Mode transition in any inappropriate mode can be a common cause of any mishap in a complex health-care system. This paper presents an approach for formalizing and reasoning about optimal mode transition in a health-care system that uses several operating modes in various operating states. Modes are formalized and their relation to a state-based formalism is established through a refinement approach. The efficiency of this approach is presented by formalizing an ideal operating mode transition of a cardiac pacemaker case study. An incremental approach is used to develop the system and its detailed design is verified through a series of refinements. The consequence of this approach is to improve system structuring, elicitation of system assumptions and expected functionality, as well as requirement traceability using modes in state-based modeling. Models are expressed in Event B modeling language and validated by a model checker tool: ProB.


Abstract model Event-B Proof-based development Refinement Modes Pacemaker 


  1. 1.
    Castellanos Jr., A., Lemberg, L., Rodriguez-Tocker, L., Berkovits, B.V.: Atrial synchronized pacemaker arrhythmias: revisited. Am. Heart, Pub. Med. 2, 199–208 (1968)CrossRefGoogle Scholar
  2. 2.
    Steinbach, K., Forohner, K., Meisl, F.: Atrial stimulation. In: Perez Gomez, F. (ed.) Cardiac Pacing, p. 629 (1985)Google Scholar
  3. 3.
    Abrial, J.-R.: Modeling in Event-B: System and Software Engineering. Cambridge University Press (2009) (forthcoming book)Google Scholar
  4. 4.
    Ausubel, K., Furman, S.: The Pacemaker Syndrome. Annals of Internal Medicine 103(3), 420–429 (1985)CrossRefGoogle Scholar
  5. 5.
    Back, R.: On correct refinement of programs. Journal of Computer and System Sciences 23(1), 49–68 (1979)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Allen, A., Clarke, M.: Rate responsive atrial pacing resulting in pacemaker syndrome. PACE 10, 1209 (1987)Google Scholar
  7. 7.
    Dotti, F.L., Iliasov, A., Ribeiro, L., Romanovsky, A.: Modal systems: Specification, refinement and realisation. In: Breitman, K., Cavalcanti, A. (eds.) ICFEM 2009. LNCS, vol. 5885, pp. 601–619. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  8. 8.
    Grumberg, O., Clarke, E.M., Peled, D.: Model Checking. MIT Press (1999) ISBN 978-0262032704Google Scholar
  9. 9.
    Elmqvist Rune, S.A.: An implantable pacemaker for the heart. In: Medical Electronics. International Conference on Medical Electronics, vol. 2, pp. 253–254. Iliffe, London (1959)Google Scholar
  10. 10.
    Fohler, G.: Realizing changes of operational modes with a pre run-time scheduled hard real-time system. In: Proceedings of the Second International Workshop on Responsive Computer Systems, pp. 287–300. Springer (1992)Google Scholar
  11. 11.
    Gomes, A.O., Oliveira, M.V.M.: Formal specification of a cardiac pacing system. In: Cavalcanti, A., Dams, D.R. (eds.) FM 2009. LNCS, vol. 5850, pp. 692–707. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  12. 12.
    Jackson, D.: Alloy: a lightweight object modelling notation. ACM Trans. Softw. Eng. Methodol. 11(2), 256–290 (2002)CrossRefGoogle Scholar
  13. 13.
    Jahanian, F., Mok, A.K.: Modechart: A specification language for real-time systems. IEEE Trans. Softw. Eng. 20(12), 933–947 (1994)CrossRefGoogle Scholar
  14. 14.
    Leuschel, M., Butler, M.: Michael Leuschel and Michael Butler. In: Araki, K., Gnesi, S., Mandrioli, D. (eds.) FME 2003. LNCS, vol. 2805, pp. 855–874. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  15. 15.
    Macedo, H.D., Larsen, P.G., Fitzgerald, J.S.: Incremental Development of a Distributed Real-Time Model of a Cardiac Pacing System Using VDM. In: Cuellar, J., Sere, K. (eds.) FM 2008. LNCS, vol. 5014, pp. 181–197. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  16. 16.
    Méry, D., Singh, N.K.: Functional behavior of a cardiac pacing system. International Journal of Discrete Event Control Systems 1 (2010) (in Press)Google Scholar
  17. 17.
    Parnas, D.L., Madey, J.: Functional documents for computer systems. Sci. Comput. Program. 25(1), 41–61 (1995)CrossRefGoogle Scholar
  18. 18.
    Project RODIN. Rigorous open development environment for complex systems (2004),
  19. 19.
    Real, J., Crespo, A.: Mode change protocols for real-time systems: A survey and a new proposal. Real-Time Syst. 26(2), 161–197 (2004)zbMATHCrossRefGoogle Scholar
  20. 20.
    Report. Recommendations for pacemaker prescription for symptomatic bradycardia. British Heart Journal 66(2),185–189 (1991)Google Scholar
  21. 21.
    Sutton, R., Stack, Z., Heaven, D., Ingram, A.: Mode switching for atrial tachyarrhythmias. The American Journal of Cardiology 83(5, suppl. 2), 202–210 (1999)Google Scholar
  22. 22.
    Epstein, A.E., DiMarco, J.P., Ellenbogen, K.A., Estes III, N.A.M., Freedman, R.A., Gettes, L.S., Gillinov, A.M., Gregoratos, G., Hammill, S.C., Hayes, D.L., Hlatky, M.A., Newby, L.K., Page, R.L., Schoenfeld, M.H., Silka, M.J., Stevenson, L.W., Sweeney, M.O.: ACC/AHA/HRS 2008 Guidelines for Device-Based Therapy of Cardiac Rhythm Abnormalities. Circulation, 117(21):2820–2840 (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Dominique Méry
    • 1
  • Neeraj Kumar Singh
    • 2
  1. 1.Université de Lorraine, LORIAVandœuvre-lès-NancyFrance
  2. 2.Department of Computer ScienceUniversity of YorkUnited Kingdom

Personalised recommendations