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Recurrence Plots and Their Quantifications: Expanding Horizons pp 169–183Cite as

Recurrence Analysis of Cardiac Restitution in Human Ventricle

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Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 180))

Abstract

The cardiac restitution curve describes functional relationships between diastolic intervals and their corresponding action potential durations. Although the simplest relationship is that restitution curves are monotonic, empirical studies have suggested that cardiac patients present a more complex dynamical process characterized, for instance, by a non-monotonic restitution curve. The purpose of this chapter is to analyze the dynamical properties of a non-monotonic cardiac restitution curve model derived from previously published clinical data. To achieve this goal, we use Recurrence Quantitative Analysis combined with Lyapunov exponents and Supertrack Functions in order to describe the complex dynamics underlying non-monotonic restitution curves. We conclude by highlighting that a consequence of the advanced complex dynamics that emerges from the aforementioned non-monotonicity, is the increasing risk of alternant rhythms.

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References

  1. J.M. Pastore, S.D. Girouard, K.R. Laurita, F.G. Akar, D.S. Rosenbaum, Mechanism linking T-wave alternans to the genesis of cardiac fibrillation. Circulation 99, 1385–1394 (1999)

    Article  Google Scholar 

  2. M.R. Guevara, G. Ward, A. Shrier, L. Glass, Electrical alternans and period doubling bifurcation. IEEE Comput. Cardiol. 167, 18–24 (1984)

    Google Scholar 

  3. J.B. Nolasco, R.W. Dahlen, A graphic method for the study of alternation in cardiac action potentials. J. Appl. Physiol. 25, 191–196 (1968)

    Article  Google Scholar 

  4. M.R. Franz, The electrical restitution curve revisited: steep or flat slope—which is better? J. Cardiovasc. Electrophysiol. 14, S140–S147 (2003)

    Google Scholar 

  5. J.N. Weiss, A. Garfinkel, H.S. Karagueuzian, T.P. Nguyen, R. Olcese, P.S. Chen, Z. Qu, Perspective: a dynamics-based classification of ventricular arrhythmias. J. Mol. Cell. Cardiol. 82, 136–154 (2015)

    Article  Google Scholar 

  6. P.N. Jordan, D.J. Christini, Determining the effects of memory and action potential duration alternans on cardiac restitution using a constant-memory restitution protocol. Physiol. Meas. 25(4), 1013 (2004)

    Google Scholar 

  7. S.D. McIntyre, V. Kakade, Y. Mori, E.G. Tolkacheva, Heart rate variability and alternans formation in the heart: The role of feedback in cardiac dynamics. J. Theor. Biol. 350, 90–97 (2014)

    Article  MathSciNet  Google Scholar 

  8. F. Fenton, E.M. Cherry, Cardiac Dynamics: Restitution (2012) http://www.scholarpedia.org/article/User:Flavio_H_Fenton/Proposed/Restitution

  9. A. Garfinkel, Y.H. Kim, O. Voroshilovsky, Z. Qu, J.R. Kil, M.H. Lee, H.S. Karagueuzian, J.N. Weiss, P.S. Chen, Preventing ventricular fibrillation by flattening cardiac restitution. Proc. Natl. Acad. Sci. USA 97, 6061–6066 (2000)

    Article  ADS  Google Scholar 

  10. A. Karma, New paradigm for drug therapies of cardiac fibrillation. PNAS 97(11) (2000)

    Google Scholar 

  11. M. Watanabe, N.F. Otani, R.F. Gilmour Jr, Biphasic restitution of action potential duration and complex dynamics in ventricular myocardium. Circ. Res. 76, 915–921 (1995)

    Article  Google Scholar 

  12. H. Dvir, S. Zlochiver, The Interrelations among stochastic pacing, stability, and memory in the Heart. Biophys. J. 107, 1023–1034 (2014)

    Google Scholar 

  13. H. Jiang, D. Zhao, B. Cui, Z. Lu, J. Lü, F. Chen, M. Bao, Electrical restitution determined by epicardial contact mapping and surface electrocardiogram: its role in ventricular fibrillation inducibility in swine. J. Electrocardiol. 41, 152–159 (2008)

    Article  Google Scholar 

  14. B.C. Knollmann, T. Schober, A.O. Petersen, S.G. Sirenko, M.R. Franz, Action potential characterization in intact mouse heart: steady-state cycle length dependence and electrical restitution. Am. J. Physiol.- Heart Circul. Physiol. 292(1), H614–H621 (2006). doi:10.1152/ajpheart.01085.2005

    Article  Google Scholar 

  15. M. Watanabe, D.P. Zipes, R.F. Gilmour Jr, Oscillations of diastolic interval and refractory period following premature and postmature stimuli in canine cardiac Purkinje fibers. Pacing Clin. Electrophysiol. 12, 1089–1103 (1989)

    Article  Google Scholar 

  16. R. Wu, A. Patwardhan, Restitution of action potential duration during sequential changes in diastolic intervals shows multimodal behavior. Circ. Res. 96, 634–641 (2012)

    Google Scholar 

  17. M.R. Guevara, L. Glass, A. Shrier, Phase locking, period-doubling bifurcations, and irregular dynamics in periodically stimulated cardiac cells. Science 214, 1350–1353 (1981)

    Article  ADS  Google Scholar 

  18. G.M. Hall, S. Bahar, D.J. Gauthier, Prevalence of rate-dependent behaviors in cardiac muscle. Phys. Rev. Lett. 82, 2995 (1999)

    Article  ADS  Google Scholar 

  19. A. Karma, Electrical alternans and spiral wave breakup in cardiac tissue. Chaos 4, 461–72 (1994)

    Google Scholar 

  20. O.E. Osadchii, Effects of ventricular pacing protocol on electrical restitution assessments in guinea-pig heart. Exp. Physiol. 97(7), 807–821 (2012)

    Google Scholar 

  21. H. Arce, A. Xu, H. González, M.R. Guevara, Alternans and higher-order rhythms in an ionic model of a sheet of ischemic ventricular muscle. Chaos 10(2), 411 (2000)

    Article  ADS  MATH  Google Scholar 

  22. B.J. Bas, Restitution of the action potential in cat papillary muscle. J. Physiol. 228, 1717–1724 (1975)

    Google Scholar 

  23. M.R. Franz, C.D. Swerdlow, L.B. Liem, J. Schaefer, Cycle length dependence of human action potential duration in vivo. J. Clin. Investig. 82(3), 972–979 (1988)

    Article  Google Scholar 

  24. A.M. Yue, M.R. Franz, P.R. Roberts, J.M. Morgan, Global endocardial electrical restitution in human right and left ventricles determined by noncontact mapping. J. Am. Coll. Cardiol. 46(6), 1067 (2005)

    Google Scholar 

  25. L.L. Trulla, A. Giuliani, J.P. Zbilut, C.L. Webber Jr, Recurrence quantification analysis of the logistic equation with transients. Phys. Lett. A 223(4), 255–260 (1996)

    Google Scholar 

  26. J. Gao, Recurrence time statistics for chaotic systems and their applications. Phys. Rev. Lett. 83(16), 3178–3181 (1999)

    Article  ADS  Google Scholar 

  27. J.P. Eckmann, S.O. Kamphorst, D. Ruelle, S. Ciliberto, Liapunov exponents from time series. Phys. Rev. A 34(6), 4971–4979 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  28. C.L. Webber Jr, J.P. Zbilut, Dynamical assessment of physiological systems and states using recurrence plot strategies. J. Appl. Physiol. 76, 965–973 (1994)

    Google Scholar 

  29. J.P. Zbilut, C.L. Webber Jr, Embeddings and delays as derived from quantification of recurrence plots. Phys. Lett. A 171, 199–203 (1992). doi:10.1161/01.CIR.99.10.1385

    Article  ADS  Google Scholar 

  30. N. Marwan, N. Wessel, U. Meyerfeldt, A. Schirdewan, J. Kurths, Recurrence plot based measures of complexity and its application to heart rate variability data. Phys. Rev. E 66(2), 026702 (2002)

    Google Scholar 

  31. N. Marwan, C.M. Romano, M. Thiel, J. Kurths, Recurrence plots for the analysis of complex systems. Phys. Rep. 438(5–6), 237–329 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  32. E.M. Oblow, Supertracks, supertrack functions and chaos in the quadratic map. Phys. Lett. A 128(8), 406–412 (1988). doi:10.1016/0375-9601(88)90119-3

    Article  ADS  MathSciNet  Google Scholar 

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Acknowledgment

We thank JoAnn Miller her valuable help in reviewing this manuscript.

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Authors and Affiliations

  1. Laboratorio de Biofísica de Sistemas Excitables, Facultad de Ciencias, Universidad Nacional Autónoma de México, Mexico, Mexico

    Humberto Arce & G. Hortensia González

  2. Centro de Ciencias Genómicas, Universidad Nacional Autónoma de México, Mexico, Mexico

    Ayari Fuentes

Authors
  1. Humberto Arce
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  2. Ayari Fuentes
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  3. G. Hortensia González
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Corresponding author

Correspondence to Humberto Arce .

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Editors and Affiliations

  1. Dept. of Cell and Molecular Physiology, Loyola University Chicago, Maywood, Illinois, USA

    Charles L. Webber, Jr.

  2. GIPSA-Lab, University Grenoble Alpes, Grenoble, France

    Cornel Ioana

  3. Potsdam Ins. for Climate Impact Research, Potsdam, Germany

    Norbert Marwan

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© 2016 Springer International Publishing Switzerland

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Arce, H., Fuentes, A., González, G.H. (2016). Recurrence Analysis of Cardiac Restitution in Human Ventricle. In: Webber, Jr., C., Ioana, C., Marwan, N. (eds) Recurrence Plots and Their Quantifications: Expanding Horizons. Springer Proceedings in Physics, vol 180. Springer, Cham. https://doi.org/10.1007/978-3-319-29922-8_9

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