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Biophysics

, Volume 62, Issue 5, pp 842–847 | Cite as

Theoretical evaluation of the parameters of glucose metabolism on the basis of continuous glycemia monitoring data using mathematical modeling

  • A. N. Sveshnikova
  • M. A. Panteleev
  • A. V. Dreval
  • T. P. Shestakova
  • O. S. Medvedev
  • O. A. Dreval
Biophysics of Complex Systems
  • 30 Downloads

Abstract

The aim of this paper is to construct a mathematical model that takes the main physiological parameters of blood-glucose regulation into account, in order to identify these parameters for an individual patient according to continuous glucose-monitoring data. The constructed mathematical model consists of six ordinary differential equations that describe the dynamics of changes in glucose concentrations, as well as insulin and anti-insulin factors in the blood. Estimation of the parameters of the equations was performed using an evolutionary programming method. The model predictions were fitted to the continuous glucosemonitoring data. As a result of the identification of the model parameters for two patients with type 1 diabetes mellitus, the estimated insulin secretion was close to zero and the estimated glucose utilization and insulin clearance were increased in comparison with the data for healthy donors. Here, we present a personalized model of the regulation of blood glucose, which can be used to predict the results of continuous glucose monitoring depending on modification of the prescribed glucose-lowering therapy. This approach can significantly reduce the number of iterations of the selection of medical hypoglycemic therapy and therefore increase the effectiveness of treatment according to glucose-monitoring data.

Keywords

mathematical modeling pharmacological modeling type 1 diabetes evolutionary programming continuous glucose monitoring 

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References

  1. 1.
    P. H. van der Graaf and N. Benson, Pharm. Res. 28, 1460 (2011). doi: doi 10.1007/s11095-011-0467-9CrossRefGoogle Scholar
  2. 2.
    I. I. Dedov, Vestn. Ross. Akad. Med. Nauk 67 (1), 7 (2012).CrossRefGoogle Scholar
  3. 3.
    A. Dreval’, Diabetes Mellitus: Diagnosis and Treatment Standards. A Pharmacologocal Guidebook (Litres, 2014) [in Russian].Google Scholar
  4. 4.
    P. Palumbo, S. Ditlevsen, A. Bertuzzi, and A. De Gaetano, Math. Biosci. 244, 69 (2013). doi 10.1016/j.mbs.2013.05.006MathSciNetCrossRefGoogle Scholar
  5. 5.
    M. Danhof, E. C. M. de Lange, O. E. Della Pasqua, et al., Trends Pharmacol. Sci. 29, 186 (2008). doi 10.1016/j.tips.2008.01.007CrossRefGoogle Scholar
  6. 6.
    S. Schaller, S. Willmann, J. Lippert, et al., CPT Pharmacometr. Syst. Pharmacol. 2, e65 (2013). doi 10.1038/psp.2013.40CrossRefGoogle Scholar
  7. 7.
    J. T. Sorensen, A Physiologic Model of Glucose Metabolism in Man and Its Use to Design and Assess Improved Insulin Therapies for Diabetes (1985). http://dspace.mit.edu/handle/1721.1/15234 (accessed April 28, 2016).Google Scholar
  8. 8.
    V. K. Ramanujan, Methods 66, 222 (2014). doi 10.1016/j.ymeth.2013.08.027CrossRefGoogle Scholar
  9. 9.
    Yu. M. Aponin and E. A. Aponina, Matem. Biol. Bioinform. 2, 347 (2007).CrossRefGoogle Scholar
  10. 10.
    T. P. Shestakova, A. V. Dreval’, and O. A. Dreval’, in Abstr. VII All-Russia Diabetological Congress (2015) [in Russian].Google Scholar
  11. 11.
    M. G. Markakis, G. D. Mitsis, and V. Z. Marmarelis, in Proc. Annu. Int. Conf. IEEE Eng. Med. Biol. Soc. (2008), pp. 5445–5448. doi 10.1109/IEMBS.2008. 4650446Google Scholar
  12. 12.
    A. G. Zalevskaya, N. I. Verbovaya, T. I. Rodionova, et al., Sakharnyi Diabet No. 2, 106 (2010).Google Scholar
  13. 13.
    S. Hoops, S. Sahle, R. Gauges, et al., Bioinformatics 22, 3067 (2006).CrossRefGoogle Scholar
  14. 14.
    T. Back, Evolutionary Algorithms in Theory and Practice: Evolution Strategies, Evolutionary Programming, Genetic Algorithms (Oxford Univ. Press, Oxford, 1996). https://www.google.com/books?hl=ru&lr=&id=htJHI1UrL 7IC&oi=fnd&pg=PR9&ots=fzsZ1PZFlR&sig=sOg- CEjGdE5kjqyXmjsnmZwux3M.zbMATHGoogle Scholar
  15. 15.
    B. J. Zikmund-Fisher, N. L. Exe, and H. O. Witteman, J. Med. Internet Res. 16, e187 (2014). doi 10.2196/jmir.3241CrossRefGoogle Scholar
  16. 16.
    T. O. Shepelyuk, M. A. Panteleev, and A. N. Sveshnikova, Math. Model. Nat. Phenom. 11, 103 (2016).MathSciNetCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2017

Authors and Affiliations

  • A. N. Sveshnikova
    • 1
    • 2
  • M. A. Panteleev
    • 1
    • 2
  • A. V. Dreval
    • 3
  • T. P. Shestakova
    • 3
  • O. S. Medvedev
    • 4
  • O. A. Dreval
    • 3
  1. 1.Department of PhysicsLomonosov Moscow State UniversityMoscowRussia
  2. 2.Federal Research and Clinical Center of Pediatric HematologyOncology and Immunology named after D. RogachevMoscowRussia
  3. 3.Moscow Regional Research and Clinical Institute named after M.F. VladimirskiiMoscowRussia
  4. 4.Faculty of Basic MedicineMoscow State UniversityMoscowRussia

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