WAVELET SAMPLE ENTROPY OPTIMIZATION

THROUGH OPTIMAL MOTHER FUNCTION SELECTION

FOR ATRIAL FIBRILLATION ANALYSIS

Ra´ul Alcaraz

Innovation in Bioengineering Research Group, University of Castilla-La Mancha, Cuenca, Spain

Jos´e Joaqu´ın Rieta

Biomedical Synergy, Electronic Engineering Dept., Universidad Polit´ecnica de Valencia, Spain

Keywords:

Atrial ﬁbrillation, Electrical cardioversion, Sample entropy, Wavelet family, Wavelet transform.

Abstract:

Wavelet Sample Entropy (WSE) has been previously introduced as a successful methodology to predict electri-

cal cardioversion (ECV) outcome of persistent atrial ﬁbrillation (AF). The method estimates AF organization

based on the combination of Wavelet decomposition and non-linear regularity metrics, such as Sample En-

tropy (SampEn). However, WSE has been only computed by applying a speciﬁc wavelet function, such as the

fourth-order biorthogonal wavelet. In the present work, with the objective of improving WSE robustness and

its diagnostic ability in ECV outcome prediction, several orthogonal wavelet families were tested, and their

performances were compared. Results indicated that, for all the functions of the same wavelet family, the same

sensitivity and speciﬁcity were obtained. Additionally, all the wavelet families reached the same diagnostic

ability (80.95% sensitivity and 85.71% speciﬁcity), being the same patients incorrectly classiﬁed by all the

families. These results suggest that any wavelet family could be indistinctly used to estimate successfully

AF organization with the WSE methodology. As a consequence, the design of a customized wavelet function

adapted to the speciﬁc characteristics of AA would not improve the WSE diagnostic ability in the prediction

of ECV outcome in AF.

1 INTRODUCTION

For patients in persistent atrial ﬁbrillation (AF),

restoration and maintenance of normal sinus rhythm

(NSR) is the main therapeutic goal because symp-

toms, cardiac output, and exercise tolerance are im-

proved whereas the risk of stroke is reduced (Fuster

et al., 2006). Thus, the ﬁrst step in the rhythm control

strategy is generally cardioversion. While chemical-

induced cardioversion is sometimes possible, particu-

larly with amiodarone (Gall and Murgatroyd, 2007),

it is generally more unsuccessful than electrical car-

dioversion (ECV), specially if the arrhythmia has

been present for more than 24 hours (Gall and Mur-

gatroyd, 2007). However, although the ECV suc-

cess rate is high, AF recurrence is common, espe-

cially during the ﬁrst 2 weeks following the proce-

dure (Tieleman et al., 1998). Moreover, ECV also

has the potential of causing severe collateral effects,

such as post-shock bradycardia, malignant ventricular

arrhythmias, arterial thromboembolism and compli-

cations related to anaesthesia (Gall and Murgatroyd,

2007). Hence, it would be clinically very useful to

predict NSR maintenance after ECV, before it is at-

tempted. In this way, the risks of cardioversion could

be avoided for those patients with high risk of short-

term recurrence and, for the health care provider,

clinical costs could be reduced because unproductive

treatment time and bed usage could be reduced.

Recently, a strategy deﬁned as Wavelet Sample

Entropy (WSE) has been introduced as a success-

ful methodology to predict ECV outcome (Alcaraz

and Rieta, 2008). The method estimates AF organi-

zation based on the combination of Wavelet decom-

position and non-linear regularity metrics, such as

Sample Entropy (SampEn), showing that in patients

with a more organized AF, the arrhythmia recurrence

likelihood was lower after ECV (Alcaraz and Rieta,

2008). However, WSE was only computed by apply-

ing a speciﬁc wavelet function, such as the fourth-

order biorthogonal wavelet. Thereby, in the present

work, with the objective of improving the robustness

389

Alcaraz R. and Joaquín Rieta J. (2010).

WAVELET SAMPLE ENTROPY OPTIMIZATION THROUGH OPTIMAL MOTHER FUNCTION SELECTION FOR ATRIAL FIBRILLATION ANALYSIS.

In Proceedings of the Third International Conference on Bio-inspired Systems and Signal Processing, pages 389-392

DOI: 10.5220/0002692003890392

 SciTePress

of WSE and its diagnostic ability in ECV outcome

prediction, several orthogonal wavelet families were

tested, and their performances were compared.

2 MATERIALS

2.1 Study Population

Thirty-ﬁve patients (12 men and 23 women) with per-

sistent AF lasting more than 30 days, undergoing

the ﬁrst attempt of ECV were followed during four

weeks. All patients were in drug treatment with amio-

darone. A standard 12-lead ECG was acquired prior

to cardioversion. All signals were digitized at a sam-

pling rate of 1024 Hz and 16-bit resolution with a

Cardiolab System in the electrophysiology laboratory

during ECV protocol. In order to process these sig-

nals, a 30 seconds-length AF segment preceding the

ECV was extracted for each patient. After the ECV,

in 21 patients (60%) NSR duration was below one

month, whereas en the remaining 14 patients (40%)

NSR was maintained.

2.2 Data Preprocessing

Lead V

was chosen for the analysis because previous

works have shown that atrial activity (AA) is domi-

nant in this lead (Petrutiu et al., 2006). The signal

was preprocessed in order to improve later analysis.

Firstly, baseline wander was removed making use of

bidirectional high pass ﬁltering with 0.5 Hz cutt-off

frequency(Dotsinsky and Stoyanov, 2004). Secondly,

high frequency noise was reduced with an eight order

bidirectional IIR Chebyshev low pass ﬁltering, whose

cut-off frequency was 70 Hz (Sun et al., 2002). Fi-

nally, powerline interference was removed through

adaptive notch ﬁltering, which preserves the ECG

spectral information (Ferdjallah and Barr, 1994).

3 METHODS

3.1 Wavelet Sample Entropy

The WSE methodology has shown an ability to de-

tect regularity variations in the AA signal that would

be left masked in other cases (Alcaraz and Rieta,

2008). However, this strategy requires the combina-

tion of Wavelet decomposition and SampEn together

with some additional previous steps, such as it will be

next described.

The analysis of the AA from the surface ECG

is complicated by the simultaneous presence of ven-

tricular activity, which is of much greater amplitude.

Whereby, the AA signal has to be ﬁrstly extracted be-

fore the application of any other analysis. Although

a variety of different techniques exist for this pur-

pose, a QRST cancellation method was used. Thus,

the highest variance eigenvector of all the ECG beats

was considered as the ventricular template for the

cancellation. This QRST template was selected be-

cause it provided a more accurate ventricular activity

representation and, hence, higher quality AA extrac-

tion in short AF recordings, such as the analyzed in

this work, than those obtained by averaging all the

beats (Alcaraz and Rieta, 2007).

Next, eight levels of wavelet decomposition were

applied to the AA signals because the seventh detail

scale (sub-band corresponding to 4− 8 Hz) covers the

most typical AA frequency range (Bollmann et al.,

2006). The wavelet coefﬁcients vector corresponding

to the scale containing the dominant atrial frequency,

those with the largest amplitude within the AA fre-

quency range (Bollmann et al., 2006), was linearly

interpolated by the factor 2

m−1

, being m the discrete

wavelet scale. Hence, a vector of wavelet coefﬁcients

with a number of samples equal to the original sig-

nal was obtained for the chosen scale. Considering

that different scales present wavelet coefﬁcients vec-

tors with different number of samples, this interpo-

lation was necessary. Moreover, unsuccessful results

were obtained when non-interpolated wavelet coefﬁ-

cients vectors were analyzed. Finally, the regularity

of this vector was estimated making use of SampEn

to discern between ECVs relapsing to AF and result-

ing in NSR.

3.2 Wavelet Family Selection

Given that there are no established rules for the choice

of a speciﬁc wavelet family for each particular ap-

plication, several orthogonal wavelet families were

tested in this work. Only experiments with orthogonal

families were developed because only in an orthogo-

nal basis any signal can be uniquely decomposed and

the decomposition can be inverted without loosing in-

formation (Mallat, 1999). Concretely, all the different

functions from Haar, Daubechies, Coiﬂet, Biorthogo-

nal, Reverse Biorthogonal and Symlet wavelet fami-

lies were tested.

3.3 Statistical Analysis

The obtained SampEn values were expressed as mean

± standard deviation, because ECVs relapsing to AF

BIOSIGNALS 2010 - International Conference on Bio-inspired Systems and Signal Processing

390

Table 1: Mean and standard deviation SampEn values for ECVs relaping to AF and resulting in NSR, statistical signiﬁcance

(p value), sensitivity and speciﬁcity for each tested wavelet family.

Wavelet family (order) ECVs relapsing AF ECVs maintaining NSR p-value Sensitivity (%) Speciﬁcity (%)

Haar 0.030 ± 0.006 0.026 ± 0.005 0.0100 80.95 (17/21) 85.71 (12/14)

Daubechies (5) 0.031 ± 0.006 0.027 ± 0.006 0.0112 80.95 (17/21) 85.71 (12/14)

Coiﬂet (3) 0.030 ± 0.007 0.025 ± 0.006 0.0098 80.95 (17/21) 85.71 (12/14)

Biorthogonal (4.4) 0.032 ± 0.005 0.027 ± 0.004 0.0072 80.95 (17/21) 85.71 (12/14)

Reverse Biorthogonal (4.4) 0.033 ± 0.006 0.029 ± 0.004 0.0115 80.95 (17/21) 85.71 (12/14)

Symlets (5) 0.031 ± 0.006 0.026 ± 0.005 0.0086 80.95 (17/21) 85.71 (12/14)

Figure 1: Results obtained with the third-order Coiﬂet wavelet family. (a) ROC curve constructed with the obtained SampEn

values for persistent AF patients. The closest point to 100% sensitivity and speciﬁcity is selected as optimum SampEn

threshold. Symbol • indicates the optimum threshold. (b) Classiﬁcation into patients resulting in NSR and relapsing to AF

after 4 weeks following ECV.

and resulting in NSR had a normal and homoscedastic

distribution as the Kolmogorov–Smirnov and Levene

tests proved, respectively. Thereby, The t Student test

was also used to determine whether there was any sig-

niﬁcant difference between the groups. A two-tailed

value of p < 0.05 was considered statistically signiﬁ-

cant.

In order to evaluate the predictive ability for

the NSR maintenance reached through each wavelet

function, receiver operating characteristic (ROC)

curves were constructed. Different thresholds or cut-

off points (SampEn values) were selected and the sen-

sitivity/speciﬁcity pair for each one of them was cal-

culated. Sensitivity (the true positive rate) was con-

sidered as the ECVs relapsing to AF proportion cor-

rectly classiﬁed (SampEn value higher than the cutoff

point), whereas speciﬁcity (the true negativerate) rep-

resented the ECVs resulting in NSR percentage cor-

rectly recognized (SampEn value lower than the cut-

off point). The closest point to 100% sensitivity and

speciﬁcity was selected as optimum SampEn thresh-

old.

4 RESULTS

For all the functions of the same wavelet family, the

same sensitivity and speciﬁcity values were obtained.

Thereby, only the function that showed lower p value

is presented in Table 1 for each wavelet family.

As can be appreciated in the table, all the wavelet

families reached the same efﬁciency, i.e. a sensi-

tivity of 80.95% (17 out of 21) and a speciﬁcity of

85.71% (12 out of 14), being the same patients incor-

rectly classiﬁed by all the families. Additionally, for

all the cases, the ROC curves provided an optimum

SampEn discrimination threshold between 0.029 and

0.030. Similarly, for all the wavelet families, the pa-

tients relapsing to AF presented higher SampEn val-

ues than those resulting in NSR after one month, and

both groups were statistically distinguishable, since a

statistical signiﬁcance lower than 0.001 was obtained.

Fig. 1 shows the ROC curve and the classiﬁcation

into patients resulting in NSR and relapsing to AF ob-

tained with the third-order Coiﬂet family as an exam-

ple.

WAVELET SAMPLE ENTROPY OPTIMIZATION THROUGH OPTIMAL MOTHER FUNCTION SELECTION FOR

ATRIAL FIBRILLATION ANALYSIS

391

5 DISCUSSION AND

CONCLUSIONS

The wavelet coefﬁcients vector organization analysis

checks the regularity of a time series. This time se-

ries is constituted by the correlation coefﬁcients be-

tween the scaled mother wavelet and consecutive and

non-overlapping signal segments. In this respect, re-

sults provided by all the tested wavelet families can

be considered as coherent and prove that the dis-

crete Wavelet transform translation variance has no

effect in this application. Additionally, a high regular-

ity value in this time series indicates constant wave-

form across the studied time period. On the contrary,

low regularity implies variable waveforms. Thus, the

presence of more structured f waves in organized

atrial activities (Petrutiu et al., 2006) could justify

the obtained results, which show that patients who

relapsed to AF presented lower wavelet coefﬁcients

vector regularity than those who remained in NSR.

Hence, the obtained results suggest that the de-

sign of a customized wavelet function adapted to

the atrial activity waveform characteristics would not

considerably improve prediction of ECV result. In

fact, in other studies, where different ECG problems

were solved making use of WT, a new wavelet func-

tion adapted to the analyzed signal characteristics was

considered but, ﬁnally, discarded (Addison, 2005).

ACKNOWLEDGEMENTS

This work was supported by the projects TEC2007-

64884 from the Spanish Ministry of Science and

Innovation, PII2C09-0224-5983 and PII1C09-0036-

3237 from Junta de Comunidades de Castilla La Man-

cha and PAID-05-08 from Universidad Polit´ecnica de

Valencia.

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