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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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.
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.
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.
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.
Fenton, F., and A. Karma. Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: Filament instability and fibrillation. Chaos 8:20–47, 1998.
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.
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.
Hall, G. M., S. Bahar, and D. J. Gauthier. Prevalence of rate-dependent behaviors in cardiac muscle. Phys. Rev. Lett. 82:2995–2998, 1999.
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.
Hogan, P. M., and L. D. Davis. Evidence for specialized fibers in the canine right atrium. Circ. Res. 23:387–396, 1968.
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.
Mines, G. R. On dynamic equilibrium in the heart. J. Physiol. 46:349–383, 1913.
Moulopoulos, S. D., N. Kardaras, and D. A. Sideris. Stimulus-response relationship in dog ventricle in vivo. Am. J. Physiol. 208:154–157, 1965.
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.
Netter, F. H. The Ciba Collection of Medical Illustrations, vol. 5. Cincinnati, OH: The Hennegan Co., 1969.
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.
Oliver, R. A., and W. Krassowska. Reproducing cardiac restitution properties using the Fenton-Karma membrane model. Ann. Biomed. Eng. submitted.
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.
Pormann, J. B. A modular system for the bidomain equations. Durham, NC: Duke University, 1999, Ph.D. Dissertation.
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.
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.
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.
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.
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.
Vinet, A. Quasiperiodic circus movement in a loop model of cardiac tissue: Multistability and low dimensional equivalence. Ann. Biomed. Eng. 28:704–720, 2000.
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.
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.
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.
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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