Quantitative Regular Expressions for Arrhythmia Detection Algorithms

  • Houssam AbbasEmail author
  • Alena Rodionova
  • Ezio Bartocci
  • Scott A. Smolka
  • Radu Grosu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10545)


Motivated by the problem of verifying the correctness of arrhythmia-detection algorithms, we present a formalization of these algorithms in the language of Quantitative Regular Expressions. QREs are a flexible formal language for specifying complex numerical queries over data streams, with provable runtime and memory consumption guarantees. The medical-device algorithms of interest include peak detection (where a peak in a cardiac signal indicates a heartbeat) and various discriminators, each of which uses a feature of the cardiac signal to distinguish fatal from non-fatal arrhythmias. Expressing these algorithms’ desired output in current temporal logics, and implementing them via monitor synthesis, is cumbersome, error-prone, computationally expensive, and sometimes infeasible.

In contrast, we show that a range of peak detectors (in both the time and wavelet domains) and various discriminators at the heart of today’s arrhythmia-detection devices are easily expressible in QREs. The fact that one formalism (QREs) is used to describe the desired end-to-end operation of an arrhythmia detector opens the way to formal analysis and rigorous testing of these detectors’ correctness and performance. Such analysis could alleviate the regulatory burden on device developers when modifying their algorithms. The performance of the peak-detection QREs is demonstrated by running them on real patient data, on which they yield results on par with those provided by a cardiologist.


Peak Detection Electrocardiograms Arrythmia discrimination ICDs Quantitative Regular Expressions 



The authors would like to thank Konstantinos Mamouras for insightful discussions about QREs and for providing the QRE Java library we used in this paper. This work is supported in part by AFOSR Grant FA9550-14-1-0261 and NSF Grants IIS-1447549, CNS-1446832, CNS-1446664, CNS-1445770, and CNS-1445770, and Austrian National Research Network grants S 11405-N23 and S 11412-N23 (RiSE/SHiNE of the FWF) and the ICT COST Action IC1402 Runtime Verification beyond Monitoring.


  1. 1.
    Alur, R., Fisman, D., Raghothaman, M.: Regular programming for quantitative properties of data streams. In: Thiemann, P. (ed.) ESOP 2016. LNCS, vol. 9632, pp. 15–40. Springer, Heidelberg (2016). doi: 10.1007/978-3-662-49498-1_2 CrossRefGoogle Scholar
  2. 2.
    Alur, R., Freilich, A., Raghothaman, M.: Regular combinators for string transformations. In: Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), CSL-LICS 2014, pp. 9:1–9:10. ACM, New York (2014)Google Scholar
  3. 3.
    Asarin, E., Caspi, P., Maler, O.: Timed regular expressions. J. ACM 49(2), 172–206 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Bartocci, E., Bortolussi, L., Sanguinetti, G.: Data-driven statistical learning of temporal logic properties. In: Legay, A., Bozga, M. (eds.) FORMATS 2014. LNCS, vol. 8711, pp. 23–37. Springer, Cham (2014). doi: 10.1007/978-3-319-10512-3_3 Google Scholar
  5. 5.
    Bozzelli, L., Sánchez, C.: Foundations of boolean stream runtime verification. In: Bonakdarpour, B., Smolka, S.A. (eds.) RV 2014. LNCS, vol. 8734, pp. 64–79. Springer, Cham (2014). doi: 10.1007/978-3-319-11164-3_6 Google Scholar
  6. 6.
    Brim, L., Dluhos, P., Safránek, D., Vejpustek, T.: STL-*: extending signal temporal logic with signal-value freezing operator. Inf. Comput. 236, 52–67 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Bufo, S., Bartocci, E., Sanguinetti, G., Borelli, M., Lucangelo, U., Bortolussi, L.: Temporal logic based monitoring of assisted ventilation in intensive care patients. In: Margaria, T., Steffen, B. (eds.) ISoLA 2014. LNCS, vol. 8803, pp. 391–403. Springer, Heidelberg (2014). doi: 10.1007/978-3-662-45231-8_30 Google Scholar
  8. 8.
    Chakarov, A., Sankaranarayanan, S., Fainekos, G.: Combining time and frequency domain specifications for periodic signals. In: Khurshid, S., Sen, K. (eds.) RV 2011. LNCS, vol. 7186, pp. 294–309. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-29860-8_22 CrossRefGoogle Scholar
  9. 9.
    D’Angelo, B., Sankaranarayanan, S., Sánchez, C., Robinson, W., Finkbeiner, B., Sipma, H.B., Mehrotra, S., Manna, Z.: LOLA: runtime monitoring of synchronous systems. In: Proceedings of the 12th International Symposium of Temporal Representation and Reasoning (TIME 2005), pp. 166–174. IEEE Computer Society Press (2005)Google Scholar
  10. 10.
    Demri, S., Lazic, R., Nowak, D.: On the freeze quantifier in constraint LTL: decidability and complexity. Inf. Comput. 205(1), 2–24 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Donzé, A., Maler, O., Bartocci, E., Nickovic, D., Grosu, R., Smolka, S.A.: On temporal logic and signal processing. In: Chakraborty, S., Mukund, M. (eds.) ATVA 2012. LNCS, vol. 7561, pp. 92–106. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-33386-6_9 CrossRefGoogle Scholar
  12. 12.
    Ferrère, T., Maler, O., Ničković, D., Ulus, D.: Measuring with timed patterns. In: Kroening, D., Păsăreanu, C.S. (eds.) CAV 2015. LNCS, vol. 9207, pp. 322–337. Springer, Cham (2015). doi: 10.1007/978-3-319-21668-3_19 CrossRefGoogle Scholar
  13. 13.
    Haghighi, I., Jones, A., Kong, Z., Bartocci, E., Grosu, R., Belta, C.: Spatel: a novel spatial-temporal logic and its applications to networked systems. In: Proceedings of HSCC 2015: The 18th International Conference on Hybrid Systems: Computation and Control, pp. 189–198. ACM (2015)Google Scholar
  14. 14.
    Harel, E., Lichtenstein, E., Pnueli, A.: Explicit clock temporal logic. IEEE (1990)Google Scholar
  15. 15.
    Koymans, R.: Specifying real-time properties with metric temporal logic. Real-Time Syst. 2(4), 255–299 (1990)CrossRefGoogle Scholar
  16. 16.
    Krishna, S.N., Madnani, K., Pandya, P.K.: Metric temporal logic with counting. In: Jacobs, B., Löding, C. (eds.) FoSSaCS 2016. LNCS, vol. 9634, pp. 335–352. Springer, Heidelberg (2016). doi: 10.1007/978-3-662-49630-5_20 CrossRefGoogle Scholar
  17. 17.
    Maler, O., Nickovic, D.: Monitoring temporal properties of continuous signals. In: Lakhnech, Y., Yovine, S. (eds.) FORMATS/FTRTFT -2004. LNCS, vol. 3253, pp. 152–166. Springer, Heidelberg (2004). doi: 10.1007/978-3-540-30206-3_12 CrossRefGoogle Scholar
  18. 18.
    Mallat, S., Hwang, W.L.: Singularity detection and processing with wavelets. IEEE Trans. Inf. Theor. 38(2), 617–643 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Mallat, S.G.: A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way. Academic Press, Amsterdam (2008)zbMATHGoogle Scholar
  20. 20.
    Mamouras, K., Raghothaman, M., Alur, R., Ives, Z., Khanna, S.: StreamQRE: modular specification and efficient evaluation of quantitative queries over streaming data. In: Proceedings of 38th ACM SIGPLAN Conference on Programming Language Design and Implementation, pp. 693–708 (2017)Google Scholar
  21. 21.
    Nenzi, L., Bortolussi, L., Ciancia, V., Loreti, M., Massink, M.: Qualitative and quantitative monitoring of spatio-temporal properties. In: Bartocci, E., Majumdar, R. (eds.) RV 2015. LNCS, vol. 9333, pp. 21–37. Springer, Cham (2015). doi: 10.1007/978-3-319-23820-3_2 CrossRefGoogle Scholar
  22. 22.
    Stroobandt, R.X., Barold, S.S., Sinnaeve, A.F.: Implantable Cardioverter - Defibrillators Step by Step. Wiley, Hoboken (2009)CrossRefGoogle Scholar
  23. 23.
    Swerdlow, C.D., Asirvatham, S.J., Ellenbogen, K.A., Friedman, P.A.: Troubleshooting implanted cardioverter defibrillator sensing problems I. Circ. Arrhythm. Electrophysiol. 7(6), 1237–1261 (2014)CrossRefGoogle Scholar
  24. 24.
    Ulus, D.: Montre: a tool for monitoring timed regular expressions. In: Majumdar, R., Kunĉak, V. (eds.) CAV 2017. LNCS, vol. 10426. Springer, Cham (2017). doi: 10.1007/978-3-319-63387-9_16 CrossRefGoogle Scholar
  25. 25.
    Ulus, D., Ferrère, T., Asarin, E., Maler, O.: Timed pattern matching. In: Legay, A., Bozga, M. (eds.) FORMATS 2014. LNCS, vol. 8711, pp. 222–236. Springer, Cham (2014). doi: 10.1007/978-3-319-10512-3_16 Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Houssam Abbas
    • 1
    Email author
  • Alena Rodionova
    • 2
  • Ezio Bartocci
    • 2
  • Scott A. Smolka
    • 3
  • Radu Grosu
    • 2
  1. 1.Department of Electrical and Systems EngineeringUniversity of PennsylvaniaPhiladelphiaUSA
  2. 2.Cyber-Physical Systems GroupTechnische Universität WienViennaAustria
  3. 3.Department of Computer ScienceStony Brook UniversityStony BrookUSA

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