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Bistability and Correlation with Arrhythmogenesis in a Model of the Right Atrium

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Abstract

Rapid pacing is an important tool for understanding cardiac arrhythmias. A recent experiment involving rapid pacing of sheep atria indicated that the initiation of atrial arrhythmias may be related to the 1:1/2:1 bistability. To elucidate the mechanism of this relation, this study applied the pacing protocol from the sheep study to an idealized model of the right atrium. The model included all major anatomical features, the sino-atrial node, and the regional differences in the action potential duration (APD). A pacing protocol was applied, in which the basic cycle length (BCL) was decreased in steps of 10 ms until the response switched to 2:1, then BCL was increased. The 1:1-to-2:1 transitions occurred at shorter BCLs than the 2:1-to-1:1 transitions yielding a global bistability window of 60 ms. As in the sheep study, idiopathic waves were observed at BCLs within or near the bistability window. The model was used to quantify the types, prevalence, and persistence of idiopatic waves, study their initiation and termination, and relate them to the model components. The results demonstrate that idiopatic waveforms move with the shift of the bistability window and that they disappear when bistability is eliminated. Thus, this modeling study supports causal relationship between the 1:1/2:1 bistability and the initiation of arrhythmias.

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References

  1. Cabrera, J. A., D. Sanchez-Quintana, S. Y. Ho, A. Medina, and R. H. Anderson. The architecture of the atrial musculature between the orifice of the inferior caval vein and the tricuspid valve: The anatomy of the isthmus. J. Cardiovasc. Electrophysiol. 9:1186–1195, 1998.

    CAS  PubMed  Google Scholar 

  2. Cohen, G., M. White, R. Sochowski, A. Klein, P. Bridge, W. Stewart, and K. L. Chan. Reference values for normal adult transesophageal echocardiographic measurements. J. Am. Soc. Echocardiogr. 8:221–230, 1995.

    CAS  PubMed  Google Scholar 

  3. Courtemanche, M., R. J. Ramirez, and S. Nattel. Ionic mechanisms underlying human atrial action potential properties: Insights from a mathematical model. Am. J. Physiol. 275:H301–H321, 1998.

    CAS  PubMed  Google Scholar 

  4. Feng, J., L. Yue, Z. Wang, and S. Nattel. Ionic mechanisms of regional action potential heterogeneity in the canine right atrium. Circ. Res. 83:541–551, 1998.

    CAS  PubMed  Google Scholar 

  5. Fenton, F., and A. Karma. Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: Filament instability and fibrillation. Chaos 8:20–47, 1998.

    Article  PubMed  Google Scholar 

  6. Guevara, M. R., F. Alonso, D. Jeandupeux, and A. C. G. V. Ginneken. Alternans in periodically stimulated isolated ventricular myocytes: Experiment and model. In Cell to Cell Signalling: From Experiments to Theoretical Models, edited by A. Goldbeter. London, UK: Academic Press, 1989, 551–563.

    Google Scholar 

  7. Guevara, M. R., A. Shrier, and L. Glass. Chaotic and complex cardiac rhythms. In: Cardiac Electrophysiology, From Cell to Bedside, edited by D. P. Zipes and J. Jalife. Philadelphia, PA: W. B. Saunders Co., 1990, 192–201.

    Google Scholar 

  8. Hall, G. M., S. Bahar, and D. J. Gauthier. Prevalence of rate-dependent behaviors in cardiac muscle. Phys. Rev. Lett. 82:2995–2998, 1999.

    Article  CAS  Google Scholar 

  9. Hescheler, J., and R. Speicher. Regular and chaotic behaviour of cardiac cells stimulated at frequencies between 2 and 20,Hz. Eur. Biophy. J. 17:273–280, 1989.

    CAS  Google Scholar 

  10. Hogan, P. M., and L. D. Davis. Evidence for specialized fibers in the canine right atrium. Circ. Res. 23:387–396, 1968.

    CAS  PubMed  Google Scholar 

  11. Janse, M. J., and M. A. Allessie. Experimental observations on atrial fibrillation. In: Atrial Fibrillation: Mechanisms and Management, edited by R. H. Falk and P. J. Podrid. Philadelphia, PA: Lippincott-Raven Publishers, 1997, 53–73.

    Google Scholar 

  12. Mines, G. R. On dynamic equilibrium in the heart. J. Physiol. 46:349–383, 1913.

    Google Scholar 

  13. Moulopoulos, S. D., N. Kardaras, and D. A. Sideris. Stimulus-response relationship in dog ventricle in vivo. Am. J. Physiol. 208:154–157, 1965.

    CAS  PubMed  Google Scholar 

  14. Nattel, S., M. Courtemanche, and Z. Wang. Functional and ionic mechanisms of antiarrhythmic drugs in atrial fibrillation. In: Atrial Fibrillation: Mechanisms and Management, edited by R. H. Falk and P. J. Podrid. Philadelphia, PA: Lippincott-Raven Publishers, 1997, 75–90.

    Google Scholar 

  15. Netter, F. H. The Ciba Collection of Medical Illustrations, vol. 5. Cincinnati, OH: The Hennegan Co., 1969.

    Google Scholar 

  16. Oliver, R. A., G. M. Hall, S. Bahar, W. Krassowska, P. D. Wolf, E. G. Dixon-Tulloch, and D. J. Gauthier. Existence of bistability and correlation with arrhythmogenesis in paced sheep atria. J. Cardiovasc. Electrophysiol. 11:797–805, 2000.

    CAS  PubMed  Google Scholar 

  17. Oliver, R. A., and W. Krassowska. Reproducing cardiac restitution properties using the Fenton-Karma membrane model. Ann. Biomed. Eng. submitted.

  18. Paes-de-Carvalho, A., W. C. de-Mello, and B. F. Hoffman. Electrophysiological evidence for specialized fiber types in rabbit atrium. Am. J. Physiol. 196:483–488, 1959.

    PubMed  Google Scholar 

  19. Pormann, J. B. A modular system for the bidomain equations. Durham, NC: Duke University, 1999, Ph.D. Dissertation.

  20. Pressler, M. L., P. N. Münster, and X-di Huang. Gap junction distribution in the heart: Functional relevance. In: Cardiac Electrophysiology. From Cell to Bedside, Second Edition, edited by D. P. Zipes and J. Jalife. Philadelphia, PA: W.B. Saunders Co., 1995, 144–150.

    Google Scholar 

  21. Qu, Z. L., A. Garfinkel, P.-S. Chen, and J. N. Weiss. Mechanisms of discordant alternans and induction of reentry in simulated cardiac tissue. Circulation 102:1664–1670, 2000.

    CAS  PubMed  Google Scholar 

  22. Roithinger, F. X., M. R. Karch, P. R. Steiner, A. Sippens Groenewegen, and M. D. Lesh. The spatial dispersion of atrial refractoriness and atrial fibrillation vulnerability. J. Interv. Card. Electr. 3:311–319, 1999.

    Article  CAS  Google Scholar 

  23. Schoels, W. Mechanisms of atrial flutter. In: Atrial Flutter and Fibrillation: From Basic to Clinical Applications, edited by N. Saoudi, W. Schoels, and N. El-Sherif. Armonk, NY: Futura Publishing Co., Inc., 1998, 53–65.

    Google Scholar 

  24. Tolkacheva, E. G., D. G. Schaeffer, D. J. Gauthier, and C. C. Mitchell. Analysis of the Fenton-Karma model through an approximation by a one-dimensional map. Chaos 12:1034–1042, 2002.

    Article  PubMed  Google Scholar 

  25. Vinet, A. Quasiperiodic circus movement in a loop model of cardiac tissue: Multistability and low dimensional equivalence. Ann. Biomed. Eng. 28:704–720, 2000.

    Article  CAS  PubMed  Google Scholar 

  26. Waldo, A. L., and A. L. Wit. Mechanisms of cardiac arrhythmias and conduction disturbances. In: The Heart, Arteries and Veins, edited by R. C. Schlant and R. W. Alexander. New York, NY: McGraw-Hill Inc., 1994, 659–704.

    Google Scholar 

  27. Yamashita, T., T. Nakajima, H. Hazama, E. Hamada, Y. Murakawa, K. Sawada, and M. Omata. Regional differences in transient outward current density and inhomogeneities of repolarization in rabbit right atrium. Circulation 92:3061–3069, 1995.

    CAS  PubMed  Google Scholar 

  28. Yehia, A. R., D. Jeandupeux, F. Alonso, and M. R. Guevara. Hysteresis and bistability in the direct transition from 1:1 to 2:1 rhythm in periodically driven single ventricular cells. Chaos 9:916–931, 1999.

    Article  PubMed  Google Scholar 

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Correspondence to Robert A. Oliver.

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Oliver, R.A., Henriquez, C.S. & Krassowska, W. Bistability and Correlation with Arrhythmogenesis in a Model of the Right Atrium. Ann Biomed Eng 33, 577–589 (2005). https://doi.org/10.1007/s10439-005-1473-z

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  • DOI: https://doi.org/10.1007/s10439-005-1473-z

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