Medical & Biological Engineering & Computing

, Volume 55, Issue 2, pp 271–282 | Cite as

Modelling the effect of insulin on the disposal of meal-attributable glucose in type 1 diabetes

  • Fernando García-García
  • Roman Hovorka
  • Malgorzata E. Wilinska
  • Daniela Elleri
  • M. Elena Hernando
Original Article


The management of postprandial glucose excursions in type 1 diabetes has a major impact on overall glycaemic control. In this work, we propose and evaluate various mechanistic models to characterize the disposal of meal-attributable glucose. Sixteen young volunteers with type 1 diabetes were subject to a variable-target clamp which replicated glucose profiles observed after a high-glycaemic-load (\(n=8\)) or a low-glycaemic-load (\(n=8\)) evening meal. [6,6-\(^{2}\hbox {H}_2\)] and [U-\(^{13}\hbox {C}\);1,2,3,4,5,6,6-\(^{2}\hbox {H}_{7}\)] glucose tracers were infused to, respectively, mimic: (a) the expected post-meal suppression of endogenous glucose production and (b) the appearance of glucose due to a standard meal. Six compartmental models (all a priori identifiable) were proposed to investigate the remote effect of circulating plasma insulin on the disposal of those glucose tracers from the non-accessible compartments, representing e.g. interstitium. An iterative population-based parameter fitting was employed. Models were evaluated attending to physiological plausibility, posterior identifiability of their parameter estimates, accuracy—via weighted fitting residuals—and information criteria (i.e. parsimony). The most plausible model, best representing our experimental data, comprised: (1) a remote effect x of insulin active above a threshold \(x_{C}\) = 1.74 (0.81–2.50) \(\cdot \,10^{-2}\) min\(^{-1}\) [median (inter-quartile range)], with parameter \(x_{C}\) having a satisfactory support: coefficient of variation CV = 42.33 (31.34–65.34) %, and (2) steady-state conditions at the onset of the experiment (\(t=0\)) for the compartment representing the remote effect, but not for the masses of the tracer that mimicked endogenous glucose production. Consequently, our mechanistic model suggests non-homogeneous changes in the disposal rates for meal-attributable glucose in relation to plasma insulin. The model can be applied to the in silico simulation of meals for the optimization of postprandial insulin infusion regimes in type 1 diabetes.


Compartmental model Glucose disposal Glucose tracer Mass balance Parameter estimation Type 1 diabetes 


Compliance with ethical standards

Informed consent

Informed consent was obtained from all individual participants included in the study, which was approved by the Addenbrooke’s Hospital (University of Cambridge, UK) ethics committee.

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Abu-Rmileh A, Garcia-Gabin W, Zambrano D (2010) A robust sliding mode controller with internal model for closed-loop artificial pancreas. Med Biol Eng Comput 48(12):1191–1201. doi: 10.1007/s11517-010-0665-3 CrossRefPubMedGoogle Scholar
  2. 2.
    Ahola AJ, Mäkimattila S, Saraheimo M, Mikkilä V, Forsblom C, Freese R, Groop P, FinnDIANE Study Group (2010) Many patients with type 1 diabetes estimate their prandial insulin need inappropriately. J Diabetes 2(3):194–202. doi: 10.1111/j.1753-0407.2010.00086.x CrossRefPubMedGoogle Scholar
  3. 3.
    Basu R, Di Camillo B, Toffolo G, Basu A, Shah P, Vella A, Rizza R, Cobelli C (2003) Use of a novel triple-tracer approach to assess postprandial glucose metabolism. Am J Physiol Endocrinol Metab 284(1):E55–69. doi: 10.1152/ajpendo.00190.2001 CrossRefPubMedGoogle Scholar
  4. 4.
    Borg R, Kuenen JC, Carstensen B, Zheng H, Nathan DM, Heine RJ, Nerup J, Borch-Johnsen K, Witte DR, ADAG Study Group (2010) Associations between features of glucose exposure and A1C: the A1C-derived average glucose (ADAG) study. Diabetes 59(7):1585–1590. doi: 10.2337/db09-1774 CrossRefPubMedPubMedCentralGoogle Scholar
  5. 5.
    Carson ER, Cobelli C, Finkelstein L (1983) The mathematical modeling of metabolic and endocrine systems: model formulation, identification, and validation, 1st edn. Wiley, New YorkGoogle Scholar
  6. 6.
    Clarke WL, Anderson S, Breton M, Patek S, Kashmer L, Kovatchev B (2009) Closed-loop artificial pancreas using subcutaneous glucose sensing and insulin delivery and a model predictive control algorithm: the Virginia experience. J Diabetes Sci Technol 3(5):1031–1038CrossRefPubMedPubMedCentralGoogle Scholar
  7. 7.
    Dalla Man C, Camilleri M, Cobelli C (2006) A system model of oral glucose absorption: validation on gold standard data. IEEE Trans Bio Med Eng 53(12 Pt 1):2472–2478. doi: 10.1109/TBME.2006.883792 Google Scholar
  8. 8.
    Dalla Man C, Rizza RA, Cobelli C (2007) Meal simulation model of the glucose-insulin system. IEEE Trans Bio Med Eng 54(10):1740–1749. doi: 10.1109/TBME.2007.893506 CrossRefGoogle Scholar
  9. 9.
    Elleri D, Allen JM, Harris J, Kumareswaran K, Nodale M, Leelarathna L, Acerini CL, Haidar A, Wilinska ME, Jackson N, Umpleby AM, Evans ML, Dunger DB, Hovorka R (2013) Absorption patterns of meals containing complex carbohydrates in type 1 diabetes. Diabetologia 56(5):1108–1117. doi: 10.1007/s00125-013-2852-x CrossRefPubMedGoogle Scholar
  10. 10.
    Galvanin F, Barolo M, Macchietto S, Bezzo F (2010) Optimal design of clinical tests for the identification of physiological models of type 1 diabetes in the presence of model mismatch. Med Biol Eng Comput 49(3):263–277. doi: 10.1007/s11517-010-0717-8 CrossRefPubMedGoogle Scholar
  11. 11.
    Grosman B, Dassau E, Zisser HC, Jovanovic L, Doyle FJ (2010) Zone model predictive control: a strategy to minimize hyper- and hypoglycemic events. J Diabetes Sci Technol 4(4):961–975CrossRefPubMedPubMedCentralGoogle Scholar
  12. 12.
    Haidar A, Elleri D, Allen JM, Harris J, Kumareswaran K, Nodale M, Acerini CL, Wilinska ME, Jackson N, Umpleby AM, Evans ML, Dunger DB, Hovorka R (2012) Validity of triple- and dual-tracer techniques to estimate glucose appearance. Am J Physiol Endocrinol Metab 302(12):E1493–1501. doi: 10.1152/ajpendo.00581.2011 CrossRefPubMedPubMedCentralGoogle Scholar
  13. 13.
    Hovorka R (2011) Closed-loop insulin delivery: from bench to clinical practice. Nat Rev Endocrinol 7(7):385–395. doi: 10.1038/nrendo.2011.32 CrossRefPubMedGoogle Scholar
  14. 14.
    Hovorka R, Jayatillake H, Rogatsky E, Tomuta V, Hovorka T, Stein DT (2007) Calculating glucose fluxes during meal tolerance test: a new computational approach. Am J Physiol Endocrinol Metab 293(2):E610–619. doi: 10.1152/ajpendo.00546.2006 CrossRefPubMedGoogle Scholar
  15. 15.
    Hovorka R, Shojaee-Moradie F, Carroll PV, Chassin LJ, Gowrie IJ, Jackson NC, Tudor RS, Umpleby AM, Jones RH (2002) Partitioning glucose distribution/transport, disposal, and endogenous production during IVGTT. Am J Physiol Endocrinol Metab 282(5):E992–1007. doi: 10.1152/ajpendo.00304.2001 CrossRefPubMedGoogle Scholar
  16. 16.
    Hovorka R, Vicini P (2001) Parameter estimation. In: Carson E, Cobelli C (eds) Modeling methodology for physiology and medicine. Academic Press, London, pp 107–151CrossRefGoogle Scholar
  17. 17.
    Lanzola G, Toffanin C, Di Palma F, Del Favero S, Magni L, Bellazzi R (2015) Designing an artificial pancreas architecture: the AP@home experience. Med Biol Eng Comput 53(12):1271–1283. doi: 10.1007/s11517-014-1231-1 CrossRefPubMedGoogle Scholar
  18. 18.
    Laurenzi A, Bolla AM, Panigoni G, Doria V, Uccellatore A, Peretti E, Saibene A, Galimberti G, Bosi E, Scavini M (2011) Effects of carbohydrate counting on glucose control and quality of life over 24 weeks in adult patients with type 1 diabetes on continuous subcutaneous insulin infusion: a randomized, prospective clinical trial (GIOCAR). Diabetes Care 34(4):823–827. doi: 10.2337/dc10-1490 CrossRefPubMedPubMedCentralGoogle Scholar
  19. 19.
    Magni L, Forgione M, Toffanin C, Dalla Man C, Kovatchev B, De Nicolao G, Cobelli C (2009) Run-to-run tuning of model predictive control for type 1 diabetes subjects: in silico trial. J Diabetes Sci Technol 3(5):1091–1098CrossRefPubMedPubMedCentralGoogle Scholar
  20. 20.
    Priebe MG, Wachters-Hagedoorn RE, Heimweg JAJ, Small A, Preston T, Elzinga H, Stellaard F, Vonk RJ (2008) An explorative study of in vivo digestive starch characteristics and postprandial glucose kinetics of wholemeal wheat bread. Eur J Nutr 47(8):417–423. doi: 10.1007/s00394-008-0743-6 CrossRefPubMedGoogle Scholar
  21. 21.
    Rosenblatt J, Chinkes D, Wolfe M, Wolfe RR (1992) Stable isotope tracer analysis by GC-MS, including quantification of isotopomer effects. Am J Physiol 263(3 Pt 1):E584–596PubMedGoogle Scholar
  22. 22.
    Steimer JL, Mallet A, Golmard JL, Boisvieux JF (1984) Alternative approaches to estimation of population pharmacokinetic parameters: comparison with the nonlinear mixed-effect model. Drug Metab Rev 15(1–2):265–292. doi: 10.3109/03602538409015066 CrossRefPubMedGoogle Scholar
  23. 23.
    Toffolo G, Dalla Man C, Cobelli C, Sunehag AL (2008) Glucose fluxes during OGTT in adolescents assessed by a stable isotope triple tracer method. J Pediatr Endocrinol Metab 21(1):31–45CrossRefPubMedGoogle Scholar
  24. 24.
    Turksoy K, Bayrak ES, Quinn L, Littlejohn E, Cinar A (2013) Multivariable adaptive closed-loop control of an artificial pancreas without meal and activity announcement. Diabetes Technol Ther 15(5):386–400. doi: 10.1089/dia.2012.0283 CrossRefPubMedPubMedCentralGoogle Scholar
  25. 25.
    Vahidi O, Kwok KE, Gopaluni RB, Knop FK (2015) A comprehensive compartmental model of blood glucose regulation for healthy and type 2 diabetic subjects. Med Biol Eng Comput. doi: 10.1007/s11517-015-1406-4 PubMedGoogle Scholar
  26. 26.
    Wachters-Hagedoorn RE, Priebe MG, Heimweg JAJ, Heiner AM, Elzinga H, Stellaard F, Vonk RJ (2007) Low-dose acarbose does not delay digestion of starch but reduces its bioavailability. Diabet Med 24(6):600–606. doi: 10.1111/j.1464-5491.2007.02115.x CrossRefPubMedGoogle Scholar
  27. 27.
    Wachters-Hagedoorn RE, Priebe MG, Heimweg JAJ, Heiner AM, Englyst KN, Holst JJ, Stellaard F, Vonk RJ (2006) The rate of intestinal glucose absorption is correlated with plasma glucose-dependent insulinotropic polypeptide concentrations in healthy men. J Nutr 136(6):1511–1516PubMedGoogle Scholar
  28. 28.
    Wald A, Wolfowitz J (1940) On a test whether two samples are from the same population. Ann Math Stat 11(2):147–162CrossRefGoogle Scholar
  29. 29.
    Wilinska M, Chassin L, Schaller H, Schaupp L, Pieber T, Hovorka R (2005) Insulin kinetics in type-1 diabetes: continuous and bolus delivery of rapid acting insulin. IEEE Trans Biomed Eng 52(1):3–12. doi: 10.1109/TBME.2004.839639 CrossRefPubMedGoogle Scholar
  30. 30.
    Wilinska ME, Budiman ES, Taub MB, Elleri D, Allen JM, Acerini CL, Dunger DB, Hovorka R (2009) Overnight closed-loop insulin delivery with model predictive control: assessment of hypoglycemia and hyperglycemia risk using simulation studies. J Diabetes Sci Technol 3(5):1109–1120CrossRefPubMedPubMedCentralGoogle Scholar
  31. 31.
    Zisser H, Robinson L, Bevier W, Dassau E, Ellingsen C, Doyle FJ, Jovanovic L (2008) Bolus calculator: a review of four ‘smart’ insulin pumps. Diabetes Technol Ther 10(6):441–444. doi: 10.1089/dia.2007.0284 CrossRefPubMedGoogle Scholar

Copyright information

© International Federation for Medical and Biological Engineering 2016

Authors and Affiliations

  1. 1.Bioengineering and Telemedicine GroupUniversidad Politécnica de MadridMadridSpain
  2. 2.Networking Research Center on Bioengineering, Biomaterials and Nanomedicine (CIBER-BBN)MadridSpain
  3. 3.Wellcome Trust-MRC Institute of Metabolic ScienceUniversity of CambridgeCambridgeUK

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