Formalizing the Glucose Homeostasis Mechanism

  • Neeraj Kumar Singh
  • Hao Wang
  • Mark Lawford
  • Thomas S. E. Maibaum
  • Alan Wassyng
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8529)

Abstract

The failure of hardware or software in the medical domain can lead to injuries and loss of life. Design errors are a major source of the defects that are introduced during the system development process. Traditional validation and verification techniques such as simulation and testing are effective methods for detecting these defects, but are seriously limited in that they cannot guarantee to find all existing defects. Formal methods provide a complementary alternative to testing and simulation, and, although we do not yet have a ‘theory of coverage’ when combining formal validation and verification techniques with testing and simulation, the combination provides better coverage than any one of them on its own. The insulin infusion pump (IIP) is a critical system that is used by millions of people around the world. IIP failures are responsible for a large number of serious illnesses and deaths. This paper presents the formalization of the glucose homeostasis mechanism that provides an environmental model for the IIP. We can then use this model to validate the appropriateness and correctness of system behaviours at an early stage of development.

Keywords

Homeostasis Diabetes Event-B Formal methods Proof-based development Refinement 

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References

  1. 1.
    Li, J., Kuang, Y., Mason, C.C.: Modeling the glucoseinsulin regulatory system and ultradian insulin secretory oscillations with two explicit time delays. Journal of Theoretical Biology 242(3), 722–735 (2006)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Bolie, V.W.: Coefficients of normal blood glucose regulation. Journal of Applied Physiology 16(5), 783–788 (1961)Google Scholar
  3. 3.
    Ajmera, I., Swat, M., Laibe, C., Novère, N.L., Chelliah, V.: The impact of mathematical modeling on the understanding of diabetes and related complications. CPT: Pharmacometrics & Systems Pharmacology 2, e54 (2013)Google Scholar
  4. 4.
    Chen, Y., Lawford, M., Wang, H., Wassyng, A.: Insulin pump software certification. In: Gibbons, J., MacCaull, W. (eds.) FHIES 2013. LNCS, vol. 8315, pp. 87–106. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  5. 5.
    Center for Devices and Radiological Health: Safety of Marketed Med. Devices, FDA (2006)Google Scholar
  6. 6.
    A Reseach and Development Needs Report by NITRD: High-Confidence Medical Devices: Cyber-Physical Systems for 21st Century Health Care, http://www.nitrd.gov/About/MedDevice-FINAL1-web.pdf
  7. 7.
    Keatley, K.L.: A review of the fda draft guidance document for software validation: Guidance for industry. Qual. Assur. 7(1), 49–55 (1999)Google Scholar
  8. 8.
    Lee, I., Pappas, G.J., Cleaveland, R., Hatcliff, J., Krogh, B.H., Lee, P., Rubin, H., Sha, L.: High-confidence medical device software and systems. Computer 39(4), 33–38 (2006)CrossRefGoogle Scholar
  9. 9.
    Bowen, J., Stavridou, V.: Safety-critical systems, formal methods and standards. Software Engineering Journal 8(4), 189–209 (1993)CrossRefGoogle Scholar
  10. 10.
    Singh, N.K.: Using Event-B for Critical Device Software Systems. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  11. 11.
    Méry, D., Singh, N.K.: Real-time animation for formal specification. In: Aiguier, M., Bretaudeau, F., Krob, D. (eds.) Complex Systems Design & Management, pp. 49–60. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  12. 12.
    Wassyng, A.: Though this be madness, yet there is method in it? In: Proc. FormaliSE, pp. 1–7. IEEE (2013)Google Scholar
  13. 13.
    Project RODIN: Rigorous open development environment for complex systems (2004), http://rodin-b-sharp.sourceforge.net/
  14. 14.
    Leuschel, M., Butler, M.: ProB: A Model Checker for B. In: Araki, K., Gnesi, S., Mandrioli, D. (eds.) FME 2003. LNCS, vol. 2805, pp. 855–874. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  15. 15.
    Silber, H.E., Jauslin, P.M., Frey, N., Gieschke, R., Simonsson, U.S.H., Karlsson, M.O.: An integrated model for glucose and insulin regulation in healthy volunteers and type 2 diabetic patients following intravenous glucose provocations. The Journal of Clinical Pharmacology 47(9), 1159–1171 (2007)CrossRefGoogle Scholar
  16. 16.
    Chay, T.R., Keizer, J.: Theory of the effect of extracellular potassium on oscillations in the pancreatic beta-cell. Biophysical Journal 48(5), 815 (1985)CrossRefGoogle Scholar
  17. 17.
    Han, K., Kang, H., Kim, J., Choi, M.: Mathematical models for insulin secretion in pancreatic β-cells. ISLETS 4, 94–107 (2012)CrossRefGoogle Scholar
  18. 18.
    De Gaetano, A., Arino, O.: Mathematical modelling of the intravenous glucose tolerance test. Journal of Mathematical Biology 40(2), 136–168 (2000)CrossRefMATHMathSciNetGoogle Scholar
  19. 19.
    Drozdov, A., Khanina, H.: A model for ultradian oscillations of insulin and glucose. Mathematical and Computer Modelling 22(2), 23 (1995)CrossRefMATHMathSciNetGoogle Scholar
  20. 20.
    Siperstein, M.D.: The glucose tolerance test: A pitfall in the diagnosis of diabetes mellitus. Adv. Intern. Med. 20, 297–323 (1975)Google Scholar
  21. 21.
    Abrial, J.R.: Modeling in Event-B: System and Software Engineering (2010)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Neeraj Kumar Singh
    • 1
  • Hao Wang
    • 1
  • Mark Lawford
    • 1
  • Thomas S. E. Maibaum
    • 1
  • Alan Wassyng
    • 1
  1. 1.McMaster Centre for Software CertificationMcMaster UniversityHamiltonCanada

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