BioMed Signal Processing and Control

8/14/2019 BioMed Signal Processing and Control

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Review

A review on sample entropy applications for the non-invasive analysis of atrialfibrillation electrocardiograms

R. Alcaraz a,*, J.J. Rieta b

a Innovation in Bioengineering Research Group, University of Castilla-La Mancha, Campus Universitario, 16071 Cuenca, Spainb Biomedical Synergy, Electronic Engineering Department, Universidad Polite cnica de Valencia, Campus de Gandia, 46730 Gandia, Spain

Contents

1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2. Short description of atrial fibrillation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

3. Surface ECG recordings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

4. The concept of sample entropy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

5. Atrial activity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

5.1. Paroxysmal AF termination prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

5.2. Paroxysmal AF organization time course. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

5.3. Electrical cardioversion outcome prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

6. Ventricular activity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

6.1. Paroxysmal AF onset prediction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

7. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Biomedical Signal Processing and Control 5 (2010) 114

A R T I C L E I N F O

Article history:

Received 19 May 2009Received in revised form 24 September 2009

Accepted 18 November 2009

Available online 29 December 2009

Keywords:

Atrial fibrillation

Electrocardiogram

Electrical cardioversion

Heart rate variability

Main atrial wave

Non-linear regularity metrics

Sample entropy

A B S T R A C T

The application of non-linear metrics to physiological signals is a valuable tool because hidden

information related to underlying mechanisms can be obtained. In this respect, approximate entropy

(ApEn)is the most popularnon-linear regularityindex thathas beenapplied to physiological time series.

However, ApEn presents some shortcomings, such as bias, relative inconsistency and dependence on the

sample length. A modification of ApEn, named sample entropy (SampEn), was introduced to overcome

these deficiencies. Recently, in the context of electrocardiography, SampEn has been applied to study

non-invasively atrial fibrillation (AF), which is the most common arrhythmia encountered in clinical

practice with unknown mechanisms provoking its onset and termination. Useful clinical information,

that could help for a better understanding of AF mechanisms, has been obtained through the application

of SampEn to electrocardiographic (ECG) recordings. This work reviews its application in the context of

non-invasive analysis of AF. During this arrhythmia, atrial and ventricular components can be regarded

as unsynchronizedactivities, whereby, the application of SampEn to the analysis of eachcomponentwill

be described separately.In first place, clinical challenges in which SampEn has beensuccessfully applied

to estimate AF organization from the atrial activity pattern are presented. The AF organization study can

provide information on the number of active reentries, which can help to improve AF treatment and to

take the appropriate decisions on its management. Next, the heart rate variability study via SampEn, to

characterize ventricular response and predict AF onset, is described. Through the aforementionedapplications it is remarked throughout this review that SampEn can be considered as a very promising

and useful tool towards the non-invasive understanding of AF.

2009 Elsevier Ltd. All rights reserved.

* Corresponding author. Postal Address: E.U. Politecnica de Cuenca, Campus Universitario, 16071 Cuenca, Spain. Tel.: +34 969 179 100x4847; fax: +34 969 179 119.

E-mail address: [email protected] (R. Alcaraz).

Contents lists available at ScienceDirect

Biomedical Signal Processing and Control

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1746-8094/$ see front matter 2009 Elsevier Ltd. All rights reserved.

doi:10.1016/j.bspc.2009.11.001
mailto:[email protected]://www.sciencedirect.com/science/journal/17468094http://dx.doi.org/10.1016/j.bspc.2009.11.001http://dx.doi.org/10.1016/j.bspc.2009.11.001http://www.sciencedirect.com/science/journal/17468094mailto:[email protected]


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1. Introduction

Non-linear analysis metrics are valuable in the assessment of

physiological time series, because hidden information related to

underlying mechanisms can be sometimes obtained [1,2]. To this

day, a high amount of non-linear complexity measures exists, such

as dimensions, Lyapunov exponents and entropies. However, their

computation is frequently compared with the problem of

insufficient number of data points [3]. Additionally, most

dimension and entropy definitions present application limitations

associated to real world time series, since all recorded data are of

limited duration and, to a certain degree, contaminated by noise. In

this respect, a 2% noise is serious enough to prevent accurate

estimation [4]. To solve the problems of short and noisy recordings

in physiological signals, Pincus [5] presented approximate entropy

(ApEn) as a measure of complexity that is applicable to noisy and

medium-sized datasets. ApEn determines the conditional proba-

bility of similarity between a chosen data segment andthe next set

of segments of the same duration. The higher the probability, the

smaller the ApEn value,indicating less irregularity of thedata. This

index has been successfully applied to analyze physiological

signals in diverse applications. For instance, ApEn has been used to

study intracranial hypertension episodes in pediatric patients with

traumatic brain injury [6,7], to analyze temperature registers withthe objective of predicting survival of critical patients [8,9], to

analyze time series generated by schizophrenic patients [6], to

study heart rate variability in disease and aging [10], etc.

Despiteits popularity, ApEn has some knownshortcomings, such

as bias, relative inconsistency, anddependence on thesamplelength

[2]. These shortcomings have led to the development of a related

non-linear measure, sample entropy (SampEn) [2]. Theoretically,

SampEnreduces thebias of ApEn by avoiding counting self-matches,

it is independent of the time series length, and it is more consistent

than ApEn. Additionally, SampEn is easier to compute than ApEn.

Thereby, this index has been also applied to analyze physiolog-

ical signals in several recent studies. Some examples are the study

of heart rate dynamics during episodes of mechanical ventilation

and acute anoxia in rats [11], the analysis of heart rate variabilityindisease and aging [10], the electroencephalographic background

activity characterization in Alzheimers disease patients [12], the

decision assessment of weaning from mechanical ventilation [13],

the neonatal sepsis diagnosis improvement by evaluating reduced

baseline variability and transient decelerations of heart rate [14],

the exercise work load influence analysis on RR and QT time-series

regularity [15], etc.

Moreover, a very recent application of SampEn has been the

non-invasive study of atrial fibrillation (AF). This disease is a

significant public health problem worldwide, affecting up to 1% of

the general populationand nearly 1 in 10 peopleover80 years [16].

Despite its high prevalence, the physiological mechanisms

provoking AF onset and termination are still unexplained and

the current AF treatments are not completely satisfactory [17]. A s aconsequence, the study of AF has been considered as a challenge

for researchers and a requirement for clinicians.

Within this context, useful clinical information that could

improve the understanding of AF mechanisms and the existing

treatments through the use of SampEn has been reported during

the last years. The purpose of this article is to review the use of

SampEn in the non-invasive analysis of AF. The manuscript

describes initially the concept of AF and how the surface

electrocardiographic (ECG) recordings were acquired. Next, a

formal description of SampEn together with the most widely used

parameters for its computation are introduced. Considering that

the atrial activity (AA) can be viewed as uncoupled to the

ventricular activity (VA) during AF [18], the applicationsof SampEn

to AA and VA are described separately. Firstly, clinical challenges in

which SampEn has been successfully applied to estimate AF

organization from the AA patterns are presented. The AF

organization study is a key aspect in the knowledge of the

arrhythmia, because it provides information on the number of

active reentries, which maintain and can perpetuate AF [1922].

Secondly, different applications of SampEn to VA analysis are

described. In this case, a non-invasive measure, such as the

heart rate variability (HRV), has been used for the VA study.

The HRVanalysis is a valuable tool,because it allows to observe the

hearts regulation by the autonomic nervous system, which is

believed to play an important role in the initiation of AF [23,24].

Finally, the concluding remarks will lead the paper to its end.

2. Short description of atrial fibrillation

Atrial fibrillation is the most commonly supra-ventricular

tachy-arrhythmia encountered in the daily clinical practice [17],

affecting roughly 2.2 million people in the US and 2 millions in

Europe, with a prevalence that doubles with each advancing

decade above 50 years and reaches almost 10% in octogenarians

[25]. This arrhythmia may appear on three different forms, namely

paroxysmal AF, i.e., self-terminating within 7 days, persistent AF, in

which intervention is required for its termination, and permanent

AF, in which sinus rhythm cannot be restored or maintained [17].Data from the Framingham heart study show that a patient with

AF has twice the risk of death than a healthy person [26,27], which

may be due to the fact that AF is one of the main causes of embolic

events, developing complications associated with cerebrovascular

accidents in 75% of the cases [28]. In addition, AF may cause

systemic thromboembolic complications, decrease exercise capac-

ity, impair ventricular function, reduce quality of life and incur

significant health care costs [27,29,30]. As a consequence, AF itself

does not represent a life-threatening condition, but it considerably

reduces the patients quality of life.

One normal cardiac cycle is started at the sinus node with the

depolarization of the right atrium, and spreads towards the entire

atria in a well-ordered manner. Atrial depolarization defines the P

wave in the ECG, see Fig. 1(a). Next, the depolarization impulsereaches the ventricles and their fast contraction produces the QRS

complex in the ECG. Finally, ventricular repolarization produces

the T wave and concludes the cardiac cycle. The manifestation of

AF is characterized by uncoordinated atrial activation with

consequent deterioration of atrial mechanical function. AF occurs

when the electrical activity in the atria degenerates from its usual

organized pattern into a rapid chaotic pattern. This disruption

results in an irregular and often rapid heartbeat that is classically

described as irregularly irregular and is due to the unpredictable

conduction of these disordered impulses across the atrioventricu-

lar node [17], see Fig. 1(b).

However, the physiological mechanisms provoking the onset

and termination of AF episodes arestill unexplained [17]. The most

widely accepted theory to explain AF mechanisms is based on thecontinuous propagation of multiple wavelets wandering through-

out the atria [17]. The fractionation of the wavefronts as they

propagate results in self-perpetuating independent wavelets,

called reentries. The number of simultaneous reentries depends

on the refractory period, mass and conduction velocity along the

atria, and these parameters present severe inhomogeneities in AF

[17]. It hasbeen also demonstratedthat thenumber of propagating

reentries into the atrial tissue is related to AF organization [1922],

therefore, a reliable organization estimation can provide very

useful information on the arrhythmia. In this respect, when AF

occurs, a notably disorganized atrial activity (AA) has been

observed on internal recordings [20,21,3133].

Through the aforementioned invasive recordings, such as

epicardial mapping and atrial electrograms, a characterization of

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the atrial electrical activity with high degree of detail have beenreached. Specially, the situations where the arrhythmia behaves

with remarkable variations, like spontaneous AF onset and AF

termination (spontaneous or induced by cardioversion), have been

studied. In this respect, a progressive increase in the number of

reentries during the first minutes after paroxysmal AF onset has

been suggested in a recent work [34]. Additionally, it has been

reported that the likelihood of spontaneous AF termination is

inversely related to the number of wavefronts propagating

throughout the atrial tissue [20]. In fact, several studies have

demonstrated a decrease in the number of reentries prior to

spontaneous AF termination, thus producing simpler wavefronts

[31,32,35]. Regarding the forced termination of AF through

electrical cardioversion (ECV), it has been shown that the higher

the number of propagating wavelets, the larger the atrial volumethat could support reentry propagation after the shock. As a

consequence, a negative ECV outcome could be more likelihood for

those patients [36].

An additional challenge in the understandingof AF should be to

obtain non-invasively the aforesaid information, such as some

authors have attempted [22]. Obviously, surface ECG recordings

can be obtained easily and cheaply, which is essential from a

clinical point of view. In addition, the risks for the patient

associated to invasive procedures could be avoided thanks to the

ECG [37]. Therefore, although the authors are conscious about the

remarkable existing applications of SampEn to biomedical signals,

this review is focused on a recent and challenging side of SampEn,

such as its application to study AF from the surface ECG.

3. Surface ECG recordings

The surface ECG recording provides a widely used and non-

invasive way to study AF. Some advantages of using the ECG include

the ability to record data for a long period of time and the minimal

costs and risks involved for the patient, in comparisonwith invasive

procedures [37]. However, because of ECG represents the hearts

electrical activity recorded on the thoraxs surface, the signal is

corrupted by different types of noise, which are picked up by the

volumeconductorconstitutingthe humanbody. Thereby, inorder to

improve later analysis, these recordings need to be preprocessed.

Filtering operations have been classically applied to the ECG for the

reduction of noise sources like, i.e., baseline wandering, high

frequency noise and powerline interference [38]. Concretely, in the

studies that will be next described, baseline wander was removed

making use of bidirectional zero-phase high-pass filtering with

0.5 Hz cut-off frequency [39], high frequency noise was reduced

withan eight-orderbidirectionalzero-phaseIIR Chebyshev low pass

filtering, whose cut-off frequency was 70 Hz [40], and powerline

interference was removed through adaptive notch filtering, which

preserves the ECG spectral information [41].

As described before, the ECG in AF is characterized by the

replacement of consistent P waves by rapid oscillations or

fibrillatory waves ( f waves) that vary in size, shape, and timing

[37], associated with an irregular ventricular response [17], see

Fig. 1. The f waves analysis from surface ECG recordings is

complicated by the simultaneous presence of ventricular activity,

which is of much higher amplitude. Thereby, the dissociation of

atrial and ventricular components is mandatory [42]. Nowadays,

several methods to extract the AA signal from surface ECG

recordings exist. The most powerful techniques are those that

exploit the spatial diversity of the multilead ECG [43], such as the

method that solves the blind source separation problem [18] or the

spatiotemporal QRST cancellation strategy [44]. However, the

performance of these techniques is seriously reduced when

recordings are obtained from Holter systems for paroxysmal AF

analysis. The reason is that, generally, Holter systems use no more

than two or three leads, which are not enough to exploit the ECGspatial information. For single-lead applications the most widely

used alternative to extract the AA is the averaged beat subtraction

(ABS). This method relies on the assumption that the average beat

can represent, approximately, each individual beat [42]. In the

studies that will be next described, ABS or some variant [45] have

been used to extract the AA from lead V1. This lead was chosen for

analysis because it contains the highest AA amplitude [37].

Additionally, in those cases where the sampling frequency was

originally low, the lead had to be upsampled to 1024 Hz to allow

better alignment for QRST complex averaging and subtraction, as

suggested in previous works [46].

4. The concept of sample entropy

Sample entropy examines a time series for similar epochs and

assigns a non-negative number to the sequence, with larger values

corresponding to more irregularity in the data [2]. Two input

parameters, a run length m and a tolerance window r, must

be specified for SampEn to be computed. SampEnm; r; N, being N

the length of the time series, is the negative logarithm of

the conditional probability that two sequences similar for m

points remainsimilar at the next point, whereself-matches are not

included in calculating the probability. Thus, a lower value of

SampEn also indicates more self-similarity in the time series [2].

Formally, given N data points from a time series

fxng x1;x2; . . . ;xN, SampEn can be defined as follows [2]:

(1) Form vector sequences of size m, Xm1;. . .

;XmN m 1,defined by Xmi fxi;xi 1; . . . ;xi m 1g, for 1 i

N m 1. These vectors represent m consecutive x values,

starting with the i th point.

(2) Define the distance between vectors Xmi and Xmj,

dXmi; Xmj, as the absolute maximum difference between

their scalar components:

dXmi; Xmj max k0;...;m1 jxi k xj kj : (1)

(3) For a given Xmi, count the number of j (1 j N m; j 6 i),

denoted as Bi, such that the distance between Xmi and Xmj is

less than or equal to r. Then, for 1 i N m:

Bmi r 1

N m 1

Bi: (2)

Fig. 1. Example of surface ECG recordings corresponding to (a) a patient in normal

sinus rhythm and (b) a patient affected by atrial fibrillation.

R. Alcaraz, J.J. Rieta / Biomedical Signal Processing and Control 5 (2010) 114 3


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(4) Define Bmr as

Bmr 1

N m

XNmi1

Bmi r: (3)

(5) Increase the dimension to m 1 and calculateAi as thenumber

ofXm1i within r ofXm1j, where j ranges from 1 to N m

(j 6 i). Then, Ami r is defined as

Ami r 1

N m 1Ai: (4)

(6) Set Amr as

Amr 1

N m

XNmi1

Ami r: (5)

Thus, Bmr is the probability that two sequences will match for

m points, whereas Amr is the probability that two sequences will

match for m 1 points. Finally, SampEn can be defined as

SampEnm; r limN! 1

lnAmr

Bmr

; (6)

which is estimated by the statistic

SampEnm; r; N lnAmr

Bmr

: (7)

Although m and r are critical in determining the outcome of

SampEn, no guidelines exist for optimizing their values. In

principle, the accuracy and confidence of the entropy estimate

improve as the number of lengthm matches increases. The number

of matches can be increased by choosingsmall m (short templates)

and large r (wide tolerance). However, penalties appear when too

relaxed criteria are used [5]. For smaller rvalues, poor conditional

probability estimates are achieved, while for larger r values, too

much detailed system information is lost and SampEn tends to 0

for all processes. To avoid a significant noise contribution on

SampEn calculation, one must choose r larger than most of thenoise [5].

The most widely established values for m and r are m 1 or

m 2 and r between 0.1 and 0.25 times the standard deviation of

the original time series fxng, such as Pincus suggested [47].

Normalizing r in this manner gives to SampEn a translation and

scale invariance, in the sense that it remains unchanged under

uniform process magnification, reduction, or constant shift to

higher or lower values [47]. These parameters produce a good

statistical reproducibility in time series of length larger than 60

samples, as considered herein [5,48,49]. In the majority of studies

where SampEn was applied to analyze physiologic signals, the

parameters m and r were studied in the range defined by Pincus

[14,50,51]. In addition, in studies where these parameters were

analyzedin a wider range, the best results were obtained forvalueswithin the Pincus range [13,15] or very close to it [3,23,52,53].

Thus, for the application of SampEn to AF organization estimation

fromrepetitive AA patterns, several combinations ofm and rvalues

within the range defined by Pincus were tested, but the optimal

results were achieved with m 2 and r 0:25 [51,54]. On the

other hand, for the study of HRV complexity via SampEn, the most

widely used parameters have been r 0:2 and m 2 [15,55,56] or

m 3 [14,23,52].

5. Atrial activity analysis

As the first part of the review, in this section several

applications of SampEn to the non-invasive study of AF are

introduced. To start, the varying number of reentries circulating

within the atria affects f waves regularity, since it is directly

related to the periodicity and repetitive morphology of the AA

pattern, such as invasive recordings have reported [1921]. Hence,

given that the AA organization provides information on the

number of active reentries, its non-invasive successful estimation

could improve AF treatment, which still is unsatisfactory, and

contribute to take the appropriate decisions on its management

[22]. In this respect, very recent studies have applied SampEn to

evaluate f waves regularity as a successful non-invasive AF

organization estimator [51,54,57]. The use of this non-linear index

is justified because non-linearity, as necessary condition for a

chaotic behavior,is present in thediseasedheartwithAF at cellular

level, and atrial electrical remodeling in AF is a far-from-linear

process [58,59]. Electrical remodeling can be described as the

progressive shortening of effective atrial refractory periods, thus

increasing the number of simultaneous reentries and, as a

consequence, the possibility of AF perpetuation [17]. In the next

subsections, the state of the art related to the non-invasive AF

organization estimation based on SampEn is summarized. These

applications demonstrate how non-linear biomedical signal

processing could contribute in the improvement of AF treatments.

5.1. Paroxysmal AF termination prediction

About 18% of paroxysmal AF degenerates into persistent AF in

less than 4 years [60]. The associated risks of persistentAF arequite

serious because it predisposes to thrombus formation within the

atria that can cause stroke or any other thromboembolic events

[28]. Therefore, the early prediction of paroxysmal AF maintenance

is crucial, because appropriate interventions may terminate the

arrhythmia and prevent AF chronification. In contrast, the

prediction of spontaneous AF termination could avoid unnecessary

therapy, reduce the associated clinical costs, and improve the

patients quality of life.

In previous invasive studies where AF termination was

achieved by using different therapies, a decrease in the number

of reentries prior to AF termination was observed [21,31,32,35].

This decrease in the number of reentries produces simplerwavefronts into the atrial tissue and irregular f waves evolve to

regular P waves [37]. Therefore, the AA slightly evolves to a more

organized pattern before AF termination. This feature has been

used to predict paroxysmal AF termination.

In thissense, someauthors applied non-linearregularity indexes

to characterize AA organization from the surface ECG, but their

results did not reveal significative differences between terminating

and non-terminating paroxysmal AF episodes. The low signal to

noiseratio ofthe AAwas believed tobe the main reason tothisresult

[61,62]. In orderto reduce the nuisance signals and enhance the AA,

the application of two wavelet decomposition analyses to this atrial

signal has been proposed [54], such as Fig. 2 shows. In the first

analysis (block 1), the wavelet coefficient vector related to the scale

containing the dominant atrial frequency (DAF), i.e., the frequencywith the highest amplitude within the typical 39 Hz AF frequency

range [63,64], was reconstructed back to the time-domain. As a

result, nuisance signals were removed and the fundamental

waveform associated to the AA, called main atrial wave (MAW),

was obtained. In the second case (block 2), the same wavelet

coefficient vector was linearly interpolated to obtain a vector with a

number of samples equal to the original AA signal. Finally, the

organization of the two provided time series was estimated via

SampEn to obtain two different and independent classifications of

paroxysmal AF into terminating and non-terminating episodes.

In order to validate this methodology, the database generated

forthe Computers in Cardiology Challenge 2004, whichis available

on Physionet [65], was used. This data set is composed by a

learning set consisting of 20 paroxysmal AF recordings withknown



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termination properties and a test set of 30 recordings. The non-terminating paroxysmal AF episodes were observed to continue in

AF for, at least, 1 h following the end of the excerpt (group N). In

contrast, spontaneously terminating AF episodes terminated

immediately after the end of the extracted segment (group T).

The independent application of each analysis block to the

learning set allowed to obtain a predictive accuracy of 90% (18 out

of 20) with 80% sensitivity (i.e., proportion of non-terminating

episodes correctly classified) and 100% specificity (i.e., percentage

of terminating episodes correctly discerned) for the first block and

85%(17 out of 20), with 100% sensitivity and70% specificity, forthe

second block, see Fig 3. The observation on these results in which

non-terminating AF recordings that presented a high DAF, and

terminating episodes having a low DAF, were incorrectly classified,

suggested the combination of both blocks to obtain an improvedclassification strategy. Thus, when both blocks classified different-

ly an AF episode and the DAF was lower than 5.5 Hz, the

classification provided by block 1 was considered. On the contrary,

if the DAF was higher than the mentioned threshold, the

classification provided by block 2 was chosen. With this combined

methodology, 100% (20 out of 20) and 93.33% (28 out of 30) of the

learning and test recordings were correctly discriminated,

respectively, with 93.75% sensitivity and 92.86% specificity for

the test set.

Additionally, the results provided by block 1 showed that

terminating episodes presented lower SampEn values and,

consequently, higher AA organization, than non-terminating

episodes, see Fig. 3(a). This observation was in agreement with

the AA organization increase prior to AF termination reportedthrough invasive recordings [21,31,32,35] which, at this moment,

is clinically accepted [66]. As a consequence, it can be considered

thatthe invasively observed increase in AF organizationis reflected

on the surface ECG when proper analysis tools are used.

Regarding a specific scale of block 2, the wavelet coefficient

vector contained the similarity evolution along time between the

analyzed signal and the scaled mother wavelet. A high regularity

value in this time series indicated a constant waveform across the

time period under analysis. On the contrary, low regularity implied

variable waveforms that, for instance, may evolve to a more

organized pattern. This fact was considered to justify the results

obtained in block 2, where terminating paroxysmal AF episodes

presented higher vector irregularity, see Fig. 3(b). Hence, the AA

evolution from disorganized f waves to organized P waves, that

Fig. 2. Block diagram describing the proposed methodology to predict AF termination [54]. Firstly, the ventricular activity is removed from the input ECG to obtain the AA.

Next, a seven levels wavelet decomposition was applied using bior4.4 as wavelet family. The scale or frequency sub-band containing the DAF was selected and two

organization analyses were carried out. In block 1, the organization of this scale, reconstructed back to time-domain, was obtained using SampEn to discern between

terminating and non-terminating AF episodes. In block 2, the wavelet coefficient vector organization of the selected scale was estimated to perform a more robust

discrimination process.

Fig. 3. Learning signal classification into terminating and non-terminating AF

episodes obtained with (a) block 1 and (b) block 2 of the methodology presented in

Fig. 2[54]. SampEn values obtained for the 20 learning episodes together with the

mean and standard deviation for each group are displayed. Optimal thresholds are

represented with a dashed line.



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takes place in AF recordings prior to itstermination [37], maycause

the described behavior in the wavelet coefficient vector.

Finally, notice that several previous works have tried to predict

the spontaneous AF termination from surface ECG recordings

[6770]. To this respect, Table 1 presents some of the most recently

proposed methods. Most of them analyzed the DAF decrease,

which was previously reported through invasive studies during

catheter ablation [71]. However, in order to improve AF termina-

tion prediction, other parameters were analyzed and combined

with the DAF. In this respect, Petrutiu et al. [72] studied the AA

peak power evolution within the two last seconds of the

recordings. This so short studied time interval couldlimit seriouslytheir methods reliability, especially when other works did not find

significative differences between the peak power of terminating

and non-terminating AF episodes [67]. In Hayn et al. [73], an

evolution of the averaged RR time interval was studied to correlate

ventricular with atrial activities (represented by the DAF). In this

method, two coefficients were empirically fitted to the analyzed

signal set, but results were very variable, such as the poor

outcomes obtained analyzing other databases have corroborated

[68]. In addition, the relation between atrial and ventricular

activities was also studied in other works, but lower predictive

capacity than in the previous method was obtained [67]. In other

studies, different timefrequency transforms were used to

evaluate the AA timefrequency evolution [61,70,74]. However,

the reported results did not reveal notable improvements in theprediction of AF termination. Parameters relative to the AA energy

distribution, such as AA amplitude [70] or exponential decay [75] ,

were also studied, but low significant differences between

terminating and non-terminating AF episodes were obtained

[76]. Therefore, the combined methodology described in this

review could be considered as the most robust and reliable

discrimination procedure, because it is completely based on AF

physiological observations, which have been reported through

invasive studies [20,21,3133]. In addition, a predictive capacity

higher than the majority of the indicated studies was obtained.

5.2. Paroxysmal AF organization time course

As previously described, the treatment of AF patients is still

unsatisfactory, due to the progressing nature of this arrhythmiaand its physiological mechanisms, making the onset and termina-

tion of AF episodes still unexplained [17]. Thus, the progressing

evolution analysis of paroxysmal AF could help for a better

understanding of its mechanisms. In this sense, as previously

mentioned, recent invasive studies have evaluated AF organization

time course during different episode parts. Concretely, the

organization in the first minutes after AF onset has been evaluated

by means of a cycle length beat-to-beat analysis and wave

similarity [34]. On the other hand, organization before AF

termination has been successfully evaluated by using different

techniques [21,31,32,35].

From a non-invasive point of view, a very recent study has

applied SampEn to the onset and offset of paroxysmal AF episodes

to evaluate their organization time course [57]. In this work, forreducing noise, nuisance signals and enhancing the AA, the MAW

was obtained through selective filtering of the AA by tracking its

DAF, such as Fig.4 shows. The MAW organization was estimated by

Table 1

Comparison between some of the most recent studies presented to predict paroxysmal AF termination.

Study Database Database description a Short descript ion of m et hods Best results b

Alcaraz and Rieta [54] Cinc/Challenge 2004 [65] Learning set: 10 T and 10 N

Test set: 14 T and 16 N

Regularity analysis via SampEn of

time and wavelet domains of the AA

100% learning, 93.33% test

Alcaraz et al. [70] Own Database with 5 0 episodes 2 1 N and 2 9 T Analy sis of t ime and f requency

parameters obtained from the AA

92%

Chiarugi et al. [67] Cinc/Challenge 2004 [65] Learning set: 10 T and 10 N


Discriminant model based on time and

frequency parameters obtained from

the atrial and ventricular activities

100% learning, 90% test

Hayn et al. [68] Cinc/Challenge 2004 together

with MIT-BIT Atrial Fibrillation

database [65]

Not speci fied Expe rimental combination o f the

DAF with the mean RR interval

< 60%

Nilsson et al. [61] Cinc/Challenge 2004 [65] Learning set: 10 T and 10 N


Analysis of time and frequency

parameters and non-linear indices

obtained from the AA


Petrutiu et al. [72] Cinc/Challenge 2004 [65] Learning set: 10 T and 10 N


Experimental combination of AA peak

power evolution within the two last

seconds of the episode with the DAF


Mainardi et al. [62] Cinc/Challenge 2004 [65] Learning set: 10 T and 10 N


Neural network with time, frequency

and non-linear parameters obtained

from the AA and RR series


Hayn et al. [73] Cinc/Challenge 2004 [65] Learning set: 10 T and 10 N


Same methodology than in

Hayn et al 2007 [68]


Mora et al. [74] Cinc/Challenge 2004 [65] Learning set: 10 T and 10 N


Evaluation of time and frequency

parameters obtained from the AA


a

T = terminating paroxysmal AF episodes; N = non-terminating episodes.b Percentage of episodes correctly classified.

Fig. 4. Blockdiagram describingthe strategy proposed for AF organizationvariationassessment [57]. Thin selectivefilteris appliedto theatrial signal. Thefilteris trackingthe

dominant atrial frequency. Finally, SampEn is computed on the resulting signal.



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applying SampEn in non-overlapping segments of 2 s. Overlappingbetween segments was discarded in order to not benefit the

organization assessment, to obtain more consistent results and to

increase the proposed strategy reliability.

With the described method, 25 ECG recordings continuously

registered during the first 5 min following paroxysmal AF onset

and available on Physionet [65] were studied. A progressive

organization deterioration in the first 3 min after the onset takes

place, as it can be observed in Fig. 5(a). This finding was in

agreement with the conclusions reported from invasive recordings

by several authors [34,77,78] and suggested that higher rates of

success to revert the arrhythmia could be obtained through the

early delivery of pacing, that is, when the episodes are more

organized.

On the other hand, 20 ECGs, also available on Physionet [65],containing the last 2 min before spontaneous AF termination were

also analyzed. In this case, the MAW organization analysis showed

a progressive organization increase during the last minute, see Fig

5(b). This organization variation was in agreement with the results

presented for AF termination prediction in the previous subsection

and those obtained by other authors, such as Takahashi et al [31]

and Hoekstra et al [33], from invasive recordings.

5.3. Electrical cardioversion outcome prediction

When a patient is in persistent AF, it is a common practice to

restore and maintain normal rhythm. In this respect, sinus rhythm

restoration is required to reduce the risk of stroke and improve

cardiac output [17]. This approach is based, in part, on dataindicating that AF is a predictor of death in patients with heart

failure and suggesting that the suppression of AF may favorably

affect the outcome.

Generally, electrical cardioversion (ECV) is the most effective

alternative to revertAF back to sinus rhythm[79]. However, because

of the high risk of AF recurrence, especially during the first 2 weeks

following the procedure [80], and because of potential collateral

effects of ECV [79], it is clinically important to predict normal sinus

rhythm (NSR) maintenance after ECV before it is attempted. With

this objective, in a recent work [51], the AA organization was non-

invasively estimated relying on the hypothesis that NSR mainte-

nance would be more likelihood in patients who present a more

organized AA. This assumption was based on the observation that

themore disorganized theAA, thehigher thenumber of propagating

wavelets [20], and the larger the atrial volume that could supportpropagation of reentries after the shock [36].

As for paroxysmal AF termination prediction, in this work, a

wavelet bidomain sample entropy methodology was used to

reduce nuisance signals and enhance the AA [51]. In this case,

however, when the classification result provided by blocks E1 and

E2 in Fig. 2 was different, two indices indicating the closeness

between the SampEnvalue of the analyzedsignal and the optimum

discrimination threshold for both time and wavelet domains were

defined. Thus,only theresult from the block presenting thehighest

index was considered.

Forty patients with persistent AF lasting for more than 30 days,

undergoing the first attempt of ECV, were analyzed to validate the

proposed method and to predict the ECV outcome. All the patients

were under drug treatment with amiodarone and were followedduring the first 4 weeks. The wavelet bidomain technique was

applied to the 30 s length segment preceding the ECV of each

patient. A diagnostic accuracy of 85.71% (30 out of 35) with 90.48%

sensitivity (i.e., proportion of ECVs relapsing to AF correctly

classified) and 78.57% specificity (i. e. percentage of ECVs resulting

in NSR correctly discerned) was obtained for the first block, see

Fig. 6(a). The accuracy for the second block was 82.86% (29 out of

35) with 80.95% sensitivity and 85.71% specificity, see Fig. 6(b).

Finally, by combining both organization estimation strategies, an

accuracy of 94.29% (33 out of 35), with 95.24% sensitivity and

92.86% specificity, was achieved.

Moreover, block 1 results showed that patients relapsing to AF

presented higher SampEn values and, therefore, lower AA

organization, than those resulting in NSR after 4 weeks, seeFig.6(a). This observation was in agreement withfindings reported

by other works, such as the higher the AA organization, the higher

the success rates in cardioversion of AF [19,20] and the lower the

energy required for successful cardioversion [36]. Therefore,

obtained results suggested that the higher the number of reentries

wandering throughout the atrial tissue, the lower the probability of

successful ECV. Regarding the block 2, the presence of a more

stable AA waveform in organized atrial activities [37] was

considered to justify that patients who relapsed to AF presented

lower wavelet coefficient vector regularity than those who

remained in NSR. In addition, it is noteworthy that five patients,

in which NSR was not immediately restored after ECV, presented

the lowestAA organizationbothin time and wavelet domains,thus

increasing the obtained results consistency.

Fig. 5. Atrialactivity organizationtime course for all the analyzed recordings [57]: (a)average organizationresults forthe first 5 min after AF onset and(b) average results for

the last 2 min before AF termination.



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In previous works, some of which are summarized in Table 2,

several clinical, electrophysiological and demographic features,

such as AF duration, type of underlying disease, patient age, left

atriumdiameter, left ventricularfunction or continuationof therapy

with antiarrhythmic drugs, were proposed as predictors of

successful AF cardioversion and sinus rhythm maintenance.

However, the predictive value of these parameters was far from

optimal [81]. Regarding the explicit analysis of AF organization,

Holmqvist et al. [82] evaluated a parameter obtained from time

frequency analysis of theatrial signals, such as harmonic decay. This

parameter was designed to be an indexof the waveform shape(and

indirectlyorganization) of theatrialcomponent in theECG,but a lownumber of patients relapsing to AF were correctlyidentified(47%,14

out of30). InBerget als work [83], ventricular rhythmwas analyzed

usingthree-dimensionalRR intervals plots,quantifyingclusteringof

RR intervals. The authors speculated that RR intervals clustering

represents a relatively high organization degree of atrial fibrillatory

activity, and hypothesized that ECV would be more effective in

patients with clustering. However, only 50%(11 outof 22)of patients

who relapsed to AF during the first 4 weeks following ECV were

correctly discerned. With respect to the use of advanced digital

signal processing tools, Watson et al. [84] examined a variety of

wavelet transform-based statistical markersas potential candidates

to predict the post-cardioversion patient status after 1 month

followingECV,and 88% (15 out of 17) sensitivityand 100% (13 out of

13) specificity were obtained. Zohar et al. [85] developed a non-deterministic model for predicting sinus rhythm maintenance after

ECV, obtaining 71% (15 out of 21) sensitivity and 96% (22 out of 23)

specificity when the patients were followed up during the first 3

months after ECV. Lombardi et al. [86] used spectral analysis of

short-term heart rate variability (HRV) to evaluate the role of the

autonomic nervous system after sinus rhythm restoration, and 76%

(19 out of 25) sensitivity and 90% (61 out of 68) specificity were

obtained after thefirst 2 weeks followingECV. Other works analyzed

the DAF as a predictor ofECV outcome [8789]. However, the results

were conflicting and, therefore, inconclusive. The latest investiga-

tion suggested that the confounding effect of antiarrhythmic drug

therapy could explain the differences among these results [88];

however, this aspect still remains unclear. Finally, a recent study

showed that the amplitude of f waves had the ability of predicting

ECV result with a sensitivity of 83.87% and a specificity of 72.73%,

which could be improved with a discriminant model based on this

amplitude and the DAF (83.87% sensitivity and 86.36% specificity)

[90]. As a consequence, havingall these methods andtheiroutcomes

in mind, the methodology based on AF organization estimation [51]

wasconsidered by theauthors as a promising predictor of successful

cardioversion and NSR maintenance following ECV of persistent AF

patients, given that its diagnostic ability was higher than those

provided by other presented methods.

6. Ventricular activity analysis

The second part of this review summarizes the applications of

SampEn, focused on theventricular activity,to thesurface ECGin AF.

In this respect, ventricular response has been widely characterized

making use of the heart rate variability (HRV) analysis, since the

state of the autonomic nervous system, and related diseases, can be

investigated non-invasively using relatively basic signal processing

techniques [91]. Thus, in recent years, numerous measures have

been suggested to characterize HRV. In this sense, several time

domain metrics, which quantify the correlation between different

RR intervals, have been proposed. However, the exclusion of non-

normal RR intervals, provoked by false detection of R peaks, is an

important step to obtain more reliable outcomes [92]. The resulting

interval series is commonly referred as the normal-to-normal

intervals (NN intervals), see Fig. 7(a). Thus, somemetrics commonlyobtained from this series have been the standard deviation of NN

intervals(SDNN), thenumber of successivepairs of NN intervals that

differ more than 50 ms (pNN50) and the root mean square of the

differences between consecutive NN intervals (RMSSD) [92]. More

advanced measures are those based on spectral analysis of the heart

rhythm, since oscillations embedded in the rhythm, for example,

due to respiratory activity or variations in blood pressure, can be

quantified from the corresponding peaks in the estimated power

spectrum [93]. The oscillations are characterized by low-frequency

components, which typically are located in the interval below

0.5 Hz, see Fig. 7(b). Unfortunately, the oscillations are sometimes

poorly pronounced. This problem is commonly alleviated by

quantifying, instead, the power of low-frequency (LF) and high-

frequency (HF) components in the intervals 0.040.15 Hz and

Table 2

Comparison between some of the most recent studies presented to predict ECV outcome.

Study Database Database description Short description of methods Best results a

Alcaraz and

Rieta [90]

Own database

with 63 patients

31 relapsed to AF,

22 maintained NSR and

10 presented unsuccessful ECV

Discriminant model based on time and

frequency parameters obtained from

the AA

83.87% sensitivity,

86.36% specificity

Alcaraz and

Rieta [51]

Own database

with 40 patients

21 relapsed to AF, 14 maintained NSR and


Regularity analysis via SampEn of time

and wavelet domains of the AA

95% sensitivity, 93% specificity

Watson

et al. [84]

Own database

with 30 patients

17 relapsed to AF and 13 maintained NSR Assessment of several wavelet

transform-based statistical markers


Holmqvist

et al. [88]

Own database

with 175 patients

90 relapsed to AF, 77 maintained NSR

and 8 presented unsuccessful ECV

Analysis of atrial fibrillation rate

(i.e., DAF multiplied by 60)


Holmqvist

et al. [82]

Own database

with 54 patients

30 relapsed to AF and 24 maintained NSR Assessment of the atrial harmonic

decay with time-frequency analysis

of the ECG


Meurling

et al. [89]

Own database

with 37 patients

10 relapsed to AF, 22 maintained NSR and


Analysis of the dominant atrial cycle

length and clinical characteristics

Non-significant differences

between groups

Zohar

et al. [85]

Own database

with 44 patients

21 relapsed to AF and 23 maintained NSR Non-deterministisc model based on

genetic programming


Berg

et al. [83]

Own database

with 66 patients

32 relapsed to AF, 22 maintained NSR

and 12 presented unsuccessful ECV

Analysis of 3D RR intervals as a

quantifier of AF organization


Bollmann

et al. [87]

Own database

with 44 patients

13 relapsed to AF, 2 to atrial flutter

and 29 maintained NSR

Experimental combination of atrial

fibrillatory rate with the left atrium

diameter


Lombardi [86] Own database

with 93 patients

25 relapsed to AF and

68 maintained NSR

Spectral analysis of short-term HRV 76% sensitivity and 90% specificity

a

Sensitivity= proportion of patients who relapsed to AF correctly identified. Specificity = percentage of patients who resulted in NSR properly classified.



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0.150.40 Hz, respectively [93]. The spectral power measured in

these two intervals has been closely associated with autonomic

balance. An increase in sympatheticactivity is related to an increase

of the LF power, whereas an increase in parasympathetic or vagal

activity is primarily related to an increase of the HF power [93,94].

Hence, the ratio between these two spectral power measures has

beenconsidered as an index of autonomicbalance [86]. However, in

an increasingnumber of recentpapers, controversialopinionson the

role of vagal and sympathetic systems in AF have been reported

[94,95]. Thereby, to obtain relevant clinical information and a better

understanding of the underlying mechanisms of HRV, several non-

linear complexity metrics have been studied in recent works.

Moreover, relationships with the classical time and frequency

domains linear measures have been also found out [15,94]. The

application of non-linear metrics for HRV analysis is justified given

that non-linear processes are involved in the genesis of heart rate

modulation [96,97]. Within the aforementioned context, the next

subsection summarizes how SampEn has been applied to HRV

analysis in an attempt to predict the onset of paroxysmal AF.

6.1. Paroxysmal AF onset prediction

The prediction of spontaneous AF onset is clinically important

because the possibility of electrically stabilizing and preventing theonset of atrial arrhythmias with different atrial pacing techniques

increases notably. Dual chamber atrial pacing may reduce the

heterogeneity of atrialrefractoriness, manifested by P waveduration

changes on the surface ECG recording. Preliminary studies by

Prakash et al. [98] have indicated that acute suppression of

paroxysmal AF is possible in selected patients with dual-site right

atrial pacing from the coronary sinus ostium and high right atrium.

Theadvances in anti-arrhythmia pacingand drug managementmay

be applied to prevent the acute onset of paroxysmal AF prior to the

loss of sinus rhythm. The maintenance of sinus rhythm can lead to

decreased symptoms, improved hemodynamics and, possibly, a

decrease in the atrial remodeling that causes increased susceptibili-

ty to future episodes of paroxysmal AF [99]. In addition, a reduction

in the risk of thromboembolic events can also be remarkable.Themechanisms leading to the initiation of AF have been under

intensive investigationwithin the last decade. It has beenproposed

that the autonomic nervous system might have a role in the

initiation of this arrhythmia. Concretely, increased vagal tone can

predispose to the development of AF [23]. Thereby, in several

works, SampEn has been applied to study the HRV complexity

evolution in the minutes preceding spontaneous AF onset. In this

sense, Tuzcu et al. [23] studied the HRV complexity of 30 min

Fig. 6. Classification into ECVs resulting in NSR and relapsing to AF after 4 weeks

following the procedure obtained with the organization analysis of (a) block 1

(time-domain) and (b) block 2 (wavelet-domain) showed in Fig. 2[51]. SampEn

values obtained for all the analyzed signals together with the mean and standard

deviation for each group are displayed. Optimal thresholds are represented with a

dashed line.

Fig. 7. For the analysis of HRV time series, the exclusion of non-normal RR intervals, provoked by false detection of R peaks, is crucial in the outcomes [92]. The resulting

interval seriesis referred as thenormal-to-normalintervals, whichare presentedin (a)acquired duringAF conditions. On theotherhand, thepowerspectrumof theprevious

series is plotted in (b).



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length segments containing the ECG immediately preceding a

paroxysmal AF episode (pre-AF) and 30 min length segments of

ECG during a perioddistant,at least 45 min, from any episode of AF

(AFd). This data set was available on Physionet [65] and called

unedited data. SampEn of the HRV was found to be significantly

reduced in the segments preceding AF compared with those

distant from any AF occurrence, see Fig. 8(a). The same study wasrepeated, but premature atrial complexes were previously

removed. In this case, the data set was called edited data and a

less pronounced difference was provided, such as Fig. 8(b) shows.

The authors considered that decreased heart rate complexity, for

both edited and unedited data, reflects a change in cardiovascular

autonomic regulation that preconditions AF onset.

Additionally, the segments preceding AF onset were divided

into three successive 10 minperiods and analyzed with SampEn in

order to show the presence of a possible trend. A decreasing trend

towards the onset of AF in the unedited data was observed, see

Fig. 9(a). After the removal of ectopic beats, a similar decrease in

entropy towards AF onset was also noticed, but it was less

pronounced, such as Fig. 9(b) shows. According to the authors, the

decrease in SampEn before the onset of AF resulted mainly from

Fig. 8. Error bar plots of SampEn values revealing 95% of the confidence interval for

HRV complexity of 30 min length segments during a period distant from any

episode of AF (AFd) and immediately preceding a paroxysmal AF episode (pre-AF).

The unedited data are plotted in (a), whereas the edited data, after removing the

premature atrialcomplexes, areplotted in (b). Theplot hasbeen recreatedfrom the

data in [23].

Fig. 9. Analysis of the segments preceding AF onset, divided into three successive

10 min periods, in order to show the presence of a possible trend. The plots show

mean SampEn values of (a) unedited and (b) edited RR intervals [23].

Fig. 10. Analysis of the HRV complexity considering the autonomic profile and the

clinical history of patients before AF onset. Theplot showsSampEn values of the RR

interval data from vagally mediated and sympathetically mediated AF before its

onset [55].



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atrial ectopy. Moreover, the decrease was in consistent agreement

with the observed ectopic firing significance, that serves as a

trigger of paroxysmal AF, in subjects without evidence of other

structural cardiac abnormalities [100].

On theother hand,becauseof AF hasbeen classifiedinto vagally

mediated and sympathetically mediated types, based on theautonomic profile and the clinical history [24], Shin et al [55]

analyzedthe HRV complexity in these types of AF. In this study, for

44 episodes, divided in three subgroups (vagal, sympathetic and

non-related types), the 60 min segment of normal sinus rhythm

preceding AF onset was divided into 6 periods of 10 min. The

application of SampEn to the HRV of these segments revealed a

linear decrease of complexity irrespective of AF type, see Fig. 10. In

addition, this result in SampEn before AF onset was not affected

whether excluding the ectopic beats or not. In theauthors opinion,

the meaning of this progressive SampEn reduction before the start

of AF was that the heart rate became more orderly before AF; that

is, there is a loss of normal healthy complexity, thus leading to a

cardiac environment vulnerable to the occurrence of AF.

In the aforesaid work, classical linear parameters, suchas SDNN,RMSSD, pNN50, LF and HF,were also computed. However, SampEn

showed to be a better predictor of AF onset than the mentioned

features [55]. Nevertheless, a very recent study has proposed a

successful method to predict AF onset. The method is based on an

artificial neural network (ANN) with spectral and non-linear

complexity parameters (including SampEn) of the HRV as input

features [53]. As in Tuzcu et al. [23], the proposed method was

validated making use of a data set available on Physionet [65] and

composed by 30 min length ECG segments preceding AF onset and

distant 45 min from any AF occurrence. A diagnostic accuracy

higher than 82% was reached. Additionally, the possibility of long-

term paroxysmal AF onset prediction was studied making use of

other database also availableon Physionet [65]. Thus,sinus rhythm

recordings with duration from 60 to 360 min preceding AF onset

were tested. Concretely, each recording was split into consecutive

30 min overlapped segments and the ANN output was investigat-

ed. As a result, classification between distant from AF HRV

segments and AF preceding segments was performed before AF

onset. Thismethod producedpositive results, leading to predict the

onset of paroxysmal AF with 6221 min in advance. This resultproved that theANN classifierwas sensible to thevariations in HRV

dynamics that take place before a paroxysmal AF event. Moreover,

the classifier successfully identified these variations during distant

AF prognosis. This fact is in agreementwith other studies reporting

the possibility of predicting paroxysmal AF onset within 60 min

time [101,102].

In the literature, other methods based on different approaches

to those previously explainedcan also be found, see Table 3. Tothis

respect, considering that an abnormal P wave prolongation reflects

the presence of intra-atrial conduction defects [103], significant

information was extracted by evaluating the normal atrial

activation extent through the study of the P wave time domain

features. Thus, some deeply analyzed characteristics of the P wave

were its duration, obtained from each individual beat [104] or anaveraging of several beats [105], the dispersion [104] and variance

[106] of its duration, its morphology forpremature heart beats [68]

or theamplitude of atrial late potentials [107]. However, the lack of

a standard definition of P wave onset and termination provokes

that the method based on time domain analysis of P wave cannot

be easily compared [108].

On the otherhand, Vikmanet al. [109] found that thenumber of

ectopic beats seems to increase prior to the arrhythmia onset. This

phenomenon is known as being the trigger for the arrhythmia on a

predisposing substrate. Thereby, several works tried to find a

correlation between premature complexes rate and AF onset. Most

of them were presented at the Computers in Cardiology 2001

Challenge [110]. However, the most relevant work was the

presented by Thong et al. [111], in which an analysis of isolated

Table 3

Comparison between some of the most recent studies presented to predict AF onset.

Study Database Database description Short description of methods Best results a

Chesnokov [53] Some segments extracted from

the episodes of Cinc/Challenge

2001 database [65]

85 before AF and 67

distant from AF

Neural network based on spectral

and non-lineal parameters obtained

from HRV

76.19% sensitivity,

93.75% specificity

Hayn et al. [68] Episodes selected from Cinc/

Challenge 2001 and MIT-BIT

Atrial Fibrillation databases [65]

91 before AF and 94

distant from AF

Morphology analysis of the P waves

of premature heart beats

77% sensitivity,

72% specificity

Budeus et al. [107] Own database with 250 episodesbefore AF Not specified Assessment of pathologicalchemoreflexsensitivity and atrial

late potentials

Classification resultsnot provided

Tuzcu et al. [23] Learning episodes of Cinc/

Challenge 2001 database [65]

25 before AF and 25

distant from AF

Analysis of HRV complexity through

SampEn

Classification results

not provided

Shin et al. [55] Own database with 44 episodes

preceding AF onset

Not specified Evaluation of linear and non-linear

parameters from HRV


not provided

Thong et al. [111] All the episodes of Cinc/


Learning: 25 before

AF and 25 distant

from AF. Test: 50

before AF, 50 distant

from AF

Analysis of isolated premature atrial

complexes not followed by a regular

RR interval

89% sensitivity, 91% s

pecificity for test set

Hickey et al. [112] Episodes selected from several

databases. Some are available

on Physionet [65]

53 before AF and 94

distant from AF

Discriminant model based on HRV spectral

parameters and the number of atrial

premature complexes

81.1% sensitivity and

85.1% specificity

Ros et al. [113] Learning episodes of Cinc/


25 before AF and

25 distant from AF

Modular classification algorithm based on

the nearest K-neighbors and parameters

related to both P wave and QRS complex

96% sensitivity,

88% specificity

Andrikopoulos et al. [106] Own database with 110 episodes 60 before AF and

50 distant from AF

Evaluation of P wave duration variance 88% sensitivity,

75% specificity

Vikman et al. [109] Own database with 92 episodes

preceding AF onset

Not specified Assessment of traditional time-frequency

and non-linear parameters from HRV


not provided

Dilaveris et al. [104] Own database with 100 episodes 60 before AF and

40 distant

from AF

Analysis of the maximum P wave duration

and its dispersion

83% sensitivity and

85% specificity

a Sensitivity= proportion of episodes preceding AF onset correctly identified. Specificity = percentage of episodes distant from AF onset properly classified.



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premature atrial complexes not followed by a regular RR interval

reached a sensitivity of 89% and specificity of 91%.

Finally, some works considered the possible relationship

between AA and VA prior to AF onset [112]. To this respect, a

proposed method was basedon a combination of techniques which

assess autonomic tone (through HRV) and atrial ectopic beat

occurrence. Depending on whether there is a significant correla-

tion between observed low-frequency and high-frequency spectral

power in the RR power spectral density, HRV or premature atrial

complexes analysis was considered. Precisely, If there is high

correlation, a discriminant analysis based on spectral features of

HRV was used to predict AF onset, whereas in the low-correlation

case, atrial premature contractions are also added to the

discriminant model. However, this method was characterized by

a notably low sensitivity, although it was robust in the presence of

no episodes. Other work presented a modular classification

algorithm based on the nearest K-neighbors and parameters

related to both the P wave and the QRS complex [113]. Thus, some

analyzed metrics were QR voltage amplitude, RR interval,

amplitude and time width of P wave, time distance between P

wave and R peak, etc. Making use of a forward stepwise approach

to maximize classification performance, this method provided a

sensitivity of 96% and specificity of 88%.

7. Conclusions

The present review has shown the applications of sample

entropy to the electrocardiogram of atrial fibrillation. Regarding

atrial activity, SampEn has demonstrated to be a robust organiza-

tion estimator able to provide information about several aspects of

the arrhythmia. In this respect, clinical relevant information

related to spontaneous AF termination, to the organization time

course variation in the onset and termination of AF and to sinus

rhythm maintenance after electrical cardioversion, are some of its

applications. On the other hand, SampEn can also play an

important role in the ventricular activity analysis of AF, thus,

being able to reflect cardiovascular autonomic regulation changes

in the instants preceding AF onset. The studies summarized in thepresent work suggest that sample entropy can be considered as a

useful non-linear metric to quantify accurately atrial and

ventricular cardiac dynamics from the surface ECG in atrial

fibrillation.

Acknowledgements

This work was supported by the projects TEC200764884 from

the Spanish Ministry of Science and Innovation, PII2C09-0224-

5983 from Junta de Comunidades de Castilla La Mancha and PAID

0508 from Universidad Politecnica de Valencia.

References

[1] S.M. Pincus, A.L. Goldberger, Physiological time-series analysis: what doesregularity quantify? Am. J. Physiol. 266 (4 Pt 2) (1994) H1643H1656.

[2] J.S.Richman,J.R. Moorman, Physiological time-seriesanalysisusing approximateentropy and sample entropy, Am. J. Physiol. Heart Circ. Physiol. 278 (6) (2000)H2039H2049.

[3] W. Chen, J. Zhuang, W. Yu, Z. Wang, Measuring complexity using FuzzyEn, ApEn,and SampEn, Med. Eng. Phys. 31 (1) (2009) 6168.

[4] D. Yu, M. Small, R.G. Harrison, C. Diks, Efficient implementation of the Gaussiankernel algorithm in estimating invariants and noise level from noisy time seriesdata, Phys.Rev. E: Stat. Phys. Plasmas FluidsRelat. Interdiscipl. Topics61 (4 Pt A)(2000) 37503756.

[5] S.M. Pincus, Approximate entropy as a measure of systemcomplexity,Proc.Natl.Acad. Sci. U.S.A. 88 (6) (1991) 22972301.

[6] R. Hornero, M. Aboy, D. Abasolo, J. McNames, W. Wakeland, B. Goldstein,Complex analysis of intracranial hypertension using approximate entropy, Crit.Care Med. 34 (1) (2006) 8795.

[7] R. Hornero, M. Aboy, D. Abasolo, J. McNames, B. Goldstein, Interpretation of

approximate entropy: analysis of intracranial pressure approximate entropy

during acute intracranial hypertension, IEEE Trans. Biomed. Eng. 52 (10) (2005)16711680.

[8] M. Varela, L. Jimenez, R. Farina, Complexity analysis of the temperature curve:new information from body temperature, Eur. J. Appl. Physiol. 89 (34) (2003)230237.

[9] M. Varela, J. Churruca, A. Gonzalez, A. Martin, J. Ode, P. Galdos, Temperaturecurve complexity predicts survival in critically ill patients, Am. J. Respir. Crit.Care Med. 174 (3) (2006) 290298.

[10] M.M. Platisa, V. Gal, Dependence of heart rate variability on heart period indisease and aging, Physiol. Meas. 27 (10) (2006) 989998.

[11] H. Goncalves,T. Henriques-Coelho, J. Bernardes, A.P. Rocha,A. Nogueira,A. Leite-

Moreira, Linear and nonlinear heart-rate analysis in a rat model of acute anoxia,Physiol. Meas. 29 (9) (2008) 11331143.[12] D. Abasolo, R. Hornero, P. Espino, D. Alvarez, J. Poza, Entropy analysis of the EEG

background activity in Alzheimersdisease patients, Physiol. Meas.27 (3) (2006)241253.

[13] P. Casaseca, M. Martn, C. Alberola, Weaning from mechanical ventilation: aretrospective analysis leading to a multimodal perspective, IEEE Trans. Biomed.Eng. 53 (7) (2006) 13301345.

[14] D.E. Lake, J.S. Richman, M.P. Griffin, J.R. Moorman, Sample entropy analysis ofneonatal heart rate variability, Am. J. Physiol. Regul. Integr. Comp. Physiol. 283(3) (2002) R789R797.

[15] M.J. Lewis, A.L. Short, Sample entropy of electrocardiographic RR and QT time-series data during rest and exercise, Physiol. Meas. 28 (6) (2007) 731744.

[16] W.B.Kannel, R.D.Abbott, D.D.Savage, P.M.McNamara,Epidemiologicfeatures ofchronic atrialfibrillation: theFramingham study,N. Engl.J. Med. 306(17) (1982)10181022.

[17] V. Fuster, L.E. Ryden, D.S. Cannom, H.J. Crijns, A.B. Curtis, ACC/AHA/ESC 2006guidelines forthe management ofpatients with atrial fibrillation:a reportof theAmerican College of Cardiology/American Heart Association Task Force on

practice guidelines and the European Society of Cardiology Committee forpractice guidelines (writing committee to revise the 2001 guidelines for themanagement of patients withatrial fibrillation): developed in collaboration withthe European heartrhythm associationand the heartrhythm society, Circulation114 (7) (2006) e257e354.

[18] J.J. Rieta, F. Castells, C. Sanchez, V. Zarzoso, J. Millet, Atrial activity extraction foratrial fibrillationanalysis usingblind sourceseparation, IEEE Trans.Biomed.Eng.51 (7) (2004) 11761186.

[19] T.H. Everett, L.C. Kok, R.H. Vaughn,J.R. Moorman, D.E. Haines, Frequency domainalgorithm for quantifying atrial fibrillation organization to increase defibrilla-tion efficacy, IEEE Trans. Biomed. Eng. 48 (9) (2001) 969978.

[20] H.J. Sih, D.P. Zipes, E.J. Berbari, J.E. Olgin, A high-temporal resolution algorithmfor quantifying organization during atrial fibrillation, IEEE Trans. Biomed. Eng.46 (4) (1999) 440450.

[21] K.T. Konings, C.J. Kirchhof, J.R. Smeets, H.J. Wellens, O.C. Penn, M.A. Allessie,High-density mapping of electrically induced atrial fibrillation in humans,Circulation 89 (4) (1994) 16651680.

[22] M.S. Guillem, A.M.Climent, F. Castells, D. Husser, J. Millet, A. Arya, C. Piorkowski,A. Bollmann, Noninvasive mapping of human atrial fibrillation, J. Cardiovasc.

Electrophysiol. 20 (5) (2009) 507513.[23] V. Tuzcu, S.Nas, T.Borklu, A. Ugur, Decrease in theheart ratecomplexity prior to

the onset of atrial fibrillation, Europace 8 (6) (2006) 398402.[24] P. Coumel, Paroxysmal atrial fibrillation: a disorder of autonomic tone? Eur.

Heart. J. 15 (Suppl. A) (1994) 916.[25] W.B. Kannel, P.A. Wolf, E.J. Benjamin, D. Levy, Prevalence, incidence, prognosis,

and predisposing conditions for atrial fibrillation: population-based estimates,Am. J. Cardiol. 82 (8A) (1998) 2N9N.

[26] E.J. Benjamin, P.A. Wolf, R.B. DAgostino, H. Silbershatz, W.B. Kannel, D. Levy,Impact of atrial fibrillation on the risk of death: the Framingham Heart Study,Circulation 98 (10) (1998) 946952.

[27] P.A. Wolf, R.D. Abbott, W.B. Kannel, Atrial fibrillation as an independent riskfactor for stroke: the Framingham Study, Stroke 22 (8) (1991) 983988.

[28] C. Blomstrom-Lundqvist, M.M. Scheinman, E.M. Aliot, J.S. Alpert, ACC/AHA/ESCguidelines for the management of patients with supraventricular arrhythmias-executive summary: a report of the American College of Cardiology/AmericanHeart Association task force on practice guidelines and the European society ofcardiology committee for practice guidelines (writing committee to develop

guidelines for the management of patients with supraventricular arrhythmias),Circulation 108 (15) (2003) 18711909.[29] G. Gronefeld, S.H. Hohnloser,Towards a consensus in rate versusrhythm control

for management of atrial fibrillation: Insights from the PIAF trial, Card. Electro-physiol. Rev. 7 (2) (2003) 113117.

[30] G.C.Gronefeld,J. Lilienthal,K.H. Kuck, S.H.Hohnloser,Impactof rateversusrhythmcontrolon qualityof lifein patientswithpersistentatrialfibrillation. Resultsfromaprospective randomized study, Eur. Heart J. 24 (15) (2003) 14301436.

[31] Y. Takahashi, P. Sanders, P. Jas, M. Hocini, R. Dubois, M. Rotter, T. Rostock, C.J.Nalliah, F. Sacher, J. Clementy, M. Hassaguerre, Organization of frequencyspectra of atrial fibrillation: relevance to radiofrequency catheter ablation, J.Cardiovasc. Electrophysiol. 17 (4) (2006) 382388.

[32] J. Kneller, J. Kalifa, R. Zou, A.V. Zaitsev, M. Warren, O. Berenfeld, E.J. Vigmond, L.J.Leon, S. Nattel, J. Jalife, Mechanisms of atrial fibrillation termination by puresodium channelblockade in an ionically-realistic mathematicalmodel, Circ.Res.96 (5) (2005) e35e47.

[33] B.P.T. Hoekstra, C.G.H. Diks, M.A. Allessie, J. DeGoede, Nonlinear analysis of thepharmacological conversion of sustained atrial fibrillation in conscious goats bythe class Ic drug cibenzoline, Chaos 7 (3) (1997) 430446.



13/14

[34] F.Ravelli,M. Mase, M.D.Greco, L. Faes,M. Disertori,Deteriorationof organizationin the first minutes of atrial fibrillation: a beat-to-beat analysis of cycle lengthand wave similarity, J. Cardiovasc. Electrophysiol. 18 (1) (2007) 6065.

[35] Z. Qu, J.N. Weiss, Dynamics and cardiac arrhythmias, J. Cardiovasc. Electrophy-siol. 17 (9) (2006) 10421049.

[36] G. Calcagnini, F. Censi, A. Michelucci, P. Bartolini, Descriptors of wavefrontpropagation. Endocardial mapping of atrial fibrillation with basket catheter,IEEE Eng. Med. Biol. Mag. 25 (6) (2006) 7178.

[37] S. Petrutiu, J. Ng, G.M. Nijm, H. Al-Angari, S. Swiryn, A.V. Sahakian, Atrialfibrillation and waveform characterization. A time domain perspective in thesurface ECG, IEEE Eng. Med. Biol. Mag. 25 (6) (2006) 2430.

[38] L. So

rnmo, P. Laguna, Bioelectrical Signal Processing in Cardiac and NeurologicalApplications, Elsevier Academic Press, 2005.[39] I. Dotsinsky, T. Stoyanov, Optimization of bi-directional digital filtering for drift

suppression in electrocardiogram signals, J. Med. Eng. Technol. 28 (4) (2004)178180.

[40] Y. Sun, K. Chan, S.M. Krishnan, ECG signal conditioning by morphologicalfiltering, Comput. Biol. Med. 32 (6) (2002) 465479.

[41] S.M.M. Martens, M. Mischi, S.G. Oei, J.W.M. Bergmans, An improved adaptivepower line interference canceller for electrocardiography, IEEE Trans. Biomed.Eng. 53 (11) (2006) 22202231.

[42] J. Slocum, A. Sahakian, S. Swiryn, Diagnosis of atrial fibrillation from surfaceelectrocardiograms based on computer-detected atrial activity, J. Electrocardiol.25 (1) (1992) 18.

[43] P. Langley, J.J. Rieta, M. Stridh, J. Millet, L. Sornmo, A. Murray, Comparison ofatrial signal extraction algorithms in 12-lead ECGs with atrial fibrillation, IEEETrans. Biomed. Eng. 53 (2) (2006) 343346.

[44] M. Stridh, L. Sornmo, Spatiotemporal QRST cancellation techniques for analysisof atrial fibrillation, IEEE Trans. Biomed. Eng. 48 (1) (2001) 105111.

[45] R. Alcaraz, J.J.Rieta, Adaptive singular valuecancellation of ventricularactivityin

single-lead atrial fibrillation electrocardiograms, Physiol. Meas. 29 (12) (2008)13511369.

[46] A.Bollmann,D. Husser, L.Mainardi, F.Lombardi,P. Langley,A. Murray, J.J. Rieta,J.Millet, S.B. Olsson, M. Stridh, L. Sornmo, Analysis of surface electrocardiogramsin atrial fibrillation: techniques, research, and clinical applications, Europace 8(11) (2006) 911926.

[47] S.M. Pincus, Assessing serial irregularity and its implications for health, Ann. N.Y. Acad. Sci. (2001) 245267.

[48] S.M.Pincus, D.L.Keefe, Quantification of hormone pulsatility via an approximateentropy algorithm, Am. J. Physiol. 262 (5 Pt 1) (1992) E741E754.

[49] D.T. Kaplan, M.I. Furman, S.M. Pincus, S.M. Ryan, L.A. Lipsitz, A.L. Goldberger,Aging and the complexity of cardiovascular dynamics, Biophys. J. 59 (4) (1991)945949.

[50] M. Aboy, D. Cuesta-Frau, D. Austin, P. Mico-Tormos, Characterization of sampleentropy in the context of biomedical signal analysis, in: Conf. Proc. IEEE Eng.Med. Biol. Soc., 2007, 59435946.

[51] R. Alcaraz, J.J. Rieta, A non-invasive method to predict electrical cardioversionoutcome of persistent atrial fibrillation, Med. Biol. Eng. Comput. 46 (7) (2008)625635.

[52] H.M. Al-Angari, A.V. Sahakian, Use of sample entropy approach to study heartratevariability in obstructivesleep apneasyndrome,IEEE Trans. Biomed. Eng.54(10) (2007) 19001904.

[53] Y.V. Chesnokov, Complexity and spectral analysis of the heart rate variabilitydynamics for distant prediction of paroxysmal atrial fibrillation with artificialintelligence methods, Artif. Intell. Med. 43 (2) (2008) 151165.

[54] R. Alcaraz, J.J. Rieta, Wavelet bidomain sample entropy analysis to predictspontaneous termination of atrial fibrillation, Physiol. Meas. 29 (1) (2008)6580.

[55] D.-G. Shin, C.-S. Yoo, S.-H. Yi, J.-H. Bae, Y.-J. Kim, J.-S. Park, G.-R. Hong, Predictionof paroxysmal atrial fibrillation using nonlinear analysis of the RR intervaldynamics before the spontaneous onset of atrial fibrillation, Circ. J. 70 (1) (2006)9499.

[56] M.M. Platisa, S. Mazic, Z. Nestorovic, V. Gal, Complexity of heartbeat intervalseries in young healthy trained and untrained men, Physiol. Meas. 29 (4) (2008)439450.

[57] R. Alcaraz, J.J.Rieta, Non-invasive organizationvariation assessment in the onsetand termination of paroxysmal atrial fibrillation, Comput. Methods Programs

Biomed. 93 (2) (2009) 148154.[58] A. Bollmann, Quantification of electrical remodeling in human atrial fibrillation,Cardiovasc. Res. 47 (2) (2000) 207209.

[59] A. Goette, C. Honeycutt, J.J. Langberg, Electrical remodeling in atrial fibrillation.Time course and mechanisms, Circulation 94 (11) (1996) 29682974.

[60] S.M. Al-Khatib, W.E. Wilkinson, L.L. Sanders, E.A. McCarthy, E.L. Pritchett,Observationson the transitionfrom intermittentto permanent atrial fibrillation,Am. Heart J. 140 (1) (2000) 142145.

[61] F. Nilsson, M. Stridh, A. Bollmann, L. Sornmo, Predicting spontaneous termina-tion of atrial fibrillation using the surface ECG, Med. Eng. Phys. 28 (8) (2006)802808.

[62] L.T. Mainardi, M. Matteucci, R. Sassi, On predicting the spontaneous terminationof atrial fibrillation episodes using linear and non-linear parameters of ECGsignal and RR series, Conf. Proc. IEEE Comput. Cardiol. 31 (2004) 665668.

[63] A. Bollmann, N.K.Kanuru, K.K.McTeague,P.F. Walter, D.B.DeLurgio,J.J. Langberg,Frequency analysis of human atrial fibrillation using the surface electrocardio-gram and its response to ibutilide, Am. J. Cardiol. 81 (12) (1998) 14391445.

[64] M. Holm, S. Pehrson, M. Ingemansson, L. Sornmo, R. Johansson, L. Sandhall, M.Sunemark, B. Smideberg, C. Olsson, S.B. Olsson, Non-invasive assessment of the

atrial cycle length during atrial fibrillation in man: introducing, validating andillustrating a new ECG method, Cardiovasc. Res. 38 (1) (1998) 6981.

[65] A.L. Goldberger, L.A. Amaral, L. Glass, J.M. Hausdorff, P.C. Ivanov, R.G. Mark, J.E.Mietus, G.B. Moody, C.K. Peng, H.E. Stanley, Physiobank, physiotoolkit, andphysionet: components of a new research resource for complex physiologicsignals, Circulation 101 (23) (2000) E215E220.

[66] A. Bollmann, F. Lombardi, Electrocardiology of atrial fibrillation. Current knowl-edge and future challenges, IEEE Eng. Med. Biol. Mag. 25 (6) (2006) 1523.

[67] F.Chiarugi, M.Varanini,F. Cantini, F.Conforti,G. Vrouchos,NoninvasiveECG as atool for predicting termination of paroxysmal atrial fibrillation, IEEE Trans.Biomed. Eng. 54 (8) (2007) 13991406.

[68] D. Hayn, A. Kollmann, G. Schreier, Predicting initiation and termination of atrialfibrillation from the ECG, Biomed. Technol. (Berl.) 52 (1) (2007) 510.[69] G.B. Moody, Spontaneous termination of atrial fibrillation: a challenge from

physionet and computers in cardiology, Conf. Proc. IEEE Comput. Cardiol. 31(2004) 101104.

[70] R. Alcaraz, J.J. Rieta, F. Hornero, Atrial activity non-invasive characterization inprevious instants before paroxysmal atrial fibrillation termination, Rev. Esp.Cardiol. 61 (2) (2008) 154160.

[71] M. Hassaguerre, P. Sanders, M. Hocini, L.-F. Hsu, D.C. Shah, C. Scavee, Y.Takahashi, M. Rotter, J.-L. Pasquie, S. Garrigue, J. Clementy, P. Jas, Changes inatrial fibrillation cycle length and inducibility during catheter ablation and theirrelation to outcome, Circulation 109 (24) (2004) 30073013.

[72] S. Petrutiu, A.V. Sahakian, J. Ng, S. Swiryn, Analysis of the surface electrocardio-gram to predict termination of atrial fibrillation: the 2004 computers in cardi-ology/physionet challenge, Conf. Proc.IEEE Comput. Cardiol. 31 (2004)105108.

[73] D. Hayn, K. Edegger, D. Scherr, P. Lercher, B. Rotman, W. Klein, G. Schreier,Automated prediction of spontaneous termination of atrial fibrillation fromelectrocardiograms, Conf. Proc. IEEE Comput. Cardiol. 31 (2004) 117120.

[74] C. Mora, F. Castells, R. Ruiz, J.J. Rieta, J. Millet, C. Sanchez, S. Morell, Prediction of

spontaneous termination of atrial fibrillation using time frequency analysis oftheatrial fibrillatory wave, Conf. Proc. IEEEComput. Cardiol. 31 (2004)109112.

[75] M. Stridh, L. Sornmo, C.J. Meurling, S.B. Olsson, Sequential characterization ofatrial tachyarrhythmias based on ECG time-frequency analysis, IEEE Trans.Biomed. Eng. 51 (1) (2004) 100114.

[76] F. Nilsson, M. Stridh, A. Bollmann, L. Sornmo, Predicting spontaneous termina-tion of atrial fibrillation with time-frequency information, Conf. Proc. IEEEComput. Cardiol. 31 (2004) 657660.

[77] C.W. Israel, J.R. Ehrlich, G. Gronefeld, A. Klesius, T. Lawo, B. Lemke, S.H. Hohn-loser, Prevalence, characteristics and clinical implications of regular atrialtachyarrhythmias in patients with atrial fibrillation: insights from a study usinga new implantable device, J. Am

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