Mathematical model to describe regulation of carbohydrate metabolism taking into account functional disorders for predicting increased risk of associated diseases

UDC: 
517.91:[613.2+612.3]
DOI: 
10.21668/health.risk/2025.3.13.eng
Authors: 

M.R. Kamaltdinov1,2, E.G. Movsisyan2

Organization: 

1Federal Scientific Center for Medical and Preventive Health Risk Management Technologies, 82 Monastyrskaya Str., Perm, 614045, Russian Federation
2Perm National Research Polytechnic University, 29 Komsomol'skii prospect, Perm, 614990, Russian Federation

Abstract: 

Diseases of the endocrine system, including those associated with increased consumption of carbohydrates and high-calorie foods, are common throughout the world. Existing complex mathematical models for describing carbohydrate metabolism processes contain many parameters, which makes their use difficult at the individual level. The aim of this work is to develop a mathematical model to describe regulation of carbohydrate metabolism, taking into account the endocrine function of the pancreas and functional disorders in the body under various diets. The new basic mathematical formulation proposed by the authors of this article takes into account the main processes in the system of glucose, insulin and glucagon balance in blood and glucose in the liver as well as functional disorders of certain organs (liver, kidneys, pancreas), time delays in the transmission of regulatory signals, as well as various diets (fast food with a high content of fast carbohydrates, high-calorie food, and unbalanced daily diets). A system of differential equations with a delayed argument is used as a mathematical apparatus and the Euler method is used for the numerical solution of the system.

Numerical experiments consider the results for four scenarios: a process without functional disorders in the body; impaired pancreatic and liver function in type I diabetes; impaired insulin-dependent glucose intake in type II diabetes; and unbalanced consumption of fast carbohydrates. In case of diabetes or when consuming fast carbohydrates, periods of elevated blood glucose as well as excess levels themselves (up to 8.8–15 mmol/l) are significantly higher than in case the disease is absent. Elevated glucose levels and periods of exceeding normal levels are the output parameters of the model, risk-inducing factors of diseases of the endocrine and cardiovascular systems. In addition, the carbohydrate balance is violated in scenarios with diabetes. The body begins to store excess glucose in the liver on a daily basis, which can lead to further conversion of carbohydrates into fats, increasing the obesity risk.

Depending on the simulation results, disease prevention measures can include optimal individual recommendations for balancing the amount of consumed carbohydrates and meals per day. In future studies, it is advisable to consider carbohydrate metabolism in combination with fat, which allows for more detailed consideration of pathways typical for diabetes and concomitant pathologies.

Keywords: 
mathematical model, carbohydrate metabolism, diabetes mellitus, insulin, glucose, glucagon, liver, functional disorders, fast carbohydrates, unbalanced diet, risk
Kamaltdinov M.R., Movsisyan E.G. Mathematical model to describe regulation of carbohydrate metabolism taking into ac-count functional disorders for predicting increased risk of associated diseases. Health Risk Analysis, 2025, no. 3, pp. 122–133. DOI: 10.21668/health.risk/2025.3.13.eng
References: 
  1. Valaiyapathi B., Gower B., Ashraf A.P. Pathophysiology of type 2 diabetes in children and adolescents. Curr. Diabetes Rev., 2020, vol. 16, no. 3, pp. 220–229. DOI: 10.2174/1573399814666180608074510
  2. Dashti H.M., Mathew T.C., Al-Zaid N.S. Efficacy of low-carbohydrate ketogenic diet in the treatment of type 2 dia-betes. Med. Princ. Pract., 2021, vol. 30, no. 3, pp. 223–235. DOI: 10.1159/000512142
  3. Karpova O.B., Shchepin V.O., Zagoruychenko A.A. The prevalence of adolescent obesity in the world and the Russian Federation in 2012–2018. Gigiena i sanitariya, 2021, vol. 100, no. 4, pp. 365–372. DOI: 10.47470/0016-9900-2021-100-4-365-372 (in Russian).
  4. Shestakova M.V., Sukhareva O.Yu. Type 2 diabetes mellitus: ease of diagnosis, and choice of treatment. Doktor.Ru, 2017, no. 13 (142)–14 (143), pp. 44–51 (in Russian).
  5. Dedov I.I., Shestakova M.V., Vikulova O.K., Zheleznyakova A.V., Isakov M.A., Sazonova D.V., Mokrysheva N.G. Diabetes mellitus in the Russian Federation: dynamics of epidemiological indicators according to the Federal Register of Diabetes Mellitus for the period 2010–2022. Sakharnyi diabet, 2023, vol. 26, no. 2, pp. 104–123. DOI: 10.14341/DM13035 (in Russian).
  6. Balabolkin M.I., Klebanova E.M., Kreminskaya V.M. Novaya klassifikatsiya, kriterii diagnostiki i kompensatsii sakharnogo diabeta [New classification, criteria for diagnosis and compensation of diabetes mellitus]. Consilium Medicum, 2000, vol. 2, no. 5, pp. 204–211 (in Russian).
  7. Hovorka R., Shojaee-Moradie F., Carroll P.V., Chassin L.J., Gowrie I.J., Jackson N.C., Tudor R.S., Umpleby A.M., Jones R.H. Partitioning glucose distribution/transport, disposal, and endogenous production during IVGTT. Am. J. Physiol. En-docrinol. Metab., 2002, vol. 282, no. 5, pp. E992–E1007. DOI: 10.1152/ajpendo.00304.2001
  8. Fabietti P.G., Canonico V., Federici M.O., Benedetti M.M., Sarti E. Control oriented model of insulin and glucose dynamics in type 1 diabetics. Med. Biol. Eng. Comput., 2006, vol. 44, no. 1–2, pp. 69–78. DOI: 10.1007/s11517-005-0012-2
  9. Bergman R.N. The minimal model of glucose regulation: a biography. Adv. Exp. Med. Biol., 2003, vol. 537, pp. 1–19. DOI: 10.1007/978-1-4419-9019-8_1
  10. Lombarte M., Lupo M., Campetelli G., Basualdo M., Rigalli A. Mathematical model of glucose-insulin homeostasis in healthy rats. Math. Biosci., 2013, vol. 245, no. 2, pp. 269–277. DOI: 10.1016/j.mbs.2013.07.017
  11. Dalla Man C., Raimondo D.M., Rizza R.A., Cobelli C. GIM, simulation software of meal glucose-insulin model. J. Diabetes Sci. Technol., 2007, vol. 1, no. 3, pp. 323–330. DOI: 10.1177/193229680700100303
  12. Gallenberger M., zu Castell W., Hense B.A., Kuttler C. Dynamics of glucose and insulin concentration connected to the β-cell cycle: model development and analysis. Theor. Biol. Med. Model., 2012, vol. 9, pp. 46. DOI: 10.1186/1742-4682-9-46
  13. Topp B., Promislow K., deVries G., Miura R.M., Finegood D.T. A model of β-cell mass, insulin, and glucose kinetics: pathways to diabetes. J. Theor. Biol., 2000, vol. 206, no. 4, pp. 605–619. DOI: 10.1006/jtbi.2000.2150
  14. De Gaetano A., Arino O. Mathematical modelling of the intravenous glucose tolerance test. J. Math. Biol., 2000, vol. 40, no. 2, pp. 136–168. DOI: 10.1007/s002850050007
  15. Shirokova N.A. Matematicheskoe modelirovanie balansa insulin-glyukoza v krovi i sistemy regulyatsii glikemii u patsientov s sakharnym diabetom [Mathematical modeling of insulin-glucose balance in blood and glycemic regulation system in patients with diabetes mellitus]. Matematicheskie struktury i modelirovanie, 2002, iss. 10, pp. 106–115 (in Russian).
  16. Shirokova N.A. Matematicheskoe modelirovanie istochnikov glyukozy i insulinov v modeli balansa «insulin – glyu-koza» [Mathematical modeling of glucose and insulin sources in the ‘insulin-glucose’ balance model]. Matematicheskie struktury i modelirovanie, 2004, iss. 14, pp. 47–52 (in Russian).
  17. Hussain J., Zadeng D. A mathematical model of glucose-insulin interaction. Sci. Vis., 2014, vol. 14, no. 2, pp. 84–88.
  18. Trusov P.V., Zaitseva N.V., Kiryanov D.A., Kamaltdinov M.R., Tsinker M.Yu., Chigvintsev V.M., Lanin D.V. A mathematical model for evolution of human functional disorders influenced by environment factors. Mathematical Biology and Bioinformatics, 2023, vol. 18, suppl., pp. t73–t93. DOI: 10.17537/2023.18.t73
  19. Kamaltdinov M., Zaitseva N., Trusov P. A mathematical model of the multiphase flow in the antroduodenum: Con-sideration of the digestive enzymes and regulation processes. Series on Biomechanics, 2018, vol. 32, no. 3, pp. 36–42.
  20. Kamaltdinov M.R., Zaitseva N.V., Shur P.Z. Numerical modeling of acidity distribution in antroduodenum aimed at identifying anomalous zones at consuming drinks with different pH level. Health Risk Analysis, 2017, no. 1, pp. 38–46. DOI: 10.21668/health.risk/2017.1.05.eng
  21. Sievenpiper J.L. Low-carbohydrate diets and cardiometabolic health: the importance of carbohydrate quality over quantity. Nutr. Rev., 2020, vol. 78, suppl. 1, pp. 69–77. DOI: 10.1093/nutrit/nuz082
  22. Almourani R., Chinnakotla B., Patel R., Kurukulasuriya L.R., Sowers J. Diabetes and Cardiovascular Disease: an Update. Curr. Diab. Rep., 2019, vol. 19, no. 12, pp. 161. DOI: 10.1007/s11892-019-1239-x
  23. Li J., Lee D.H., Hu J., Tabung F.K., Li Y., Bhupathiraju S.N., Rimm E.B., Rexrode K.M. [et al.]. Dietary Inflammatory Potential and Risk of Cardiovascular Disease Among Men and Women in the U.S. J. Am. Coll. Cardiol., 2020, vol. 76, no. 19, pp. 2181–2193. DOI: 10.1016/j.jacc.2020.09.535
  24. Jiang Y., Zheng W. Cardiovascular toxicities upon manganese exposure. Cardiovasc. Toxicol., 2005, vol. 5(4), pp. 345–354. DOI: 10.1385/ct:5:4:345
  25. Yagudina R.I., Kulikov A.Yu., Arinina E.E., Shestakova M.V., Suntsov Yu.I., Dedov I.I. Pharmacoeconomics mod-eling of long term results of type 2 diabetes mellitus treatment in patients using modern insulin analogues in contrast to oral antidiabetic drugs or diet in Russia. Farmakoekonomika. Sovremennaya farmakoekonomika i farmakoepidemiologiya, 2010, vol. 3, no. 3, pp. 11–20 (in Russian).
  26. Watkins P.J. ABC of Diabetes. In: D.E. Koloda translation from English; M.I. Balabolkin ed. Moscow, Binom Publ., 2006, 134 p. (in Russian).
  27. Fadeev P.A. Sakharnyi diabet v detalyakh diagnostiki i lecheniya [Diabetes Mellitus in Details of Diagnosis and Treatment]. Moscow, Eksmo Publ., 2016, 304 p. (in Russian).
Received: 
23.07.2025
Approved: 
11.08.2025
Accepted for publication: 
26.09.2025

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