ASSESSMENT OF NOISE IMPACT IN SAMPLE

ENTROPY FOR THE NON-INVASIVE ORGANIZATION

ESTIMATION OF ATRIAL FIBRILLATION

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, Electrocardiogram, Organization Estimation, Sample Entropy, Noise Effect.

Abstract:

In recent studies, Sample Entropy (SampEn) has demonstrated that can be a very promising non-linear index

to assess atrial ﬁbrillation (AF) organization from surface ECG recordings. However, non-linear regularity

metrics are notably sensitive to noise. Thereby, in the present work, the effect that noise provokes in AF or-

ganization estimation based on SampEn is analyzed. Given that AF organization was estimated by computing

SampEn over the atrial activity (AA) signal, to evaluate the noise impact on AA regularity, 25 synthetic signals

with different organization degrees were generated following a published model. Noise coming from real ECG

recordings with different energy levels was added to the synthesized AA signals to obtain different signal to

noise ratios (SNR). Results showed that SampEn, i.e., the AA irregularity, increased with noise, thus hiding

the differences between organized and disorganized recordings. Precisely, in the presence of noise, SampEn

values were increased, in average, by factors of 1.64, 4.46, 9.46 and 14.23 for SNRs of 24, 15, 9 and 3 dB,

respectively. As a conclusion, a successful AF organization evaluation via SampEn requires a proper noise

reduction in the AA signal.

1 INTRODUCTION

Non-linear analysis metrics are valuable in the as-

sessment of physiological time series, because ”hid-

den information” related to underlying mechanisms

can be sometimes obtained (Pincus and Goldberger,

1994; Richman and Moorman, 2000). To date, a

high amount of non-linear complexity measures ex-

ists, such as dimensions, Lyapunov exponents and

entropies. However, their computation is frequently

confronted with the problem of insufﬁcient number

of data points (Chen et al., 2009). Additionally, most

dimension and entropy deﬁnitions present application

limitations associated to real world time series, since

all recorded data are, to a certain degree, contami-

nated by noise. In this respect, a 2% noise is seri-

ous enough to prevent accurate estimation (Yu et al.,

2000).

Recently, a method based on sample entropy

(SampEn) has been proposed to estimate organization

of atrial ﬁbrillation (AF) (Alcaraz and Rieta, 2009),

which is the most common cardiac arrhythmia in clin-

ical practice and whose onset and termination mech-

anisms are still unknown (Fuster et al., 2006). The

study of AF organization is a key aspect in the ar-

rhythmia’s knowledge, because it provides informa-

tion on the number of active reentries (Sih et al., 1999;

Everett et al., 2001), which maintain and can perpet-

uate AF. Thereby, in the present work, the noise ef-

fect on this method, which could be useful to predict

spontaneous AF termination or the result of aggres-

sive therapies, such as electrical cardioversion or ab-

lation, is exhaustively analyzed.

2 MATERIALS

Given that AF organization has to be estimated by

computing SampEn over the atrial activity (AA) sig-

nal (Alcaraz and Rieta, 2009) and because AA with

393

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

ASSESSMENT OF NOISE IMPACT IN SAMPLE ENTROPY FOR THE NON-INVASIVE ORGANIZATION ESTIMATION OF ATRIAL FIBRILLATION.

In Proceedings of the Third International Conference on Bio-inspired Systems and Signal Processing, pages 393-396

DOI: 10.5220/0002692103930396

 SciTePress

no noise or ventricular residues cannot be obtained

from real ECG recordings, 25 one minute synthetic

AA signals were generated. Thus, the noise effect on

AA organization estimation could be evaluated. The

synthetic AA signals were obtained making use of the

model proposed by Stridh et al (Stridh and S¨ornmo,

2001). In this model, a sinusoid and M − 1 harmon-

ics are used to generate a sawtooth-like shape of AF.

The non-stationary behavior is created by introducing

a time-varying amplitude and cycle length of the saw-

tooth signal. In every lead of N samples in length, the

AA is modelled by:

y(n) = −

∑

i=1

(n)sin(iθ(n)), n = 1, . . . , N (1)

where the term a

(n) with the sawtooth amplitude, a,

the modulation peak amplitude, ∆a, and amplitude

modulation frequency, f

, is given by:

(n) =

iπ



a+ ∆asin2π



(2)

The fundamental frequency of the ﬁbrillation wave-

form is assumed to vary around f

with a maximum

frequency deviation of ∆f and modulation frequency

given by f

. The phase, θ(n), is then given by:

θ(n) = 2π



∆f



sin2π

n (3)

After several tests, the selected parameters were

∆f = 3 Hz, f

= 4 Hz, ∆a = 10µV, f

= 9 Hz and

= 1024 Hz in order to synthesize a signal as close

as possible to the real AA. In this respect, Figs. 1(a)

and (b) show a real AA signal obtained by applying

the averaged QRST cancellation technique and a syn-

thetic AA signal generated with the indicated param-

eters, respectively. Because of the typical AA fun-

damental frequency range is 3-9Hz (Bollmann et al.,

2006; Stridh et al., 2001), a fundamental frequency f

equal to 6 Hz was selected. In order to obtain differ-

ent regularities, the number of harmonics M and their

amplitude a were varied, such that, a higher num-

ber of harmonics with lower amplitude will gener-

ate a more irregular AA. In this way, M and a were

randomly selected between 5 and 15 and between

6 and 18 µV, respectively. Hence, the most irreg-

ular AA signal presented 15 harmonics with 6 µV

of amplitude. The set of AA signals with different

regularities were used to evaluate if the noise effect

was regularity-dependent. Finally, available noise

in Physionet (Goldberger et al., 2000) coming from

real ECG recordings with different energy levels was

added to the synthesized AA signals. Concretely,

this noise was the recorded signal when the patient

front-end is disconnected from the skin electrodes. In

Figure 1: Comparison example between real and synthe-

sized AA signals depending on added noise.(a) Real AA

signal obtained from the ECG through averaged QRST can-

cellation technique. (b) Synthetic AA signal without noise.

dB. (d) Synthetic AA signal with added noise and SNR of 9

dB.

Figs. 1(c) and (d), a synthetic AA signal that has been

added to the described noise with two differentenergy

levels is shown.

3 METHODS

The 25 synthetic signals were used in order to evalu-

ate the noise impact on AA regularity. The same noise

signal was superimposed to all synthetic AA signals,

which were generated with different degrees of regu-

larity. Firstly, SampEn values of the AA signals with-

out noise were computed. Next, the noise recording

was weighed by different gain factors and added to

the synthetic signals in order to obtain different signal

to noise ratios (SNR). Finally, SampEn values of the

synthetic AA signals contaminated with noise were

calculated. This methodology allowed us to evaluate

the evolution of AA regularity estimation in the pres-

ence of noise.

The SNR of an ECG recording is normally lower

than 30 dB (Laguna and Sornmo, 2000). In addi-

tion, because of the real AA signal is obtained from

ECG recordings using ventricular activity cancella-

tion techniques, the SNR of an AA signal must be

lower than the SNR of an ECG signal. In fact, the

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

394

Figure 2: Each plot shows SampEn values of 25 synthetic noise-free AA signals stacked with their corresponding result when

SNR is 24, 15, 9, and 3 dB. The presence of noise produces a disorganization increase in the AA signals and reduces the

differences between initially organized and disorganized signals. Therefore, noise reduction is essential to assess successfully

AF organization with SampEn.

SNRs of the AA signals obtained from 50 real ECGs

analyzed in a previous work were within the 16.4–2.7

dB range (Nilsson et al., 2006). In the study, the SNR

is deﬁned as the ratio between the mean of the funda-

mental and ﬁrst harmonic power magnitudes and the

power magnitude of the background noise. Whereby,

AA signals with SNR of 24, 15, 9 and 3 dB were gen-

erated.

4 RESULTS

Fig. 2 shows the evaluation results of noise effect on

AA organization estimation via SampEn. As can be

seen, SampEn values for the 25 noise-free synthetic

AA signals are shown and increased with their corre-

sponding SampEn values for 24, 15, 9 and 3 dB SNR,

respectively. It can be observed that SampEn, i.e., the

AA irregularity, increases with noise, thus hiding the

differences between organized and disorganized ac-

tivities. Precisely, in the presence of noise, SampEn

values were increased, in average, by factors of 1.64,

4.46, 9.46 and 14.23 for SNRs of 24, 15, 9 and 3 dB,

respectively. In addition, the difference between the

two signals without noise that presented the highest

and lowest SampEn values was reduced by factors of

1.07, 1.29, 2.05 and 4.67 for the signals with SNRs of

24, 15, 9, and 3 dB, respectively.

We also tested the same experiment by adding

Gaussian noise instead of ECG noise to the synthe-

sized AA signals and results were very similar, hence,

they have been omitted. However, bearing this simi-

lar behavior in mind, any other kind of random and

non-deterministic contaminating signal should pro-

voke similar results of SampEn.

5 DISCUSSION AND

CONCLUSIONS

Results showed that the noise presence masks the dif-

ferences, evaluated with SampEn, between organized

and disorganized activities. Thereby, it could be con-

sidered that when AA is contaminated by noise or any

other undesired signal, the organization difference be-

tween AF episodes are considerably reduced. This

fact is crucial, for example, in the successful pre-

diction of paroxysmal AF termination. Considering

ASSESSMENT OF NOISE IMPACT IN SAMPLE ENTROPY FOR THE NON-INVASIVE ORGANIZATION

ESTIMATION OF ATRIAL FIBRILLATION

395

that the AA obtained from the ECG often presents

QRS residua and noise (Petrutiu et al., 2006), the ob-

tained results with synthetic AA signals can be used

to justify the poor discrimination outcome reported

by other groups when direct AA organization analy-

sis was applied (Nilsson et al., 2006).

Moreover, the results are also coherent with the

highly improved paroxysmal AF termination predic-

tion reached by applying SampEn to the fundamental

waveform associated to the AA (Alcaraz and Rieta,

2009), its wavelength being the inverse of the domi-

nant atrial frequency (DAF) (Holm et al., 1998). As

this signal is obtained by applying a selective ﬁlter-

ing to the AA centered on the DAF, most part of the

undesired contaminating signals are avoided. As a

consequence, to obtain a successful AF organization

assessment through SampEn, noise and nuisance in-

terferences in the AA signal should be considerably

reduced prior to the computation of the non-linear in-

dex.

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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