- Friis-Jensen E. Modeling and simulation of glucose-insulin metabolism. Kongens Lyngby, Denmark: Technical University; 2007.
- Association AD. Economic costs of diabetes in the US in 2007. Diabetes Care. 2008;31:596-615. doi: 10.2337/dc08-9017.
- De Gaetano A, Arino O. Mathematical modelling of the intravenous glucose tolerance test. J Math Biol. 2000;40:136-68. doi: 10.1007/s002850050007. PubMed PMID: 10743599.
- Salzsieder E, Albrecht G, Fischer U, Freyse EJ. Kinetic modeling of the glucoregulatory system to improve insulin therapy. IEEE Trans Biomed Eng. 1985;32:846-55. doi: 10.1109/TBME.1985.325500. PubMed PMID: 3902618.
- Ogurtsova K, Da Rocha Fernandes J, Huang Y, Linnenkamp U, Guariguata L, Cho NH, et al. IDF Diabetes Atlas: Global estimates for the prevalence of diabetes for 2015 and 2040. Diabetes Res Clin Pract. 2017;128:40-50. doi: 10.1016/j.diabres.2017.03.024. PubMed PMID: 28437734.
- O’Sullivan SB, Schmitz TJ, Fulk G. Physical Rehabilitation: Chapter 6, Examination of Coordination and Balance. Philsdelphia: F.A Davis; 2019.
- Schwitzgebel VM, Somm E, Klee P. Modeling intrauterine growth retardation in rodents: Impact on pancreas development and glucose homeostasis. Mol Cell Endocrinol. 2009;304:78-83. doi: 10.1016/j.mce.2009.02.019. PubMed PMID: 19433251.
- Watts M, Sherman A. Modeling the pancreatic alpha-cell: dual mechanisms of glucose suppression of glucagon secretion. Biophys J. 2014;106:741-51. doi: 10.1016/j.bpj.2013.11.4504. PubMed PMID: 24507615. PubMed PMCID: PMC3944880.
- Netter FH, Colacino S. Atlas of human anatomy. Summit, New Jersey: CIBA-GEIGY Corporation; 1989.
- Stern MP. Diabetes and cardiovascular disease, the “common soil” hypothesis. Diabetes. 1995;44:369-74. doi: 10.2337/diab.44.4.369. PubMed PMID: 7698502.
- Surwit RS, Feinglos MN. The effects of relaxations on glucose tolerance in non-insulin-dependent diabetes. Diabetes Care. 1983;6:176-9. doi: 10.2337/diacare.6.2.176. PubMed PMID: 6343022.
- Jie S. Study on Effects of Ganoderma Lucidum Peptides on Alloxan-induced Diabetes Mice Modle. Food Science. 2002;11.
- Hall JE. Guyton and Hall Textbook of Medical Physiology. Elsevier; 2015.
- Deiss D, Bolinder J, Riveline JP, Battelino T, Bosi E, Tubiana-Rufi N, et al. Improved glycemic control in poorly controlled patients with type 1 diabetes using real-time continuous glucose monitoring. Diabetes Care. 2006;29:2730-2. doi: 10.2337/dc06-1134. PubMed PMID: 17130215.
- Ackerman E, Gatewood LC, Rosevear JW, Molnar GD. Model studies of blood-glucose regulation. The Bulletin of Mathematical Biophysics. 1965;27:21-37. doi: 10.1007/bf02477259.
- Bergman RN, Cobelli C. Minimal modeling, partition analysis, and the estimation of insulin sensitivity. Fed Proc. 1980;39:110-5. PubMed PMID: 6985867.
- Wang Y, Sun Y-c, Tong T. Non-linear dynamics model of blood glucose regulation by hypothalamus-pancreatic island axis. Journal of Northeast Normal University (Natural Science Edition). 2010;1.
- Drozdov A, Khanina H. A model for ultradian oscillations of insulin and glucose. Mathematical and Computer Modelling. 1995;22:23-38. doi: 10.1016/0895-7177(95)00108-e.
- Ricken T, Werner D, Holzhutter HG, Konig M, Dahmen U, Dirsch O. Modeling function-perfusion behavior in liver lobules including tissue, blood, glucose, lactate and glycogen by use of a coupled two-scale PDE-ODE approach. Biomech Model Mechanobiol. 2015;14:515-36. doi: 10.1007/s10237-014-0619-z. PubMed PMID: 25236798.
- Picchini U, Ditlevsen S, De Gaetano A. Maximum likelihood estimation of a time-inhomogeneous stochastic differential model of glucose dynamics. Math Med Biol. 2008;25:141-55. doi: 10.1093/imammb/dqn011. PubMed PMID: 18504247.
- Li J, Kuang Y, Mason CC. Modeling the glucose-insulin regulatory system and ultradian insulin secretory oscillations with two explicit time delays. J Theor Biol. 2006;242:722-35. doi: 10.1016/j.jtbi.2006.04.002. PubMed PMID: 16712872.
- Panunzi S, Palumbo P, De Gaetano A. A discrete Single Delay Model for the Intra-Venous Glucose Tolerance Test. Theor Biol Med Model. 2007;4:35. doi: 10.1186/1742-4682-4-35. PubMed PMID: 17850652. PubMed PMCID: PMC2072949.
- Sorensen JT, Colton CK, Hillman RS, Soeldner JS. Use of a physiologic pharmacokinetic model of glucose homeostasis for assessment of performance requirements for improved insulin therapies. Diabetes Care. 1982;5:148-57. doi: 10.2337/diacare.5.3.148. PubMed PMID: 6756834.
- Eren-Oruklu M, Cinar A, Quinn L, Smith D. Adaptive control strategy for regulation of blood glucose levels in patients with type 1 diabetes. Journal of Process Control. 2009;19:1333-46. doi: 10.1016/j.jprocont.2009.04.004.
- Clarke WL, Cox D, Gonder-Frederick LA, Carter W, Pohl SL. Evaluating clinical accuracy of systems for self-monitoring of blood glucose. Diabetes Care. 1987;10:622-8. doi: 10.2337/diacare.10.5.622. PubMed PMID: 3677983.
- Mahata A, Mondal SP, Alam S, Roy B. Mathematical model of glucose-insulin regulatory system on diabetes mellitus in fuzzy and crisp environment. Ecological Genetics and Genomics. 2017;2:25-34. doi: 10.1016/j.egg.2016.10.002.
- Kumar D. Mathematical Model for Glucose-Insulin Regulatory System of Diabetes Mellitus. Advances in Applied Mathematical Biosciences. 2011;2:39-46.
- Bede B, Gal SG. Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations. Fuzzy Sets and Systems. 2005;151:581-99. doi: 10.1016/j.fss.2004.08.001.
- Bennett DL, Gourley SA. Asymptotic properties of a delay differential equation model for the interaction of glucose with plasma and interstitial insulin. Applied Mathematics and Computation. 2004;151:189-207. doi: 10.1016/s0096-3003(03)00332-1.
|