Modeling the glucose-insulin regulatory system and ultradian insulin secretory oscillations with two explicit time delays

Journal of Theoretical Biology

Volumn 242, Issue 3, 2006, Pages 722-735

  Li, Jiaxu ^a   Kuang, Yang ^a   Mason, Clinton C ^a  

^a ARIZONA STATE UNIVERSITY   (United States)

Author keywords

Delay differential equation model; Glucose insulin regulatory system; Insulin secretion; Time delay; Ultradian oscillation

Indexed keywords

GLUCOSE; INSULIN;

GLUCOSE; HORMONE; NUMERICAL MODEL; SECRETION; SIMULATION;

ARTICLE; ENTERIC FEEDING; GLUCONEOGENESIS; GLUCOSE INFUSION; GLUCOSE METABOLISM; GLUCOSE UTILIZATION; INSULIN CLEARANCE; INSULIN DEGRADATION; INSULIN METABOLISM; INSULIN RELEASE; INSULIN SYNTHESIS; MATHEMATICAL MODEL; NEGATIVE FEEDBACK; OSCILLATION; PRIORITY JOURNAL; REGULATORY MECHANISM; SIMULATION; ULTRADIAN RHYTHM;

ACTIVITY CYCLES; COMPUTER SIMULATION; DIABETES MELLITUS, TYPE 2; ENTERAL NUTRITION; GLUCOSE; HUMANS; INSULIN; ISLETS OF LANGERHANS; LIVER; MODELS, BIOLOGICAL; SECRETORY RATE; TIME FACTORS;

EID: 33747876336     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2006.04.002     Document Type: Article

References (25)

1. Ahren, B., Taborsky Jr., G.J., 2002. B-cell function and insulin secretion. In: Porte, D., Sherwin, R.S., Baron, A. (Eds.), Ellenberg and Rifkin's Diabetes Mellitus, sixth ed. McGraw-Hill Professional, New York, pp. 43-65 (Chapter 4).
2. Bennett D.L., and Gourley S.A. Asymptotic properties of a delay differential equation model for the interaction of glucose with the plasma and interstitial insulin. Appl. Math. Comput. 151 (2004) 189-207
3. Bergman R.N. Pathogenesis and prediction of diabetes mellitus: lessons from integrative physiology. Irving L. Schwartz Lecture, Mount Sinai J. Med. 60 (2002) 280-290
4. Bergman R.N., Finegood D.T., and Ader M. Assessment of insulin sensitivity in vivo. Endocr. Rev. 6 (1985) 45-86
5. Bergman R.N., Finegood D.T., and Kahn S.E. The evolution of beta-cell dysfunction and insulin resistance in type 2 diabetes. Eur. J. Clin. Invest. 32 Suppl. 3 (2002) 35-45
6. Bolie V.W. Coefficients of normal blood glucose regulation. J. Appl. Physiol. 16 (1961) 783-788
7. Cherrington A.D., Sindelar D., Edgerton D., Steiner K., and McGuinness O.P. Physiological consequences of phasic insulin release in the normal animal. Diabetes 51 Suppl. 1 (2002) S103-S108
8. DeGaetano A., and Arino O. Mathematical modeling of the intravenous glucose tolerance test. J. Math. Biol. 40 (2000) 136-168
9. Derouich M., and Boutayeb A. The effect of physical exercise on the dynamics of glucose and insulin. J. Biomechanics 35 (2002) 911-917
10. Duckworth W.C., Bennett R.G., and Hamel F.G. Insulin degradation: progress and potential. Endocr. Rev. 19 (1998) 608-624
11. Engelborghs K., Lemaire V., Belair J., and Roose D. Numerical bifurcation analysis of delay differential equations arising from physiological modeling. J. Math. Biol. 42 (2001) 361-385
12. Gilon P., Ravier M.A., Jonas J.C., and Henquin J.C. Control mechanisms of the oscillations of insulin secretion in vitro and in vivo. Diabetes 51 Suppl. 1 (2002) S144-S151
13. Keener J., and Sneyd J. Mathematical Physiology (1998), Springer, New York
14. Luzi L., and DeFrenzo R.A. Effect of loss of first-phase insulin secretion on hepatic glucose production and tissue glucose disposal in humans. Am. J. Physiol. 257 (1989) E241-E246
15. Li J., Kuang Y., and Li B. Analysis of IVGTT glucose-insulin interaction models with time delay. Discrete Contin. Dyn. Syst. Ser. B 1 1 (2001) 103-124
16. Makroglou, A., Li, J., Kuang, Y., 2006. Mathematical models and software tools for the glucose-insulin regulatory system and diabetes: an overview. Appl. Numer. Math. 56, 559-573.
17. Mari A. Mathematical modeling in glucose metabolism and insulin secretion. Curr. Opin. Clin. Nutr. Metab. Care 5 (2002) 495-501
18. Mukhopadhyay A., DeGaetano A., and Arino O. Modeling the intra-venous glucose tolerance test: a global study for a single-distributed-delay model. Discrete Contin. Dyn. Syst. Ser. B 4 2 (2004) 407-417
19. Pørksen N., Hollingdal M., Juhl C., Butler P., Veldhuis J.D., and Schmitz O. Pulsatile insulin secretion: detection, regulation, and role in diabetes. Diabetes 51 Suppl. 1 (2002) S245-S254
20. Prager R., Wallace P., and Olefsky J.M. In vivo kinetics of insulin action on peripheral glucose disposal and hepatic glucose output in normal and obese subjects. J. Clin. Invest. 78 (1986) 472-481
21. Shampine L.F., and Thompson S. Solving DDEs in MATLAB. Appl. Numer. Math. 37 (2001) 441-458. http://www.radford.edu/thompson 〈http://www.radford.edu/∼thompson〉
22. Simon C., and Brandenberger G. Ultradian oscillations of insulin secretion in humans. Diabetes 51 Suppl. 1 (2002) S258-S261
23. Sturis J., Polonsky K.S., Mosekilde E., and Van Cauter E. Computer model for mechanisms underlying ultradian oscillations of insulin and glucose. Am. J. Physiol. 260 (1991) E801-E809
24. Tolic I.M., Mosekilde E., and Sturis J. Modeling the insulin-glucose feedback system: the significance of pulsatile insulin secretion. J. Theor. Biol. 207 (2000) 361-375
25. Topp B., Promislow K., De Vries G., Miura R.M., and Finegood D.T. A model of β-cell mass, insulin, and glucose kinetics: pathways to diabetes. J. Theor. Biol. 206 (2000) 605-619