Simulating Insulin Infusion Pump Risks by In-Silico Modeling of the Insulin-Glucose Regulatory System

  • Sriram Sankaranarayanan
  • Georgios Fainekos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7605)


We present a case study on the use of robustness-guided and statistical model checking approaches for simulating risks due to insulin infusion pump usage by diabetic patients. Insulin infusion pumps allow for a continuous delivery of insulin with varying rates and delivery profiles to help patients self-regulate their blood glucose levels. However, the use of infusion pumps and continuous glucose monitors can pose risks to the patient including chronically elevated blood glucose levels (hyperglycemia) or dangerously low glucose levels (hypoglycemia).

In this paper, we use mathematical models of the basic insulin-glucose regulatory system in a diabetic patient, insulin infusion pumps, and the user’s interaction with these pumps defined by commonly used insulin infusion strategies for maintaining normal glucose levels. These strategies include common guidelines taught to patients by physicians and certified diabetes educators and have been implemented in commercially available insulin bolus calculators. Furthermore, we model the failures in the devices themselves along with common errors in the usage of the pump. We compose these models together and analyze them using two related techniques: (a) robustness guided state-space search to explore worst-case scenarios and (b) statistical model checking techniques to assess the probabilities of hyper- and hypoglycemia risks. Our technique can be used to identify the worst-case effects of the combination of many different kinds of failures and place high confidence bounds on their probabilities.


Sugar Entropy Starch Carbohydrate Syringe 


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  1. 1.
    Ackerman, E., Gatewood, L., Rosevear, J., Molnar, G.: Blood glucose regulation and diabetes. In: Heinmets, F. (ed.) Concepts and Models of Biomathematics, pp. 131–156. Marcel Dekker (1969)Google Scholar
  2. 2.
    Ackerman, E., Rosevear, J., McGuckin, W.: A mathematical model of the insulin-glucose tolerance test. Physics in Medicine and Biology 9, 202–213 (1964)CrossRefGoogle Scholar
  3. 3.
    Annapureddy, Y.S.R., Fainekos, G.E.: Ant colonies for temporal logic falsification of hybrid systems. In: Proceedings of the 36th Annual Conference of IEEE Industrial Electronics, pp. 91–96 (2010)Google Scholar
  4. 4.
    Annpureddy, Y., Liu, C., Fainekos, G., Sankaranarayanan, S.: S-TaLiRo: A Tool for Temporal Logic Falsification for Hybrid Systems. In: Abdulla, P.A., Leino, K.R.M. (eds.) TACAS 2011. LNCS, vol. 6605, pp. 254–257. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  5. 5.
    Arney, D.E., Jetley, R., Jones, P., Lee, I., Ray, A., Sokolsky, O., Zhang, Y.: Generic infusion pump hazard analysis and safety requirements: Version 1.0, CIS Technical Report, University of Pennsylvania (2009), (accessed May 2011)
  6. 6.
    Bergman, R.N.: Minimal model: Perspective from 2005. Hormone Research, 8–15 (2005)Google Scholar
  7. 7.
    Bergman, R.N., Urquhart, J.: The pilot gland approach to the study of insulin secretory dynamics. Recent Progress in Hormone Research 27, 583–605 (1971)Google Scholar
  8. 8.
    Castle, J., Ward, K.: Amperometric glucose sensors: Sources of error and potential benefit of redundancy. J. Diabetes Sci. and Tech. 4(1) (January 2010)Google Scholar
  9. 9.
    Chee, F., Fernando, T.: Closed-Loop Control of Blood Glucose. Springer (2007)Google Scholar
  10. 10.
    Clarke, E., Donzé, A., Legay, A.: Statistical Model Checking of Mixed-Analog Circuits with an Application to a Third Order Δ − Σ Modulator. In: Chockler, H., Hu, A.J. (eds.) HVC 2008. LNCS, vol. 5394, pp. 149–163. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  11. 11.
    Cobelli, C., Federspil, G., Pacini, G., Salvan, A., Scandellari, C.: An integrated mathematical model of the dynamics of blood glucose and its hormonal control. Mathematical Biosciences 58, 27–60 (1982)CrossRefMATHGoogle Scholar
  12. 12.
    Cobelli, C., Man, C.D., Sparacino, G., Magni, L., Nicolao, G.D., Kovatchev, B.P.: Diabetes: Models, signals and control (methodological review). IEEE Reviews in Biomedical Engineering 2, 54–95 (2009)CrossRefGoogle Scholar
  13. 13.
    Cobelli, C., Mari, A.: Control of diabetes with artificial systems for insulin delivery — algorithm independent limitations revealed by a modeling study. IEEE Trans. on Biomed. Engg. BME-32(10) (October 1985)Google Scholar
  14. 14.
    Dalla Man, C., Rizza, R.A., Cobelli, C.: Meal simulation model of the glucose-insulin system. IEEE Transactions on Biomedical Engineering 1(10), 1740–1749 (2006)Google Scholar
  15. 15.
    Facchinetti, A., Sparacino, G., Cobelli, C.: Modeling the error of continuous glucose monitoring sensor data: Critical aspects discussed through simulation studies. J. Diabetes Sci. and Tech. 4(1) (January 2010)Google Scholar
  16. 16.
    Fainekos, G., Pappas, G.J.: Robustness of temporal logic specifications for continuous-time signals. Theoretical Computer Science 410, 4262–4291 (2009)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Fainekos, G.E.: Robustness of Temporal Logic Specifications. PhD thesis, Department of Computer and Information Science, University of Pennsylvania (2008)Google Scholar
  18. 18.
    Fox, L., Buckloh, L., Smith, S.D., Wysocki, T., Mauras, N.: A randomized controlled trial of insulin pump therapy in young children with type 1 diabetes. Diabetes Care, 28(6) (June 2005)Google Scholar
  19. 19.
    Hovorka, R.: Continuous glucose monitoring and closed-loop systems. Diabetic Medicine 23(1), 1–12 (2005)CrossRefGoogle Scholar
  20. 20.
    Hovorka, R., Allen, J.M., Elleri, D., Chassin, L.J., Harris, J., Xing, D., Kollman, C., Hovorka, T., Larsen, A.M., Nodale, M., Palma, A.D., Wilinska, M., Acerini, C., Dunger, D.: Manual closed-loop delivery in children and adoloscents with type 1 diabetes: a phase 2 randomised crossover trial. Lancet 375, 743–751 (2010)CrossRefGoogle Scholar
  21. 21.
    Hovorka, R., Canonico, V., Chassin, L., Haueter, U., Massi-Benedetti, M., Frederici, M., Pieber, T., Shaller, H., Schaupp, L., Vering, T., Wilinska, M.: Nonlinear model predictive control of glucose concentration in subjects with type 1 diabetes. Physiological Measurement 25, 905–920 (2004)CrossRefGoogle Scholar
  22. 22.
    Hovorka, R., Shojaee-Moradie, F., Carroll, P., Chassin, L., Gowrie, I., Jackson, N., Tudor, R., Umpleby, A., Hones, R.: Partitioning glucose distribution/transport, disposal and endogenous production during IVGTT. Am. J. Physiol. Endocrinol. Metab. 282, 992–1007 (2002)CrossRefGoogle Scholar
  23. 23.
    Jha, S.K., Clarke, E.M., Langmead, C.J., Legay, A., Platzer, A., Zuliani, P.: A Bayesian Approach to Model Checking Biological Systems. In: Degano, P., Gorrieri, R. (eds.) CMSB 2009. LNCS, vol. 5688, pp. 218–234. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  24. 24.
    Jha, S.K., Datta, R., Langmead, C., Jha, S., Sassano, E.: Synthesis of insulin pump controllers from safety specifications using bayesian model validation. In: Proceedings of 10th Asia Pacific Bioinformatics Conference, APBC (2012)Google Scholar
  25. 25.
    Koymans, R.: Specifying real-time properties with metric temporal logic. Real-Time Systems 2(4), 255–299 (1990)CrossRefGoogle Scholar
  26. 26.
    Man, C., Camilleri, M., Cobelli, C.: A system model of oral glucose absorption: Validation on gold standard data. IEEE Transactions on Biomedical Engineering 53(12), 2472–2478 (2006)CrossRefGoogle Scholar
  27. 27.
    Man, C.D., Raimondo, D.M., Rizza, R.A., Cobelli, C.: GIM, simulation software of meal glucose-insulin model. J. Diabetes Sci. and Tech. 1(3) (May 2007)Google Scholar
  28. 28.
    Nghiem, T., Sankaranarayanan, S., Fainekos, G.E., Ivančić, F., Gupta, A., Pappas, G.J.: Monte-carlo techniques for falsification of temporal properties of non-linear hybrid systems. In: Hybrid Systems: Computation and Control, pp. 211–220. ACM Press (2010)Google Scholar
  29. 29.
    Patek, S., Bequette, B., Breton, M., Buckingham, B., Dassau, E., Doyle III, F., Lum, J., Magni, L., Zisser, H.: In silico preclinical trials: methodology and engineering guide to closed-loop control in type 1 diabetes mellitus. J. Diabetes Sci. Technol. 3(2), 269–282 (2009)CrossRefGoogle Scholar
  30. 30.
    Rizk, A., Batt, G., Fages, F., Soliman, S.: On a Continuous Degree of Satisfaction of Temporal Logic Formulae with Applications to Systems Biology. In: Heiner, M., Uhrmacher, A.M. (eds.) CMSB 2008. LNCS (LNBI), vol. 5307, pp. 251–268. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  31. 31.
    Roy, A., Parker, R.: Dynamic modeling of exercise effects on plasma glucose and insulin levels. J. Diabetes Sci. and Tech. 1(3), 338–347 (2007)CrossRefGoogle Scholar
  32. 32.
    Sankaranarayanan, S., Fainekos, G.E.: Falsification of temporal properties of hybrid systems using the cross-entropy method. In: HSCC, pp. 125–134. ACM (2012)Google Scholar
  33. 33.
    Sankaranarayanan, S., Homaei, H., Lewis, C.: Model-Based Dependability Analysis of Programmable Drug Infusion Pumps. In: Fahrenberg, U., Tripakis, S. (eds.) FORMATS 2011. LNCS, vol. 6919, pp. 317–334. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  34. 34.
    Scheiner, G.: Think like a pancreas: A Practical guide to managing diabetes with insulin. Da Capo Press (2011)Google Scholar
  35. 35.
    Skyler, J.S.: Atlas of Diabetes, 4th edn. Springer Science+Business Media (2012)Google Scholar
  36. 36.
    Sorensen, J.: A Physiological Model of Glucos Metabolism in Man and its use to Design and Access Improved Insulin Therapies for Diabetes. PhD thesis, Massachussetts Inst. of Technology. MIT (1985)Google Scholar
  37. 37.
    Teixeira, R.E., Malin, S.: The next generation of artificial pancreas control algorithms. J. Diabetes Sci. and Tech. 2, 105–112 (2008)CrossRefGoogle Scholar
  38. 38.
    Thimbleby, H.: Ignorance of interaction programming is killing people. ACM Interactions, 52–57 (2008)Google Scholar
  39. 39.
    Thimbleby, H.: Is it a dangerous prescription? BCS Interfaces 84, 5–10 (2010)Google Scholar
  40. 40.
    Wilinska, M., Chassin, L., Acerini, C.L., Allen, J.M., Dunber, D., Hovorka, R.: Simulation environment to evaluate closed-loop insulin delivery systems in type 1 diabetes. J. Diabetes Science and Technology 4 (January 2010)Google Scholar
  41. 41.
    Worthington, D.: Minimal model of food absorption in the gut. Medical Informatics 22(1), 35–45 (1997)CrossRefGoogle Scholar
  42. 42.
    Younes, H.L.S., Simmons, R.G.: Statistical probabilitistic model checking with a focus on time-bounded properties. Information & Computation 204(9), 1368–1409 (2006)MathSciNetCrossRefMATHGoogle Scholar
  43. 43.
    Zhang, Y., Jones, P.L., Jetley, R.: A hazard analysis for a generic insulin infusion pump. J. Diabetes Sci. and Tech. 4(2), 263–282 (2010)CrossRefGoogle Scholar
  44. 44.
    Zuliani, P., Platzer, A., Clarke, E.M.: Bayesian statistical model checking with application to simulink/stateflow verification. In: HSCC, pp. 243–252. ACM (2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Sriram Sankaranarayanan
    • 1
  • Georgios Fainekos
    • 2
  1. 1.University of ColoradoBoulderUSA
  2. 2.Arizona State UniversityTempeUSA

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