Cover
Vol. 16 No. 1 (2020)

Published: June 30, 2020

Pages: 1-8

Original Article

A New Model For Endocrine Glucose-Insulin Regulatory System

Abstract

To gain insight into complex biological endocrine glucose-insulin regulatory system where the interactions of components of the metabolic system and time-delay inherent in the biological system give rise to complex dynamics. The modeling has increased interest and importance in physiological research and enhanced the medical treatment protocols. This brief contains a new model using time delay differential equations, which give an accurate result by utilizing two explicit time delays. The bifurcation analysis has been conducted to find the main system parameters bifurcation values and corresponding system behaviors. The results found consistent with the biological experiments results.

References

  1. “International Diabetes Federation (IDF).” [Online]. Available: https://idf.org/. [Accessed: 03-Feb-2020].
  2. A. Mondal, M. Islam, and N. Islam, “Linear feedback- based control of blood glucose in a modified model for glucose-insulin kinetics: A theoretical study,” Int. J. Biomath., vol. 10, no. 4, pp. 1–20, 2017.
  3. B. Topp, K. Promislow, G. Devries, R. M. Miura, and D. T. Finegood, “A model of β-cell mass, insulin, and glucose kinetics: Pathways to diabetes,” J. Theor. Biol., vol. 206, no. 4, pp. 605–619, 2000.
  4. B. Ahren and G. J. Taborsky, “Beta-cell function and insulin secretion,” Ellenberg and Rifkin’s diabetes mellitus. New York, McGraw Hill, pp. 43–65, 2003.
  5. C. Simon and G. Brandenberger, “Ultradian oscillations of insulin secretion in humans,” Diabetes, vol. 51, no. suppl 1, pp. S258–S261, 2002.
  6. J. Sturis, K. S. Polonsky, E. Mosekilde, and E. Van Cauter, “Computer model for mechanisms underlying ultradian oscillations of insulin and glucose,” Am. J. Physiol. - Endocrinol. Metab., vol. 260, no. 5 23-5, 1991.
  7. K. S. Polonsky et al., “Abnormal patterns of insulin secretion in non-insulin-dependent diabetes mellitus,” N. Engl. J. Med., vol. 318, no. 19, pp. 1231–1239, 1988.
  8. E. W. Kraegen, J. D. Young, E. P. George, and L. Lazarus, “Oscillations in blood glucose and insulin after oral glucose,” Horm. Metab. Res., vol. 4, no. 06, pp. 409–413, 1972.
  9. C. Simon, G. Brandenberger, and M. Follenius, “Ultradian oscillations of plasma glucose, insulin, and c peptide in man during continuous enteral nutrition,” J. Clin. Endocrinol. Metab., vol. 64, no. 4, pp. 669–674, 1987.
  10. E. V. E. V. A. N. CAUTER, D. Désir, C. Decoster, F. FERY, and E. O. BALASSE, “Nocturnal decrease in glucose tolerance during constant glucose infusion,” J. Clin. Endocrinol. Metab., vol. 69, no. 3, pp. 604–611, 1989.
  11. I. M. Tolić, E. Mosekilde, and J. Sturis, “Modeling the insulin-glucose feedback system: The significance of pulsatile insulin secretion,” J. Theor. Biol., vol. 207, no. 3, pp. 361–375, 2000.
  12. R. N. Bergman, Y. Z. Ider, C. R. Bowden, and C. Cobelli, “Quantitative estimation of insulin sensitivity,” Am. J. Physiol. Endocrinol. Metab. Gastrointest. Physiol., vol. 5, no. 6, 1979.
  13. R. N. Bergman, “Minimal model: Perspective from 2005,” Horm. Res., vol. 64, no. SUPPL. 3, pp. 8–15, 2005.
  14. K. Engelborghs, V. Lemaire, J. Belair, and D. Roose, “Numerical bifurcation analysis of delay differential equations arising from physiological modeling,” J. Math. Biol., vol. 42, no. 4, pp. 361–385, 2001.
  15. D. L. Bennett and S. A. Gourley, “Asymptotic properties of a delay differential equation model for the interaction of glucose with plasma and interstitial insulin,” Appl. Math. Comput., vol. 151, no. 1, pp. 189–207, 2004.
  16. J. Li, Y. Kuang, and C. C. Mason, “Modeling the glucose-insulin regulatory system and ultradian insulin secretory oscillations with two explicit time delays,” J. Theor. Biol., vol. 242, no. 3, pp. 722–735, 2006.
  17. Z. Wu, C. K. Chui, G. S. Hong, and S. Chang, “Physiological analysis on oscillatory behavior of glucose- insulin regulation by model with delays,” J. Theor. Biol., vol. 280, no. 1, pp. 1–9, 2011.
  18. R. J. Strilka, S. T. Trexler, T. J. Sjulin, and S. B. Armen, “A qualitative numerical study of glucose dynamics in patients with stress hyperglycemia and diabetes receiving intermittent and continuous enteral feeds,” Informatics Med. Unlocked, vol. 10, pp. 108–116, 2018.
  19. A. De Gaetano and O. Arino, “Mathematical modelling of the intravenous glucose tolerance test,” J. Math. Biol., vol. 40, no. 2, pp. 136–168, 2000.