The impact of mathematical modeling on the understanding of diabetes and related complications

CPT: Pharmacometrics and Systems Pharmacology

Volumn 2, Issue 7, 2013, Pages

  Ajmera, I ^a,b   Swat, M ^a   Laibe, C ^a   Novére, N Le ^a,c   Chelliah, V ^a  

^a WELLCOME TRUST SANGER INSTITUTE   (United Kingdom)

^b UNIVERSITY OF NOTTINGHAM   (United Kingdom)

^c BABRAHAM INSTITUTE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

GLUCAGON; GLUCOSE; INSULIN; INSULIN RECEPTOR;

ABSORPTION; BASAL METABOLIC RATE; DIABETES MELLITUS; DISEASE COURSE; ELECTRIC ACTIVITY; ELECTROPHYSIOLOGY; GLUCOSE HOMEOSTASIS; HUMAN; INSULIN DEPENDENT DIABETES MELLITUS; INSULIN RELEASE; INSULIN SENSITIVITY; INTRAVENOUS GLUCOSE TOLERANCE TEST; MACROPHAGE; MATHEMATICAL MODEL; NON INSULIN DEPENDENT DIABETES MELLITUS; NONHUMAN; ORAL GLUCOSE TOLERANCE TEST; OSCILLATION; PANCREAS ISLET BETA CELL; PRIORITY JOURNAL; REVIEW; SIGNAL TRANSDUCTION;

EID: 84881162079     PISSN: None     EISSN: 21638306     Source Type: Journal    
DOI: 10.1038/psp.2013.30     Document Type: Review

References (75)

1. Li, C. et al. BioModels Database: an enhanced, curated and annotated resource for published quantitative kinetic models. BMC Syst. Biol. 4, 92 (2010).
2. Bolie, V.W. Coefficients of normal blood glucose regulation. J. Appl. Physiol. 16, 783-788 (1961).
3. Bergman, R.N., Phillips, L.S. & Cobelli, C. Physiologic evaluation of factors controlling glucose tolerance in man: measurement of insulin sensitivity and beta-cell glucose sensitivity from the response to intravenous glucose. J. Clin. Invest. 68, 1456-1467 (1981). (Pubitemid 12194400)
4. Bergman, R.N., Ider, Y.Z., Bowden, C.R. & Cobelli, C. Quantitative estimation of insulin sensitivity. Am. J. Physiol. 236, E667-E677 (1979). (Pubitemid 9220487)
5. Bergman, R.N. et al. Assessment of insulin sensitivity in vivo: a critical review. Diabetes. Metab. Rev. 5, 411-429 (1989). (Pubitemid 19194684)
6. Cobelli, C., Man, C.D., Sparacino, G., Magni, L., De Nicolao, G. & Kovatchev, B.P. Diabetes: models, signals, and control. IEEE Rev. Biomed. Eng. 2, 54-96 (2009).
7. De Gaetano, A. & Arino, O. Mathematical modelling of the intravenous glucose tolerance test. J. Math. Biol. 40, 136-168 (2000).
8. Silber, H.E., Jauslin, P.M., Frey, N., Gieschke, R., Simonsson, U.S. & Karlsson, M.O. An integrated model for glucose and insulin regulation in healthy volunteers and type 2 diabetic patients following intravenous glucose provocations. J. Clin. Pharmacol. 47, 1159-1171 (2007).
9. Landersdorfer, C.B. & Jusko, W.J. Pharmacokinetic/pharmacodynamic modelling in diabetes mellitus. Clin. Pharmacokinet. 47, 417-448 (2008). (Pubitemid 351861956)
10. Mari, A. Mathematical modeling in glucose metabolism and insulin secretion. Curr. Opin. Clin. Nutr. Metab. Care 5, 495-501 (2002c). (Pubitemid 40684644)
11. Wallace, T.M., Levy, J.C. & Matthews, D.R. Use and abuse of HOMA modeling. Diabetes Care 27, 1487-1495 (2004). (Pubitemid 38680001)
12. Kjems, L.L., Vlund, A. & Madsbad, S. Quantification of beta-cell function during IVGTT in type II and non-diabetic subjects: assessment of insulin secretion by mathematical methods. Diabetologia 44, 1339-1348 (2001). (Pubitemid 33010513)
13. Eaton, R.P., Allen, R.C., Schade, D.S., Erickson, K.M. & Standefer, J. Prehepatic insulin production in man: kinetic analysis using peripheral connecting peptide behavior. J. Clin. Endocrinol. Metab. 51, 520-528 (1980). (Pubitemid 10022835)
14. Pedersen, M.G., Toffolo, G.M. & Cobelli, C. Cellular modeling: insight into oral minimal models of insulin secretion. Am. J. Physiol. Endocrinol. Metab. 298, E597-E601 (2010).
15. Wilinska, M.E. & Hovorka, R. Simulation models for in silico testing of closed-loop glucose controllers in type 1 diabetes. Drug Discov. Today Dis. Mod. 5, 289-298 (2008).
16. Huang, M., Li, J., Song, X. & Guo, H. Modeling impulsive injections of insulin: towards artificial pancreas. SIAM J. Appl. Math. 72, 1524-1548 (2012).
17. Nucci, G. & Cobelli, C. Models of subcutaneous insulin kinetics. A critical review. Comput. Methods Programs Biomed. 62, 249-257 (2000).
18. Li, J. & Johnson, J.D. Mathematical models of subcutaneous injection of insulin analogues: a mini-review. Discrete Continuous Dyn. Syst. Ser. B 12, 401-414 (2009).
19. Balakrishnan, N.P., Rangaiah, G.P. & Samavedham, L. Review and analysis of blood glucose (BG) models for type 1 diabetic patients. Ind. Eng. Chem. Res. 50, 12041-12066 (2011).
20. Hovorka, R. et al. Nonlinear model predictive control of glucose concentration in subjects with type 1 diabetes. Physiol. Meas. 25, 905-920 (2004). (Pubitemid 39121173)
21. Dalla Man, C., Rizza, R.A. & Cobelli, C. Meal simulation model of the glucose-insulin system. IEEE Trans. Biomed. Eng. 54, 1740-1749 (2007). (Pubitemid 47450539)
22. Sorensen, J.T. A Physiologic Model of Glucose Metabolism in Man and Its Use to Design and Assess Improved Insulin Therapies for Diabetes (Massachusetts Institute of Technology, 1985).
23. Topp, B., Promislow, K., deVries, G., Miura, R.M. & Finegood, D.T. A model of beta-cell mass, insulin, and glucose kinetics: pathways to diabetes. J. Theor. Biol. 206, 605-619 (2000).
24. De Gaetano, A. et al. Mathematical models of diabetes progression. Am. J. Physiol. Endocrinol. Metab. 295, E1462-E1479 (2008).
25. Waugh, H.V. & Sherratt, J.A. Macrophage dynamics in diabetic wound dealing. Bull. Math. Biol. 68, 197-207 (2006). (Pubitemid 44195592)
26. Waugh, H.V. & Sherratt, J.A. Modeling the effects of treating diabetic wounds with engineered skin substitutes. Wound Repair Regen. 15, 556-565 (2007). (Pubitemid 47087655)
27. Al-Hashmi, S., Ekanayake, M. & Martin, C. Type II diabetes and obesity: a control theoretic model. In Emergent Problems in Nonlinear Systems and Control Vol. 393 (eds. Ghosh, B., Martin, C. and Zhou, Y.) 1-19 (Springer, Berlin/Heidelberg, 2009).
28. Toghaw, P., Matone, A., Lenbury, Y. & De Gaetano, A. Bariatric surgery and T2DM improvement mechanisms: a mathematical model. Theor. Biol. Med. Model. 9, 16 (2012).
29. Tiran, J., Galle, K.R. & Porte, D. Jr. A simulation model of extracellular glucose distribution in the human body. Ann. Biomed. Eng. 3, 34-46 (1975).
30. Guyton, J.R. et al. A model of glucose-insulin homeostasis in man that incorporates the heterogeneous fast pool theory of pancreatic insulin release. Diabetes 27, 1027-1042 (1978). (Pubitemid 9050233)
31. Alvehag, K. & Martin, C. The feedback control of glucose: on the road to type II diabetes. In Decision and Control 45th IEEE Conference, 2006, 685-690. (Pubitemid 351283312)
32. König, M., Bulik, S. & Holzhütter, H.G. Quantifying the contribution of the liver to glucose homeostasis: a detailed kinetic model of human hepatic glucose metabolism. PLoS Comput. Biol. 8, e1002577 (2012a).
33. Koenig, M. & Holzhuetter, H.G. Kinetic modeling of human hepatic glucose metabolism in T2DM predicts higher risk of hypoglycemic events in rigorous insulin therapy. J. Biol. Chem. (2012b).
34. Gaohua, L. & Kimura, H. A mathematical model of brain glucose homeostasis. Theor. Biol. Med. Model. 6, 26 (2009).
35. Grodsky, G.M., Curry, D., Landahl, H. & Bennett, L. [Further studies on the dynamic aspects of insulin release in vitro with evidence for a two-compartmental storage system]. Acta Diabetol. Lat. 6(suppl. 1), 554-578 (1969).
36. Grodsky, G.M. A threshold distribution hypothesis for packet storage of insulin and its mathematical modeling. J. Clin. Invest. 51, 2047-2059 (1972).
37. Sturis, J., Polonsky, K.S., Mosekilde, E. & Van Cauter, E. Computer model for mechanisms underlying ultradian oscillations of insulin and glucose. Am. J. Physiol. 260, E801-E809 (1991).
38. Tolic, I.M., Mosekilde, E. & Sturis, J. Modeling the insulin-glucose feedback system: the significance of pulsatile insulin secretion. J. Theor. Biol. 207, 361-375 (2000).
39. Keener, J.P. Diffusion induced oscillatory insulin secretion. Bull. Math. Biol. 63, 625-641 (2001). (Pubitemid 32721006)
40. Farhy, L.S. & McCall, A.L. Pancreatic network control of glucagon secretion and counterregulation. Meth. Enzymol. 467, 547-581 (2009).
41. Farhy, L.S. & McCall, A.L. Optimizing reduction in basal hyperglucagonaemia to repair defective glucagon counterregulation in insulin deficiency. Diabetes. Obes. Metab. 13(suppl. 1), 133-143 (2011).
42. Freiesleben De Blasio, B., Bak, P., Pociot, F., Karlsen, A.E. & Nerup, J. Onset of type 1 diabetes: a dynamical instability. Diabetes 48, 1677-1685 (1999). (Pubitemid 29415183)
43. Marée, A.F., Kublik, R., Finegood, D.T. & Edelstein-Keshet, L. Modelling the onset of Type 1 diabetes: can impaired macrophage phagocytosis make the difference between health and disease? Philos. Trans. A. Math. Phys. Eng. Sci. 364, 1267-1282 (2006). (Pubitemid 43706609)
44. Bertram, R. & Sherman, A. Dynamical complexity and temporal plasticity in pancreatic beta-cells. J. Biosci. 25, 197-209 (2000).
45. Bertram, R., Sherman, A. & Satin, L.S. Metabolic and electrical oscillations: partners in controlling pulsatile insulin secretion. Am. J. Physiol. Endocrinol. Metab. 293, E890-E900 (2007). (Pubitemid 47535819)
46. Pedersen, M.G. Contributions of mathematical modeling of beta cells to the understanding of beta-cell oscillations and insulin secretion. J. Diabetes Sci. Technol. 3, 12-20 (2009).
47. Han, K., Kang, H., Kim, J. & Choi, M. Mathematical models for insulin secretion in pancreatic b-cells. Islets 4, 94-107 (2012).
48. Chay, T.R. & Keizer, J. Theory of the effect of extracellular potassium on oscillations in the pancreatic beta-cell. Biophys. J. 48, 815-827 (1985). (Pubitemid 16234579)
49. Sherman, A., Rinzel, J. & Keizer, J. Emergence of organized bursting in clusters of pancreatic beta-cells by channel sharing. Biophys. J. 54, 411-425 (1988).
50. De Vries, G. & Sherman, A. Channel sharing in pancreatic beta cells revisited: enhancement of emergent bursting by noise. J. Theor. Biol. 207, 513-530 (2000).
51. Magnus, G. & Keizer, J. Minimal model of beta-cell mitochondrial Ca2+ handling. Am. J. Physiol. 273, C717-C733 (1997).
52. Fridlyand, L.E. & Philipson, L.H. Glucose sensing in the pancreatic beta cell: a computational systems analysis. Theor. Biol. Med. Model. 7, 15 (2010).
53. Bertram, R. et al. A role for calcium release-activated current (CRAC) in cholinergic modulation of electrical activity in pancreatic beta-cells. Biophys. J. 68, 2323-2332 (1995).
54. Mears, D., Sheppard, N.F. Jr, Atwater, I., Rojas, E., Bertram, R. & Sherman, A. Evidence that calcium release-activated current mediates the biphasic electrical activity of mouse pancreatic beta-cells. J. Membr. Biol. 155, 47-59 (1997). (Pubitemid 27046531)
55. Chay, T.R. Effects of extracellular calcium on electrical bursting and intracellular and luminal calcium oscillations in insulin secreting pancreatic beta-cells. Biophys. J. 73, 1673-1688 (1997). (Pubitemid 27360756)
56. Bertram, R., Previte, J., Sherman, A., Kinard, T.A. & Satin, L.S. The phantom burster model for pancreatic beta-cells. Biophys. J. 79, 2880-2892 (2000).
57. Bertram, R., Satin, L., Zhang, M., Smolen, P. & Sherman, A. Calcium and glycolysis mediate multiple bursting modes in pancreatic islets. Biophys. J. 87, 3074-3087 (2004b). (Pubitemid 40468566)
58. Westermark, P.O. & Lansner, A. A model of phosphofructokinase and glycolytic oscillations in the pancreatic beta-cell. Biophys. J. 85, 126-139 (2003). (Pubitemid 36753622)
59. Jiang, N., Cox, R.D. & Hancock, J.M. A kinetic core model of the glucose-stimulated insulin secretion network of pancreatic beta cells. Mamm. Genome 18, 508-520 (2007). (Pubitemid 47360412)
60. Quon, M.J. & Campfield, L.A. A mathematical model and computer simulation study of insulin receptor regulation. J. Theor. Biol. 150, 59-72 (1991a).
61. Wanant, S. & Quon, M.J. Insulin receptor binding kinetics: modeling and simulation studies. J. Theor. Biol. 205, 355-364 (2000).
62. Koschorreck, M. & Gilles, E.D. Mathematical modeling and analysis of insulin clearance in vivo. BMC Syst. Biol. 2, 43 (2008).
63. Kiselyov, V.V., Versteyhe, S., Gauguin, L. & De Meyts, P. Harmonic oscillator model of the insulin and IGF1 receptors' allosteric binding and activation. Mol. Syst. Biol. 5, 243 (2009).
64. Brännmark, C., Palmér, R., Glad, S.T., Cedersund, G. & Strålfors, P. Mass and information feedbacks through receptor endocytosis govern insulin signaling as revealed using a parameter-free modeling framework. J. Biol. Chem. 285, 20171-20179 (2010).
65. Sedaghat, A.R., Sherman, A. & Quon, M.J. A mathematical model of metabolic insulin signaling pathways. Am. J. Physiol. Endocrinol. Metab. 283, E1084-E1101 (2002). (Pubitemid 35216969)
66. Liu, W., Hsin, C. & Tang, F. A molecular mathematical model of glucose mobilization and uptake. Math. Biosci. 221, 121-129 (2009).
67. Cedersund, G. & Strålfors, P. Putting the pieces together in diabetes research: towards a hierarchical model of whole-body glucose homeostasis. Eur. J. Pharm. Sci. 36, 91-104 (2009).
68. Nyman, E. et al. A hierarchical whole-body modeling approach elucidates the link between in Vitro insulin signaling and in Vivo glucose homeostasis. J. Biol. Chem. 286, 26028-26041 (2011).
69. Hetherington, J. et al. A composite computational model of liver glucose homeostasis. I. Building the composite model. J. R. Soc. Interface 9, 689-700 (2012).
70. Kansal, A.R. Modeling approaches to type 2 diabetes. Diabetes Technol. Ther. 6, 39-47 (2004). (Pubitemid 38233744)
71. Makroglou, A. Mathematical models and software tools for the glucose-insulin regulatory system and diabetes: an overview. Appl. Numer. Math. 56, 559-573 (2006).
72. Boutayeb, A. & Chetouani, A. A critical review of mathematical models and data used in diabetology. Biomed. Eng. Online 5, 43 (2006).
73. Pattaranit, R. & van den Berg, H.A. Mathematical models of energy homeostasis. J. R. Soc. Interface 5, 1119-1135 (2008).
74. Smith, J.M. et al. Mathematical modeling of glucose homeostasis and its relationship with energy balance and body fat. Obesity (Silver Spring). 17, 632-639 (2009).
75. Nyman, E., Cedersund, G. & Strålfors, P. Insulin signaling-mathematical modeling comes of age. Trends Endocrinol. Metab. 23, 107-115 (2012b).