"تحليل مقارن لهياكل تحكم PID لتنظيم الجلوكوز في مرض السكري من النوع الأول: دراسة قائمة على المحاكاة باستخدام نموذج بيرغمان"

[1]International Diabetes Federation, IDF Diabetes Atlas Ninth Edition 2019.

[2]Ajmera, I., Swat, M., Le Novere, N. And Chelliah, V. (2013) ‘The impact of mathematical modelling on the understanding of diabetes and related complications’ CPT Pharmacometrics& Systems Pharmacology, vol. 2, no. 2, pp. E54.

[3]Z. Trajanoski and P. Wach, “Neural predictive controller for insulin delivery using the subcutaneous route,” IEEE Trans. Biomed. Eng., vol. 45,no. 9, pp. 1122–1134, Sep. 1998.

[4] R. S. Parker, F. J. Doyle III, and N. A. Peppas, “A model-based algorithm for blood glucose control in type I diabetic patients,” IEEE Trans. Biomed. Eng., vol. 46, no. 2, pp. 148–157, Feb. 1999.

[5]Chew YH, Shia YL, Lee CT, Majid FA, Chua LS, Sarmidi MR, et al. Modeling of oscillatory bursting activity of pancreatic β-cells under regulated glu¬cose stimulation. Mol Cell Endocrinol 2009; 307:57- 67; PMID:19524127; http://dx.doi.org/10.1016/j. mce.2009.03.005.

[6]Han K, Kang H, Choi MY, Kim J. Mathematical model of the glucose-insulin regulatory system: From the bursting electrical activity in pancreatic β-cells to the glucose dynamics in the whole body. (preprint).

[7]G. W. Swan, “An optimal control model of diabetes mellitus,” Bull.Math. Biol., vol. 44, no. 6, pp. 793–808, 1982.

[8]World Health Organization. Classification of Diabetes Mellitus; World Health Organization: Geneva, Switzerland, 2019.

[9] Boutayeb, A.; Chetouani, A. A population model of diabetes and prediabetes. Int. J. Comput. Math. 2007, 84, 57–66. [CrossRef]

[10] An, J.; Nichols, G.A.; Qian, L.; Munis, M.A.; Harrison, T.N.; Li, Z.;Wei, R.;Weiss, T.; Rajpathak, S.; Reynolds, K. Prevalence and incidence of microvascular and macrovascular complications over 15 years among patients with incident type 2 diabetes. BMJ Open Diabetes Res. Care 2021, 9, e001847. [CrossRef]

[11]Gatwood, J.; Chisholm-Burns, M.; Davis, R.; Thomas, F.; Potukuchi, P.; Hung, A.; Kovesdy, C.P. Evidence of chronic kidneydisease in veterans with incident diabetes mellitus. PLoS ONE 2018, 13, e0192712.

[12]P. Saeedi, I. Petersohn, P. Salpea, B. Malanda, S. Karuranga, N. Unwin,S. Colagiuri, L. Guariguata, A.A. Motala, K. Ogurtsova, J.E. Shaw, D. R. Williams, Global and regional diabetes prevalence estimates for 2019 andprojections for 2030 and 2045: results from the international diabetes federation diabetes Atlas, 9th edition, Diabetes Res. Clin. Pract. 157 (2019), 107843.

[13] M.A. Atkinson, G.S. Eisenbarth, A.W. Michels, Type 1 diabetes, Lancet 383 (2014)69–82.A.D. Cherrington, Banting lecture 1997, Diabetes 48 (1999) 1198–1214.

[14]A. Cinar, Advances in artificial pancreas control systems, J. Process Control 81(2019) 221–222.

[15] J.C. Pickup, H. Keen, J.A. Parsons, K.G. Alberti, Continuous subcutaneous insulin infusion: an approach to achieving normoglycaemia, Br. Med. J. 1 (1978) 204–207.

[16]El Haout, S.; Fatani, M.; Farha, N.A.; AlSawaftah, N.; Mortula, M.; Husseini, G.A. Modeling the Effects of Chemotherapy and Immunotherapy on Tumor Growth. J. Biomed. Nanotechnol. 2021, 17, 2505–2518. [CrossRef]

[17]Centers for Disease Control and Prevention. Incidence of Newly Diagnosed Diabetes. Available online: https://www.cdc.gov/ diabetes/data/statistics-report/newly-diagnosed-diabetes.html (accessed on 9 October 2022).

[18]F. Chee, T. Fernando, and P. V. van Heerden, “Closed-loop glucose control in critically-ill patients using continuous glucose monitoring system (CGMS) in real-time,” IEEE Trans. Inf. Technol. Biomed., vol. 7, no. 1, pp. 43–53, Mar. 2003.

[19]Bergman, R. N., Ider, Y. Z., Bowden, G. R. &Cobelli, C. (1979). Quantitative estimation of insulin sensitivity, Am. J. Physiol. Vol. 236, pp. E667-E677

[20] Bergman, R. N. &Cobelli, C. (1980). Minimal modeling, partition analysis and the estimation of insulin sensitivity, Fed. Proc. Vol. 39, pp. 110-115.

[21] Bergman, R. N., Bortolan, G., Cobelli, C. &Toffolo, G. (1980). Identification of a minimal model of glucose disappearance for estimating insulin sensitivity, in Proceedings of the 5th IFAC Symposium on Identification and System Parameter Estimation, (Isermann, Ed.), Bergman, Oxford, Vol. 2, pp. 883-890

[22]Mitsis, G. D., Markakis, M. G., &Marmarelis, V. Z. (2009). Nonlinear modeling of the dynamic effects of infused insulin on glucose: comparison of compartmental with Volterra models, IEEE Transactions on Biomedical Engineering, Vol. 56, No. 10, pp. 2347-2358.

[23]Gyorgy, E., Jozef, K. T. &Levente, K. (2015). Adaptive control solution for type 1 diabetes control. Applied Computational Intelligence and Informatics, IEEE 10th Jubilee Int. Symposium, 215-220.

[24]Gomez, A. M., Marin Carrillo, L. F., &MunosVelandia, O. M. (2017). Long-term efficacy and safety of sensor augmented insulin pump therapy with low-glucose suspend feature in patients with type 1 diabetes. Diabetes Tech. Ther. Vol. 19, No. 2, pp. 109-114

[25]Forlenza, G. P., Pinhas-Hamiel, O., &Liljenquist, D. R. (2019). Safety evaluation of the Minimed 670G System in children 7-13 years of age with type 1 diabetes, Diabetes Tech. Ther. Vol. 21, No. 1, pp. 11-19

[26]Gomez, A. M., Marin Carrillo, L. F., &MunosVelandia, O. M. (2017). Long-term efficacy and safety of sensor augmented insulin pump therapy with low-glucose suspend feature in patients with type 1 diabetes. Diabetes Tech. Ther. Vol. 19, No. 2, pp. 109-114

[27]Hassan, F. U., Adil, M., Khaqan, A., Shuja, S., Tiwana, M. I., Hassan, Q. U., Malik, S. and Riaz, R. A. (2017). Closed loop blood glucose control in diabetics. Biomedical Research, Vol. 28, No.16, pp. 7230-7236.

[28]Kwach, B., Ongati, O., &Simwa, R. (2011). Mathematical model for detecting diabetes in the blood, Applied Mathematical Sciences, Vol. 56, pp. 279-286

[29]J. D. Bronzino and D. R. Peterson, The Biomedical Engineering Handbook, 4th ed. Boca Raton, FL, USA: CRC Press, 2015.

[30]C. Ionescu, Y. Zhou, and J. A. T. Machado, ``Special Issue: Advances in fractional dynamics and control,'' J. Vib. Control, vol. 22, no. 8, pp. 1969_1971, 2016.

[31]A. Haidar, ``The arti_cial pancreas: How closed-loop control is revolutionizing diabetes,'' IEEE Control Syst. Mag., vol. 36, no. 5, pp. 28_47, Oct. 2016.

[32]E.Ackerman,L.C.Gatewood,J.W.Rosevear,G.D.Molnar. “Model studies of blood glucose regulation, ” Bull. Math. Biophys.vol.27,pp.21-37,1965

[33]R.N.Bergman,L.S.Phillips,C.Cobelli. “Physiologic evaluation of factors controlling glucose tolerance in man,” J.Clin.Invest,vol.68,pp.1456- 1467,1981.

[34] C.Cobelli, A.Mari. “Validation of mathematical models of complex endocrine-metabolic systems. A case study on a model of glucose regulation, ” Med. Biol. Eng. Comput,vol.21,pp.390-399,1983.

[35]R.Hovorka,V.Canonico,L.J.Chassin,U.Haueter,M.MassiBenedetti,M.O.Federici,T.R.Pieber,H.C.Schaller,L.Schaupp,T.Vering,M.E.Wilinska“Non- linear model predictive control of glucose concentration in subjects with type 1 diabetes,”Physiol.Meas,vol.25, pp.905-920,2004.

[36]Lind, M., Polonsky, W., Hirsch, I.B, et al.: ‘Continuous glucose monitoring vs. conventional therapy for glycemic control in adults with type 1 diabetes treated with multiple daily insulin injections: the goldrandomized clinical trial’, J. Am. Med. Assoc., 2017, 317, (4), pp. 379–387.

[37]Steil, G.M., Rebrin, K., Janowski, R., et al.: ‘Modeling-cell insulin secretion implications for closed-loop glucose homeostasis’, Diabetes Technol. Ther., 2003, 5, (6), pp. 953–964

[38] Athena Makroglou, Jiaxu Li, Yang Kuang, Mathematical models and software tools for the glucose-insulin regulatory system and diabetes: an overview, Applied Numerical Mathematics, Volume 56, Issues 3–4, 2006, Pages 559-573, ISSN 0168-9274,https://doi.org/10.1016/j.apnum.2005.04.023.