This Article Abstract Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Citation Map Services Email this article to a friend Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Request Permissions Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Google Scholar Articles by Weiss, J. N. Articles by Garfinkel, A. Search for Related Content PubMed PubMed Citation Articles by Weiss, J. N. Articles by Garfinkel, A. Related Collections Electrophysiology Arrhythmias, clinical electrophysiology, drugs Chronic ischemic heart disease Myocardial cardiomyopathy disease Arrythmias-basic studies

(Circulation Research. 2000;87:1103.)
© 2000 American Heart Association, Inc.

Review

Ventricular Fibrillation

How Do We Stop the Waves From Breaking?

James N. Weiss, Peng-Sheng Chen, Zhilin Qu, Hrayr S. Karagueuzian, Alan Garfinkel

From the Cardiovascular Research Laboratory and the Departments of Medicine (Cardiology), Physiology and Physiological Science, UCLA School of Medicine and Cedars-Sinai Medical Center, Los Angeles, Calif.

Correspondence to James N. Weiss, MD, Division of Cardiology, 3641 MRL Building, UCLA School of Medicine, Los Angeles, CA 90095-1760. E-mail jweiss{at}mednet.ucla.edu

	Abstract

Top Abstract Introduction Cardiac Excitation as a... Wavebreak and Preexisting... Wavebreak Attributable to... Electrical Alternans, a... Interactions Between Preexisting... Implications for Developing... Conclusions References

 
Abstract—Combined experimental and theoretical developments have demonstrated that in addition to preexisting electrophysiological heterogeneities, cardiac electrical restitution properties contribute to breakup of reentrant wavefronts during cardiac fibrillation. Developing therapies that favorably alter electrical restitution properties have promise as a new paradigm for preventing fibrillation.

Key Words: fibrillation • electrical restitution • cardiac action potential • antiarrhythmic drugs • arrhythmias

	Introduction

Top Abstract Introduction Cardiac Excitation as a... Wavebreak and Preexisting... Wavebreak Attributable to... Electrical Alternans, a... Interactions Between Preexisting... Implications for Developing... Conclusions References

 
Ventricular fibrillation (VF) remains the most common cause of sudden death. We briefly review the recent synergism between simulation and experiment, providing new insights into its pathogenesis. For more extensive treatment, see the excellent review by Jalife.¹

Figure 1A illustrates an ECG of a person suddenly developing VF, typifying the clinical observation that VF is almost always preceded by ventricular tachycardia (VT), lasting from a few to many beats.² In his seminal 1930 high-speed cinematographic study of electrically induced canine VF, Carl Wiggers³ divided VF into 4 stages, the first of which (the tachysystolic phase) is rapid VT, shown in later studies^{4 5} to correspond to figure-eight reentry. The progression from sinus rhythm to VF can be logically considered in 3 stages: initiation of VT, degeneration of VT to VF, and maintenance of VF.

View larger version (51K): [in this window] [in a new window]   Figure 1. Figure 1. A, ECG illustrating the onset of VF. B, Propagating cardiac action potential (AP, above) in simulated tissue. Wavefront (AP upstroke) is white, waveback (repolarization) is dark gray, and wavelength () is the distance between them.

	Cardiac Excitation as a Wave

Top Abstract Introduction Cardiac Excitation as a... Wavebreak and Preexisting... Wavebreak Attributable to... Electrical Alternans, a... Interactions Between Preexisting... Implications for Developing... Conclusions References

 
What is responsible for the sequence in Figure 1A? Cardiac excitation can be viewed as an electrical wave, with a wavefront corresponding to the action potential upstroke (phase 0) and a waveback corresponding to rapid repolarization (phase 3). The wavelength is the distance between the wavefront and waveback and is equivalent to the product of action potential duration (APD) and conduction velocity (CV) (Figure 1B). The 3 stages of VF all depend on electrical waves in the ventricle breaking up.

In sinus rhythm, cardiac waves emerge focally and spread throughout the ventricle. If the wave breaks at one point, the 2 broken ends become the tips of potential reentrant (spiral or scroll) waves. If successful at propagating, the tips circulate around either a functional core or an anatomic obstacle to create monomorphic VT, polymorphic VT, or, in hearts from small mammals, even VF.⁶ If additional wavebreaks develop, multiple reentrant waves are created, and VT degenerates to the classic VF of large mammal hearts characterized by multiple wavelets (Figure 2D). The message is that if we understand how to prevent wavebreak, we may have the key to curing VF.

View larger version (51K): [in this window] [in a new window]   Figure 2. Figure 2. Electrical restitution and spiral wave stability. A, S1S2 method of measuring APD restitution by introducing a progressively more premature stimulus (S2) in Luo-Rudy action potential model.34 B, APD restitution curve, constructed by plotting APD of the S2 beat versus diastolic interval (DI). Dashed line shows the effect of reducing the Ca2+ current (ICa) by 50%. C, CV restitution curve, determined analogously; ICa reduction (dashed line) had no effect. D, Spiral wave breakup. Snapshot of membrane voltage (white depolarized, black repolarized) several seconds after initiation of a spiral wave in homogeneous 2-dimensional cardiac tissue. APD and CV restitution corresponded to the control curves in panels B and C. E, Stable spiral wave in the same tissue, when APD restitution slope was flattened by reducing ICa (dashed lines in panels B and C).

Wavebreak leading to spiral wave reentry and other complex pattern formation is a generic property of excitable media (also called reaction-diffusion or activator-inhibitor systems), of which cardiac tissue is a classic example. Other examples include chemical reactions in the Belousov-Zhabotinski category,⁷ growth patterns of the slime mold Dictyostelium,⁸ and Ca²⁺-induced Ca²⁺ release in oocytes⁹ and cardiac myocytes.¹⁰ That spiral wave reentry might be relevant to cardiac arrhythmias was first suggested by Krinsky¹¹ and later by Winfree.¹² In the 1970s, Allessie et al^{13 14 15} provided key experimental documentation by showing that cardiac reentry could occur in the absence of an anatomical obstacle, a phenomenon they termed functional or leading circle reentry. However, the connection between functional reentry and spiral wave reentry was not made explicit until 1992, when Davidenko et al¹⁶ published their seminal study documenting spiral wave reentry in ventricle and subsequently proposed this as a mechanism of VF.⁶

	Wavebreak and Preexisting Tissue Heterogeneity

Top Abstract Introduction Cardiac Excitation as a... Wavebreak and Preexisting... Wavebreak Attributable to... Electrical Alternans, a... Interactions Between Preexisting... Implications for Developing... Conclusions References

 
The first quantitative theory of fibrillation, the multiple wavelet hypothesis, predated the recognition that spiral waves might be relevant to cardiac arrhythmias. Moe et al^16A used a minimal 2-dimensional cardiac tissue model composed of automata with resting, excited, and refractory states, ie, the bare essentials of a cardiac cell. They discovered that by introducing sufficient electrophysiological heterogeneity into the tissue by randomly assigning different refractory periods to different cells, cardiac waves spontaneously broke up into patterns of random reentry. This process was self-sustaining, provided the tissue was large enough. Direct experimental evidence for the multiple wavelet hypothesis was subsequently provided by Allessie et al,¹⁷ who mapped the surface of the fibrillating atrium with multielectrode plaques and observed the predicted multiple wavelets meandering in complex random-appearing patterns. Similar findings were subsequently reported in ventricle.¹⁸

In the multiple wavelet hypothesis, wavebreak depends on preexisting electrophysiological heterogeneity, particularly dispersion of refractoriness. For a wave to break, its wavelength must become zero at a discrete point somewhere along the wave. This can happen if the wave encounters a local heterogeneity (refractoriness) that creates block (wavelength=zero) locally, while propagating (ie, nonzero wavelength) elsewhere. In Moe’s simple model, this was achieved by randomly introducing local differences in refractory period (dispersion of refractoriness) to cells throughout the tissue. Subsequently, a large body of experimental work confirmed the importance of preexisting heterogeneity to both atrial and ventricular fibrillation. The clinical observation that diseased hearts fibrillate more easily than normal hearts has been largely attributed to their increased susceptibility to wavebreak because of increased anatomical and electrophysiological heterogeneity from the disease process.

	Wavebreak Attributable to Dynamic Instability

Top Abstract Introduction Cardiac Excitation as a... Wavebreak and Preexisting... Wavebreak Attributable to... Electrical Alternans, a... Interactions Between Preexisting... Implications for Developing... Conclusions References

 
However, cardiac modeling studies have shown that preexisting heterogeneity is not the only cause of wavebreak. Dynamically induced heterogeneity is another mechanism that requires no preexisting heterogeneity of any kind, just an intervention (eg, very rapid pacing or a large premature stimulus) to create the first wavebreak. After that, wavebreak proceeds spontaneously on its own to create VF. This type of wavebreak is determined primarily by the electrical restitution properties, ie, the dependence of APD and CV on the preceding diastolic interval (DI), defined as the interval between repolarization and the next action potential (Figures 2A through 2C). Intuitively, this makes sense: because wavelength is defined as the product of APD·CV, then either APD or CV must become zero for wavelength to be zero. Because APD and CV are controlled dynamically by DI (ie, restitution), APD and CV restitution are therefore key determinants of wavebreak.

The steepness of APD restitution is a critical parameter for spiral wave stability. When the slope of the APD restitution curve exceeds one, a small change in DI gets magnified into a larger change in APD, which translates into a larger change in wavelength. This creates yet a larger change in DI for the next wave, and so forth. The positive feedback causes small wavelength oscillations to grow progressively until the DI becomes too short for the wave to propagate, resulting in wavebreak (Figure 3B). The analogy is to an amplifier with gain >1. In contrast, an APD restitution slope <1 acts like an attenuator, allowing perturbations in the wave to heal rather than expand (Figure 3A). The role of steep APD restitution in causing APD alternation during pacing¹⁹ and unstable reentry around anatomic obstacles²⁰ was appreciated from the 1960s. However, it was not until 1993 that Karma²¹ showed that the same mechanism could produce wavebreak in spiral wave reentry. In 2-dimensional and 3-dimensional tissue simulations, dynamic instability arising from steep APD restitution causes spiral waves (VT) to break up into a VF-like state, even in completely homogeneous isotropic tissue (Figure 2D). Furthermore, by reducing APD restitution steepness, spiral or scroll wave breakup can be prevented and spiral and scroll wave behavior can be progressively stabilized (Figure 2E). This concept, termed the restitution hypothesis, has now been validated experimentally in several VF models.^{22 23} Note that in Figure 2D, spiral wave breakup has caused the multiple wavelets to lose their morphological resemblance to spirals, and rarely does a broken wave make a complete revolution before it is pushed off course by a competing wave. Yet the generic reaction-diffusion processes are identical in Figures 2D and 2E. APD restitution slope should be thought of as a global parameter that controls phenotypical behavior of the tissue.

View larger version (85K): [in this window] [in a new window]   Figure 3. Figure 3. Electrical restitution and wavelength oscillations in 2-dimensional tissue paced at a fixed cycle length (diamonds). A, With APD restitution slope (APDR) <1 and no CV restitution (CVR), APD and wavelength remain constant for each wave (1 through 7) once the DI is set. Concordant APD/wavelength alternans progressively attenuates with APDR <1. B, If APDR >1, however, APD/wavelength alternation can progressively amplify until the DI is too short for the next wave (6) to propagate. (In this example, the whole planar wave would fail, whereas a break in symmetry is required for localized conduction failure to initiate reentry.) C, Effect of adding CVR, showing snapshots of 2 waves (1 and 2) at 3 successive time points. Between t=1and t=2, the short DI facing wave 2 caused it to slow, increasing its DI and prolonging its APD/wavelength. Between t=2 and t=3, wave 1 approached the preceding wave (0, not shown), shortening its DI and APD/wavelength. This increased the DI of wave 2 additionally, causing additional APD/wavelength prolongation as well. Variation of APD/wavelength of the same wave as it propagates because of CVR is discordant alternans.

	Electrical Alternans, a Harbinger of Dynamic Instability

Top Abstract Introduction Cardiac Excitation as a... Wavebreak and Preexisting... Wavebreak Attributable to... Electrical Alternans, a... Interactions Between Preexisting... Implications for Developing... Conclusions References

 
A natural consequence of steep APD restitution is APD alternans, in which successive waves alternate between short and long APD, illustrated in Figures 3A and 3B. Electrocardiographically, this is manifested as T wave (repolarization) alternans, a clinically established harbinger of ventricular arrhythmia vulnerability.²⁴ CV restitution plays an equally important role, especially in facilitating initiation of VT/VF. With no CV restitution present (Figures 3A and 3B), each wave by definition propagates at identical velocity. Therefore, once a wavefront emerges, its DI with respect to the wave ahead is set and cannot change over time. Even though different waves have different wavelengths, the APD and wavelength of a given wave will remain fixed as it propagates. When APD restitution slope is >1, wavelengths of successive waves typically alternate between long and short, which is called concordant alternans.

For the case in which CV varies with DI because of CV restitution, a sufficiently short DI causes the wavefront to slow (Figure 3C). As it slows, its distance from the wave ahead increases, resulting in a longer DI. As its DI increases, APD also lengthens, thereby changing the wavelength of the wave. (Whether the wavelength prolongs or shortens depends on the relative degree of APD change versus CV slowing.) Meanwhile, the wave’s changing wavelength also affects the DI of the wave behind it, so that the next wave’s wavelength will also oscillate, and so forth for each successive wave, like a car braking and accelerating on the freeway in response to cars ahead. The important consequence is that the wavelength of the same wave changes while propagating through the tissue, becoming short in some areas and long in others. This discordant alternans markedly enhances dispersion of refractoriness, arising purely from the dynamics of electrical restitution. For the planar waves illustrated in Figure 3, spatial APD dispersion can occur only along the horizontal axis. However, if preexisting heterogeneities are present, asymmetries will develop along the vertical axis as well. The resulting spatial variation in wavelength along the wave amplifies both source-sink mismatches and head-to-tail interactions with adjacent waves to cause localized wavebreak and reentry.²⁵

Although other mechanisms may also be involved, simulations of concordant and discordant APD alternans²⁵ on the basis of electrical restitution properties show close agreement with experimental data,^{26 27} including reproducing electrocardiographic T and QRS alternans and enhanced arrhythmia susceptibility. The message is that electrical alternans reflects the underlying dynamic instability of cardiac tissue, measuring the likelihood that rapid pacing or extrasystoles will induce wavebreak leading to initiation of VT with subsequent degeneration to VF.

	Interactions Between Preexisting Heterogeneity and Dynamic Instability

Top Abstract Introduction Cardiac Excitation as a... Wavebreak and Preexisting... Wavebreak Attributable to... Electrical Alternans, a... Interactions Between Preexisting... Implications for Developing... Conclusions References

 
Simulation and experiment support the existence of 2 main mechanisms of wavebreak: preexisting heterogeneity and dynamic instability. The real heart contains both features, but their relative importance to fibrillation is debated at present. One possibility is that dynamic instability plays only an ancillary role during fibrillation and that most wavebreaks observed during fibrillation are epiphenomena related to fibrillatory conduction block. That is, a wavefront arising from a relatively stable but rapid scroll wave (mother rotor) develops complex Wenckebach conduction block patterns as it propagates outward because of heterogeneous tissue refractoriness.²⁸ This mechanism is consistent with the typical short life span (<1 rotation) of wavebreaks during VF and the finding of quasi-stable regions with unique dominant frequencies. In addition, Wenckebach-like conduction block patterns have been detected at the borders of these regions. If the driving scroll wave is relatively stable dynamically, then restitution-based dynamic instability is unlikely to play a major role in maintenance of fibrillation.

Alternatively, preexisting heterogeneity may dominate VT initiation,²⁹ with dynamic instability playing larger roles in the VT to VF transition and VF maintenance. This possibility is supported by experimental observations that in the normal ventricle of humans and other mammals, APD restitution slope is typically steep enough (ie, >1) to promote self-regenerating wavebreak leading to VF when spiral wave reentry is induced. In addition, flattening APD restitution slope with drugs converts VF to VT,^{22 23} as predicted by simulations (although alternative explanations have also been proposed^{30 31 32} ). The inherent dynamical instability of normal human ventricle is clinically manifested as the VF threshold, in which initiation of functional (scroll wave) reentry by a critically large electrical stimulus invariably degenerates to VF. However, in normal ventricle, physiological triggers such as premature ventricular contractions are extremely unlikely to induce the initial wavebreak, because the degree of preexisting heterogeneity is insufficient. To achieve the VF threshold requires a markedly supraphysiological electrical stimulus, also facilitated in part by normal preexisting heterogeneities such as the His-Purkinje system.³³ In contrast, in diseased ventricle, preexisting heterogeneity increases, thereby raising the probability that a physiological trigger will induce wavebreak. Even so, the probability remains low, recalling that 2 extrasystoles per minute (a modest degree of ventricular ectopy) corresponds to a million extrasystoles per year. After induction of reentry, the outcome of the arrhythmia (stable VT versus VF) then depends on the subsequent history of wavebreak, as influenced by preexisting heterogeneity and dynamic instability.

	Implications for Developing Effective Antiarrhythmic Drugs

Top Abstract Introduction Cardiac Excitation as a... Wavebreak and Preexisting... Wavebreak Attributable to... Electrical Alternans, a... Interactions Between Preexisting... Implications for Developing... Conclusions References

 
Which of the above mechanisms are most important in clinical VF remains to be determined but is very important with respect to the prospects for developing effective antifibrillatory drug therapy. Preexisting heterogeneity is difficult as a therapeutic target: it is often made worse by antiarrhythmic drugs, because any differential sensitivity to the drug’s effects on CV or APD is likely to increase dispersion of electrophysiological properties. Reducing dynamical instability by flattening APD restitution slope may be more promising. Figure 4 summarizes schematically the interaction between preexisting heterogeneity and dynamic instability. The hypothetical curve divides stable VT (gray area) from VT that degenerates to VF (white area). In general, increasing either preexisting heterogeneity or dynamic instability increases the probability of VF. The curve is not necessarily monotonic: sometimes preexisting heterogeneities (such as anatomic obstacles) can anchor and stabilize reentry (ie, convert functional reentry to anatomic reentry). The present challenge of researchers in this field is to define the contour of this curve more accurately to determine whether the restitution hypothesis can be translated into the development of effective antifibrillatory drugs. Standard antiarrhythmic drugs (classes 1 to 4) were developed primarily to prevent initiation of VT by suppressing the triggering events or altering properties of reentrant circuits, with no regard for how they affected electrical restitution. Perhaps this partly explains their failure at preventing sudden cardiac death. It now seems timely to investigate whether a combined antitachycardia (classes 1 to 4) and antifibrillatory (restitution-based) strategy can produce more successful results.

View larger version (48K): [in this window] [in a new window]   Figure 4. Figure 4. Hypothetical interaction between dynamic and preexisting heterogeneity with respect to VT stability. Increased preexisting heterogeneity generally decreases the degree of dynamically induced heterogeneity required for wavebreak. The goal of the restitution hypothesis is to determine whether drugs that reduce normal dynamical instability (from point a to b) can prevent VT from degenerating to VF despite preexisting heterogeneity, which the drugs may also alter favorably or unfavorably.

	Conclusions

Top Abstract Introduction Cardiac Excitation as a... Wavebreak and Preexisting... Wavebreak Attributable to... Electrical Alternans, a... Interactions Between Preexisting... Implications for Developing... Conclusions References

 
We have argued that the question "What causes VF?" can be stated more precisely as "What causes wavebreak?" and even more specifically as "How do preexisting heterogeneity and dynamically induced heterogeneity interact to promote VF?" If dynamic instability plays a key role, then developing drugs that favorably alter electrical restitution properties is a promising new approach to a vexing problem.

	Acknowledgments

 
This work was supported by National Institutes of Health Specialized Center of Research in Sudden Cardiac Death P50 HL53219, the Laubisch Fund, and the Chizuko Kawata and the Pauline and Harold Price endowments. We thank Dr Alain Karma for his suggestion for Figure 4.

Received September 5, 2000; revision received October 23, 2000; accepted October 23, 2000.

	References

Top Abstract Introduction Cardiac Excitation as a... Wavebreak and Preexisting... Wavebreak Attributable to... Electrical Alternans, a... Interactions Between Preexisting... Implications for Developing... Conclusions References

 

1. Jalife J. Ventricular fibrillation: mechanisms of initiation and maintenance. Annu Rev Physiol. 2000;62:25–50.[Medline] [Order article via Infotrieve]
2. Kempf FC Jr, Josephson ME. Cardiac arrest recorded on ambulatory electrocardiograms. Am J Cardiol. 1984;53:1577–1582.[Medline] [Order article via Infotrieve]
3. Wiggers CJ. Studies of ventricular fibrillation caused by electric shock, II: cinematographic and electrocardiographic observation of the natural process in the dog’s heart. Its inhibition by potassium and the revival of coordinated beats by calcium. Am Heart J. 1930;5:351–365.
4. Chen PS, Wolf PD, Dixon EG, Danieley ND, Frazier DW, Smith WM, Ideker RE. Mechanism of ventricular vulnerability to single premature stimuli in open-chest dogs. Circ Res. 1988;62:1191–1209.[Abstract/Free Full Text]
5. Bonometti C, Hwang C, Hough D, Lee JJ, Fishbein MC, Karagueuzian HS, Chen PS. Interaction between strong electrical stimulation and reentrant wavefronts in canine ventricular fibrillation. Circ Res. 1995;77:407–416.[Abstract/Free Full Text]
6. Gray RA, Jalife J, Panfilov AV, Baxter WT, Cabo C, Davidenko JM, Pertsov AM. Mechanisms of cardiac fibrillation. Science. 1995;270:1222–1223.[Abstract/Free Full Text]
7. Winfree A. Spiral waves of chemical activity. Science. 1972;175:634–636.[Abstract/Free Full Text]
8. Devreotes PN, Potel MJ, MacKay SA. Quantitative analysis of cyclic AMP waves mediating aggregation in Dictyostelium discoideum. Dev Biol. 1983;96:405–415.[Medline] [Order article via Infotrieve]
9. Lechleiter J, Girard S, Peralta E, Clapham D. Spiral calcium wave propagation and annihilation in Xenopus laevis oocytes. Science. 1991;252:123–126.[Abstract/Free Full Text]
10. Lipp P, Niggli E. Microscopic spiral waves reveal positive feedback in subcellular calcium signaling. Biophys J. 1993;65:2272–2276.[Abstract/Free Full Text]
11. Krinsky VI. Spread of excitation in an inhomogeneous medium. Biophysica (USSR). 1966;11:776–784.
12. Winfree AT. When Time Breaks Down. Princeton, NJ: Princeton University Press; 1987.
13. Allessie M, Bonke F, Shopman F. Circus movement in rabbit atrial muscle as a mechanism of tachycardia. Circ Res. 1977;41:9–18.[Free Full Text]
14. Allessie MA, Bonke FIM, Schopman FJC. Circus movement in rabbit atrial muscle as a mechanism of tachycardia, II: the role of nonuniform recovery of excitability in the occurrence of unidirectional block as studied with multiple microelectrodes. Circ Res. 1976;39:168–181.[Abstract/Free Full Text]
15. Allessie MA, Bonke FIM, Schopman FJC. Circus movement in rabbit atrial muscle as a mechanism of tachycardia. Circ Res. 1973;33:54–77.[Abstract/Free Full Text]
16. Davidenko JM, Pertsov AV, Salomonsz JR, Baxter W, Jalife J. Stationary and drifting spiral waves of excitation in isolated cardiac muscle. Nature. 1992;355:349–351.[Medline] [Order article via Infotrieve]
16. Moe GK, Rheinboldt WC, Abildshov JA. A computer model of atrial fibrillation. Am Heart J. 1964;67:200–220.[Medline] [Order article via Infotrieve]
17. Allessie MA, Lammers WJEP, Bonke FIM, Hollen J. Experimental evaluation of Moe’s multiple wavelet hypothesis of atrial fibrillation. In: Zipes DP, Jalife J, eds. Cardiac Arrhythmias. New York: Grune & Stratton; 1985:265–276.
18. Lee JJ, Kamjoo K, Hough D, Hwang C, Fan W, Fishbein MC, Bonometti C, Ikeda T, Karagueuzian HS, Chen PS. Reentrant wave fronts in Wiggers’ stage II ventricular fibrillation: characteristics and mechanisms of termination and spontaneous regeneration. Circ Res. 1996;78:660–675.[Abstract/Free Full Text]
19. Nolasco JB, Dahlen RW. A graphic method for the study of alternation in cardiac action potentials. J Appl Physiol. 1968;25:191–196.[Free Full Text]
20. Frame LH, Simson MB. Oscillations of conduction, action potential duration, and refractoriness: a mechanism for spontaneous termination of reentrant tachycardias. Circulation. 1988;78:1277–1287.[Abstract/Free Full Text]
21. Karma A. Spiral breakup in model equations of action potential propagation in cardiac tissue. Phys Rev Lett. 1993;71:1103–1106.[Medline] [Order article via Infotrieve]
22. Riccio M, Koller M, Gilmour RF Jr. Electrical restitution and spatiotemporal organization during ventricular fibrillation. Circ Res. 1999;84:955–963.[Abstract/Free Full Text]
23. Garfinkel A, Kim Y, Voroshilovsky O, Qu Z, Kil JR, Lee M-Y, Karagueuzian HS, Weiss JN, Chen P-S. Preventing ventricular fibrillation by flattening cardiac restitution. Proc Natl Acad Sci U S A. 2000;97:6061–6066.[Abstract/Free Full Text]
24. Nearing BD, Huang AH, Verrier RL. Dynamic tracking of cardiac vulnerability by complex demodulation of the T wave. Science. 1991;252:437–440.[Abstract/Free Full Text]
25. Qu Z, Garfinkel A, Chen P-S, Weiss JN. Mechanisms of discordant alternans and induction of reentry in a simulated cardiac tissue. Circulation. 2000;102:1664–1670.[Abstract/Free Full Text]
26. Laurita KR, Girouard SD, Rosenbaum DS. Modulation of ventricular repolarization by a premature stimulus: role of epicardial dispersion of dispersion of repolarization kinetics demonstrated by optical mapping of the intact guinea pig heart. Circ Res. 1996;79:493–503.[Abstract/Free Full Text]
27. Pastore JM, Girouard SD, Laurita KR, Akar FG, Rosenbaum DS. Mechanism linking T-wave alternans to the genesis of cardiac fibrillation. Circulation. 1999;99:1385–1394.[Abstract/Free Full Text]
28. Zaitsev AV, Berenfeld O, Mironov SF, Jalife J, Pertsov AM. Distribution of excitation frequencies on the epicardial and endocardial surfaces of fibrillating ventricular wall of the sheep heart. Circ Res. 2000;86:408–417.[Abstract/Free Full Text]
29. Weiss JN, Garfinkel A, Karaguezian HS, Qu Z, Chen P-S. Chaos and the transition to ventricular fibrillation: a new approach to antiarrhythmic drug evaluation. Circulation. 1999;99:2819–2826.[Abstract/Free Full Text]
30. Fenton F, Karma A. Vortex dynamics in three-dimensional continuous medium with fiber rotation: filament instability and fibrillation. Chaos. 1998;8:20–47.[Medline] [Order article via Infotrieve]
31. Beaumont J, Davidenko N, Davidenko JM, Jalife J. Spiral waves in two-dimensional models of ventricular muscle: formation of a stationary core. Biophys J. 1998;75:1–14.[Abstract/Free Full Text]
32. Samie FH, Mandapati R, Gray RA, Watanabe Y, Zuur C, Beaumont J, Jalife J. A mechanism of transition from ventricular fibrillation to tachycardia: effect of calcium channel blockade on the dynamics of rotating waves. Circ Res. 2000;86:684–691.[Abstract/Free Full Text]
33. Berenfeld O, Jalife J. Purkinje-muscle reentry as a mechanism of polymorphic ventricular arrhythmias in a 3-dimensional model of the ventricles. Circ Res. 1998;82:1063–77.[Abstract/Free Full Text]
34. Luo CH, Rudy Y. A model of the ventricular cardiac action potential: depolarization, repolarization and their interaction. Circ Res. 1991;68:1501–1526.[Abstract/Free Full Text]

This article has been cited by other articles:

				S. E. Ahlberg, A. M. Yue, N. D. Skadsberg, P. R. Roberts, P. A. Iaizzo, and J. M. Morgan Investigation of pacing site-related changes in global restitution dynamics by non-contact mapping Europace, January 1, 2008; 10(1): 40 - 45. [Abstract] [Full Text] [PDF]

				P Jones and N Lode Ventricular fibrillation and defibrillation Arch. Dis. Child., October 1, 2007; 92(10): 916 - 921. [Abstract] [Full Text] [PDF]

				G. A. Ng, K. E. Brack, V. H. Patel, and J. H. Coote Autonomic modulation of electrical restitution, alternans and ventricular fibrillation initiation in the isolated heart Cardiovasc Res, March 1, 2007; 73(4): 750 - 760. [Abstract] [Full Text] [PDF]

				A. Baher, Z. Qu, A. Hayatdavoudi, S. T. Lamp, M.-J. Yang, F. Xie, S. Turner, A. Garfinkel, and J. N. Weiss Short-term cardiac memory and mother rotor fibrillation Am J Physiol Heart Circ Physiol, January 1, 2007; 292(1): H180 - H189. [Abstract] [Full Text] [PDF]

				B. C. Knollmann, T. Schober, A. O. Petersen, S. G. Sirenko, and M. R. Franz Action potential characterization in intact mouse heart: steady-state cycle length dependence and electrical restitution Am J Physiol Heart Circ Physiol, January 1, 2007; 292(1): H614 - H621. [Abstract] [Full Text] [PDF]

				R. D. Simitev and V. N. Biktashev Conditions for Propagation and Block of Excitation in an Asymptotic Model of Atrial Tissue Biophys. J., April 1, 2006; 90(7): 2258 - 2269. [Abstract] [Full Text] [PDF]

				M. M. Scheinman and E. Keung The Year in Clinical Electrophysiology J. Am. Coll. Cardiol., March 21, 2006; 47(6): 1207 - 1213. [Full Text] [PDF]

				Z. Qu Critical mass hypothesis revisited: role of dynamical wave stability in spontaneous termination of cardiac fibrillation Am J Physiol Heart Circ Physiol, January 1, 2006; 290(1): H255 - H263. [Abstract] [Full Text] [PDF]

				A. M. Yue, M. R. Franz, P. R. Roberts, and J. M. Morgan Global Endocardial Electrical Restitution in Human Right and Left Ventricles Determined by Noncontact Mapping J. Am. Coll. Cardiol., September 20, 2005; 46(6): 1067 - 1075. [Abstract] [Full Text] [PDF]

				J. N. Weiss, Z. Qu, P.-S. Chen, S.-F. Lin, H. S. Karagueuzian, H. Hayashi, A. Garfinkel, and A. Karma The Dynamics of Cardiac Fibrillation Circulation, August 23, 2005; 112(8): 1232 - 1240. [Abstract] [Full Text] [PDF]

				S.-m. Hwang, T. Y. Kim, and K. J. Lee From The Cover: Complex-periodic spiral waves in confluent cardiac cell cultures induced by localized inhomogeneities PNAS, July 19, 2005; 102(29): 10363 - 10368. [Abstract] [Full Text] [PDF]

				S. S. Po, Y. Li, D. Tang, H. Liu, N. Geng, W. M. Jackman, B. Scherlag, R. Lazzara, and E. Patterson Rapid and Stable Re-Entry Within the Pulmonary Vein as a Mechanism Initiating Paroxysmal Atrial Fibrillation J. Am. Coll. Cardiol., June 7, 2005; 45(11): 1871 - 1877. [Abstract] [Full Text] [PDF]

				J. I. Goldhaber, L.-H. Xie, T. Duong, C. Motter, K. Khuu, and J. N. Weiss Action Potential Duration Restitution and Alternans in Rabbit Ventricular Myocytes: The Key Role of Intracellular Calcium Cycling Circ. Res., March 4, 2005; 96(4): 459 - 466. [Abstract] [Full Text] [PDF]

				S. B. Danik, F. Liu, J. Zhang, H. J. Suk, G. E. Morley, G. I. Fishman, and D. E. Gutstein Modulation of Cardiac Gap Junction Expression and Arrhythmic Susceptibility Circ. Res., November 12, 2004; 95(10): 1035 - 1041. [Abstract] [Full Text] [PDF]

				G. F. Tomaselli and D. P. Zipes What Causes Sudden Death in Heart Failure? Circ. Res., October 15, 2004; 95(8): 754 - 763. [Abstract] [Full Text] [PDF]

				Z. Qu, H. S. Karagueuzian, A. Garfinkel, and J. N. Weiss Effects of Na+ channel and cell coupling abnormalities on vulnerability to reentry: a simulation study Am J Physiol Heart Circ Physiol, April 1, 2004; 286(4): H1310 - H1321. [Abstract] [Full Text] [PDF]

				H.-N. Pak, Y.-S. Oh, Y.-B. Liu, T.-J. Wu, H. S. Karagueuzian, S.-F. Lin, and P.-S. Chen Catheter Ablation of Ventricular Fibrillation in Rabbit Ventricles Treated With {beta}-Blockers Circulation, December 23, 2003; 108(25): 3149 - 3156. [Abstract] [Full Text] [PDF]

				H. Hayashi, C. Omichi, Y. Miyauchi, W. J. Mandel, S.-F. Lin, P.-S. Chen, and H. S. Karagueuzian Age-related sensitivity to nicotine for inducible atrial tachycardia and atrial fibrillation Am J Physiol Heart Circ Physiol, November 1, 2003; 285(5): H2091 - H2098. [Abstract] [Full Text] [PDF]

				F. G. Akar and D. S. Rosenbaum Transmural Electrophysiological Heterogeneities Underlying Arrhythmogenesis in Heart Failure Circ. Res., October 3, 2003; 93(7): 638 - 645. [Abstract] [Full Text] [PDF]

				M. C. Sanguinetti and P. B. Bennett Antiarrhythmic Drug Target Choices and Screening Circ. Res., September 19, 2003; 93(6): 491 - 499. [Abstract] [Full Text] [PDF]

				Y. Miyauchi, S. Zhou, Y. Okuyama, M. Miyauchi, H. Hayashi, A. Hamabe, M. C. Fishbein, W. J. Mandel, L. S. Chen, P.-S. Chen, et al. Altered Atrial Electrical Restitution and Heterogeneous Sympathetic Hyperinnervation in Hearts With Chronic Left Ventricular Myocardial Infarction: Implications for Atrial Fibrillation Circulation, July 22, 2003; 108(3): 360 - 366. [Abstract] [Full Text] [PDF]

				M. Valderrabano, P.-S. Chen, and S.-F. Lin Spatial Distribution of Phase Singularities in Ventricular Fibrillation Circulation, July 22, 2003; 108(3): 354 - 359. [Abstract] [Full Text] [PDF]