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Computational Mapping Identifies Localized
Mechanisms for Ablation of Atrial Fibrillation
Sanjiv M. Narayan1, David E. Krummen1, Michael W. Enyeart1, Wouter-Jan Rappel2*
1 Department of Medicine and Veterans Affairs Medical Center, University of California San Diego, San Diego, California, United States of America, 2 Department of Physics
and Center for Theoretical Biological Physics, University of California San Diego, San Diego, California, United States of America

Atrial fibrillation (AF) is the most common heart rhythm disorder in the Western world and a common cause of
hospitalization and death. Pharmacologic and non-pharmacologic therapies have met with limited success, in part due to
an incomplete understanding of the underlying mechanisms for AF. AF is traditionally characterized by spatiotemporally
disorganized electrical activation and, although initiating triggers for AF are described, it is unclear whether AF is sustained
by spatially meandering continuous excitation (re-entrant waves), localized electrical sources within the atria, or some other
mechanism. This has limited therapeutic options for this condition. Here we show that human AF is predominantly caused
by a small number (1.860.9) of localized re-entrant waves or repetitive focal beats, that remain stable with limited spatial
migration over prolonged periods of time. Radiofrequency ablation that selectively targeted the sites of these sources was
able to immediately terminate fibrillation and eliminate the arrhythmia with high success. Our results show that human AF,
despite apparent spatiotemporal disorganization, is often perpetuated by a few spatially-constrained and temporally
conserved sources whose targeted ablation can eliminate this complex rhythm disorder.
Citation: Narayan SM, Krummen DE, Enyeart MW, Rappel W-J (2012) Computational Mapping Identifies Localized Mechanisms for Ablation of Atrial
Fibrillation. PLoS ONE 7(9): e46034. doi:10.1371/journal.pone.0046034
Editor: Vladimir E. Bondarenko, Georgia State University, United States of America
Received May 21, 2012; Accepted August 28, 2012; Published September 26, 2012
Copyright: ß 2012 Narayan et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: This study was funded by grants to SMN and WJR from the National Heart Lung and Blood Institute (HL70529, HL83359, HL103800) and Doris Duke
Charitable foundation. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing Interests: Intellectual property has been registered on the use of computational mapping for use as an AF ablation procedure by the University of
California Regents, with Drs. Narayan and Rappel named as inventors, and is licensed to Topera Medical Inc.. Dr. Narayan is a co-founder and holds equity in
Topera Medical Inc. Dr. Rappel is a consultant to Topera Medical. Topera Medical does not support any research conducted by Dr. Narayan nor Dr. Rappel,
including that presented here. This does not alter the authors’ adherence to all the PLOS ONE policies on sharing data and materials.
* E-mail: rappel@physics.ucsd.edu

understanding the mechanisms that sustain AF, once triggered, is
lacking [4,19], such that current ablation procedures often fail to
terminate AF and require electrical shock to restore sinus rhythm
[4]. AF subsequently recurs in 30–50% of these patients within a
1-year period [4,20] with little improvements in outcome in recent
years [21].
In some animal models, reentrant spiral waves (rotors) may act
as sources for fibrillation [22–25], and may be numerous [23], drift
within the atria [26] or ventricles [23], or extinguish over time
[23,26,27]. In other models, AF exhibits non-localized waves
within the atrium [28–30]. Due to interspecies differences,
including the rarity of spontaneous AF in animals and the fact
that human AF is age-related and the product of co-existing
diseases that are difficult to model, none of these mechanisms has
yet been proven in human AF. Indeed, the existence of rotors is
disputed in human AF [29,31]. Similarly, focal beats, small regions
of tissue from where activation emanates centrifugally and that
may drive AF in animal models [31–33], are rarely identified a
priori as sustaining mechanisms for human AF [29,31].
To define the predominant mechanisms underlying the
perpetuation of AF in humans, we developed an approach to
map human AF during minimally invasive procedures, combining
high temporospatial resolution mapping of both atria (Fig. 1A–D)
with patient-specific computational analyses of atrial activation
and recovery.

Heart rhythm disorders are defined by abnormal spatial or
temporal patterns of electrical propagation. Fibrillation, the most
prevalent human rhythm disorder, is characterized by extremely
rapid, temporally irregular and spatially disorganized electrical
activity with potentially disastrous consequences. In the ventricles,
fibrillation causes an abrupt loss of cardiac output (sudden death),
and is the leading cause of death world-wide [1]. Fibrillation of the
atria affects over 10 million individuals in the U.S. and Europe
[2,3] in whom it contributes to heart failure, stroke and death.
Despite numerous advances in therapy, AF is rarely cured [2–4]
by defibrillating electrical shocks [2,5] or anti-arrhythmic medications, both of which have modest long-term efficacy [2,4].
Organized arrhythmias [6,7], including the Wolff-ParkinsonWhite syndrome which contains an anatomically fixed reentry
pathway [8,9], exhibit rapid activity that can be destroyed by
targeted ablation for a cure. However, this is not currently true for
Several mechanisms have been proposed for the maintenance
and recurrence of AF, including electrical remodeling [10,11],
structural remodeling [12–14] and disturbed intracellular calcium
homeostasis [15]. Seminal work by Haı̈ssaguerre et al. has
described initiating triggers for AF that can be eliminated by
ablation [16] and genetic factors have been identified that
contribute to the underlying propensity to AF [17,18]. However,

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Mechanisms for Atrial Fibrillation

Figure 1. Electrical and Anatomic Mapping of Human Atria. A. Basket catheter splines are represented as colored lines registered within the
right (blue) and left (grey) atria in left anterior oblique and B. right anterior oblique projections. The figure shows alternate splines with positions D
(distal) to 4 representing electrodes 1 to 8. C. Bi-atrial schematic showing right atrium as if opened at its poles and left atrium as if opened at its
equator, with electrode positions (black dots). D. ECG leads I, aVF and V1 and electrograms of one sinus rhythm beat (red box) captured by baskets in
right and left atrium. E. Maps of sinus rhythm activation (isochrones) from high right atrium (sinus node) to low lateral left atrium created from biatrial basket recordings.

We studied 80 subjects with a broad range of AF phenotypes
including paroxysmal AF (defined as episodes that self-limit within
7 days), persistent AF (episodes that terminate only with
cardioversion) or longstanding persistent AF (continuous AF for
over 1 year) [4], and undergoing a first ablation as well as those
who had failed conventional ablation (see Table S1 for patient
characteristics). Details of our patient population and mapping
technique are presented in the Methods and Supporting Information. Our mapping technique revealed localized sources
(electrical rotors or focal beats) in almost all patients. Furthermore,
we found that these sources were few in number and stable over
prolonged periods of time that can be as long as months. These
surprising findings enabled us to terminate AF with targeted
ablation at the site of the localized sources. Finally, patients
undergoing this targeted ablation experienced a superior rate of
AF elimination in the long-term compared to patients undergoing
traditional ablation procedures focusing on trigger mechanisms
near the pulmonary veins.

Rotors and focal sources are common during AF
When applied to AF, our computational mapping technique
revealed localized and stable sources in 96% of patients. This is in
contrast to recent human studies in which localized sources for AF
were rarely or never observed [29,31]. Electrical rotors in AF,
defined in this study as continuous sequential activation rotating
around a central region, were revealed in 86% of patients (Fig. 2A–
F and Table S2). Different computational approaches gave the
same results on rotor location and characteristics (see Methods and
compare fig. 3 with Figure S1).
Repetitive focal beats in AF, defined in this study as activation
radiating from a source region, were revealed in 29% of patients
(Fig. 2GH and Table S2). Although elegant studies suggest that
focal beats in fibrillation may represent breakthrough from
reentrant waves on the opposing cardiac surface [29], simultaneous epicardial mapping would be required to resolve differences
across the cardiac wall. Analysis of the directionality of propagation across cycles confirmed that localized sources drive fibrillatory
activity (Figure S2).
Study patients often demonstrated more than one coexisting
electrical rotor or repetitive focal beat (Fig. 4, Table S2), for an
average of 1.860.9 for both atria. By comparison, single
fibrillating sheep atria [26], that are substantially smaller than
either human atrium, showed 1–3 sources. The number of
coexisting sources was higher in patients presenting with advanced
AF (i.e. persistent compared to paroxysmal AF, p,0.05), but was
unrelated to whether patients were being studied for the first time
or had previously failed conventional ablation (1.860.9 vs
1.860.6, respectively p = 0.84), patient age, left atrial diameter
or duration of AF history.

Results and Discussion
Mapping of sinus rhythm
As a validation for our approach, we first computed activation
patterns in patients during normal sinus rhythm using baskets in
both the left and right atrium. This approach led to no adverse
events in our experience. Fig. 1A–B depicts electrode locations
registered within patient-specific atrial geometry, and shows that
the baskets cover the vast majority of both atria. Fig. 1D shows the
electrograms of one sinus rhythm beat in a patient, along with
ECG leads. From this, a spatial map of normal sinus rhythm
(isochrones) can be computed and shows activation from high right
atrium (sinus node) to low lateral left atrium (Fig. 1E), consistent
with known activation patterns.

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Localized sources are stable during AF
Computational mapping showed that rotational centers and
focal beat origins in fibrillation were unexpectedly stable,

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Mechanisms for Atrial Fibrillation

Figure 2. Stable Localized sources underlie human atrial fibrillation. A. Isochrones show an LA rotor in paroxysmal AF, with electrograms
during AF (ECG lead I and CS electrodes; scale bar 1 second). Activation times are color-coded (black indicates non-activated, diastole). B. Spatially
constrained migration locus of the rotational center, computed every 25–45 ms and joined using third-order Bézier curve fitting. C. Isochrones
90 minutes later, indicating temporal conservation of the rotor. D. Isochrones of a RA rotor in persistent AF. E. Migration locus. F. Isochrones 1 hour
later. G. LA repetitive focal beat in paroxysmal AF. H. Conservation of focal beat 1 hour later. In each case, ablation only at the source locus
terminated AF within ,5 minutes. Scale bar 1 cm.

elimination. We ablated the rotational center or origin of localized
sources during ongoing AF by directly applying radiofrequency
energy in 26 patients (of the population of n = 80), of whom 19 had
persistent AF. Of 16 of 26 patients who exhibited 1 or 2 coexisting
sources, ablation targeted to the limited migration loci of
rotational centers or focal origins, with no other ablation,
terminated AF in 3.963.8 minutes of total ablation to sinus
rhythm (n = 13, Fig. 3 and 4), or organized atrial flutter (n = 3).
Ablation was typically applied 60–120 minutes after the rotor or
focal source was first recorded, further illustrating the temporal
stability of human AF sources. Targeted ablation destroyed
approximately 2 cm2 of tissue to terminate AF, via 5–10 ablation
lesions of typical area 0.25 cm2, in contrast with conventional
ablation for persistent AF that may destroy .12–50 cm2 of tissue
via 50–200 lesions [34] (each 0.25 cm2) or .30% of the area of a
4.6 cm diameter atrium [4] yet terminates persistent AF in fewer
than 20% of cases [35]. Specialist centers often aim to achieve AF
termination yet, when successful, typically convert AF to atrial
tachycardia rather than sinus rhythm [34]. The mechanism by

migrating along circumscribed loci that partially overlapped
between cycles (Fig. 2BE, 3B and 4B and Table S2) with areas
2.561.2 cm2 and 2.161.8 cm2, respectively. Notably, source
locations were conserved between maps acquired 115657 minutes
apart throughout mapping (Fig. 2), showing that sources for
human cardiac fibrillation are conserved for at least several hours.
One patient presented the unusual opportunity to demonstrate
conservation of a left atrial rotor during AF between procedures
separated by 8 months (Figure S3). Conversely, rotors in animal
models of AF may last for short periods before extinguishing [26].
Focal beats in human AF were also stable for hours (Fig. 4 and
Table S2), while focal beats in animal models of AF were spatially
variable and destabilized AF rotors [33]. This illustrates potential
differences between AF in animals and the human condition.

Targeted ablation of localized sources can eliminate AF
The spatially constrained and temporally conserved nature of a
small number of rotors and focal beat sources in human AF
presented an opportunity to establish their causal role via targeted

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Mechanisms for Atrial Fibrillation

Figure 3. AF termination by ablation of Stable LA rotor. A. Left atrial rotor during paroxysmal AF visualized using isochrones. B. Migration
locus of the rotational center, color-coded over time. C. Ablation lesions at rotor in low left atrium, applied 1 hour after initial recording of the rotor,
shown on patient specific geometry. Red lesion is where AF terminated, and 3 other lesions (gray) were also applied. D. Electrode recordings during
AF with termination to sinus rhythm by ,1 minute ablation at the rotational center (ECG lead aVF, and electrodes at ablation catheter, coronary
sinus). E. Isochronal map of sinus rhythm. The patient remains free of AF on implanted cardiac monitor at 9 months. Scale Bar 1 cm.

which localized ablation terminates rotors is unclear but likely
involves the elimination or alteration of functional or anatomical
heterogeneities such as fiber anisotropy [7,22,29], fibrosis, scar or
other factors [36] central to maintaining AF, leading to its
termination. These results demonstrate that targeted ablation of all
identified AF sources may terminate fibrillation to normal sinus

rhythm in 1–2 orders of magnitude less time and tissue destruction
than conventional ablation.
Ablation of rotors or focal beats was successful independent of
the type or location of sources. For example, targeted ablation at
the rotational center of a left atrial rotor for less than 1 minute
converted AF to sinus rhythm (Fig. 3), while targeted ablation of a

Figure 4. AF Termination by ablation of a Stable RA Rotor. A. Isochrones show a RA rotor and concurrent LA focal beat during persistent AF.
B. Spatially constrained rotational center locus. C. Ablation lesions at lateral RA rotor on patient specific geometry (performed 2 hours after initial
recording of rotor). A total of 11 lesions were applied (shown), with AF termination to sinus rhythm at 5.5 minutes. The red lesion indicates where
ablation terminated AF. D. Electrograms AF terminating to sinus rhythm with localized ablation at rotor (total duration 5.5 minutes) (ECG lead I,
intracardiac electrodes in RA, LA and CS). E. Isochrones of sinus rhythm. After ablation, the patient remains AF-free at 12 months on implanted cardiac
monitor. Scale bar 1 cm.

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Mechanisms for Atrial Fibrillation

our mapping approach (without pulmonary vein isolation)
terminated AF predominantly to sinus rhythm in seconds to
Although electrode separation in our approach is not always
equal between splines, this will not alter sequential activation
across adjacent electrodes that defines rotational or focal
activation. Additional work is required to test whether mitigation
of these basket limitations will further improve spatial targeting of
rotors or focal sources. Of note, the size of a clinical ablation lesion
(5–7 mm) defines the practical resolution required for mapping.
Clinically, while conventional ablation can isolate initiating
mechanisms for AF in the pulmonary veins, other initiating
mechanisms must remain to explain its suboptimal success [4].
Freedom from AF following a single procedure to directly
eliminate AF sustaining sources in our study (81.6%) is substantially higher than after a single procedure to isolate pulmonary
veins and other triggers (<40–50%) in several studies [4,20].
Moreover, we confirmed success using implanted subcutaneous
ECG monitors, that was not used in prior AF ablation trials and is
the most rigorous monitoring currently available. Ectopic beats or
short-lived AF from initiators may theoretically occur if AFperpetuating regions alone are destroyed. However, in 2 patients
in our study with persistent AF despite prior conventional ablation,
targeted ablation at AF sources alone acutely terminated AF and
eliminated AF on implanted monitors with no additional ablation.
This suggests that the localized sources alone were primary
mechanisms sustaining AF in these patients. Further studies are
required to identify populations in whom targeted source ablation
alone, without conventional ablation, may eliminate AF.

right atrial rotor terminated AF to sinus rhythm within 5.5 minutes (Fig. 4). Figures 3, 4 and S4 also show clinical electroanatomic
shells of the precise ablation lesions applied to terminate AF. Acute
termination of AF after localized therapy in only the right atrium is
very unusual, and contrasts with conventional ablation which is
primarily performed in the left atrium [4]. Our study finds that AF
sources often lay in the right atrium (Table S2). The distribution of
sources, or the ability of targeted ablation at sources to terminate
AF, were unrelated to whether patients were studied for the first
time or had previously failed conventional AF ablation.
Ten of the 26 patients had 3 or more organized AF sources,
although our protocol permitted ablation at only 2 regions.
Localized ablation at 2 sites slowed AF (prolonged cycle length,
measured on the coronary sinus channel in routine fashion) by
15612% in these patients after 6.364.3 minutes of targeted
ablation. These results show that ablation of all identified localized
sources can terminate fibrillation, regardless of the location of the
source and whether it is a rotor or a focal beat.

Targeted ablation results in long-term freedom of AF in
After performing targeted ablation, we also performed standard-of-care ablation per our approved protocol (further detailed
in Materials and Methods). We then implanted continuous cardiac
ECG monitors in 22 of 26 patients to detect recurrent AF,
providing more rigorous follow-up than prior studies [4]. Of
n = 16 patients with 1–2 localized sources targeted for ablation,
93.8% were continuously free of AF during followup (3596220
days; range: 90 days, blanking, to 861 days) after this single
procedure, substantially higher than the single procedure success
of conventional ablation [4,20]. Of n = 10 patients with 3 or more
sources, 60% were continuously free of AF during followup
(3476272 days; range 90 days, blanking, to 717 days) after this
single procedure. Kaplan-Meier curves in figure S5 illustrate these
data. These results demonstrate that eliminating all identified
rotors or focal impulses sources can improve elimination of AF in
the long term.
Our study differs substantially from previous studies using
alternative mapping modalities. For example, numerous studies
have centered on triggering foci for AF near the pulmonary veins
using contact electrodes [37] in populations including those with
mitral valve disease [38]. Recent studies have applied the inverse
solution to multielectrode arrays within the heart (Ensite 3000, St
Jude Medical, Minnesota) [39,40] or electrodes at the patient’s
body surface (EcVueTM, Cardioinsight, Cleveland, Ohio) [41] to
produce maps showing mixed patterns of unstable reentry, focal
discharges and less defined waves [31]. Further studies are
required using interventions such as ablation to define which of
these patterns represent sustaining mechanisms. Contact mapping
studies by Allessie and co-workers used high spatial resolution
circular electrode plaques (1.8 cm radius) to show transient reentry
of meandering wavelets, but covered relatively small atrial regions
in patients undergoing surgical valve repair (,15% of the surface
area, assuming spherical atria of mean diameter 5.9 cm as
reported) [29,42]. These studies could thus plausibly miss stable
sources revealed by our wide field of view mapping, and thus
explain why wide-field-of-view mapping revealed localized sources
in nearly all patients. Haı̈ssaguerre et al. used careful mapping
with a roving catheter to find ‘organized sources’ for AF adjacent
to sites of prior unsuccessful ablation [43]. However, our
technique revealed sources in all patients (with or without prior
ablation), and sources in patients with prior ablation often lay
remote from previously ablated left atrial tissue (for instance, in
right atrium). Ablation at only rotors and focal sources revealed by
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Our results demonstrate that cardiac fibrillation in human atria,
despite its substantial spatiotemporal variability, may be directly
caused by very few stable electrical rotors or repetitive focal beats,
that are spatially constrained and temporally conserved. Accordingly, limited and rapid ablation was able to terminate fibrillation
for long-term elimination. These results were observed in patients
with a wide range of AF phenotypes. The demonstration of
localized perpetuating sources for human AF using this approach
may enable the development of a number of targeted interventions
in addition to ablation, including pacing, pharmacologic, gene or
regenerative therapies.

Materials and Methods
Ethics Statement
The study was approved by the joint Ethics committee of the
University of California and Veterans Affairs Medical Centers,
San Diego, and written informed consent was obtained from each
subject. The authors’ responsible joint institutional review board
approved the study.

Patient population
We studied 80 consecutive patients with drug-resistant AF
referred for ablation (Table S1), all of whom provided written
informed consent for the protocol. The study was approved by our
Institutional Review Board (IRB) in two phases (I) n = 54 recruited
for procedural collection of data on AF organization; (II) n = 26 in
whom intraprocedural mapping enabled targeted ablation at
identified AF sources. We enrolled consecutive patients, the only
exclusion being an inability or unwillingness to provide informed


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Mechanisms for Atrial Fibrillation

Ablation to Demonstrate the Mechanistic Role of AF
Rotors and Focal Beats

Electrophysiological Data Acquisition
Electrophysiology study was performed after discontinuing antiarrhythmic medications for .5 half-lives (.60 days after
amiodarone). Catheters were advanced to the heart from
peripheral veins. After trans-septal puncture, 64-pole basket
catheters (Constellation, Boston Scientific, MA) were advanced
to the left atrium (all patients) and the right atrium (n = 54 patients)
(Fig. 1A–C). Catheters were manipulated carefully to ensure good
electrode contact. Electrodes are separated by 4–6 mm along each
spline and by 4–10 mm between splines, and thus are able to
resolve the <40–50 mm minimum reentrant wavelength predicted from minimum human atrial repolarization time (100–110 ms)
and slowest dynamic conduction velocity (<40 cm/s) [30,44].
Because sources should control activation over a wider area than
just the rotor core or focal origin [45], our panoramic approach
covers the vast majority of both atria (Fig. 1). This is in contrast to
previous contact mapping studies which have a higher spatial
resolution but cover far smaller atrial regions [29,42]. In general,
point-by-point (sequential) mapping has focused on electrogram
characteristics such as fractionation [46], since spatial maps of AF
vary over the timeframe required to complete sequential maps. As
discussed above, non-contact mapping techniques have been
developed that use mathematical inverse solution approaches to
perform global atrial mapping (EcVueTM, Cardioinsight, Cleveland, Ohio [41] and Ensite 3000TM, St Jude Medical, Minnesota
Electrode locations were verified within atrial geometry by
fluoroscopy and clinical mapping (NavX, St Jude Medical, MN;
Fig. 1AB) and enabled creation of spatial maps of normal sinus
rhythm (Fig. 1DE) and AF. In phase I, a deflectable 7F
monophasic action potential (MAP) catheter (EP technologies,
Sunnyvale, CA) was advanced to record MAPs from the right
atrium and, via a second trans-septal puncture (performed for
clinical ablation), from multiple sites in the left atrium. MAP
recordings in AF were used to determine MAP restitution (rateresponse) [47] and validate unipolar recordings: activation time
intervals that were smaller than the minimum MAP-derived
recovery time were discarded.

In phase II, targeted ablation was performed directly at AF
rotor and focal beat locations to demonstrate their mechanistic
role in perpetuating AF in each patient. This is quite distinct to
prior mapping studies of AF that generally did not use such
interventions to establish whether mapped features were causal or
simply associative. Targeted ablation at rotors and focal beats was
performed prior to any other intervention. Ablation was
performed using an irrigated catheter (Biosense-Webster, Diamond-Bar, CA) at 25–35 W or, in patients with heart failure, a
non-irrigated catheter (Boston Scientific, Natick, MA) at 40–50 W,
target 52uC. In n = 2 patients with prior conventional ablation in
whom targeted ablation terminated AF to sinus rhythm, the
pulmonary veins were still isolated and no other ablation was
performed. In all other patients, targeted ablation was followed by
current standard-of-care ablation [4] utilizing wide area circumferential ablation to isolate left and right pulmonary vein pairs with
electrical verification of pulmonary vein isolation. Patients with
persistent AF also received a left atrial roof line and those with
typical atrial flutter received a cavotricuspid isthmus ablation. No
other ablation was performed.
To establish that identified AF sources caused the clinical AF
phenotype, and not just AF seen acutely in the laboratory, we
rigorously followed patients for recurrent AF after targeted
elimination of sources. Anti-arrhythmic medications were discontinued after a 3 month blanking period [4], then we used
continuous subcutaneous ECG monitoring (84.6% of patients) or
external monitors in the remaining 15.4%. No additional ablation
was permitted in the blanking period. Freedom from AF was
assessed quarterly in clinic for up to 2 years after ablation, and
defined as ,1% total AF burden. The use of implanted monitors is
considerably more rigorous than patient-activated event monitors,
ECGs or symptoms alone [4,50,51] used in almost all prior AF
studies [4].

Statistical Analysis
Continuous data are represented as mean 6 standard deviation
(SD). The t-test was used to compare variables between 2 groups.
Paired continuous variables were compared using linear regression
and the paired t-test. Contingency tables were analyzed using the
Fisher exact or the Chi-tests when appropriate. A p-value of ,0.05
was considered statistically significant. Statistics were calculated
using SPSS 19 (IBM, Somers, NY, USA).

Signal Processing
Intracardiac signals were filtered at 0.05–500 Hz, and the ECG
at 0.05–100 Hz. Signals were digitized at 1 kHz to 16-bit
resolution (Bard Pro, Billerica, MA) for analysis.
We computed spatial activity in AF using 2 approaches. First,
we determined AF activation from potentials (electrograms) at
each electrode to construct isochronal maps. Second, we
performed phase analysis to fibrillation, as first described by Gray
et al. [23], by applying the Hilbert transform directly to human
unipolar electrograms (Figure S1). Phase analysis can be used to
determine spiral wave dynamics in complex computational models
[48] and has also been applied to human ventricles [49]. Both
approaches led to similar qualitative results. Tip trajectories for
each localized source were computed directly from isochronal
maps by manual processing, or from phase maps [23]. For the
latter, the phase singularity, defined as the point around which the
integral of the gradient of the phase did not equate to zero, was
assigned periodically throughout multiple cycles. Isolated extreme
outlying points representing interpolation errors were excluded.
The spatial constraint of rotors (Fig. 2–4) was maintained when
data were plotted in raw form or interpolated by third-order
Bézier curves, as shown, computed such that first and second
derivatives were continuous at the location of the migration locus.
In patients undergoing targeted ablation at sources in phase II, the
areas of source migration were calculated.
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Supporting Information
Table S1 Patient Characteristics.

Table S2 Characteristics of Human AF Sources.

Figure S1 Phase map of Human Left Atrial Activation
During AF. The phase map was computed using the Hilbert
Transform [52] and shows a phase singularity (indicated by the
white dot), corresponding to the location of a rotor (same patient
as figure 3 of the main manuscript).
Figure S2 Directionality Analysis of a Rotor During
Human Atrial Fibrillation. A. shows propagation emanating from the left atrial rotor to the remaining atrium,
in the same patient shown in figure 3 of the main manuscript. The
arrows indicate activation direction [53] between isochrones (color
bar). B. Recurrence of predominant direction, shown as the

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Mechanisms for Atrial Fibrillation

correlation at each site of the direction over consecutive cycles,
showing high recurrence (repeatability) in the annulus adjacent to
the rotational center (warm colors) with markedly reduced
correlation in a surrounding annulus of tissue (cool colors) with
some recovery of repeatability at distant sites.

clockwise left atrial rotor on the posterior left atrium near (but not
within) the left pulmonary vein antra, where localized ablation (red
dots in right panel) terminated AF to sinus rhythm within
3 minutes. Both patients are free of AF on implanted monitors.
Figure S5 Kaplan-Meier curves for freedom from AF,
detected using rigorous monitoring including implanted continuous ECG recordings.

Figure S3 Temporal Conservation of a Left atrial rotor

in human AF for 237 days. A. Isochronal map of a left atrial
rotor obtained prior to conventional ablation that passed outside
this source, and did not target it. Atrial fibrillation failed to
terminate during ablation, and recurred after the procedure. B.
Isochronal map of a left atrial rotor at the same location obtained
at repeat electrophysiology study 237 days later. Targeted ablation
at this source eliminated AF.

We are indebted to Kathleen Mills, BA for coordinating this study, and to
Antonio Moyeda, RCVT, Kenneth Hopper, RCVT, Judith Hildreth, RN,
Sherie Jaynes, RN, Stephanie Yoakum, RNP, Elizabeth Greer, RN and
Donna Cooper, RN for assisting with clinical data collection and followup.

Additional Examples of Brief Targeted Ablation at Stable Sources for Human Atrial Fibrillation. A.
Isochronal map of a left atrial focal beat source that lay outside
traditional ablation lesion locations. Localized ablation at this site
(red dot, and contiguous white dots) terminated AF directly to
sinus rhythm in ,5 minutes. B. Isochronal map of a counter-

Figure S4

Author Contributions
Conceived and designed the experiments: SMN WJR. Performed the
experiments: SMN DEK. Analyzed the data: SMN DEK MWE WJR.
Contributed reagents/materials/analysis tools: SMN WJR. Wrote the
paper: SMN WJR.

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