Skip to main content

Formalization of Heart Models Based on the Conduction of Electrical Impulses and Cellular Automata

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNPSE,volume 7151)

Abstract

Tools and techniques based on formal methods have been recognized as a promising approach to supporting the process of verification and validation of critical systems in the early stages of their development. In particular, medical devices are very prone to showing unexpected system behaviour in operation because of the stochastic nature of the systems and when traditional methods are used for system testing. Device-related problems have been responsible for a large number of serious injuries. Officials of the US Food and Drug Administration (FDA) have found that many deaths and injuries related to these devices are caused by flaws in product design and engineering. Cardiac pacemakers and implantable cardioverter–defibrillators (ICDs) are the most critical of these medical devices, requiring closed-loop modelling (integrated system and environment modelling) for verification purposes before obtaining a certificate from the certification bodies. No technique is available to provide environment modelling for verifying the developed system models. This paper presents a methodology for modelling a biological system, such as the heart, to enable modelling in a biological environment. The heart model is based mainly on electrocardiography analysis, which models the heart system at the cellular level. The main objective of this methodology is to model the heart system and integrate it with a model of a medical device such as a cardiac pacemaker to specify a closed-loop model. To build an environment model for a closed-loop system is currently an open problem. The industry has long sought such an approach to validating a system model in a virtual biological environment. Our approach involves a pragmatic combination of formal specifications of the system and the biological environment to model a closed-loop system that enables verification of the correctness of the system and helps to improve the quality of the system.

Keywords

  • Heart Model
  • ECG
  • Cellular Automata
  • Event B
  • Proof-based development
  • Refinement

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   72.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Jaakko Malmivuo, R.P.: Bioelectromagnetism. Oxford University Press (1995) ISBN 0-19-505823-2

    Google Scholar 

  2. Khan, M.G.: Rapid ECG Interpretation. Humana Press (2008)

    Google Scholar 

  3. Maisel, W.H., Sweeney, M.O., Stevenson, W.G., Ellison, K.E., Epstein, L.M.: Recalls and safety alerts involving pacemakers and implantable cardioverter-defibrillator generators. JAMA: The Journal of the American Medical Association 286(7), 793–799 (2001)

    CrossRef  Google Scholar 

  4. Center for Devices and Radiological Health: Safety of Marketed Med. Devices, FDA (2006)

    Google Scholar 

  5. A Research 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

  6. Keatley, K.L.: A review of the fda draft guidance document for software validation: guidance for industry. Qual. Assur. 7(1), 49–55 (1999)

    CrossRef  Google Scholar 

  7. 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)

    CrossRef  Google Scholar 

  8. Méry, D., Singh, N.K.: Trustable Formal Specification for Software Certification. In: Margaria, T., Steffen, B. (eds.) ISoLA 2010. LNCS, vol. 6416, pp. 312–326. Springer, Heidelberg (2010)

    CrossRef  Google Scholar 

  9. Bowen, J., Stavridou, V.: Safety-critical systems, formal methods and standards. Software Engineering Journal 8(4), 189–209 (1993)

    CrossRef  Google Scholar 

  10. Jetley, R.P., Carlos, C., Iyer, S.P.: A case study on applying formal methods to medical devices: computer-aided resuscitation algorithm. STTT 5(4), 320–330 (2004)

    CrossRef  Google Scholar 

  11. Jetley, R., Purushothaman Iyer, S., Jones, P.: A formal methods approach to medical device review. Computer 39(4), 61–67 (2006)

    CrossRef  Google Scholar 

  12. 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)

    CrossRef  Google Scholar 

  13. Abrial, J.R.: Modeling in Event-B: System and Software Engineering. Cambridge University Press (2010)

    Google Scholar 

  14. Fitzgerald, J.: Logics of Specification Languages. In: Bjørner, D., Henson, M.C. (eds.) The Typed Logic of Partial Functions and the Vienna Development Method. EATCS Textbook in Computer Science, pp. 431–465. Springer, Heidelberg (2007)

    Google Scholar 

  15. Harrild, D.M., Henriquez, C.S., Atria, T.H., Harrild, D.M., Henriquez, C.S.: Cs, a computer model of normal conduction. The Human Atria, Circ. Res. 87, 25–36 (2000)

    Google Scholar 

  16. Bayes de Luna, A., Batcharov, V.N., Malik, M.: The morphology of the Electrocardiogram. In: The ESC Textbook of Cardiovascular Medicine. Blackwell Publishing Ltd. (2006)

    Google Scholar 

  17. von Neumann, J.: Theory of Self-Reproducing Automata. University of Illinois Press (1966); edited by Burks, A.W.

    Google Scholar 

  18. Artigou, J.-Y., Monsuez, J.-J., Societe française cardiologie: Cardiologie et maladies vasculaires. Elsevier Masson (2006)

    Google Scholar 

  19. Project RODIN: Rigorous open development environment for complex systems (2004), http://rodin-b-sharp.sourceforge.net/

  20. Plonsey, R., Barr, R.C.: Mathematical modeling of electrical activity of the heart. Journal of Electrocardiology 20(3), 219–226 (1987)

    CrossRef  Google Scholar 

  21. Kye-Rok Jun, Y.R.S., Kim, T.G.: A cellular automata model of activation process in ventricular muscle. In: SCSC 1994, pp. 769–774 (1994)

    Google Scholar 

  22. Berenfeld, O., Abboud, S.: Simulation of cardiac activity and the ecg using a heart model with a reaction-diffusion action potential. Medical Engg. & Physics 18(8), 615–625 (1996)

    CrossRef  Google Scholar 

  23. Adam, D.: Propagation of depolarization and repolarization processes in the myocardium-an anisotropic model. IEEE Transactions on Biomedical Engg. 38(2), 133–141 (1991)

    CrossRef  Google Scholar 

  24. Jiang, Z., Pajic, M., Connolly, A.T., Dixit, S., Mangharam, R.: Real-time heart model for implantable cardiac device validation and verification. In: 22nd Euromicro Conference on Real-Time Systems (IEEE ECRTS 2010) (July 2010)

    Google Scholar 

  25. Barold, S.S., Stroobandt, R.X., Sinnaeve, A.F.: Cardiac Pacemakers Step by Step. Futura Publishing (2004) ISBN 1-4051-1647-1

    Google Scholar 

  26. Ellenbogen, K.A., Wood, M.A.: Cardiac Pacing and ICDs, 4th edn. Blackwell (2005) ISBN-10 1-4051-0447-3

    Google Scholar 

  27. Hesselson, A.: Simplified Interpretations of Pacemaker ECGs. Blackwell Publishers (2003) ISBN 978-1-4051-0372-5

    Google Scholar 

  28. 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)

    CrossRef  Google Scholar 

  29. Love, C.J.: Cardiac Pacemakers and Defibrillators. Landes Bioscience Publishers (2006) ISBN 1-57059-691-3

    Google Scholar 

  30. Makowiec, D.: The Heart Pacemaker by Cellular Automata on Complex Networks. In: Umeo, H., Morishita, S., Nishinari, K., Komatsuzaki, T., Bandini, S. (eds.) ACRI 2008. LNCS, vol. 5191, pp. 291–298. Springer, Heidelberg (2008)

    CrossRef  Google Scholar 

  31. Back, R., von Wright, J.: Refinement Calculus A Systematic Introduction. Graduate Texts in Computer Science. Springer (1998)

    Google Scholar 

  32. Méry, D., Singh, N.K.: Technical Report on Formalisation of the Heart using Analysis of Conduction Time and Velocity of the Electrocardiography and Cellular-Automata. Technical report (2011), http://hal.inria.fr/inria-00600339/en/

  33. Clarke, E.M., Grumberg, O., Peled, D.: Model Checking. MIT Press (1999)

    Google Scholar 

  34. Méry, D., Singh, N.K.: Functional behavior of a cardiac pacing system. International Journal of Discrete Event Control Systems 1(2), 129–149 (2011)

    Google Scholar 

  35. EB2ALL: Automatic code generation from Event-B to many Programming Languages (2011), http://eb2all.loria.fr/

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Méry, D., Singh, N.K. (2012). Formalization of Heart Models Based on the Conduction of Electrical Impulses and Cellular Automata. In: Liu, Z., Wassyng, A. (eds) Foundations of Health Informatics Engineering and Systems. FHIES 2011. Lecture Notes in Computer Science, vol 7151. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32355-3_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-32355-3_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32354-6

  • Online ISBN: 978-3-642-32355-3

  • eBook Packages: Computer ScienceComputer Science (R0)