. D. Cuthbertson, L. M. Dolan, F. Kaufman, J. P. Krischer, D. A. Schatz, N. H. White, D. M. Wilson and J. Wolfsdorf, First-phase insulin release during the intravenous glucose tolerance test as a risk factor for type 1 diabetes, J Pediatr, 138 (2001), 244-249.
doi: 10.1067/mpd.2001.111274. |
[19] |
Y. J. Cheng, E. W. Gregg, L. S. Geiss, G. Imperatore, D. E. Williams, X. Zhang, A. L. Albright, C. C. Cowie, R. Klein and J. B. Saaddine, Association of A1C and fasting plasma glucose levels with diabetic retinopathy prevalence in the U.S. population: Implications for diabetes diagnostic thresholds, Diabetes Care, 32 (2009), 2027-2032.
doi: 10.2337/dc09-0440. |
[20] |
S. Colagiuri, C. M. Lee, T. Y. Wong, B. Balkau, J. E. Shaw, K. Borch-Johnsen and D.-C. W. Group, Glycemic thresholds for diabetes-specific retinopathy: Implications for diagnostic criteria for diabetes, Diabetes Care, 34 (2011), 145-150.
doi: 10.2337/dc10-1206. |
[21] |
A. De Gaetano and O. Arino, Mathematical modeling of the intravenous glucose tolerance test, J Math Bio, 40 (2000), 136-168.
doi: 10.1007/s002850050007. |
[22] |
W. S. Eldin, M. Emara and A. Shoker, Prediabetes: A must to recognise disease state, Int J Clin Pract, 62 (2008), 642-648.
doi: 10.1111/j.1742-1241.2008.01705.x. |
[23] |
A. Festa, K. Williams, A. J. Hanley and S. M. Haffner, Beta-cell dysfunction in subjects with impaired glucose tolerance and early type 2 diabetes: comparison of surrogate markers with first-phase insulin secretion from an intravenous glucose tolerance test, Diabetes, 57 (2008), 1638-1644. |
[24] |
R. G. Hahn, S. Ljunggren, F. Larsen and T. Nyström, A simple intravenous glucose tolerance test for assessment of insulin sensitivity, Theor Biol Med Model, 8 (2011), p12.
doi: 10.1186/1742-4682-8-12. |
[25] |
J. Li, Y. Kuang and B. Li, Analysis of IVGTT glucose-insulin interaction models with time delay, Discrete and Continuous Dynamical Systems - Series B, 1 (2001), 103-124.
doi: 10.3934/dcdsb.2001.1.103. |
[26] |
M. A. Marini, E. Succurro, S. Frontoni, S. Mastroianni, F. Arturi, A. Sciacqua, R. Lauro, M. L. Hribal, F. Perticone and G. Sesti, Insulin sensitivity, beta-cell function, and incretin effect in individuals with elevated 1-hour postload plasma glucose levels, Diabetes Care, 35 (2012), 868-872. |
[27] |
R. Muniyappa, S. Lee, H. Chen and M. J. Quon, Current approaches for assessing insulin sensitivity and resistance in vivo: Advantages, limitations, and appropriate usage, Am J Physiol Endocrinol Metab, 294 (2008), E15-E26.
doi: 10.1152/ajpendo.00645.2007. |
[28] |
D. M. Nathan, M. B. Davidson, R. A. DeFronzo, R. J. Heine, R. R. Henry, R. Pratley, B. Zinman and American Diabetes Association, Impaired fasting glucose and impaired glucose tolerance: Implications for care, Diabetes Care, 30 (2007), 753-759.
doi: 10.2337/dc07-9920. |
[29] |
A. Nittala, S. Ghosh, D. Stefanovski, R. Bergman and X. Wang, Dimensional analysis of MINMOD leads to definition of the disposition index of glucose regulation and improved simulation algorithm, BioMedical Engineering OnLine, 5 (2006), 44-57. |
[30] |
T. Nozaki, H. Tamai, S. Matsubayashi, G. Komaki, N. Kobayashi and T. Nakagawa, Insulin response to intravenous glucose in patients with anorexia nervosa showing low insulin response to oral glucose, J Clin Endocrinol Metab, 79 (1994), 217-222. |
[31] |
G. Pacini and R. N. Bergman, MINMOD: A computer program to calculate insulin sensitivity and pancreatic responsivity from the frequently sampled intravenous glucose tolerance test, Comput Meth Prog Bio, 23 (1986), 113-122.
doi: 10.1016/0169-2607(86)90106-9. |
[32] |
S. Panunzi and A. DeGaetano, Pitfalls in model identification: Examples from glucose-insulin modelling, in Data-driven Modeling for Diabetes (eds. V. Marmarelis and G. Mitsis), Lecture Notes in Bioengineering, Springer Berlin Heidelberg, 2014, 117-129.
doi: 10.1007/978-3-642-54464-4_5. |
[33] |
M. Stumvoll, B. J. Goldstein and T. W. van Haeften, Type 2 diabetes: Principles of pathogenesis and therapy, Lancet, 365 (2005), 1333-1346.
doi: 10.1016/S0140-6736(05)61032-X. |
[34] |
N. van Riel, Eindhoven University of Technology, Department of Biomedical Engineering, Department of Electrical Engineering, BIOMIM & Control Systems, 1-21. |
[35] |
N. van Riel, GLUC_MM_MLE2012 Maximum Likelihood Estimation of minimal model of glucose kinetics, http://bmi.bmt.tue.nl/sysbio/parameter_estimation/gluc_mm_mle2012.m, 2012, Accessed: 2015-02-24. |
[36] |
L. Zhang, G. Krzentowski, A. Albert and P. J. Lefebvre, Risk of developing retinopathy in Diabetes Control and Complications Trial type 1 diabetic patients with good or poor metabolic control, Diabetes Care, 24 (2001), 1275-1279.
doi: 10.2337/diacare.24.7.1275. |
show all references
References:
[1] |
I. Ajmera, M. Swat, C. Laibe, N. Le Novère and V. Chelliah, The impact of mathematical modeling on the understanding of diabetes and related complications, CPT: Pharmacometrics & Systems Pharmacology, 2 (2013), 1-14.
doi: 10.1038/psp.2013.30. |
[2] |
American Diabetes Association, Standards of medical care in diabetes-2014, Diabetes Care, 37 (2014), S14-S80. |
[3] |
E. Bartoli, G. P. Fra and G. P. Carnevale Schianca, The oral glucose tolerance test (OGTT) revisited, Eur J Intern Med, 22 (2011), 8-12.
doi: 10.1016/j.ejim.2010.07.008. |
[4] |
R. N. Bergman, Lilly lecture 1989. Toward physiological understanding of glucose tolerance. Minimal-model approach, Diabetes, 38 (1989), 1512-1527.
doi: 10.2337/diabetes.38.12.1512. |
[5] |
R. N. Bergman, The minimal model of glucose regulation: A biography, 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.
doi: 10.1007/978-1-4419-9019-8_1. |
[6] |
R. N. Bergman, Minimal model: Perspective from 2005, Horm Res, 64 (2005), 8-15.
doi: 10.1159/000089312. |
[7] |
R. N. Bergman, Y. Z. Ider, C. R. Bowden and C. Cobelli, Quantitative estimation of insulin sensitivity, Am J Physiol, 236 (1979), E667-E677. |
[8] |
R. N. Bergman, L. S. Phillips and C. Cobelli, Physiologic evaluation of factors controlling glucose tolerance in man: measurement of insulin sensitivity and $\beta$-cell glucose sensititivy from the response to intravenous glucose, J Clin Invest, 68 (1981), 1456-1467.
doi: 10.1172/JCI110398. |
[9] |
P. J. Bingley, P. Colman, G. S. Eisenbarth, R. A. Jackson, D. K. McCulloch, W. J. Riley and E. A. Gale, Standardization of IVGTT to predict IDDM, Diabetes Care, 15 (1992), 1313-1316.
doi: 10.2337/diacare.15.10.1313. |
[10] |
V. Biourge, R. W. Nelson, E. Feldman, N. H. Willits, J. G. Morris and Q. R. Roger, Effect of weight gain and subsequent weight loss on glucose tolerance and insulin response in healthy cats, J. Vet Intern Med., 11 (1997), 86-91.
doi: 10.1111/j.1939-1676.1997.tb00078.x. |
[11] |
Z. T. Bloomgarden, Approaches to treatment of type 2 diabetes, Diabetes Care, 31 (2008), 1697-1703.
doi: 10.2337/dc08-zb08. |
[12] |
E. Bonora and J. Tuomilehto, The pros and cons of diagnosing diabetes with A1C, Diabetes Care, 34 (2011), S184-S190.
doi: 10.2337/dc11-s216. |
[13] |
R. Boston, D. Stefanovski, P. Moate, O. Linares and P. Greif, Cornerstones to shape modeling for the 21st Century: Introducing the AKA-Glucose project, 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.
doi: 10.1007/978-1-4419-9019-8. |
[14] |
R. C. Boston, D. Stefanovski, P. J. Moate, A. E. Sumner, R. M. Watanabe and R. N. Bergman, MINMOD Millennium: A computer program to calculate glucose effectiveness and insulin sensitivity from the frequently sampled intravenous glucose tolerance test, Diabetes technology & therapeutics, 5 (2003), 1003-1015. |
[15] |
A. Boutayeb and A. Chetouani, A critical review of mathematical models and data used in diabetology, BioMedical Engineering OnLine, 5 (2006), p43.
doi: 10.1186/1475-925X-5-43. |
[16] |
A. Caumo, R. N. Bergman and C. Cobelli, Insulin sensitivity from meal tolerance tests in normal subjects: A minimal model index, J Clin Endocrinol Metab, 85 (2000), 4396-4402.
doi: 10.1210/jcem.85.11.6982. |
[17] |
Centers for Disease Control and Prevention, National diabetes fact sheet: National estimates and general, information in diabetes and prediabetes in the United States, 2011. |
[18] |
H. P. Chase, D. D. Cuthbertson, L. M. Dolan, F. Kaufman, J. P. Krischer, D. A. Schatz, N. H. White, D. M. Wilson and J. Wolfsdorf, First-phase insulin release during the intravenous glucose tolerance test as a risk factor for type 1 diabetes, J Pediatr, 138 (2001), 244-249.
doi: 10.1067/mpd.2001.111274. |
[19] |
Y. J. Cheng, E. W. Gregg, L. S. Geiss, G. Imperatore, D. E. Williams, X. Zhang, A. L. Albright, C. C. Cowie, R. Klein and J. B. Saaddine, Association of A1C and fasting plasma glucose levels with diabetic retinopathy prevalence in the U.S. population: Implications for diabetes diagnostic thresholds, Diabetes Care, 32 (2009), 2027-2032.
doi: 10.2337/dc09-0440. |
[20] |
S. Colagiuri, C. M. Lee, T. Y. Wong, B. Balkau, J. E. Shaw, K. Borch-Johnsen and D.-C. W. Group, Glycemic thresholds for diabetes-specific retinopathy: Implications for diagnostic criteria for diabetes, Diabetes Care, 34 (2011), 145-150.
doi: 10.2337/dc10-1206. |
[21] |
A. De Gaetano and O. Arino, Mathematical modeling of the intravenous glucose tolerance test, J Math Bio, 40 (2000), 136-168.
doi: 10.1007/s002850050007. |
[22] |
W. S. Eldin, M. Emara and A. Shoker, Prediabetes: A must to recognise disease state, Int J Clin Pract, 62 (2008), 642-648.
doi: 10.1111/j.1742-1241.2008.01705.x. |
[23] |
A. Festa, K. Williams, A. J. Hanley and S. M. Haffner, Beta-cell dysfunction in subjects with impaired glucose tolerance and early type 2 diabetes: comparison of surrogate markers with first-phase insulin secretion from an intravenous glucose tolerance test, Diabetes, 57 (2008), 1638-1644. |
[24] |
R. G. Hahn, S. Ljunggren, F. Larsen and T. Nyström, A simple intravenous glucose tolerance test for assessment of insulin sensitivity, Theor Biol Med Model, 8 (2011), p12.
doi: 10.1186/1742-4682-8-12. |
[25] |
J. Li, Y. Kuang and B. Li, Analysis of IVGTT glucose-insulin interaction models with time delay, Discrete and Continuous Dynamical Systems - Series B, 1 (2001), 103-124.
doi: 10.3934/dcdsb.2001.1.103. |
[26] |
M. A. Marini, E. Succurro, S. Frontoni, S. Mastroianni, F. Arturi, A. Sciacqua, R. Lauro, M. L. Hribal, F. Perticone and G. Sesti, Insulin sensitivity, beta-cell function, and incretin effect in individuals with elevated 1-hour postload plasma glucose levels, Diabetes Care, 35 (2012), 868-872. |
[27] |
R. Muniyappa, S. Lee, H. Chen and M. J. Quon, Current approaches for assessing insulin sensitivity and resistance in vivo: Advantages, limitations, and appropriate usage, Am J Physiol Endocrinol Metab, 294 (2008), E15-E26.
doi: 10.1152/ajpendo.00645.2007. |
[28] |
D. M. Nathan, M. B. Davidson, R. A. DeFronzo, R. J. Heine, R. R. Henry, R. Pratley, B. Zinman and American Diabetes Association, Impaired fasting glucose and impaired glucose tolerance: Implications for care, Diabetes Care, 30 (2007), 753-759.
doi: 10.2337/dc07-9920. |
[29] |
A. Nittala, S. Ghosh, D. Stefanovski, R. Bergman and X. Wang, Dimensional analysis of MINMOD leads to definition of the disposition index of glucose regulation and improved simulation algorithm, BioMedical Engineering OnLine, 5 (2006), 44-57. |
[30] |
T. Nozaki, H. Tamai, S. Matsubayashi, G. Komaki, N. Kobayashi and T. Nakagawa, Insulin response to intravenous glucose in patients with anorexia nervosa showing low insulin response to oral glucose, J Clin Endocrinol Metab, 79 (1994), 217-222. |
[31] |
G. Pacini and R. N. Bergman, MINMOD: A computer program to calculate insulin sensitivity and pancreatic responsivity from the frequently sampled intravenous glucose tolerance test, Comput Meth Prog Bio, 23 (1986), 113-122.
doi: 10.1016/0169-2607(86)90106-9. |
[32] |
S. Panunzi and A. DeGaetano, Pitfalls in model identification: Examples from glucose-insulin modelling, in Data-driven Modeling for Diabetes (eds. V. Marmarelis and G. Mitsis), Lecture Notes in Bioengineering, Springer Berlin Heidelberg, 2014, 117-129.
doi: 10.1007/978-3-642-54464-4_5. |
[33] |
M. Stumvoll, B. J. Goldstein and T. W. van Haeften, Type 2 diabetes: Principles of pathogenesis and therapy, Lancet, 365 (2005), 1333-1346.
doi: 10.1016/S0140-6736(05)61032-X. |
[34] |
N. van Riel, Eindhoven University of Technology, Department of Biomedical Engineering, Department of Electrical Engineering, BIOMIM & Control Systems, 1-21. |
[35] |
N. van Riel, GLUC_MM_MLE2012 Maximum Likelihood Estimation of minimal model of glucose kinetics, http://bmi.bmt.tue.nl/sysbio/parameter_estimation/gluc_mm_mle2012.m, 2012, Accessed: 2015-02-24. |
[36] |
L. Zhang, G. Krzentowski, A. Albert and P. J. Lefebvre, Risk of developing retinopathy in Diabetes Control and Complications Trial type 1 diabetic patients with good or poor metabolic control, Diabetes Care, 24 (2001), 1275-1279.
doi: 10.2337/diacare.24.7.1275. |
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