The mathematical model of glucose dynamics in blood over 24-hour period

: pp.5-10
Volodymyr Hnatiuk National Pedagogical University of Ternopil
Ternopil National Economic University
Ternopil National Economic University

The article is concerned with the problem of controlling the glucose concentration in blood with minimal application of invasive measuring. The mathematical model of digestion of recepted glucose, which depends on the volume of consumed carbo­hydrates (instantaneous, fast, slow) has been developed. The mathematical model is built for long-term observa­tions with the use of specially organized expe­riments. The blood glucose level depends on the intensity of the effect of insulin, that is why the model of insulin dynamics has been developed either. The accu­mulated insulin is presented as combination of the insulin produced by the body and the insulin coming from injections. The Levenberg-Marquardt method is used to identify the blood glucose dynamics.

  1. C.Cobelli, C. Man, D. Raimondo, and R. Rizza, “GIM, simulation software of meal glucose–insulin model”, J Diabetes Sci Technol, vol. 1, no. 3, pp. 323-330, 2007.
  2.  T. Callegari, A. Caumo, and C. Cobelli, “Bayesian two-compartment and classic single-compartment minimal models: compa­rison on insulin modified IVGTT and effect of experiment reduction”, IEEE Trans. Biomed. Eng. vol. 50, no.12, pp. 1301–1309, 2003.
  3. B. Kovatchev, M. Breton, C. Man, and C. Cobelli, “In Silico Preclinical Trials: A Proof of Concept in Closed-Loop Control of Type 1 Diabetes”, J Diabe­tes Sci Technol, vol. 3, no. 1, pp. 44-55, 2009.
  4. R. Hovorka, M. Wilinska, and L. Chassin, “Evalua­tion of glucose controllers in virtual environment: methodology and sample application”, Artificial In­telligence in Medicine, vol. 32, no. 3, pp. 171-181, 2004.
  5. C. Man, R. Rizza, and C. Cobelli, “Meal simulation model of the glucose-insulin system”, IEEE Trans. Biomed. Eng. vol. 54, no. 10, pp. 1740–1749, 2007.
  6. P. Bergman, et al, “A comparison between the mini­mal model and the glucose clamp in the assess­ment of insulin sensitivity across the spectrum of glucose tolerance”, Diabetes, no.43, pp. 1114-1121, 2004.
  7. M.D. Breton, “Physical activity - the major unac­counted impediment to closed loop control”, J Dia­betes Sci Technol, vol.2, no. 1, pp. 169-174, 2008.
  8. G. Marchetti, M. Barolo, L.Jovanovic, H, Zisser, and D, Seborg, “A feedforward - feedback glucose control strategy for type 1 diabetes mellitus”, Journal of Process Control, vol.18, no.2, pp. 149-162, 2008.
  9. E. Renard, J. Place, M. Cantwell, H. Chevassus, and C. Palerm, “Closed-loop insulin delivery using a subcutaneous glucose sensor and intraperitoneal in­sulin delivery”, Diabetes Care, vol.33, no.1, pp. 121-127, 2010.
  10. F. El-Khatib, J. Jianq, and E. Damiano, “Adaptive closed-loop control provides blood-glucose regu­lation using dual sub­cutaneous insulin and glucagon infusion in diabetic swine”, J Diabetes Sci Technol, vol.2, no.1, pp. 181-192, 2007.
  11. О.V.Shvets, “Diet in diabetes mellitus”, Mizhna­rodnyi endokrynologichnyi zhurnal, vol.50, no.2, pp. 65-74, 2013. (Ukrainian)
  12. Yu. Chаikіvskа and R. Pаsіchnyk, “The mathema­tical model of the glucose dynamics in the digestion process”, Informatyka ta matematychni metody v modeliuvanni, vol.4, no.3, pp. 272-277, 2014. (Ukrainian)