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Modeling and simulation of glucose insulin glucagon algorithm for artificial pancreas to control the diabetes mellitus

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Abstract

Artificial pancreas systems the courage to remove this risk by taking existing pump technology to a new level. In this paper, we modified the existing model for type 1 diabetes mellitus to discuss different control strategies for the artificial pancreas. A model consists of eight states variables and various parameters, numerous of which are undefined and complicated to find out correctly. The stability of glucose-insulin in humans has been created and validated the non-negative unique solution. Controllability and observability for the glucose-insulin system is treated for feedback design to develop the artificial pancreas. We design glucose insulin algorithm for whole body having eight sub-compartments according to parameters values given in Liu and Tang (J Theor Biol 252:608–620, 2008) which provide the continues monitoring of glucose and insulin in finite time. Numerical simulation are carried out for closed-loop design which is helpful for the development of artificial pancreas. The developed model provides the estimation values for normal day life to measure the glucose-insulin system in humans.

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References

  • Ahmad A, Farman M, Yasin F, Ahmad MO (2018a) Dynamical transmission and effect of smoking in society. Int J Adv Appl Sci 5(2):71–75

    Article  Google Scholar 

  • Ahmad A, Farman M, Ahmad MO, Raza N, Abdullah (2018b) Dynamical behavior of SIR epidemic model with non-integer time fractional derivatives: a mathematical analysis. Int J Adv Appl Sci 5(1):123–129

  • Alkahtani BS, Algahtani OJ, Dubey RS, Goswami P (2017) The solution of modified fractional Bergman’s minimal blood glucose-insulin model. Entropy 19:114

    Article  Google Scholar 

  • Anguelov R, Lubuma JMS (2001) Contributions to the mathematics of the nonstandard finite difference method and applications. Numer Methods Partial Differ Equ 17:518–543

    Article  MathSciNet  Google Scholar 

  • Ashraf F, Ahmad MO (2019) Nonstandard finite difference scheme for control of measles epidemiology. Int J Adv Appl Sci 6(3):79–85

    Article  Google Scholar 

  • Ashraf F, Ahmad A, Saleem MU, Farman M, Ahmad MO (2018) Dynamical behavior of HIV immunology model with non-integer time fractional derivatives. Int J Adv Appl Sci 5(3):39–45

    Article  Google Scholar 

  • Bergman R, Phillips L, Cobelli C (1981) Physiologic evaluation of factors controlling glucose tolerance in man. J Clin Investig 68(6):1456–1467

    Article  Google Scholar 

  • Boutayeb DT, Chetouani A (2006) A critical review of mathematical models and data used in diabetology. Biomed Eng 5:43

  • Chee G, Fernando T (2007) Closed-loop control of blood glucose, number 368 in lecture notes in control and information sciences. Springer, Berlin

    Google Scholar 

  • Coron JM (2007) Control and nonlinearity. Am Math Soc 136:1–66

  • Dalla Man C, Rizza RA, Cobelli C (2007) Meal simulation model of the glucose-insulin system. IEEE Trans Biomed Eng 54(10):1740–1749

  • De Gaetano A, Panunzi S, Matone A, Samson A, Vrbikova J, Bendlova B et al (2013) Routine OGTT: a robust model including incretin effect for precise identification of insulin sensitivity and secretion in a single individual. PLoS ONE 8:e70875

    Article  Google Scholar 

  • Erlandsen M, Martinussen C, Gravholt CH (2018) Integrated model of insulin and glucose kinetics describing both hepatic glucose and pancreatic insulin regulation. Comput Methods Prog Biomed 56:121–131

    Article  Google Scholar 

  • Farman M, Saleem MU, Meraj MA (2016) Control of glucose insulin regulatory system for type 1 diabetes. Sci Int (Lahore) 28(1):27–29

    Google Scholar 

  • Farman M, Saleem MU, Ahmad MO, Ahmad A (2018) Stability analysis and control of glucose insulin glucagon system in human. Chin J Phys 56:1362–1369

  • Farman M, Saleem MU, Tabassum MF, Ahmad A, Ahmad MO (2019) A linear control of composite model for glucose insulin glucagon. Ain Shamas Eng J 10:867–872

    Article  Google Scholar 

  • Li L, Zheng W (2010) Global stability of a delay model of glucose–insulin interaction. Math Comput Model 52(4):472–480

    Article  MathSciNet  Google Scholar 

  • Liu W, Tang F (2008) Modelling a simplified regulatory system of blood glucose at molecular levels. J Theor Biol 252:608–620

    Article  Google Scholar 

  • Lunze K, Brendel MD, Leonhardt S (2011) Preliminary results of a type-1 diabetes swine model. In: 5th European IFMBE conference. Hungary, Budapest, pp 307–310

  • Makroglou A, Li J, Kuang Y (2006) Mathematical models and software tools for the glucose-insulin regulatory system and diabetes: an overview Appl Numer Math 56:559–573

  • Mickens RE (1994) Nonstandard finite difference Models of differential equations. World Scientific, Singapore

    MATH  Google Scholar 

  • Naik PA, Yavuz M, Qureshi S, Zu J, Townley S (2020) Modeling and analysis of COVID-19 epidemics with treatment in fractional derivatives using real data from Pakistan. Eur Phys J Plus 135(10):795

    Article  Google Scholar 

  • Parker RS, Doyle FJI, Peppas NA (2001) The intravenous route to blood glucose control. A review of control algorithms for noninvasive monitoring and regulation in type I diabetic patients. IEEE Eng Med Biol Mag 20(1):65–73

  • Saleem MU, Farman M, Ahmad MO, Rizwan M (2017) Control of an artificial human pancreas. Chin J Phys 55:2273–2282

    Article  MathSciNet  Google Scholar 

  • Saleem MU, Farman M, Rizwan M, Ahmad MO, Ahmad A (2018) Controllability and observability of glucose insulin glucagon systems in human. Chin J Phys 56(5):1909–1916

  • Saleem MU, Farman M, Ahmad A, Naeem M, Ahmad MO (2019) Stability analysis and control of fractional order diabetes mellitus model for artificial pancreas. Punjab Univ J Math 51(4):97-113

  • Salinari S, Bertuzzi A, Mingrone G (2011) Intestinal transit of a glucose bolus and incretin kinetics: a mathematical model with application to the oral glucose tolerance test. Am J Physiol Endocrinol Metab 300:E955–E965

    Article  Google Scholar 

  • Schmidt S, Boiroux D, Ranjan A, Jorgensen JB, Madsen H, Norgaard K (2015) An artificial pancreas for automated blood glucose control in patients with Type 1 diabetes. Ther Deliv 6:609–619

    Article  Google Scholar 

  • Yavuz M, Ozdemir N (2020) Analysis of an epidemic spreading model with exponential decay law. Math Sci Appl E-Notes 8(1):142–154

    Google Scholar 

  • Yavuz M, Sene N (2020) Stability analysis and numerical computation of the fractional predator-prey model with the harvesting rate. Fractal Fract 4(35):1–22

    Google Scholar 

  • Yavuza M, Bonyah E (2019) New approaches to the fractional dynamics of schistosomiasis disease model. Physica A Stat Mech Appl 525:373–393

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Sports Sciences and Physical Education, Faculty of Allied Health Sciences, University of Lahore, Lahore, 54590, Pakistan

    Muhammad Farhan Tabassum, Aqsa Shamim Ahmad & Saadia Mahmood ul Hassan

  2. Department of Mathematics and Statistics, University of Lahore, Lahore, 54590, Pakistan

    Muhammad Farman & Aqeel Ahmad

  3. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, Shaanxi, People’s Republic of China

    Parvaiz Ahmad Naik

Authors
  1. Muhammad Farhan Tabassum
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  2. Muhammad Farman
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  3. Parvaiz Ahmad Naik
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  4. Aqeel Ahmad
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  5. Aqsa Shamim Ahmad
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  6. Saadia Mahmood ul Hassan
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Contributions

MFT: analysis, writing-original draft. MF: methodology, writing-original draft. PAN: conceptualization, review and editing, Supervision. AA: software, validation, numerical simulations. ASA: analysis, writing-original draft. SMH: methodology, writing-original draft.

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Correspondence to Parvaiz Ahmad Naik.

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Tabassum, M.F., Farman, M., Naik, P.A. et al. Modeling and simulation of glucose insulin glucagon algorithm for artificial pancreas to control the diabetes mellitus. Netw Model Anal Health Inform Bioinforma 10, 42 (2021). https://doi.org/10.1007/s13721-021-00316-4

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  • DOI: https://doi.org/10.1007/s13721-021-00316-4

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