(Circulation. 1999;99:2819-2826.)
© 1999 American Heart Association, Inc.
Current Perspectives |
Chaos and the Transition to Ventricular Fibrillation
A New Approach to Antiarrhythmic Drug Evaluation
From the Departments of Medicine (Cardiology), Physiology, and Physiological Science and the UCLA Cardiovascular Research Laboratory, UCLA School of Medicine and Cedars-Sinai Medical Center, Los Angeles, Calif.
Correspondence to James N. Weiss, MD, Division of Cardiology, 3645 MRL Bldg, UCLA School of Medicine, Los Angeles, CA 90095-1760. E-mail jweiss{at}mednet.ucla.edu
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Abstract |
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Abstract—Sudden cardiac death resulting from ventricular fibrillation can be separated into 2 components: initiation of tachycardia and degeneration of tachycardia to fibrillation. Clinical drug studies such as CAST and SWORD demonstrated that focusing exclusively on the first component is inadequate as a therapeutic modality. The hope for developing effective pharmacological therapy rests on a comprehensive understanding of the second component, the transition from tachycardia to fibrillation. We summarize evidence that the transition from tachycardia to fibrillation is a transition to spatiotemporal chaos, with similarities to the quasiperiodic transition to chaos seen in fluid turbulence. In this scenario, chaos results from the interaction of multiple causally independent oscillatory motions. Simulations in 2-dimensional cardiac tissue suggest that the destabilizing oscillatory motions during spiral-wave reentry arise from restitution properties of action potential duration and conduction velocity. The process of spiral-wave breakup in simulated cardiac tissue predicts remarkably well the sequence by which tachycardia degenerates to fibrillation in real cardiac tissue. Modifying action potential duration and conduction velocity restitution characteristics can prevent spiral-wave breakup in simulated cardiac tissue, suggesting that drugs with similar effects in real cardiac tissue may have antifibrillatory efficacy (the Restitution Hypothesis). If valid for the real heart, the Restitution Hypothesis will support a new paradigm for antiarrhythmic drug classification, incorporating an antifibrillatory profile based on effects on cardiac restitution and the traditional antitachycardia profile (classes 1 through 4).
Key Words: arrhythmia • death, sudden • drugs • dynamics • fibrillation
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Introduction |
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TopAbstractIntroductionWhy Has the Drug...VF: Relationship to Functional...How Do Nonlinear Dynamics...Can These Findings Help...What Critical Evidence Is...ConclusionsReferences |
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Despite impressive recent advances in antiarrhythmic therapies, ventricular fibrillation (VF) remains a major health problem, accounting for
300 000 sudden cardiac deaths
annually in the United States. From a conceptual standpoint, treatment
of VF has advanced little since the development of electrical
defibrillation in the 1950s. Although implantable
cardioverter-defibrillators now save many lives, it would be highly
desirable and cost-effective to develop less invasive technologies.
Pharmacological therapy represents one such avenue but has been
largely stalemated by disappointing results of large-scale clinical
trials such as CAST1 and SWORD,2 which showed
increased mortality from sudden death in post–myocardial infarction
patients treated with class 1 or 3 antiarrhythmic drugs. |
Why Has the Drug Therapy of Cardiac Fibrillation Been So Disappointing? |
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TopAbstractIntroductionWhy Has the Drug...VF: Relationship to Functional...How Do Nonlinear Dynamics...Can These Findings Help...What Critical Evidence Is...ConclusionsReferences |
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In pioneering computer modeling studies, Moe and colleagues3 demonstrated that simulated cardiac tissue could support multiple reentrant wave fronts meandering in complex patterns resembling fibrillation, and they proposed the multiple wavelet hypothesis of fibrillation. This hypothesis was later elegantly validated experimentally by Allessie et al.4
If fibrillation is due to multiple reentrant wave fronts, how do they
arise? Clinical observations indicate that VF is almost always preceded
by ventricular tachycardia (VT), the duration
of which may vary from a few to many beats5 (Figure 1
). Cineangiographic studies by
Wiggers6 documented that the earliest
"tachysystolic" stage was characterized by rapid
coordinated contractions, which later studies7 8 showed
corresponded to a single or double (figure-8) reentrant wave front,
subsequently breaking up into multiple fractionated wave fronts
characteristic of fully developed fibrillation.
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These observations suggest that sudden death from VF is separable into
2 components: a triggering event that initiates VT and degeneration of
VT to VF (Figure 1
). CAST and SWORD1 2 were
therapeutically aimed at suppressing VT initiation. Their failure to
prevent sudden cardiac death demonstrates that exclusively targeting VT
initiation is not, in general, effective. Why not? In CAST, a positive
response to drug therapy was defined as >80% suppression of
ventricular ectopy. However, eliminating >80% of events
potentially triggering VT translates to a commensurate reduction in VF
only if the drug does not adversely potentiate the likelihood that
tachycardia, once initiated, will degenerate to
fibrillation. Obviously, if the probability of the latter is
concomitantly increased by a factor of 5, then the 80% reduction in
triggering events is negated.
At the present time, little is known about how antiarrhythmic drugs affect the propensity of VT to degenerate into VF. However, an effective pharmacological approach must take antifibrillatory properties of antiarrhythmic drugs, as well as traditional antitachycardic (ie, suppression of VT initiation) properties, into account. This is the area into which nonlinear dynamics and chaos theory is providing new insights.
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VF: Relationship to Functional Reentry and Spiral Waves |
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TopAbstractIntroductionWhy Has the Drug...VF: Relationship to Functional...How Do Nonlinear Dynamics...Can These Findings Help...What Critical Evidence Is...ConclusionsReferences |
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The mechanism by which the initial "tachysystolic phase" degenerates into fibrillation is still poorly understood. In the 1970s, Allessie et al9 made the seminal observation that functional reentry can occur in cardiac tissue in the absence of an anatomical obstacle, originally called leading circle reentry. This suggested a plausible explanation for the initial "tachysystolic phase" of fibrillation and raised the possibility that unstable functional reentry breaking up into multiple wave fronts could cause fibrillation. Subsequently, functional reentry was documented experimentally in animal10 11 12 and human ventricle.13 Meanwhile, computer simulations predicted that spiral waves might be the underlying mechanism.14 Spiral waves are a generic property of excitable media; they arise in cardiac tissue because conduction velocity depends on wave-front curvature.15 The more convexly curved a wave front is, the more slowly it propagates, because the depolarizing current at the leading edge is diluted into a larger sink of resting cells. At a critical curvature, the source of depolarizing current is too small to bring the sink (resting tissue) to threshold, and propagation fails. A spiral wave is produced when a break occurs along a propagating wave front; at the break, the end is highly curved and forms the tip of the spiral wave, which precesses around a core defined by the critical curvature. Along the arm of the spiral wave, curvature progressively decreases, allowing conduction velocity to increase with radial distance from the tip. The landmark study from Davidenko et al16 demonstrated spiral-wave reentry as a mechanism of functional reentry in real cardiac tissue. That study also documented that spiral-wave reentry could be unstable, as predicted by computer simulations.17 18 In this case, the core around which the spiral-wave arm rotates is not stationary but meanders through the tissue, producing the ECG appearance of polymorphic tachycardia or even fibrillation.19 In addition to meandering, computer simulations also demonstrated that spiral waves can break up to form multiple spiral waves,17 19 20 21 similar to wave fronts observed during fibrillation. Movement of multiple spiral waves and their cores (also called phase singularities) is complex,22 so the classic spiral morphology becomes distorted, characteristic of disorganized wave fronts in fully developed fibrillation (Figure 2
).
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How Do Nonlinear Dynamics and Chaos Theory Apply to Fibrillation? |
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TopAbstractIntroductionWhy Has the Drug...VF: Relationship to Functional...How Do Nonlinear Dynamics...Can These Findings Help...What Critical Evidence Is...ConclusionsReferences |
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The demonstration that a deterministic computer model, with no random elements, mimics fibrillation raises a strong possibility that fibrillation is not "random" reentry but arises from a deterministic process, ie, is an example of chaos. We investigated this possibility by applying nonlinear dynamics and chaos theory to experimental mapping of cardiac fibrillation and computer simulations.23 The findings strongly support the idea that cardiac fibrillation represents spatiotemporal chaos. Moreover, the analysis suggests that chaos develops by a specific route, the quasiperiodic transition to chaos.23 24 The identification of this "route to chaos" provides very specific predictions about how antiarrhythmic drugs may be designed to prevent cardiac fibrillation.
What Is Chaos Theory?
Chaos theory is the study of how highly complex behavior, with
seemingly random properties, arises from determinism (Figure 3). Determinism means that the current
state of a system is determined by its previous state. A simple way to
look for a deterministic relationship is to construct a Poincaré
plot, in which the present state (xn) is
plotted against the previous state (xn-1)
(Figure 3B). If the relationship between
xn and xn-1 is random, the
Poincaré plot yields a formless cloud of points. If the
relationship is deterministic, the Poincaré plot may exhibit
structure reflecting the underlying dependence of the present state
on previous state(s). The unpredictable behavior of a chaotic system
results from sensitivity to initial conditions; ie, small perturbations
get magnified exponentially (Figure 3F). From a therapeutic
standpoint, a key point is that chaos refers to complex behavior that a
system may exhibit depending on values of critical system
parameters (
in Figure 3). If these critical
parameters controlling behavior can be identified and
manipulated, chaotic behavior might be eliminated.
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Another important aspect illustrated in Figure 3 is that the
transition from periodic behavior to chaos is usually not abrupt but
occurs through an identifiable transition (or bifurcation sequence). A
rather astounding fact is that for all known deterministic equations
exhibiting chaotic behavior, only a small number of fundamental routes
to chaos have been identified.25 Therefore, identifying
the route to chaos may provide important insights into etiology to
guide the search for critical parameters governing system
behavior.
Evidence That Fibrillation Is Chaotic
Previous studies addressing the question of whether
fibrillation is chaotic have yielded mixed results.26 27 28 29
We looked for chaos by analyzing local extracellular electrograms
obtained at single recording sites in 3 types of
hemodynamically stable fibrillation: human atrial
fibrillation, canine VF with maintained coronary blood flow,
and VF in ventricular muscle sheets.23 The
first step was to construct Poincaré plots of the interactivation
intervals measured from the recorded electrograms. As shown by
Figure 4A through 4C, in all 3 types of
fibrillation, the Poincaré plots did not show a diffuse cloud of
points suggesting a random process but instead had definite structure:
a ring of points with a hole in the center.23
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Computer simulations showed that the ringlike pattern was not an
artifact.23 When 2-dimensional (2D) cardiac tissue was
simulated with a ventricular action potential model,
spiral-wave reentry was readily initiated and broke up into multiple
reentrant wave fronts resembling fibrillation (Figure 2). When
interactivation intervals at a local site were analyzed, the
Poincaré plot also had a ringlike appearance (Figure 4D).
The Route to Chaos in Fibrillation
The ringlike structure in the Poincaré plot has
particular significance, because it suggests that chaos arose by a
quasiperiodic transition. This route to chaos was first described in a
theoretical treatment of fluid turbulence by Newhouse et
al.30 They proved that a system containing 
3 independent
oscillatory modes is inherently unstable and becomes chaotic. Figure 5A illustrates that theorem with a stream
of smoke injected into air. Near the origin of the stream, the flow
pattern is laminar, but a bit farther away, a pair of stationary
vortices form (first oscillatory motion). A bit farther still, the
vortex develops a waviness (second oscillatory motion), which grows in
amplitude and complexity (third oscillatory motion), upon which a
sudden transition to full turbulence occurs.
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An analogous process was observed in simulated
fibrillation.23 Figure 5B shows the initiation of a
spiral wave (first oscillatory motion). The thickness of the
spiral-wave arm represents the amount of depolarized tissue
between the action potential upstroke and repolarization phase, also
known as the wavelength (the product of action potential duration
[APD] and conduction velocity [CV]). Along the spiral-wave arm,
wavelength is not uniform but is thicker in some regions and thinner in
others, as in the smoke vortices. As a result, the wave front and the
wave back of the spiral arm develop a scalloped appearance (secondary
and tertiary oscillatory motions), which are progressively amplified
until at 1 point along the spiral arm, the wavelength becomes too short
to propagate (Figure 5C). At this break in the spiral arm, the 2
"ends" form the tips of 2 "daughter" spiral waves (Figure 5D).
This breakup process repeats itself until fibrillation is
fully developed (Figure 5E).
Figure 6 shows an analogous process in a
local electrogram recorded during a spontaneous transition from VT
to VF in human right ventricular
myocardium.23 During VT, the electrogram is
monomorphic with a constant cycle length (CL) (first oscillatory
motion). At the first arrow, a transient irregularity developed that
settled into a period-2 bigeminal rhythm (second oscillatory motion).
This period-2 rhythm then developed low-frequency amplitude and period
modulation (third oscillatory motion), which grew progressively larger
until the electrogram suddenly became completely irregular, abruptly
marking the onset of VF.
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In fluid turbulence, as in cardiac fibrillation, the Poincaré
plot constructed from flow measurements typically shows a ringlike
structure (Figure 4E). More rigorous mathematical criteria, such
as nonmonotonic circle maps,25 also supported the
hypothesis that the route to chaos in fibrillation arises through
quasiperiodicity.23
What Are the Oscillatory Motions Producing Chaos in Cardiac
Fibrillation?
The close agreement between simulation and experiment
supports spiral-wave breakup in simulated cardiac tissue as a
reasonable model for the transition from tachycardia to
fibrillation. We hypothesize that the process by which a spiral wave
(the tachysystolic phase of fibrillation) meanders and then
breaks up into multiple reentrant wave fronts (fully developed
fibrillation) represents a quasiperiodic transition to
spatiotemporal chaos, resulting from the interaction of multiple
coupled oscillatory motions. Understanding the origin of these
oscillations could, in principle, provide the key to
preventing fibrillation.
As illustrated in Figure 5B through 5E, the additional
oscillatory motions that cause spiral-wave breakup are directly
observed as oscillations in wavelength along spiral-wave
arm soon after its initiation. This is an important clue to their
cellular basis. Because wavelength is by definition the product of
APD and CV, then for wavelength to change requires 1 or both
parameters to change. APD and CV are each determined by
their restitution properties. Therefore, APD and CV restitution must be
the source of wavelength oscillations that lead to
spiral-wave breakup. One method for measuring APD restitution is
illustrated in Figure 7A, in which a
premature stimulus (S2) is delivered at progressively shorter
diastolic intervals (DIs) during pacing at a fixed CL. For
short DIs (defined as the interval between the end of the previous
action potential and S2), the action potential does not recover its
full amplitude or duration. The plot of APD versus DI is an APD
restitution curve (Figure 7B). In cardiac tissue, the slower
velocity of the action potential upstroke at short DIs also slows CV,
and a similar curve of CV versus DI defines the CV restitution curve
(Figure 7C).
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It is known that the steepness of APD restitution has played a
critical role in stability of reentry around an anatomic obstacle in
both experimental31 32 and theoretical
studies.33 34 Steep APD restitution (slope >1) promotes
instability, which can terminate reentry around an obstacle (Figure 8). Karma20 realized that
the same instability, if it occurred along the arm of a spiral wave,
would produce wave break, the essential event in spiral-wave
breakup.
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To understand the mechanism, we can think of APD restitution as a
difference amplifier, providing the next value of APD as a
function of the previous DI. For a spiral wave rotating at a constant
CL, the equilibrium values of APD and DI occur at the intersection of
the APD restitution curve, with the dashed line
representing CL (Figure 8). Suppose there is a
slight perturbation in DI. Because of APD restitution, the new DI will
cause the APD of the next beat to differ. The new APD will then
generate a new DI. Whether this difference in DI is greater or smaller
is determined by the APD restitution slope. If it is <1 (Figure 8A), the next difference is smaller, and if it is >1 (Figure 8B), the next difference is larger. In this way, a shallow slope
restores APD and DI back to their equilibrium values, whereas a steeply
sloped APD restitution curve amplifies the differences so that they
progressively diverge (ie, the equilibrium is unstable). If this
oscillation grows large enough, the DI will eventually
become shorter than the refractory period, causing a wave break at some
point along the spiral-wave arm. APD restitution produces
oscillations in the wave back (repolarization phase),
whereas CV restitution creates oscillations in the wave
front (depolarization phase) by slowing CV in regions with short DIs.
This creates a spatial mode of CL oscillation. The
interaction between APD and CV restitution creates spatiotemporal
oscillations, which are quasiperiodic.
A prediction of this hypothesis is that altering cardiac
restitution properties should alter the behavior of spiral
waves.20 35 Figure 7 shows that decreasing the Ca
current by 50% in the action potential model36 reduces
the range of DIs over which APD restitution is steep (Figure 7B). This prevents spiral-wave breakup, because the DIs
experienced along the spiral-wave arm are no longer in a steep range of
APD restitution.
Wavelength also plays another important role in spiral-wave reentry by setting the minimal space required for a spiral wave to sustain itself. If wavelength is too long relative to tissue size, tachycardia or fibrillation will self-terminate24 37 the basis of the "critical mass hypothesis."38 In 2D simulations, however, spiral-wave dynamics (stationary, meandering, or breakup phenotypes) is determined primarily by underlying electrophysiological properties such as restitution, regardless of tissue size.
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Can These Findings Help Us to Develop Effective Antifibrillatory Drugs? |
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TopAbstractIntroductionWhy Has the Drug...VF: Relationship to Functional...How Do Nonlinear Dynamics...Can These Findings Help...What Critical Evidence Is...ConclusionsReferences |
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Sudden cardiac death caused by VF is separable into 2 components: initiation of tachycardia and degeneration of tachycardia to fibrillation. Clinical antiarrhythmic drug studies focusing exclusively on preventing VT initiation have not been effective at reducing sudden cardiac death, so a better understanding of the second component is critically needed to advance pharmacological therapy. The degeneration of tachycardia to fibrillation can be simulated in computer models by spiral-wave breakup, which occurs by a specific route known as the quasiperiodic transition to chaos. Experimental evidence directly supports this scenario. In simulations, APD and CV restitution creates spatiotemporal oscillations in APD and DI, leading to wave break and the onset of a fibrillationlike state. That is, they are potential critical parameters that govern the transition between periodicity (tachycardia) and chaos (fibrillation).
The key question is as follows: Is this scenario relevant to real cardiac tissue? If so, it should be possible to develop antiarrhythmic drugs that modify cardiac restitution properties appropriately to prevent tachycardia from degenerating to fibrillation. A strategy for the ideal antiarrhythmic drug would be to combine traditional antitachycardic properties (classes 1 through 4) with antifibrillatory properties on the basis of their effects on restitution as a 2-pronged attack. Like Karma,20 we refer to this scenario as the Restitution Hypothesis.
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What Critical Evidence Is Needed to Validate the Restitution Hypothesis? |
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TopAbstractIntroductionWhy Has the Drug...VF: Relationship to Functional...How Do Nonlinear Dynamics...Can These Findings Help...What Critical Evidence Is...ConclusionsReferences |
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Methods for measuring restitution properties need fuller evaluation. APD restitution is not a unique function of the previous DI but is significantly influenced by excitation history (memory effect). The restitution characteristics present during the arrhythmia determine stability or instability, and these characteristics may differ significantly from restitution measured by arbitrarily devised pacing protocols. In our own survey of 25 studies, we found that maximal APD restitution slope was either considerably >1 (15 studies) or
1 (10 studies). In none was the slope substantially
<1 at all CLs tested. The major cellular determinants of APD and CV
restitution are well characterized and include recovery from
inactivation of inward Na and Ca currents, deactivation of K currents,
and intracellular Ca dynamics.36 39 40 With a directed
approach, antiarrhythmic drugs that favorably alter factors controlling
restitution should be identifiable. The real heart is highly complex (3-dimensional, anisotropic, and electrophysiologically and anatomically heterogeneous) compared with simulated 2D tissue for which the Restitution Hypothesis is demonstrated to be valid. Others argue that fibrillation requires 3 dimensions, 2D spiral-wave breakup has limited relevance to fibrillation,41 or 3 dimensions produce restitution-independent breakup.42 However, fibrillation has been documented in relatively thin-walled cardiac preparations.24 43 This issue needs to be resolved.
Electrophysiological and anatomic heterogeneity makes the diseased heart more susceptible to VF and sudden death.44 Although heterogeneity makes reentry easier to induce, its effects on VT stability are less clear. In healthy human heart, functional reentry can invariably be induced with a sufficiently strong stimulus, and once initiated, it virtually always degenerates to VF. In contrast, stable VT is much more common in diseased hearts despite their considerably greater heterogeneity. Heterogeneity can actually promote stability by anchoring meandering spiral waves.16 45 Therefore, the common perception that heterogeneity intrinsically destabilizes reentrant wave fronts may be a misconception. The higher incidence of VT and VF in diseased hearts may reflect the greater likelihood that a triggering event (premature ventricular contraction) will initiate a sustained arrhythmia rather than a destabilizing effect of heterogeneity on reentry.
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Conclusions |
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TopAbstractIntroductionWhy Has the Drug...VF: Relationship to Functional...How Do Nonlinear Dynamics...Can These Findings Help...What Critical Evidence Is...ConclusionsReferences |
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Therapeutically, the role of electrophysiological and anatomic tissue heterogeneity in degeneration of VT to VF is the key challenge facing the restitution hypothesis. If heterogeneity by itself directly promotes spiral-wave instability, this is a difficult therapeutic target. On the other hand, if modifiable global electrophysiological properties such as APD and CV restitution determine stability, the outlook for effective pharmacological treatment of VF is bright. Resolving this issue is critical. It is testable with simulations incorporating realistic cardiac anatomy and electrophysiology, in combination with experimental arrhythmia mapping experiments.
From these findings, we recommend that comprehensive experimental evaluation of the Restitution Hypothesis is warranted and timely. A new paradigm for antiarrhythmic drug classification, incorporating an antifibrillatory profile based on cardiac restitution with the traditional antitachycardia profile (classes 1 through 4), seems highly promising. Potentially, this could resolve the stalemate over antiarrhythmic drug development that has followed in the discouraging wake of the CAST and SWORD trials.1 2
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Acknowledgments |
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This work was supported by NIH SCOR in Sudden Cardiac Death P50 HL-52319, grants from the American Heart Association and its Greater Los Angeles Affiliate, the University of California Tobacco-Related Disease Research Program, Cedars-Sinai Foundation ECHO Award, the Ralph M. Parsons Foundation, the Laubisch Fund, and the Kawata and Price endowments.
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