Skip to main content
SpringerLink
Log in
SpringerLink
Log in

Synthesising Robust and Optimal Parameters for Cardiac Pacemakers Using Symbolic and Evolutionary Computation Techniques

  • Conference paper
  • First Online:
Hybrid Systems Biology (HSB 2015)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 9271))

Included in the following conference series:

Abstract

We consider the problem of automatically finding safe and robust values of timing parameters of cardiac pacemaker models so that a quantitative objective, such as the pacemaker energy consumption or its cardiac output (a heamodynamic indicator of the human heart), is optimised in a finite path. The models are given as parametric networks of timed I/O automata with data, which extend timed I/O automata with priorities, real variables and real-valued functions, and specifications as Counting Metric Temporal Logic (CMTL) formulas. We formulate the parameter synthesis as a bilevel optimisation problem, where the quantitative objective (the outer problem) is optimised in the solution space obtained from optimising an inner problem that yields the maximal robustness for any parameter of the model. We develop an SMT-based method for solving the inner problem through a discrete encoding, and combine it with evolutionary algorithms and simulations to solve the outer optimisation task. We apply our approach to the composition of a (non-linear) multi-component heart model with the parametric dual chamber pacemaker model in order to find the values of multiple timing parameters of the pacemaker for different heart diseases.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • 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

Institutional subscriptions

Notes

  1. 1.

    In order to have consistent resets, we assume that different components cannot update the same variable with different values during the same transition.

  2. 2.

    Not to be confused with the spurious counter-examples discussed before.

References

  1. André, É., Chatain, T., Fribourg, L., Encrenaz, E.: An inverse method for parametric timed automata. Int. J. Found. Comput. Sci. 20(05), 819–836 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  2. André, É., Fribourg, L.: Behavioral cartography of timed automata. In: Kučera, A., Potapov, I. (eds.) Reachability Problems. LNCS, vol. 6227, pp. 76–90. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  3. Arai, T., Lee, K., Cohen, R.J.: Cardiac output and stroke volume estimation using a hybrid of three windkessel models. In: EMBC, pp. 4971–4974. IEEE (2010)

    Google Scholar 

  4. Armando, A., Mantovani, J., Platania, L.: Bounded model checking of software using SMT solvers instead of SAT solvers. STTT 11(1), 69–83 (2009)

    Article  MATH  Google Scholar 

  5. Barbot, B., Kwiatkowska, M., Mereacre, A., Paoletti, N.: Estimation and verification of hybrid heart models for personalised medical and wearable devices. In: Roux, O., Bourdon, J. (eds.) CMSB 2015. LNCS, vol. 9308, pp. 3–7. Springer, Heidelberg (2015)

    Chapter  Google Scholar 

  6. Beyer, H.-G., Schwefel, H.-P.: Evolution strategies-a comprehensive introduction. Nat. Comput. 1(1), 3–52 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  7. Bozzelli, L., La Torre, S.: Decision problems for lower/upper bound parametric timed automata. FMSD 35(2), 121–151 (2009)

    MATH  Google Scholar 

  8. Bruyère, V., Raskin, J.-F.: Real-time model-checking: parameters everywhere. In: Pandya, P.K., Radhakrishnan, J. (eds.) FSTTCS 2003. LNCS, vol. 2914, pp. 100–111. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  9. Chen, T., Diciolla, M., Kwiatkowska, M., Mereacre, A.: Quantitative verification of implantable cardiac pacemakers over hybrid heart models. Inf. Comput. 236, 87–101 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  10. Cimatti, A., Mover, S., Tonetta, S.: SMT-based verification of hybrid systems. In: Hoffmann, J., Selman, B. (eds.) Proceedings of the Twenty-Sixth AAAI Conference on Artificial Intelligence, 22–26 July 2012, Toronto, Ontario, Canada. AAAI Press (2012)

    Google Scholar 

  11. Clarke, E., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  12. Colson, B., Marcotte, P., Savard, G.: An overview of bilevel optimization. Ann. Oper. Res. 153(1), 235–256 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  13. de Moura, L., Bjørner, N.S.: Z3: an efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  14. Deb, K.: An efficient constraint handling method for genetic algorithms. Comput. Methods Appl. Mech. Eng. 186(2), 311–338 (2000)

    Article  MATH  Google Scholar 

  15. Diciolla, M., Kim, C.H.P., Kwiatkowska, M., Mereacre, A.: Synthesising optimal timing delays for timed I/O automata. In: EMSOFT 2014. ACM (2014)

    Google Scholar 

  16. Doyen, L.: Robust parametric reachability for timed automata. Inf. Process. Lett. 102(5), 208–213 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  17. Fazeli, N., Hahn, J.-O.: Estimation of cardiac output and peripheral resistance using square-wave-approximated aortic flow signal. Front. Physiol 3, 736–743 (2012)

    Article  Google Scholar 

  18. Gao, S., Kong, S., Clarke, E.M.: Satisfiability modulo ODEs. In: Formal Methods in Computer-Aided Design (FMCAD), pp. 105–112. IEEE (2013)

    Google Scholar 

  19. 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)

    Chapter  Google Scholar 

  20. Gulwani, S., Tiwari, A.: Constraint-based approach for analysis of hybrid systems. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 190–203. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  21. Jiang, Z., Pajic, M., Moarref, S., Alur, R., Mangharam, R.: Modeling and verification of a dual chamber implantable pacemaker. In: Flanagan, C., König, B. (eds.) TACAS 2012. LNCS, vol. 7214, pp. 188–203. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  22. Jovanović, A., Kwiatkowska, M.: Parameter synthesis for probabilistic timed automata using stochastic game abstractions. In: Ouaknine, J., Potapov, I., Worrell, J. (eds.) RP 2014. LNCS, vol. 8762, pp. 176–189. Springer, Heidelberg (2014)

    Google Scholar 

  23. Jovanović, A., Lime, D., Roux, O.H.: Integer parameter synthesis for timed automata. In: Piterman, N., Smolka, S.A. (eds.) TACAS 2013. LNCS, vol. 7795, pp. 401–415. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  24. Kerner, D.R.: Solving windkessel models with mlab (2007). http://www.civilized.com/mlabexamples/windkesmodel.htmld

  25. Kindermann, R., Junttila, T., Niemelä, I.: Beyond lassos: complete SMT-based bounded model checking for timed automata. In: Giese, H., Rosu, G. (eds.) FORTE 2012 and FMOODS 2012. LNCS, vol. 7273, pp. 84–100. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  26. Kindermann, R., Junttila, T., Niemelä, I.: SMT-based induction methods for timed systems. In: Jurdziński, M., Ničković, D. (eds.) FORMATS 2012. LNCS, vol. 7595, pp. 171–187. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  27. Knapik, M., Penczek, W.: Bounded model checking for parametric timed automata. In: Jensen, K., Donatelli, S., Kleijn, J. (eds.) ToPNoC V. LNCS, vol. 6900, pp. 141–159. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  28. Kovásznai, G., Fröhlich, A., Biere, A.: On the complexity of fixed-size bit-vector logics with binary encoded bit-width. In: SMT, pp. 44–56 (2012)

    Google Scholar 

  29. Kwiatkowska, M., Lea-Banks, H., Mereacre, A., Paoletti, N.: Formal modelling and validation of rate-adaptive pacemakers. In: ICHI, pp. 23–32. IEEE (2014)

    Google Scholar 

  30. Kwiatkowska, M., Mereacre, A., Paoletti, N., Patanè, A.: Synthesising robust and optimal parameters for cardiac pacemakers using symbolic and evolutionary computation techniques. Technical Report RR-15-09, Department of Computer Science, University of Oxford (2015)

    Google Scholar 

  31. Lian, J., Krätschmer, H., Müssig, D., Stotts, L.: Open source modeling of heart rhythm and cardiac pacing. Open Pacing Electrophysiol. Ther. J. 3, 4 (2010)

    Google Scholar 

  32. Méry, D., Singh, N.K.: Closed-loop modeling of cardiac pacemaker and heart. In: Weber, J., Perseil, I. (eds.) FHIES 2012. LNCS, vol. 7789, pp. 151–166. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  33. Ouaknine, J., Worrell, J.: On the decidability of metric temporal logic. In: Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science, LICS 2005, pp. 188–197. IEEE (2005)

    Google Scholar 

  34. Rabinovich, A.: Complexity of metric temporal logics with counting and the pnueli modalities. Theor. Comput. Sci. 411(22), 2331–2342 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  35. Rudolph, G.: An evolutionary algorithm for integer programming. In: Davidor, Y., Schwefel, H.-P., Männer, R. (eds.) PPSN III. LNCS, vol. 866, pp. 139–148. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  36. Boston Scientific: Pacemaker System Specification. Boston Scientific, Boston (2007)

    Google Scholar 

  37. Sturm, T., Tiwari, A.: Verification and synthesis using real quantifier elimination. In: Proceedings of the 36th International Symposium on Symbolic and Algebraic Computation, pp. 329–336. ACM (2011)

    Google Scholar 

  38. Traonouez, L.-M.: A parametric counterexample refinement approach for robust timed specifications. arXiv preprint arXiv:1207.4269 (2012)

Download references

Acknowledgments

This work is supported by the ERC AdG VERIWARE and ERC PoC VERIPACE.

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Oxford, Oxford, UK

    Marta Kwiatkowska, Alexandru Mereacre & Nicola Paoletti

  2. Department of Mathematics and Computer Science, University of Catania, Catania, Italy

    Andrea Patanè

Authors
  1. Marta Kwiatkowska
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alexandru Mereacre
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nicola Paoletti
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Andrea Patanè
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nicola Paoletti .

Editor information

Editors and Affiliations

  1. University of Oxford, Oxford, United Kingdom

    Alessandro Abate

  2. Faculty of Informatics, Masaryk University, Brno, Czech Republic

    David Šafránek

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Kwiatkowska, M., Mereacre, A., Paoletti, N., Patanè, A. (2015). Synthesising Robust and Optimal Parameters for Cardiac Pacemakers Using Symbolic and Evolutionary Computation Techniques. In: Abate, A., Šafránek, D. (eds) Hybrid Systems Biology. HSB 2015. Lecture Notes in Computer Science(), vol 9271. Springer, Cham. https://doi.org/10.1007/978-3-319-26916-0_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-26916-0_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26915-3

  • Online ISBN: 978-3-319-26916-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation