MODIFICATION OF THE MINIMAL BERGMAN MODEL OF THE "INSULIN-GLUCOSE" SYSTEM AND ITS IMPLEMENTATION IN MATLAB/SIMULINK
DOI:
https://doi.org/10.17770/etr2021vol2.6659Keywords:
Diabetes mellitus, Insulin-glucose balance, Glycemic monitoring, Computer simulation, Model personalization, Computational experimentAbstract
The article discusses a modification of Bergman's minimal mathematical model of the "insulin-glucose" system, which allows simulating controlled exogenous sources of glucose and insulin into the patient's blood on the model and investigating the dynamics of changes in their concentrations in normal conditions, in type I DM and type II DM. A modeling scheme is presented in graphic notations of the MatLab / Simulink computer mathematics system and a number of computational experiments on it are described to determine the type of glycemic profiles of glucose and insulin concentration in the patient's blood in the noted situations. The fundamental possibility of using model mappings in the MatLab/Simulink environment for the study and tuning of the loop for automatic regulation of the "insulin-glucose" balance in the patient's blood using a controlled insulin pump is demonstrated. It was also found that the modified minimal model can be customized for a specific patient with diabetes, which makes it possible to use it to solve the problems of individual prediction of the development of a diabetic disease in a specific patient. In addition, the described model makes it possible to recreate and virtually investigate various conditions and cases on it that affect the dynamics of insulin and glucose concentrations in the patient's blood, for example, when he performs physically stressed activities, in the presence of the effects of “aging” of insulin-producing cells in the pancreas. iron, etc.
Downloads
References
Standards of specialized diabetes care. Edited by Dedov I.I., Shestakova M.V. and Mayorov A.Yu. 9th Edition. Moscow: 2019,144 p. https://doi.org/10.14341/DM221S1. (in Russian)
S.N. Okulova, Review of mathematical models of the dynamics of insulin and glucose. Materials of the XI International Student Scientific Conference "Student Scientific Forum-2019". 2019. [Online]. Available: https://scienceforum.ru/2019/article/2018012293 [Accessed Mart, 14, 2021]. (in Russian)
F., Cosentino, P.J. Grant, V. Aboyans and etc., ESC/EASD Guidelines for Diabetes Mellitus, Prediabetes and Cardiovascular Disease, Russian journal of cardiology, 2020, vol. 25, no4, p. 3839. ttps://doi.org/10.15829/1560-4071-2020-3839 (in Russian)
Definition, Diagnosis and Classification of Diabetes Mellitus and its Complications: Report of a WHO Consultation. Part 1: Diagnosis and Classification of Diabetes Mellitus. Geneva: WHO. Department of Noncommunicable Disease Surveillance, 1999, 59 p.
F.J. Doyle, L. Jovanovic, D.E. Seborg, R.S. Parker and B.W. Bequette, A tutorial on biomedical process control, J. Process Control., 2007, vol. 17, pp. 571-572. https://doi.org/10.1016/j.jprocont.2007.01.012.
N.P. Balakrishnan, G.P. Rangaiah and L. Samavedham, Review and analysis of blood glucose (BG) models for type 1 diabetic patients,. Ind. Eng. Chem. Res., 2011. vol. 50, no. 21, pp. 12041–12066. https://doi.org/10.1021/ie2004779.
V.A. Karpel'ev, Yu.I. Filippov, Yu.V. Tarasov, M.D. Boyarsky, A.Yu. Mayorov, M.V. Shestakova and I.I. Dedov, Mathematical Modeling of the Blood Glucose Regulation System in Diabetes Mellitus Patients, Vestnik RAMN, 2015, vol. 5, pp. 549-60. https://doi.org/10.15690/vramn.v70.i5.1441. (in Russian)
T. Bremer and D.A. Gough, Is blood glucose predictable from previous values? A solicitation for data, Diabetes, 1999, vol. 48, pp. 445–451. https://doi.org/10.2337/diabetes.48.3.445.
M. Eren-Oruklu, A. Cinar, L. Quinn and D. Smith, Adaptive control strategy for regulation of blood glucose levels in patients with type 1 diabetes, J. Process. Control., 2009; 19: 1333–1346. https://doi.org/10.1016/j.jprocont.2009.04.004.
T. Van Herpe, M. Espinoza, B. Pluymers, P. Wouters, F. De Smet, G. Van Berghe and B. De Moor, Development of a critically ill patient input output model. Proceedings 14th IFAC Symposium on System Indentification (SYSID 2006), Newcastle, Australia, 2006, pp. 482-486. https://doi.org/10.3182/20060329-3-AU-2901.00073.
S.G. Mougiakakou, A. Prountzou, D. Iliopoulou, K.S. Nikita and W. Vazeou, Neural network based glucose – insulin metabolism models for children with Type 1 diabetes, IEEE Eng. Med. Biol. Soc., 2006; 1: 3545–3548. https://doi.org/10.1109/IEMBS.2006.260640.
N. Auwal, D.M. Hamman, G. Ibrahim and M.J. Abdullahi, Adaptive Neuro-Fuzzy System to Determine the Blood Glucose Level of Diabetic,. Mathematics and Computer Science, 2019, vol. 4, no. 3, p. 63-67 https://doi.org/10.11648/j.mcs.20190403.11.
A. Makroglou, J. Li and Y. Kuang, Mathematical models and software tools for the glucoseinsulin regulatory system and diabetes: an overview, Proceedings of the 2005 IMACS. Applied Numerical Mathematics, 2006, vol. 56, no. 3-4, pp. 559-573. https://doi.org/10.1016/j.apnum.2005.04.023.
R.N. Bergman, Pathogenesis and prediction of diabetes mellitus: Lessons from integrative physiology, in: Irving L. Schwartz Lecture, Mount Sinai J. Medicine., 2002, vjol. 60, pp. 280–290.
I.M. Tolich, E. Mosekilde and J. Sturis, Modeling the insulin-glucose feedback system: The significance of pulsatile insulin secretion, J. Theor. Biol., 2000, vol. 207, pp. 361-375. https://doi.org/10.1006/jtbi.2000.2180.
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., 2004, vol. 151, pp. 189–207. https://doi.org/10.1016/S0096-3003(03)00332-1.
K. Engelborghs, V. Lemaire, J.Bélair and D. Roose, Numerical bifurcation analysis of delay differential equations arising from physiological modeling, J. Math. Biol., 2001, vol. 42, pp. 361–385. https://doi.org/10.1007/s002850000072.
A. De Gaetano and O. Arino, Mathematical modelling of the intravenous glucose tolerance test, J. Math. Biol., 2000, vol. 40, pp. 136–168.
A.G. Borzov A.V., Dreval and S.I. Mukhin, Modeling of blood glucose dynamics with account of systemic loop topology, Mathematical modeling, 2015, vol. 27, no. 2, pp. 3-24. (in Russian)
M.E. Fisher, A semiclosed loop algorithm for the control of blood glucose levels in diabetics. IEEE Transact. Biomed. Engineering, 1991, vol. 38, no. 1, pp. 57-61. https://doi.org/10.1109/10.68209.
N.A. Shirokova, Mathematical modeling of glucose and insulin sources in the insulin-glucose balance model, Mathematical structures and modeling, 2004, vol. 14, pp. 47-52. (in Russian)
T. Van Herpe, B. Pluymers, M. Espinoza, G. Van den Berghe and B. De Moor, A minimal model for glycemia control in critically ill patients, IEEE Eng. Med. Biol. Soc., 2006, vol. 1, pp. 5432–5435. https://doi.org/10.1109/IEMBS.2006.260613.
E. Breda, M.K. Cavaghan, G. Toffolo, K.S. Polonsky and C. Cobelli, Oral glucose tolerance test minimal model indexes of beta cell function and insulin sensitivity, Diabetes, 2001, vol. 50, no. 1, pp. 150-158. https://doi.org/10.2337/diabetes.50.1.150.
S.M. Lynch, B.W. Bequette, Model predictive control of blood glucose in type I diabetics using subcutaneous glucose measurements, Proceed. Am. Control Conf., 2002, vol. 5, pp. 4039–4043. https://doi.org/10.1109/ACC.2002.1024561.
C. Dalla Man and R.A. Rizza, C. Cobelli, Meal simulation model of the glucose insulin system, IEEE Transactions on Biomed. Engineer, 2007, vol. 54, no. 10, pp. 1740-1749. https://doi.org/10.1109/TBME.2007.893506.
A. Roy and R.S. Parker, Dynamic modeling of exercise effects on plasma glucose and insulin levels, J. Diabet. Sci Technol., 2007, vol. 1, no. 3, pp. 338-347. https://doi.org/10.1177/193229680700100305.
J.T. Sorensen, A physiologic model of glucose metabolism in man and its use to design and assess improved insulin therapies for diabetes, Submitted to the Department of Chemical Engineering in partial fulfillment of the requirements for the Degree of Doctor of Science. Massachusetts Institute of Technology. Massachusetts, 1985, 556 p.
R.S. Parker, F.J. Doyle and N.A. Peppas, A model based algorithm for blood glucose control in type I diabetic patients, IEEE Transact. Biomed. Engineer,. 1999, vol. 46, no. 2, pp. 148–157. https://doi.org/10.1109/10.740877.
R.S. Parker, F.J. Doyle, J.H. Ward and N.A. Peppas, Robust H [infinity] glucose control in diabetes using a physiological model, Am. Institute Chem. Engineers J., 2000, vol. 46, pp. 2537–2549. https://doi.org/10.1002/aic.690461220.
C. Cobelli, G. Federspil, G. Pacini, A. Salvan and C. Scandellari, An integrated mathematical model of the dynamics of blood glucose and its hormonal control, Math. Biosci. 1982, vol. 58, pp. 27–60 https://doi.org/10.1016/0025-5564(82)90050-5.
C. Cobelli and A. Mari, Validation of mathematical models of complex endocrine-metabolic systems. A case study on a model of glucose regulation. Med. Biol. Eng. Comput. 1983, vol. 21, no. 4, pp. 390–399. https://doi.org/10.1007/BF02442625.
D.M. Eddy and L. Schlessinger, Archimedes: a trial validated model of diabetes, Diabetes Care, 2003, vol. 26, no. 11, pp. 3093–3101. https://doi.org/10.2337/diacare.26.11.3093.
D.M. Eddy and L. Schlessinger, Validation of the archimedes diabetes model. Diabetes Care. 2003, vol. 26, no. 11, pp. 3102–3110. https://doi.org/10.2337/diacare.26.11.3102.
S.G. Mougiakakou, K. Prountzou and K.S. Nikita, A Real Time Simulation Model of Glucose-Insulin Metabolism for Type I Diabetes Patients, 27th Annual International Conference of the Engineering in Medicine and Biology Society, 2005, pp. 298–301. https://doi.org/10.1109/IEMBS.2005.1616403.
Yu. Lazarev, Modeling of processes and systems in MatLab, SPb.: Peter; Kiev: Publishing house group BHV, 2005, 512 p. (in Russian)
Diabetes mellitus: diagnosis, treatment, prevention. Edited by I.I. Dedov and M.V. Shestakova, Moskow: LLC "Publishing house "Medical Information Agency", 2011, 808 p. (in Russian)
N.A. Shirokova, Mathematical modeling of the insulin-glucose balance in the blood. Mathematical structures and modeling, 2002, vol. 10, pp. 106-115. (in Russian)
V.V. Smirnov, Glucose monitoring system and insulin pumps. Therapist. 2009, vol. 3, pp. 31-35. (in Russian)
Pathophysiology. Edited by N.N. Zaiko, Yu.V. Bytsya and N.V. Kryshtal, Кiev: VSI "Medicine", 2015, 744 p. (in Russian)
I.P. Bolodurina, Yu.P. Ivanova (Lugovskova) and L.M. Antsiferova, Optimal Control of Glycemia Regulation Dynamics in Patients with Type I Diabetes Mellitus. Bulletin of the South Ural State University. Ser. Computer Technologies, Automatic Control, Radio Electronics, 2020, vol. 20, no. 4, pp. 144–154. https://doi.org/10.14529/ctcr200415. (in Russian)
A.S. Ametov and L.L. Kamykina, Glycemic variability is the key to successfully managing type 2 diabetes in obesity. Russian medical journal. 2011, vol. 27, p. 1672. [Online]: Available:https://www.rmj.ru/articles/endokrinologiya/Variabelynosty_glikemii__klyuch_k_uspeshnomu_upravleniyu_saharnym_diabetom_2_tipa_na_fone_oghireniya/. [Accessed: Mart, 15, 2021]. (in Russian)
D.N. Laptev, Insulin pump therapy with automatic shutdown of insulin delivery in response to hypoglycemia. Endocrinology problems, 2012, vo, 58, no. 3, pp. 70-74. (in Russian)
