Mathematical modelling of a glucose-insulin system for type 2 diabetic patients in Chad
DOI:
https://doi.org/10.53391/mmnsa.2022.020Abstract
In this paper, we focus on modelling the glucose-insulin system for the purpose of estimating glucagon, insulin, and glucose in the liver in the internal organs of the human body. A three-compartmental mathematical model is proposed. The model parameters are estimated using a nonlinear inverse optimization problem and data collected in Chad. In order to identify insulin and glucose in the liver for type 2 diabetic patients, the Sampling Importance Resampling (SIR) particle filtering algorithm is used and implemented through discretization of the developed mathematical model. The proposed mathematical model allows further investigation of the dynamic behavior of hepatic glucose, insulin, and glucagon in internal organs for type 2 diabetic patients. During periods of hyperglycemia (i.e., after meal ingestion), whereas insulin secretion is increased, glucagon secretion is reduced. The results are in agreement with empirical and clinical data and they are clinically consistent with physiological responses.
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Tolić, I.M., Mosekilde, E., & Sturis, J. Modeling the insulin–glucose feedback system: the significance of pulsatile insulin secretion. Journal of Theoretical Biology, 207(3), 361-375, (2000).
https://fr.wikipedia.org/wiki/Afriquecentrale, 2022, Access Date: 15th May 2022.
International Diabetes Federation (IDF), Atlas, Seventh edition, 2015, Access Date: 15th May 2022.
International Diabetes Federation (IDF), Atlas, Sixth edition, 2013, Access Date: 5th June 2022.
https://www.diabete.qc.ca/fr/comprendre-le-diabete/tout-sur-le-diabete/types-de-diabete/le-diabete-de-type-2, Access Date: 5th June 2022.
Lin, C.W. Modeling glucose-insulin kinetics and development of type 2 diabetes in offspring of diabetic parents. PhD Thesis, University of Iowa, (2011).
Joshi, H., & Jha, B.K. Chaos of calcium diffusion in Parkinson’s infectious disease model and treatment mechanism via Hilfer fractional derivative. Mathematical Modelling and Numerical Simulation with Applications, 1(2), 84-94, (2021).
Joshi, H., Jha, B.K., & Yavuz, M. Modelling and analysis of fractional-order vaccination model for control of COVID-19 outbreak using real data. Mathematical Biosciences and Engineering, 20(1), 213-240, (2023).
Durai, P., Xavier, F., Zubair, B., & Fuqian, S. Fractional Reaction-Diffusion Model for Parkinson’s Disease. In: Pandian, D., Fernando, X., Baig, Z., Shi, F. (eds) Proceedings of the International Conference on ISMAC in Computational Vision and BioEngineering 2018 (ISMAC-CVB). ISMAC 2018. Lecture Notes in Computational Vision and Biomechanics, vol 30. Springer, Cham.
Uçar, S., Özdemir, N., Koca, İ., & Altun, E. Novel analysis of the fractional glucose-insulin regulatory system with nonsingular kernel derivative. The European Physical Journal Plus, 135(5), 414, (2020).
Vahidi, O., Kwok, K.E., Gopaluni, R.B., & Sun, L. Development of a physiological model for patients with type diabetes mellitus. In Proceedings of 2010, American Control Conference, pp.2027-2032, Mariott Waterfront, Baltimore, MD, USA, (2010).
Vahidi, O. Dynamic Modeling of Glucose Metabolism for the Assessment of Type II Diabetes Mellitus. Ph.D. Thesis, The University of British Columbia, (2013).
Vahidi, O., Kwok, K.E., Gopaluni, R.B., & Sun, L. Developing a physiological model for type II diabetes mellitus. Biochemical Engineering Journal, 55(1), 7-16, (2011).
Sorensen, J.T. A physiologic model of glucose metabolism in man and its use to design and assess improved insulin therapies for diabetes. Ph.D. Thesis, USA: Massachusetts Institute of Technology, (1985).
Moore, C.X., & Cooper, G.J. Co-secretion of amylin and insulin from cultured islet β-cells: modulation by nutrient secretagogues, islet hormones and hypoglycemic agents. Biochemical and Biophysical Research Communications, 179(1), 1-9, (1991).
Aronoff, S.L., Berkowitz, K., Shreiner, B., & Want, L. Glucose metabolism and regulation: beyond insulin and glucagon. Diabetes Spectrum, 17(3), 183-190, (2004).
Basu, A., Basu, R., Shah, P., Vella, A., Johnson, C.M., Nair, K.S., Jensen, M.D., Schwenk, W.F. & Rizza, R.A. Effects of type 2 diabetes on the ability of insulin and glucose to regulate splanchnic and muscle glucose metabolism: evidence for a defect in hepatic glucokinase activity. Diabetes, 49(2), 272-283, (2000).
Iozzo, P., Hallsten, K., Oikonen, V., Virtanen, K.A., Kemppainen, J., Solin, O., Ferrannini, E., Knuuti, J., & Nuutila, P. Insulinmediated hepatic glucose uptake is impaired in type 2 diabetes: evidence for a relationship with glycemic control. The Journal of Clinical Endocrinology & Metabolism, 88(5), 2055-2060, (2003).
Kahn, S.E. The importance of the beta cell in the pathogenesis of type 2 diabetes mellitus. The American Journal of Medicine, 108(6), 2-8, (2000).
Toft-Nielsen, M.B., Damholt, M.B., Madsbad, S., Hilsted, L.M., Hughes, T.E., Michelsen, B.K., & Holst, J.J. Determinants of the impaired secretion of glucagon-like peptide-1 in type 2 diabetic patients. The Journal of Clinical Endocrinology & Metabolism, 86(8), 3717-3723, (2001).
Igari, K., Kudo, T., Uchiyama, H., Toyofuku, T., & Inoue, Y. Quantitative evaluation of microvascular dysfunction in peripheral neuropathy with diabetes by indocyanine green angiography. Diabetes Research and Clinical Practice, 104(1), 121-125, (2014).
Ntaganda, J.M., Niyobuhungiro, J., Banzi, W., Mpinganzima, L., Minani, F., Gahutu, J.B., Dusabejambo, V., & Kambutse, I. Mathematical modelling of human cardiovascular-respiratory system responses to exercise in Rwanda. International Journal of Mathematical Modelling and Numerical Optimisation, 9(3), 287-308, (2019).
Hanke, M. (2000). Iterative regularization techniques in image reconstruction. In Surveys on solution methods for inverse problems (pp. 35-52). Springer, Vienna.
Arulampalam, M.S., Maskell, S., Gordon, N., & Clapp, T. A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Transactions on Signal Processing, 50(2), 174-188, (2002).
Doucet, A., Godsill, S., & Andrieu, C. On sequential Monte Carlo sampling methods for Bayesian filtering. Statistics and Computing, 10(3), 197-208, (2000).
Staehr, P., Hother-Nielsen, O., & Beck-Nielsen, H. The role of the liver in type 2 diabetes. Reviews in Endocrine & Metabolic Disorders, 5(2), 105-110, (2004).
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Copyright (c) 2022 Adam Hassan Adoum, Mahamat Saleh Daoussa Haggar, Jean Marie Ntaganda
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