Abstract
The aim of the study was to realize a mathematical model of insulin–glucose relationship in type I diabetes and test its effectiveness for the design of control algorithms in external artificial pancreas. A new mathematical model, divided into glucose and insulin sub-models, was developed from the so-called “minimal model”. The key feature is the representation of insulin sensitivity so as to permit the personalisation of the parameters. Real-time applications are based on an insulin standardised model. Clinical data were used to estimate model parameters. Root mean square error between simulated and real blood glucose profiles (Grms) was used to evaluate system efficacy. Results from parameter estimation and insulin standardisation showed a good capability of the model to identify individual characteristics. Simulation results with a Grms 1.30 mmol/l in the worst case testified the capacity of the model to accurately represent glucose–insulin relationship in type 1 diabetes allowing self tuning in real time.
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Albisser AM, Leibel BS, Ewart TG, Davidovac Z, Botz CK, Zingg W (1974) An artificial endocrine pancreas. Diabetes 23:389–404
Albisser AM, Schiffrin A, Schulz M, Tiran J, Leibel BS (1986) Insulin dosage adjustment using manual methods and computer algorithms: a comparative study. Med Biol Eng Comput 24(6):577–584
Arleth T, Andreassen S, Orsini Federici M, Massi Benedetti M (2000) A model of the endogenous glucose balance incorporating the characteristics of glucose transporters. Comput Methods Programs Biomed 62(3):219–234
Arleth T, Andreassen S, Orsini-Federici M, Timi A, Massi-Benedetti M (2000) A model of glucose absorption from mixed meals. In: IFAC proceedings. Karlsburg/Greifswald, Germany, pp 331–336
Bergman RN, Cobelli C (1981) Physiological evaluation of factors controlling glucose tolerance in men: measurement of insulin sensitivity and beta-cell glucose sensitivity from the response to intravenous glucose. J Clin Invest 68:1456–1467
Brunetti P, Orsini Federici M, Massi Benedetti M (2003) The artificial pancreas. Artif Cells Blood Substit Immobil Biotechnol 31(2):127–138
ClemensAH, Chung PH, Myers RW (1977) Development of biostator, a glucose controlled insulin infusion system (GCIIS). Horm Metab Res Suppl 7:23–33
Cobelli C, Toffolo G (1984) A model of glucose kinetics and their control by insulin, compartmental and non-compartmental approaches. Math Biosci 72:291–235
Defronzo RA, Ferrannini E, Hendler R, Felig P, Wahren J (1983) Regulation of splanchnic and peripheral glucose uptake by insulin and hyperglycemia in man. Diabetes 32:32–35
Fabietti PG, Massi Benedetti M, Bronzo F, Reboldi GP, Sarti E, Brunetti P (1991) Wearable system for acquisition, processing and storage of the signal from amperometric glucose sensors. Int J Artif Org 14(3):175–178
Fabietti PG, Calabrese G, Iorio M, Bistoni S, Brunetti P, Sarti E, Benedetti MM (2001) A mathematical model describing the glycemic response of diabetic patients to meal and i.v. infusion of insulin. Int J Artif Org 24(10):736–742
Ferrannini E, Defronzo RA (1997) Insulin actions in vivo: glucose metabolism. In: International textbook of diabetes mellitus, vol 1. Wiley, New York, pp 505–530
Heinemann L, Ampudia-Blasco FJ (1994) Glucose clamps with the Biostator: a critical reappraisal. Horm Metab Res 26(12):579–583
Heinemann L, Koschinsky T (2002) Continuous glucose monitoring: an overview of today’s technologies and their clinical applications. Int J Clin Pract Suppl 129:75–79
Heinemann L, Chantelau EA, Starke AA (1992) Pharmacokinetics and pharmacodynamics of subcutaneously administered U40 and U100 formulations of regular human insulin. Diab Metab 18:21–24
Hoffman A, Ziv E (1997) Pharmacokinetic considerations of new insulin formulations and routes of administration. Clin Pharmacokinet 33(4):285–301
Hovorka R, Chassin LJ, Wilinska ME, Canonico V, Akwi JA, Orsini Federici M, Massi-Benedetti M, Hutzli I, Zaugg C, Kaufmann H, Both M, Vering T, Schaller HC, Schaupp L, Bodenlenz M, Pieber TR (2004) Closing the loop: the adicol experience. Diab Technol Ther 6(3):307–318
Lindholm A, Jacobsen LV (2001) Clinical pharmacokinetics and pharmacodynamics of insulin aspart. Clin Pharmacokinet 40(9):641–659
Massi Benedetti M, Noy G, Johnston IDA, Worth R, Alberti KGMM (1981) Glucose controlled insulin infusion system (Biostator) application during surgery for a presumed pancreatic microinsulinoma. Diab Metab 7:41–44
Massi Benedetti M, Home PD, Gill GV, Burrin JM, Noy GA, Alberti KGMM (1987) Hormonal and metabolic responses in brittle diabetic patients during feedback intravenous insulin infusion. Diab Res Clin Pract 3:307–317
Pfeiffer EF, Thum C, Clemens AH (1974) The artificial beta cell—a continuous control of blood sugar by external regulation of insulin infusion (glucose controlled insulin infusion system). Horm Metab Res 6:339–342
Pickup J, Mccartney L, Rolinski O, Birch D (1999) In vivo glucose sensing for diabetes management: progress towards non-invasive monitoring. BMJ 319(7220):1289–1295
Regitting W, Trajanoski Z, Leis HJ, Ellmerer M, Wutte A, Sendlhofer G, Schaupp L, Brunner GA, Wach P, Pieber TR (1999) Plasma and interstitial glucose dynamics after intravenous glucose injection. Evaluation of the single-compartment glucose distribution assumption in the minimal models. Diabetes 48:1070–1081
Rizza R (1996) The role of splanchnic glucose appearance in determining carbohydrates tolerance. Diab Med 13:S23–S27
Shichiri M, Kawamori R, Yamasaki Y, Hakui N, Abe H (1982) Wearable artificial endocrine pancreas with needle-type glucose sensor. Lancet 2:1129–1131
Silverman M, Turner RJ (1992) Renal physiology. In handbook of physiology. Oxford University Press, Oxford, pp 2017–2038
Small DH, Mok SS, Williamson TG, Nurcombe V (1996) Role of proteoglycans in neural development, regeneration, and the aging brain. J Neurochem 67:889–899
Stephenson JM, Schernthaner G (1989) Dawn phenomenon and Somogyi effect in IDDM. Diab Care 12(4):245–251
The Diabetes Control and Complications Trial Research Group (1993) The effect of intensive treatment of diabetes on the development and progression of long-term complications in insulin-dependent diabetes mellitus. N Engl J Med 329:977–986
Van Den Berg BM, Vink H, Spaan JA (2003) The endothelial glycocalyx protects against myocardial edema. Circ Res 92(6):592–594
Wach P, Trajanoski Z, Kotanko P, Skrabal F (1995) Numerical approximation of mathematical model for absorption of subcutaneously injected insulin. Med Biol Eng Comput 33(1):18–23
Wise S, Nielsen M, Rizza R (1997) Effects of hepatic glycogen content on hepatic insulin action in humans: alteration in the relative contribution of glycogenolysis and gluconeogenesis to endogenous glucose production. J Clin Endocrinol Metab 82(6):1828–1833
Yamaguchi M, Kawabata Y, Kambe S, Wardell K, Nystrom FH, Naitoh K, Yoshida H (2004) Non-invasive monitoring of gingival crevicular fluid for estimation of blood glucose level. Med Biol Eng Comput 42(3):322–327
Yanagishita M, Hascall VC (1992) Cell-surface heparan sulfate proteoglycans. J Biol Chem 267:9451–9454
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Fabietti, P.G., Canonico, V., Federici, M.O. et al. Control oriented model of insulin and glucose dynamics in type 1 diabetics. Med Bio Eng Comput 44, 69–78 (2006). https://doi.org/10.1007/s11517-005-0012-2
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DOI: https://doi.org/10.1007/s11517-005-0012-2