Ventricular Fibrillation
How Do We Stop the Waves From Breaking?
James N. Weiss, Peng-Sheng Chen, Zhilin Qu, Hrayr S. Karagueuzian, Alan Garfinkel
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. (Circ Res. 2000;87:1103-1107.)
Key Words: fibrillation 䡲 electrical restitution 䡲 cardiac action potential 䡲 antiarrhythmic drugs 䡲 arrhythmias
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V
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.
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 BelousovZhabotinski 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 al13–15
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
entricular 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 studies4,5 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.
Cardiac Excitation as a Wave
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
Wavebreak and Preexisting
Tissue Heterogeneity
The first quantitative theory of fibrillation, the multiple
wavelet hypothesis, predated the recognition that spiral waves
might be relevant to cardiac arrhythmias. Moe et al16a 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
Received September 5, 2000; revision received October 23, 2000; accepted October 23, 2000.
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 [email protected]
© 2000 American Heart Association, Inc.
Circulation Research is available at http://www.circresaha.org
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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.
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
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
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).
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䡠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.
Weiss et al
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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.
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.
Electrical Alternans, a Harbinger of
Dynamic Instability
A natural consequence of steep APD restitution is APD
alternans, in which successive waves alternate between short
Ventricular Fibrillation and Wavebreak
1105
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
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
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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 selfregenerating 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
proposed30 –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
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:
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.
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.
Conclusions
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.
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Ventricular Fibrillation: How Do We Stop the Waves From Breaking?
James N. Weiss, Peng-Sheng Chen, Zhilin Qu, Hrayr S. Karagueuzian and Alan Garfinkel
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Circ Res. 2000;87:1103-1107
doi: 10.1161/01.RES.87.12.1103
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