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# Nonlinear-dynamical arrhythmia control in humans

Edited by Charles S. Peskin, New York University, New York, NY, and approved February 28, 2001 (received for review November 21, 2000)

## Abstract

Nonlinear-dynamical control techniques, also known as chaos
control, have been used with great success to control a wide range of
physical systems. Such techniques have been used to control the
behavior of *in vitro* excitable biological tissue,
suggesting their potential for clinical utility. However, the
feasibility of using such techniques to control physiological processes
has not been demonstrated in humans. Here we show that
nonlinear-dynamical control can modulate human cardiac
electrophysiological dynamics by rapidly stabilizing an unstable target
rhythm. Specifically, in 52/54 control attempts in five patients, we
successfully terminated pacing-induced period-2 atrioventricular-nodal
conduction alternans by stabilizing the underlying unstable
steady-state conduction. This proof-of-concept demonstration shows that
nonlinear-dynamical control techniques are clinically feasible and
provides a foundation for developing such techniques for more complex
forms of clinical arrhythmia.

Increasingly, it is
recognized that many cardiac arrhythmias can be characterized on the
basis of the physical principles of nonlinear dynamics (1, 2). A
nonlinear-dynamical system is one that changes with time and cannot be
broken down into a linear sum of its individual components. For certain
nonlinear systems, known as chaotic systems, behavior is aperiodic and
long-term prediction is impossible, even though the dynamics are
entirely deterministic (i.e., the dynamics of the system are completely
determined from known inputs and the previous state of the system, with
no influence from random inputs). Importantly, such determinism
actually can be exploited to control the dynamics of a chaotic system.
To this end, a variety of nonlinear-dynamical control techniques, also
known as chaos control,‡ have been developed
(3, 4) and applied successfully to a wide range of physical systems
(5–14). Such techniques are model-independent, i.e., they require no
*a priori* knowledge of the underlying equations of a system
and are therefore appropriate for systems that are essentially
“black boxes.”

The success of nonlinear-dynamical control techniques in stabilizing
physical systems, together with the facts that many physiological
systems are nonlinear (e.g., the cardiac conduction system, because of
its numerous complex nonlinear component interactions) and lack the
detailed analytical system models required for model-based control
techniques, have fostered widespread interest in applying these
model-independent techniques to biological dynamical systems (15–26).
In a pioneering application, Garfinkel *et al.* (15)
stabilized drug-induced irregular cardiac rhythms by means of
dynamically timed electrical stimulation in an *in vitro*
rabbit ventricular-tissue preparation. That work was an important
demonstration that the physical principles of nonlinear-dynamical
control could be extended into the realm of cardiac dynamics. Although
extension of that work to the control of fibrillation in intact hearts
is impeded currently by the complexity of fibrillation
[notwithstanding a recent study that showed interesting dynamical
modification of human atrial fibrillation (27)], there are clinically
important low-dimensional cardiac dynamics (e.g., reentrant
arrhythmias) for which such techniques are well suited. Control of such
dynamics has been demonstrated in computational studies of mathematical
arrhythmia models (19, 21) and in *in vitro* rabbit heart
experiments (22). In this study, we demonstrate that such dynamics also
can be controlled in humans.

## Methods

### Background.

To demonstrate clinical feasibility, we have attempted to control a dynamically tractable rhythm known as atrioventricular (AV) nodal conduction alternans (referred to hereafter as alternans). Alternans is a beat-to-beat alternation in AV-nodal conduction time that can develop if the time between consecutive AV-nodal excitations is abnormally short—the AV-nodal conduction time gradually fatigues (lengthens) and then bifurcates from its steady-state value into an alternation; such a bifurcation is a hallmark of a nonlinear-dynamical system. AV-nodal alternans is not clinically dangerous. However, alternans is of interest to nonlinear dynamicists, because it is a clinically inducible cardiac rhythm that can be used to study how nonlinear-dynamical control methods can exploit arrhythmia dynamics for arrhythmia termination. Furthermore, as will be discussed later, the underlying dynamics of alternans may be related to more dangerous cardiac dynamics.

Clinically, alternans often has been attributed to the presence of dual AV-nodal pathways (28). However, Billette and coworkers (29, 30) have demonstrated clearly that alternans can result solely from the conduction properties of a single AV-nodal pathway. In fact, alternans attributed to a single AV-nodal pathway have been observed in humans during AV orthodromic reciprocating tachycardia (ORT; refs. 31 and 32), a repetitive reentrant arrhythmia in which normal anterograde ventricular excitation by means of the AV node is followed by reexcitation of the atria by means of a pathological retrograde accessory ventriculoatrial pathway.

### Technique.

An alternans pacing and control protocol was performed, after informed written consent was obtained, as a supplementary component of routine clinically indicated electrophysiological studies in five patients (3 males, 2 females; 52 ±17 yr) with normal AV-nodal conduction (see Table 1 for patient demographics and control-algorithm results). In two patients, trials were performed preceding and after pharmacological autonomic blockade, which was administered by means of i.v. delivery of 0.2 mg/kg propranolol and 0.04 mg/kg atropine (33). The pharmacological blockade trials were used to ensure that control-algorithm results were not related to autonomic influences on AV-nodal function. In two other patients, because alternans did not occur in the absence of pharmacological autonomic blockade, the control protocol was performed only after blockade. In one patient, alternans did occur in the absence of pharmacological autonomic blockade but a second trial after blockade was not performed, because β-blockade was contraindicated due to the patient's underlying chronic obstructive pulmonary disease.

The electrophysiological studies used standardized techniques that included the introduction of multiple percutaneous catheters from the femoral veins to record intracardiac signals from the right atrium, the His bundle region, and the right ventricle, as well as to pace from the two chambers. In studies in which isoproterenol was delivered during the clinical evaluation stage, the alternans pacing and control protocol was not initiated until at least 15 min after the termination of isoproterenol delivery.

During each trial, ORT was simulated by means of a protocol
called fixed-delay stimulation (Fig. 1),
in which the right atrium was stimulated (at time *A*) at a
fixed time interval, VA (ventriculoatrial), after detection of
ventricular activation (at time *V*). When the VA interval is
reduced (simulating faster reentry), the approximately (i.e., there is
a small degree of inherent conduction variability) period-1 rhythm can
destabilize and the AV-nodal conduction time can bifurcate into
period-2 alternans. Note that in this study, rhythms more complex than
alternans were not observed; however, in a larger clinical study of
AV-nodal conduction dynamics during rapid atrial pacing, more complex
AV-nodal rhythms, including period-4 conduction, were seen (34).

A surface electrogram was sampled at 1 kHz by a National Instruments
(Austin, Texas) AT-MIO-16E-10 data acquisition board in a 266-MHz Intel
Pentium-II-powered computer running Real-Time Linux and a custom C++
experiment interface system (35). To simulate ORT, this system
automatically detected R-waves in the surface electrogram (denoted time
*V*) by means of a threshold-crossing algorithm and then, at a
predetermined VA interval after the detected R-wave, output a voltage
pulse by means of the AT-MIO-16E-10 to trigger a Bloom DTU215
stimulator (Fischer Imaging, Denver) to stimulate the right atrium (at
time *A*; Fig. 1). The nominal VA interval was decreased
gradually until an alternation (alternans) in the AV interval was
observed.

Once alternans occurred, an adaptive nonlinear-dynamical control
technique (36) was initiated to terminate the alternans. The control
algorithm is designed to stabilize the underlying unstable steady
state, *x**, of a system that can be described by a unimodal
one-dimensional function (*x*_{n+1} =
*f*(*x _{n}*,

*p*), where

_{n}*x*is the current value of the system variable of interest,

_{n}*x*(for alternans,

*x*is the AV-nodal conduction time, AV),

*x*

_{n+1}is the next value of the same variable, and

*p*is the current value of an accessible system parameter

_{n}*p*(for alternans control,

*p*is the VA-pacing interval) at index

*n*. Thus, for alternans, the system function is 1 where

*n*is the beat number. The control technique perturbs VA such that 2 where is the nominal VA-pacing interval, and δVA

_{n}is a perturbation (6, 7, 37) given by 3 where AV

^{*}

_{n}is the current estimate of the unstable steady state AV*, and

*g*is the control sensitivity

_{n}*g*at index

*n*. Thus, for each atrial stimulus, the nonlinear-dynamical control algorithm computes a perturbation to the nominal VA interval that is proportional to the difference between the current AV interval and the targeted unstable period-1 AV steady state.

Importantly, only negative perturbations (i.e., those that result in a shortening of the VA interval) are permitted. If the perturbation computed for a given VA interval is positive, the nominal VA interval is left unperturbed. This condition is imposed to simulate the ability of a pacemaker to truncate but not lengthen VA during a hypothetical episode of clinical ORT (i.e., the natural ORT impulse would excite the AV node before any stimulus attempted at a lengthened VA interval).

The dynamics of alternans and control are depicted schematically in
Fig. 2. In Fig. 2,
*f*(AV_{n}, ) is represented
by a quadratic curve fit to uncontrolled AV intervals that obeyed the
dynamics of Eq. 1. During stable alternans (i.e., without
control) (Fig. 2*a*), the AV intervals alternate indefinitely
between points 1 and 2 via the dynamic route depicted by the dotted
lines, and never move into the unstable interior region of the
function. With control (Fig. 2*b*), the appropriate VA control
perturbation of Eq. 3 shifts the function to
*f*(AV_{n}, +
δVA_{n}). By doing so, point 1 becomes point 1′
(i.e., AV_{n+1} is increased). When the
function is returned to
*f*(AV_{n},) at the next
beat (i.e., δVA = 0), AV progresses to point 2—the unstable
period-1 steady state AV*. Repetition of such perturbations, always
calculated according to the current system state, holds the system
within the neighborhood of AV*. Termination of control would be
followed by the drift of AV away from AV*, through the unstable
interior region, back to the stable alternans rhythm of Fig.
2*a*.

Both AV* and *g* are estimated adaptively at each beat,
thereby providing inherent algorithmic dynamic flexibility. For
alternans, AV* ^{*}_{n}* is reestimated
repeatedly as the midpoint of AV

_{n}and AV

_{n−1}.§ The control sensitivity

*g*is adapted in real time based on the characteristic dynamics of unimodal one-dimensional systems. Specifically, for every beat, if the sign of the computed perturbation (Eq. 3) has alternated for the four previous perturbations, the magnitude of

*g*is decreased by a factor

*ρ*(for this study

*ρ*= 0.05), otherwise, the magnitude of

*g*is increased by a factor

*ρ*(36).

Importantly, this nonlinear-dynamical control technique estimates the control parameters and target-rhythm dynamics in real time “on-the-fly” (i.e., requiring no learning stage). This feature has two significant benefits, especially for clinical applications. First, the repetitive estimation provides inherent robustness to nonstationarities, because any change in the underlying system dynamics will be immediately detected and accounted for. Second, the instantaneous onset of parameter estimation eliminates the need for a precontrol learning stage (3), which is a period often required before control activation to quantify the system dynamics. With this on-the-fly approach, the algorithm learns the dynamics at the same time that it is bringing the system under control. Thus, it is capable of applying control immediately on the detection of an arrhythmia (avoiding dangerous lag time) and is able to maintain control as the dynamics of the arrhythmia change over time.

## Results

The alternans pacing and control algorithm results for the five
patients are shown in Table 1. Control was successful in 52 of 54
control attempts (96%). To quantify control-stage efficacy, the
standard deviation of the 15 AV intervals immediately preceding each
control stage [(σ_{pk}), where
*k* is the index of a given control stage)] and the standard
deviation of the AV intervals during each control stage
(σ_{ck}) were calculated. From these
values, the mean precontrol standard deviation
( =
∑
σ_{pk}, where *N* is the
total number of control stages for the trial) and the mean
control-stage standard deviation
( =
∑
*b*_{k}σ_{ck},
where *b _{k}* is the number of beats for the

*k*th control stage and

*B*= ∑

*b*

_{k}) were computed. The control improvement was quantified as the percentage of the precontrol AV-interval standard deviation eliminated during control: Δ

_{σ}= 100(1 − /). Control improvement ranged from 35% to 68%. Control efficacy was independent of the presence of dual AV-nodal pathways [dual-pathway physiology was tested without pharmacological autonomic blockade; trials on patients with dual pathways: 48 ± 16% (Δ

_{σ}mean ± standard deviation); and without dual pathways: 51 ± 14%,

*P*= not significant (NS)], antiarrhythmic medications (trials on patients taking antiarrhythmic medications: 45 ± 9%; and not taking antiarrhythmic medications: 56 ± 18%,

*P*= NS), or autonomic blockade (trials before autonomic blockade: 42 ± 12%; and after autonomic blockade: 55 ± 13%,

*P*= NS).

Fig. 3 shows a representative example of a patient undergoing simulated ORT pacing after propranolol/atropine autonomic blockade (Patient 1). Before the initiation of control, the fixed VA-pacing interval of 60 ms caused an alternation in the atrial-His (AH) interval between 127 and 167 ms.¶ On control initiation, the VA nonlinear-dynamical control perturbations (Eq. 3) moved the AH intervals toward their underlying steady state, which lies between the bifurcated alternating values.

Fig. 4 shows the time course of a segment
of the trial shown in Fig. 3. The control perturbations made to the VA
interval (Fig. 4*b*) terminated the alternating AV-nodal
conduction by forcing the AV interval toward its underlying unstable
steady state (Fig. 4*a*). Tight, noise-free control was not
possible because of the biological noise inherent to this system.

Importantly, on termination of each control stage, the AV interval
reverted spontaneously to alternans. This spontaneous reversion
demonstrates that the steady state was unstable, that the
nonlinear-dynamical control perturbations were required for
stabilization, and that the alternans termination was not a
coincidental spontaneous occurrence. An alternative hypothesis, that
control resulted from a reversion to single-pathway conduction from
dual-pathway alternation, is refuted by the fact that period-1
conduction was at an interval between the two alternating conduction
intervals rather than at one rate or the other. The single-pathway
hypothesis is further supported by (*i*) the fact that the
onset of alternans was characterized by a bifurcation (typical of
nonlinear-dynamical function) instead of a discrete jump (typical of
dual-pathway function) and (*ii*) successful control in three
patients who did not have dual AV-nodal pathways.

The adaptive control algorithm's inherent ability to track
nonstationarities was demonstrated later in the same trial, as shown in
Fig. 5. During each control attempt, the
nominal VA interval, , was increased or decreased in
discrete steps. For example, Fig. 5*b* shows that from 2,900
≤ *n* ≤ 3,115, was increased from 15 to 55
ms. During this time, the control algorithm never lost its AV
stabilization, even as its unstable steady state shifted from 320 to
285 ms (Fig. 5*a*).

For Patient 1, nonlinear-dynamical control was applied 14 distinct
times; each control attempt successfully eliminated the alternans
rhythm ( = 17.3 ms,
= 6.1 ms, and
Δ_{σ} = 65%). In Patient 2, control was
attempted in two trials, one before and one after
propranolol/atropine autonomic blockade. In the preblockade trial,
control was attempted 8 times at four different nominal VA intervals
and was successful each time (
= 14.1 ms, = 9.0 ms, and
Δ_{σ} = 36%). In the postblockade trial,
control was attempted 8 times at four different nominal VA intervals
and was successful each time (
= 12.0 ms, = 3.9 ms, and
Δ_{σ} = 68%). In Patient 3, control also was
attempted before and after propranolol/atropine autonomic blockade.
In the preblockade trial, control was attempted twice at two different
nominal VA intervals and was successful both times
(= 43.8 ms,
= 28.5 ms, and
Δ_{σ} = 35%). In the postblockade trial,
control was attempted twice at one VA interval and was successful both
times ( = 5.4 ms,
= 3.1 ms, and
(Δ_{σ} = 43%). (Most alternans occurrences for
this patient were transient and therefore inappropriate for control
attempts.) In Patient 4, control was attempted without autonomic
blockade 10 times at three different nominal VA intervals and was
successful each time ( = 9.7
ms, = 4.3 ms, and
Δ_{σ} = 56%). In Patient 5, control was
successful in 8 of 10 attempts at a single nominal VA interval after
propranolol/atropine autonomic blockade
( = 9.1 ms,
= 5.0 ms, and
Δ_{σ} = 45%; values were computed by using only
successful control stages). The two control failures seemed to result
from the fact that = 10 ms, which left little room for
VA interval shortening, thereby increasing the difficulty of unstable
steady-state capture. The AV and VA intervals and *g*
proportionality constant for Patients 2–5 were all qualitatively
similar to those shown in Fig. 4.

## Discussion

In this study, we have demonstrated that nonlinear-dynamical control techniques can be used effectively in humans. We have shown, in 52/54 control attempts in five patients, that an adaptive on-the-fly (i.e., requiring no learning stage) nonlinear-dynamical control technique can alter cardiac dynamics by simultaneously estimating and stabilizing an unstable target rhythm. Control efficacy was not related to antiarrhythmic medications, the presence of dual AV-nodal pathways, or autonomic influences (i.e., control was effective both with and without pharmacological autonomic blockade). These findings provide support for earlier suggestions that nonlinear-dynamical control might be applicable to clinical arrhythmia control (1, 2, 15, 19, 22).

### Nonlinear-Dynamical Control.

The idea of using the dynamics of a chaotic system for system
control was proposed in the early 1990s by Ott *et al.* (3).
Their approach took advantage of the fact that the aperiodic dynamics
of a chaotic system are actually composed of an infinite number of
unstable steady-state rhythms. Chaotic aperiodicity stems from the
inability of a chaotic system to remain in any one of its repellent
unstable periodic rhythms. The Ott *et al.* technique attempts
to regularize the dynamics of a chaotic system by holding it within a
targeted unstable rhythm by exploiting the characteristic dynamics of
that rhythm. Such control is possible because, although long-term
forecasting of a chaotic system is impossible, short-term dynamical
prediction is possible. Furthermore, such short-term prediction can be
extended to account for and exploit the effects of a perturbed system
parameter. With such dynamical knowledge, a corrective parameter
perturbation can be used to move the system into, and hold it within,
the neighborhood of a desired unstable steady-state rhythm.

Importantly, the Ott *et al.* (3) technique is
model-independent, i.e., it requires no *a priori* knowledge
of the underlying equations of a system. Model-independent techniques
extract necessary quantitative information (about the functional
dependence of the variable to be controlled on a system parameter) from
system observations and then use this information to exploit the
inherent dynamics of the system to achieve a desired control result.
Thus, these techniques are applicable to systems for which analytical
models are typically unavailable or incomplete, i.e., “black
boxes.”

The Ott *et al.* (3) technique, and its derivatives, have been
applied to control a wide range of physical systems (3, 4) including
magneto-elastic ribbons (5), electronic circuits (6, 10, 11), lasers
(8, 12), chemical reactions (7, 9), and driven pendulums (13, 14). The
success of nonlinear-dynamical control in stabilizing physical systems
has fostered interest in applying these techniques to excitable
biological systems (15–19, 21, 22). It is the model-independent nature
of such techniques that make them particularly well suited for
biological systems—although many physiological mechanisms are well
understood qualitatively, quantitative relationships between
physiological system components are usually incomplete. Thus, because
accurate analytical system models cannot be developed for such systems,
model-based control techniques are often not applicable to
physiological systems. In contrast, model-independent techniques are
applicable because, before control, they require only a qualitative
understanding of the underlying dynamical mechanisms.

### Nonlinear-Dynamical Control of Cardiac Dynamics.

In a pioneering biological nonlinear-dynamical control application,
Garfinkel *et al.* (15) stabilized drug-induced irregular
cardiac rhythms in tissue from the interventricular septum of a rabbit
heart. They applied electrical nonlinear-dynamical control
perturbations directly to the interbeat intervals to hold the system
within an underlying unstable steady state. They successfully
regularized the electrical activity into low-order rhythms, but not the
period-1 rhythm they targeted. Subsequent mathematical modeling studies
have suggested dynamical mechanisms for such control-algorithm results,
along with improved adaptive algorithms that could achieve
“tighter” control (39–42).

The provocative cardiac chaos-control study by Garfinkel *et
al.* (15), combined with data suggesting that fibrillation is
chaotic (43, 44), sparked interest in nonlinear-dynamical control of
fibrillation. However, other work has questioned the chaotic
fibrillation hypothesis (45, 46). The current prevailing theory (47),
supported by a range of mathematical (48–56), *in vitro*
(57–59), and *in vivo* (57, 60–70) studies, is that
fibrillation is a complex nonlinear combination of stochastic and
deterministic components, such as scroll waves of electrical activity
meandering within the ventricular wall. Given this body of evidence, it
is apparent that fibrillation is characterized by high-dimensional
nonstationary spatiotemporal dynamics that are too complex for current
nonlinear-dynamical control techniques.

Nevertheless, nonlinear-dynamical control is still applicable to the
control of cardiac arrhythmias because, as with chaotic systems,
nonlinear-dynamical systems with regular dynamics may have underlying
unstable steady states. Such steady states can be targeted for rhythm
control by using derivatives of the Ott *et al.* (3) technique
(71). This approach has been demonstrated in mathematical modeling of
cardiac dynamics (19, 21) and *in vitro* rabbit heart studies
(22).

### Nonlinear-Dynamical Control of Clinical Cardiac Dynamics.

In this study, we now have demonstrated the utility of such techniques in humans. These results suggest that nonlinear-dynamical control could be used for clinical arrhythmia control. In particular, nonlinear-dynamical suppression of cardiac alternans may have important clinical implications given that alternans in electrocardiogram morphology, such as T-wave alternans, can precede life-threatening arrhythmias and is a risk factor for sudden death (72–76). T-wave alternans is the surface electrocardiographic marker of a beat-to-beat alternation in ventricular repolarization. The period-2 nature of T-wave alternans suggests that, like AV-nodal alternans, it may be amenable to nonlinear-dynamical control techniques. However, because T-wave alternans is distributed spatially over the surface of the ventricles (unlike the spatially localized AV-nodal alternans controlled in this study), nonlinear-dynamical methods applied to it must be capable of spatiotemporal control (25, 26, 77–81). If such control is successful, a potential route to a sustained ventricular arrhythmia may be eliminated (72–76) thereby preventing the onset of a potentially deadly arrhythmic event.

More generally, the flexibility and adaptability of nonlinear-dynamical control techniques may improve ventricular tachycardia therapies. Antitachycardia pacing algorithms used in current-generation implantable cardiac defibrillators do not use beat-to-beat feedback information during stimulation. In contrast, adaptive nonlinear-dynamical control techniques alter their intervention parameters, such as interstimulus interval, on a beat-to-beat basis according to the effects of previous stimuli on the dynamics of the arrhythmia. By doing so, such “smart” algorithms exploit the underlying dynamics of the arrhythmia they are attempting to terminate—essentially using the dynamics of the arrhythmia against the arrhythmia itself. In summary, nonlinear-dynamical control techniques, by means of their inherent adeptness at characterizing and exploiting the underlying nonlinear nature of arrhythmias, have the potential to provide novel approaches to the treatment of clinical arrhythmias.

### Limitations.

Although the findings of this study suggest the feasibility of nonlinear-dynamical control of cardiac arrhythmias in general, the applicability of this particular control algorithm to arrhythmias other than induced AV-nodal alternans is unclear, given that the alternans termination in this study corresponds to a modification of AV-nodal conduction (not actual termination of conduction) that is qualitatively different from the termination (not modification) of a reentrant wave. Another limitation of this study was that control efficacy was restricted by the 1-ms stimulus-timing resolution of the stimulator. Because unstable steady states are highly sensitive to small parameter deviations, it is possible that a finer stimulus-timing resolution could result in tighter rhythm control. An additional limitation was the need for visual alternans recognition and the corresponding manual activation (by means of a software toggle switch) of the nonlinear-dynamical control algorithm. In an arrhythmia-control device, arrhythmia recognition and control activation would have to be automated.

## Acknowledgments

This work was supported, in part, by grants from the American Heart Association (National Center no. 0030028N and New York City Affiliate no. 9950993T), the Raymond and Beverly Sackler Foundation, and the National Institutes of Health Grant R01 HL-56139.

## Footnotes

↵† To whom reprint requests should be addressed at: Cornell University Medical College, 520 East 70th Street, Starr-463, New York, NY 10021. E-mail: dchristi{at}med.cornell.edu.

This paper was submitted directly (Track II) to the PNAS office.

↵‡ Note that in this paper, “control” refers to a method of altering dynamics, not a standard comparative group for an experiment.

↵§ For higher-order rhythms, additional previous values of the system variable may be incorporated into the estimate (40).

↵¶ Note that the AH interval, which is the AV-nodal conduction time, is quantifiable during posttrial analysis of electrograms. Because reliable His-bundle detection is not possible during a control trial, the AV interval is used as a surrogate for the AH interval. This substitution is based on the assumption that the HV interval is fixed, an assumption that was verified for each patient during atrial pacing at multiple cycle lengths.

## Abbreviations

- AV,
- avioventricluar;
- ORT,
- orthodromic reciprocating tachycardia;
- VA,
- ventriculoatrial;
- AH,
- atrial-His

- Received November 21, 2000.

- Copyright © 2001, The National Academy of Sciences

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- Shulgin B V,
- Collins J J

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