1 Introduction

Atrial fibrillation (AF) is the most commonly sustained cardiac arrhythmia in clinical practice, with a prevalence of 0.5% in the adult population [21], rising to 10% or more in those over 75 years [14, 13]. AF may cause systemic thromboembolic complications, decrease exercise capacity, impair ventricular function, reduce quality of life, and incur significant health care costs [16]. After adjusting for the underlying cardiac condition, AF is associated with a 1.5–1.9-fold increase in risk of mortality in both men and women across a wide spectrum of ages [3].

This disease can be divided into different forms, namely paroxysmal AF (self-terminating within 7 days), persistent AF (interventions are required for its termination), and permanent AF (sinus rhythm cannot be restored) [14]. For patients in persistent AF, restoration and maintenance of normal sinus rhythm (NSR) can be one therapeutic goal because symptoms, cardiac output, and exercise tolerance are improved whereas the risk of stroke is reduced [14]. Thus, the first step in the rhythm control strategy is generally cardioversion. While chemical-induced cardioversion is sometimes possible, particularly with amiodarone, it is generally more unsuccessful than electrical cardioversion (ECV), especially if the arrhythmia has been present for more than 24 h [15].

Electrical cardioversion consists of delivering a controlled transthoracic electrical shock to the patient. This procedure is successful in around 80–100% of the patients. However, although the success rate is high, AF recurrence is common, especially during the first 2 weeks following the procedure [38]. Thus, approximately 40–60% of cardioverted patients revert back to AF within 3 months subsequent to the ECV, and around 60–80% within 1 year [24]. Moreover, ECV also has the potential of causing severe collateral effects, such as post-shock bradycardia, malignant ventricular arrhythmias, arterial thromboembolism, and complications related to anesthesia [40].

Hence, because of the high AF risk of recurrence and because of the potential secondary effects of ECV, it would be clinically useful to predict NSR maintenance after ECV before it is attempted. In this way, the risks of cardioversion could be avoided for those patients with low NSR maintenance probability, and for the health care provider, the clinical costs could be optimized because unproductive treatment time and bed usage could be reduced.

To date, numerous studies have attempted to find invasive and non-invasive parameters (clinical, electrophysiological, demographic, etc.) for the prediction of ECV outcome in AF. However, very different and, consequently, inconclusive results have been reported [19]. Thus, the aim of this work is to carry out a new non-invasive predictor of NSR maintenance after ECV before it is attempted. In this respect, the atrial activity (AA) organization was estimated noninvasively, because it can be hypothesized that NSR maintenance would be more likely in patients who present a more organized AA. This hypothesis is based on the observation that the more disorganized the AA, the higher the number of propagating wavelets [36], and the larger the atrial volume that could support the propagation of reentries after the shock [7].

In order to estimate the AA organization obtained from surface electrocardiographic (ECG) recordings, sample entropy (SampEn), which is a non-linear index for quantifying time series regularity [34], was selected because non-linearity, as a necessary condition for a chaotic behavior, is present in the diseased heart with AF at cellular level, and electrical remodeling in AF is a far-from-linear process [14]. 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 perpetuation of AF [14].

The paper is structured as follows. Section 2 starts describing the used database and previous preprocessing applied to ECG recordings. Next, the proposed strategy for NSR maintenance prediction after ECV, together with the performance evaluation and the statistical study that were carried out, are presented. Section 3 summarizes the obtained results, which are discussed in Sect. 4. Finally, Sect. 5 presents the concluding remarks.

2 Methods

2.1 Study population

Forty patients (15 men and 25 women) with persistent AF, lasting for more than 30 days, undergoing the first attempt of ECV, were followed for 4 weeks. A standard 12-lead ECG was acquired prior to cardioversion. All the signals were digitized at a sampling rate of 1,024 Hz with 16-bit resolution. Next, a 30 s-length AF segment preceding the ECV was extracted for each patient.

After the ECV, NSR was not restored in five patients (12.5%) whereas in 21 (52.5%), NSR duration was below 1 month. In the remaining 14 patients (35%), NSR was maintained. All patients were under drug treatment with amiodarone. The median arrhythmia duration was 10.33 months (range 1–45.67), and echocardiography demonstrated a mean left atrium diameter (LAD) of 46.20 ± 7.02 mm. Moreover, 20% of the patients presented underlying heart disease. A summary of these parameters is shown in Table 1.

Table 1 Clinical characteristics and measured parameters in the population under study
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The ECG recordings were preprocessed in order to improve later analysis. First, baseline wander was removed making use of bidirectional high pass filtering with 0.5 Hz cut-off frequency [9]. Second, high frequency noise was reduced with an eight order, bidirectional IIR, Chebyshev low pass filtering, whose cut-off frequency was 70 Hz. Finally, powerline interference was removed through adaptive notch filtering, which preserves the ECG spectral information [12].

2.2 Strategy to predict cardioversion outcome

The AA analysis from surface ECG recordings is complicated by the simultaneous presence of ventricular activity, which is of much greater amplitude; whereby, the AA signal was first extracted. Thus, each QRS complex and T wave in the ECG was assumed to be represented by an N × L matrix Y, which contains N samples from L leads:

$${{\mathbf{Y}}}=[{{\mathbf{y}}}_1, \ldots, {{\mathbf{y}}}_{L}]$$
(1)

where the vector y l contains the samples of the lth lead. The ith QRST complex start point was defined as s i  = r i −0.3 × RR min, r i being the R peak event and RR min the minimum R–R interval found in the ECG. The ith QRST complex end point was selected as e i  = r i  + 0.7 × RR min [35]. Therefore, the N samples of the ith complex are uniformly distributed between the points s i and e i . Each r i time instant was marked following the algorithm presented by Pan and Tompkins [29].

The atrial fibrillation can be viewed as being uncoupled to the ventricular activity, and thus, each observed beat can be modeled as a sum of atrial activity (Y A) and ventricular activity (Y V) [37]:

$${{\mathbf{Y}}}={{\mathbf{Y}}}_{\rm A}+{{\mathbf{Y}}}_{\rm V}$$
(2)

Because every beat was temporally aligned using its R peak timing, the median complex was obtained averaging the matrices Y corresponding to all QRST complexes in the ECG. The median QRST complex, T, was used to represent the ventricular activity [37]. Thereby, this template T was temporally aligned with each R peak in the ECG, and the AA estimation inside the complex Y i was taken to be the residual difference Y i −T.

Making use of this general process, the AA of lead V 1 was obtained and denoted as y(k). Previous works have shown that AF is dominant in this lead, whereby it was chosen for the analysis [30].

Bearing in mind that the median beat cannot represent each individual beat accurately, since QRST morphology is affected by respiration, patient movement, etc., QRST residua and noise are often present in the remainder ECG [30]. These nuisance signals can degrade AA organization estimation using non-linear regularity indexes, which could provoke unsuccessful results. In fact, non-significative differences between terminating and non-terminating paroxysmal AF recordings were observed in other studies when direct sample entropy analysis of the remainder ECG was applied [27]. On the contrary, 96% of the same analyzed AF episodes were correctly classified when these nuisance signals were removed and the AA properly enhanced. The technique was based on wavelet bidomain regularity analysis [2], which is similar to the one that will be proposed next to predict ECV outcome.

Hence, in order to reduce the presence of noise, ventricular residues, and enhance the AA, two different wavelet decomposition analysis of y(k) are proposed. Mathematically speaking, a wavelet is a smooth and quickly vanishing oscillating function with good localization, both in time and frequency. A wavelet family Ψa,b(t) is the set of elementary functions generated by dilations and translations of a unique admissible mother wavelet Ψ(t) [25]:

$$\Psi_{a,b}(t)=|a|^{-\frac{1}{2}}\Psi\left(\frac{t-b}{a}\right)$$
(3)

where a, b ∈ ℜ, a ≠ 0 are the scale and translation parameters, respectively, and t is the time. As a increases, the wavelet becomes narrower. Thus, one has a unique analytic pattern and its replications at different scales, with variable time localization.

Because the methodology that will be proposed next requires to reconstruct back to time the sub-band containing the dominant atrial frequency (DAF) of the analyzed AF recordings, discrete wavelet transform (DWT) was used. In DWT, the parameters a and b are sampled using a logarithmic discretization of the a scale (a = 2m) and linking this, in turn, to the size of steps taken between the b locations. To link b to a, each location b, which is proportional to the a scale, is moved in discrete steps (b = n × 2m). Thus, the discretized mother wavelet is:

$$\Psi_{m,n}(k)=2^{-\frac{m}{2}}\Psi(2^{-m}k-n)$$
(4)

m and n being the new scale and translation discrete parameters, respectively, and k the discrete time.

The atrial signal wavelet decomposition can be defined as the correlation between y(k) and the chosen wavelet family Ψm,n(k) for each m and n:

$$C_m(n)=\sum_k y(k) \Psi_{m,n}(k)$$
(5)

The decomposition results are wavelet coefficients C, which depend on scale and position. In fact, a vector of wavelet coefficients C m is obtained for each analyzed discrete scale m. The information stored in this wavelet coefficients vector is not repeated elsewhere and allows the complete regeneration of the original signal without redundancy, because the used discretization of the wavelet mother employs orthonormal wavelet basis functions [25].

Seven levels of wavelet decomposition were applied to AA signals because the seventh discrete scale (sub-band corresponding to 4–8 Hz) covers the most typical AA frequency range [6] and contains the DAF of all the analyzed AF recordings. Thereby, the two aforementioned alternatives for reducing noise, ventricular residues, and enhancing the AA, that will be introduced later, were applied to the wavelet coefficients vector in this scale, which is denoted as m AA. Regarding the wavelet family selection, there are no established rules for the choice of wavelet functions. A cautious and still exploratory approach is to test different wavelet families, and then, to compare their efficiency in the specific problem [8]. Unfortunately, on each electrocardiographic application where the WT has been used, a different wavelet family was chosen [1]. In this study, several orthogonal wavelet families were tested (see Sect. 3), because only in an orthogonal basis any signal can be uniquely decomposed and the decomposition can be inverted without losing information [25].

In the first proposed alternative, \({\bf C}_{m_{\rm AA}}\) was reconstructed back to the time-domain, obtaining \(y_{m_{\rm AA}}(k):\)

$$y_{m_{\rm AA}}(k)=\sum_k C_{m_{\rm AA}}(n)\Psi_{m,n}(k)$$
(6)

The organization of \(y_{m_{\rm AA}}(k)\) was estimated making use of SampEn, which will be mathematically described in the next subsection. SampEn was chosen because it is notably independent on record length and obtains coherent results when short and noisy data sets are analyzed [34].

In the second alternative, the wavelet coefficients vector corresponding to the scale m AA was linearly interpolated by the factor \(2^{m_{\rm AA}-1}\) in order to obtain a vector \({\bf C}_{m_{\rm AA}}(2^{m_{\rm AA}-1}k)\) with equal number of samples than the original signal y(k). The organization of this vector was also estimated using SampEn.

When the organization analysis of \(y_{m_{\rm AA}}(k)\) and \({\bf C}_{m_{\rm AA}}(2^{m_{\rm AA}-1}k)\) were independently evaluated, a high accuracy in the prediction of sinus rhythm maintenance was obtained, as will be presented in Sect. 3. However, by combining both organization analysis strategies, the predictive capability was additionally improved. Thus, two indexes that indicate the closeness between the SampEn value of the analyzed signal and the optimum discrimination threshold were obtained as:

$$d_1=\frac{{\rm SampEn}(y_{m_{\rm AA}}(k))-Th1}{Th1}$$
(7)
$$d_2=\frac{{\rm SampEn}({\bf C}_{m_{\rm AA}}(2^{m_{\rm AA}-1}k))-Th2}{Th2}$$
(8)

where Th1 and Th2 allow the optimal discrimination between ECVs relapsing to AF and resulting in NSR after 1 month. These threshold values were obtained making use of receiver operating characteristic (ROC) curves; see Sect. 2.4. Finally, the discrimination process was carried out following these rules:

  • if the ECV result was differently classified by both organization analysis, and:

    • d1 > d2, the classification provided by \(y_{m_{\rm AA}}(k)\) was considered

    • d1 < d2, the classification result of \({\bf C}_{m_{\rm AA}}(2^{m_{\rm AA}-1}k))\) was chosen

  • On the contrary, the result of both analysis was coincident and any of them can be selected indistinguishably.

2.3 Sample entropy

Sample entropy examines time series for similar epochs and assigns a non-negative number to the sequence, with larger values corresponding to more irregularity in the data [34]. Two input parameters, a run length m and a tolerance window r, must be specified for SampEn to be computed. SampEn is the negative logarithm of the conditional probability that two sequences similar for m points remain similar at the next point, where self-matches are not included in calculating the probability.

Formally, given N data points from a time series {x(n)} = x(1), x(2),..., x(N), SampEn can be defined as follows [34]:

  1. 1.

    Form m vectors X m (1),..., X m (N − m + 1) defined by X m (i) = [x(i), x(i + 1),..., x(i + m − 1)], for 1 ≤ i ≤ N − m + 1. These vectors represent m consecutive x values, starting with the ith point.

  2. 2.

    Define the distance between vectors X m (i) and X m (j), d[X m (i), X m (j)], as the absolute maximum difference between their scalar components:

    $$d[X_m(i),X_m(j)]=\max_{k=0,\ldots,m-1}\left(|x(i+k)-x(j+k)|\right)$$
    (9)
  3. 3.

    For a given X m (i), count the number of j (1 ≤ j ≤ N − m, j ≠ i), denoted as B i , such that the distance between X m (i) and X m (j) is less than or equal to r. Then, for 1 ≤ i ≤ N − m,

    $$B_i^m(r)=\frac{1}{N-m-1}B_i$$
    (10)
  4. 4.

    Define B m(r) as

    $$B^m(r)=\frac{1}{N-m}\sum_{i=1}^{N-m}B_i^m(r)$$
    (11)
  5. 5.

    Increase the dimension to m + 1 and calculate B m+1(r).

Thus, B m(r) is the probability that two sequences will match for m points, whereas B m+1(r) is the probability that two sequences will match for m + 1 points. Finally, sample entropy can be estimated as:

$${\rm SampEn}(x(n),m,r)=-\ln\left[\frac{B^{m+1}(r)}{B^m(r)}\right]$$
(12)

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 length m matches increases. The number of matches can be increased by choosing small m (short templates) and large r (wide tolerance). However, penalties appear when too relaxed criteria are used [31]. For smaller r values, 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 the noise [31]. As suggested by Pincus [32], SampEn was estimated using the widely established parameters values of m = 1 and m = 2 and r between 0.1 and 0.25 × the standard deviation (SD) of the original time series {x(n)}. Normalizing r in this manner gives a translation and scale invariance to SampEn, in the sense that it remains unchanged under uniform process magnification, reduction, or constant shift to higher or lower values [32]. These parameters produce a good statistical reproducibility in time series of length larger than 60 samples, as considered herein [31, 33].

2.4 Performance evaluation and statistical analysis

The proposed methodology performance was compared with the results provided by two parameters, which were widely studied in previous works, such as the DAF [5, 19, 26] and the LAD [11, 17]. The DAF was defined as the frequency component with the largest amplitude within the typical AA range (3–9 Hz) [6]. The AA power spectral density was obtained using the Welch Periodogram. A Hamming window of 4,096 points in length, a 50% overlapping between adjacent windowed sections and a 8,192-points fast Fourier transform (FFT) were used as computational parameters. The DAF, whose inverse can be considered as the dominant atrial cycle length (DACL) [6], has been possibly the most typically analyzed parameter in previous studies for predicting NSR maintenance after ECV [5, 19, 26]. On the other hand, the LAD was obtained from the echocardiographic study.

Because the number of available ECG recordings is reduced, leave-one-out cross validation was used. In this manner, the approach is trained multiple times using all but one of the database recordings. ROC curves were constructed in order to evaluate the predictive ability of each organization analysis. For each strategy and each analyzed parameter, different thresholds or cutoff points were selected and the sensitivity/specificity pair for each one of them were calculated. Sensitivity (the true positive rate) is the proportion of correctly classified ECVs relapsing to AF (parameter value higher than the cutoff point), whereas specificity (the true negative rate) represents the percentage of correctly recognized ECVs resulting in NSR (parameter value lower than the cutoff point). The closest point to 100% sensitivity and specificity was selected as optimum discrimination threshold. Results were expressed as mean ± SD, unless otherwise specified. Additionally, the t Student test was used to determine whether there was any significant difference between the groups. Thus, a two-tailed value of p < 0.05 was considered statistically significant.

3 Results

As suggested by Pincus [32], m = 1 and m = 2 and four different values of r: 0.1, 0.15, 0.2, and 0.25× the SD of data, were studied to independently estimate the organization degree of \(y_{m_{\rm AA}}(k)\) and \({\bf C}_{m_{\rm AA}}(2^{m_{\rm AA}-1}k).\) The results were compared making use of the mean and SD of SampEn values, the statistical significance (P value) computed by the t Student, the sensitivity, and the specificity, as shown in Tables 2 and 3. In both organization analysis, the best results (lower P value) were obtained with m = 2 and r = 0.25; hence, these values were selected. Nevertheless, in all the cases the outcomes were very similar.

Table 2 Organization analysis results of \(y_{m_{\rm AA}}(k)\) when different m and r values are employed in the computation of SampEn
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Table 3 Organization analysis results of \({\bf C}_{m_{\rm AA}}(2^{m_{\rm AA}-1}k)\) when different m and r values are employed in the computation of SampEn
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The wavelet functions considered in this work were independently tested in the two proposed organization analysis. As before, in order to compare the different wavelet functions performance, mean and SD of SampEn values were computed together with the statistical significance, sensitivity, and specificity of the classification approach. All the different functions from Haar, Daubechies, Coiflet, Biorthogonal, Reverse Biorthogonal, and Symlet wavelet families were tested. In all the functions of the same wavelet family, the same sensitivity and specificity values were obtained. Thus, only the function that presented a lower P value is included in Tables 4 and 5 for each wavelet family.

Table 4 Mean and standard deviation SampEn values for ECVs relaping to AF and resulting in NSR, statistical significance (P value), sensitivity, and specificity for each wavelet family tested in the organization analysis of \(y_{m_{\rm AA}}(k)\)
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Table 5 Mean and standard deviation SampEn values for ECVs relaping to AF and resulting in NSR, statistical significance (P value), sensitivity, and specificity for each wavelet family tested in the organization analysis of \({\bf C}_{m_{\rm AA}}(2^{m_{\rm AA}-1}k)\)
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The obtained results with the organization analysis of \(y_{m_{\rm AA}}(k)\) are shown in Table 4, where several differences can be appreciated. Nevertheless, the best discrimination results were obtained making use of the Biorthogonal wavelet (order 4.4). By using this family, 90% (19 out of 21) sensitivity and 79% (11 out of 21) specificity was obtained; see Fig. 1a. The ROC curve provided 0.0990 as optimum SampEn discrimination threshold between patients relapsing to AF and resulting in NSR after 1 month. Figure 2a shows the SampEn values for all the analyzed signals, together with the mean and SD values for each group. Note that the patients who resulted in NSR presented lower SampEn values (0.0930 ± 0.0150) than those who relapsed to AF (0.1136 ± 0.0151); see Table 2. Indeed, both groups were statistically distinguishable, given that statistical significance was lower than 0.0001. Additionally, Fig. 3a shows a couple of illustrative examples of reconstructed back to time-domain AA signals presenting different degrees of organization.

Fig. 1
figure 1

Receiver operating characteristic (ROC) curve obtained with the organization analysis of a \(y_{m_{\rm AA}}(k)\) and b \({\bf C}_{m_{\rm AA}}(2^{m_{\rm AA}-1}k)\) . The closest point to 100% sensitivity and specificity is selected as optimum SampEn threshold. Symbol • indicates the optimum threshold

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Fig. 2
figure 2

Classification into ECVs resulting in NSR and relapsing to AF after 4 weeks following ECV obtained with the organization analysis of a \(y_{m_{\rm AA}}(k)\) and b \({\bf C}_{m_{\rm AA}}(2^{m_{\rm AA}-1}k)\)

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Fig. 3
figure 3

Examples of a time reconstructed AA signals, after wavelet processing, with different organization degrees, and b their interpolated wavelet coefficients vectors

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Regarding the organization analysis of the interpolated wavelet coefficients vector, the obtained results are shown in Table 5. In this case, all the wavelet families reached the same efficiency. Moreover, the same recordings were incorrectly classified by all the families. Consequently, any wavelet family could be used indistinctly. Considering that only one wavelet function can be applied to the proposed methodology, Biorthogonal family (order 4.4) was selected. Making use of this wavelet function, 81% (17 out of 21) sensitivity and 86% (12 out of 14) specificity was obtained; see Fig. 1b. The ROC curve provided 0.0301 as optimum SampEn discrimination threshold. Again, the patients relapsing to AF presented higher SampEn values (0.0320 ± 0.0053) than those resulting in NSR after 1 month (0.0271 ± 0.0045), as Fig. 2b and Table 6 show. Also, both groups were statistically distinguishable, since a statistical significance lower than 0.001 was obtained. Figure 3b presents two interpolated wavelet coefficients vectors corresponding to AA signals with different degrees of organization.

Table 6 Results obtained with the proposed strategies, compared with the dominant atrial frequency and left atrium diameter analysis
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Figure 4 shows the leave-one-out cross validation results obtained with both the proposed organization analysis. Note that a slight SampEn threshold variation was observed in both cases. Indeed, in the analysis of \(y_{m_{\rm AA}}(k),\) the maximum and minimum thresholds were 0.1008 and 0.0981, respectively, whereas the threshold obtained with all the patients was 0.0990, thus implying a variation lower than 1.82%. In the wavelet coefficients vector analysis, the maximum and minimum thresholds were 0.0302 and 0.0298, respectively, whereas for all the signals it was 0.0301, giving a variation lower than 1%. Additionally, it can be observed that the sensitivity and specificity were similar to those obtained with all the patients, reaching slightly higher values in some cases because the ECV result was correctly predicted in one extra patient. Hence, the analyzed patients database included in this study can be considered as a representative data set.

Fig. 4
figure 4

Leave-one-out cross validation results obtained with the proposed organization analysis in a time, and b wavelet domains

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By combining both organization analysis strategies, 95% (20 out of 21) sensitivity and 93% (13 out of 14) specificity was obtained; therefore, the ECV result in 33 out of 35 patients (94%) was correctly predicted. In addition, the five patients who relapsed to AF immediately after ECV were also studied separately. In this case, the organization analysis of \(y_{m_{\rm AA}}(k)\) and \({\bf C}_{m_{\rm AA}}(2^{m_{\rm AA}-1}k)\) provided the highest SampEn values both in time (0.1255 ± 0.0165) and wavelet (0.0350 ± 0.0028) domains, thus reinforcing the consistency of the obtained results.

On the other hand, Table 6 also presents the results obtained with the DAF and LAD analysis. It can be observed that non-significative differences were obtained in both cases, the statistical significance being greater than 0.05. Moreover, the predictive ability of these parameters was quite lower than that obtained with the aforementioned proposed organization analysis.

4 Discussion

First, regarding the wavelet family selection, orthogonal wavelet filters larger than two coefficients must present asymmetrical impulse response. Therefore, linear phase behavior is impossible [25]. Given that each wavelet family filter provokes different phase distortion, dissimilar waveforms will be reconstructed back to time-domain. This fact could justify the different results obtained with the organization analysis of \(y_{m_{\rm AA}}(k)\) (presented in Table 4). Moreover, the Biorthogonal family introduces the lowest phase distortion, because it reaches the best compromise between asymmetrical impulse response and orthogonality [25]. Therefore, it provided the best results, as shown in Table 4. However, remarkable differences among the tested wavelet families were not noticed. Thus, the design of a customized wavelet function adapted to AA characteristics would not considerably improve results. In fact, other studies in which WT was applied to different ECG problems, a new wavelet function adapted to the analyzed signal characteristics was not designed [1].

On the other hand, the wavelet coefficients vector organization analysis checks the regularity of a time series. This time series is constituted by the correlation coefficients between the scaled mother wavelet and consecutive and non-overlapping signal segments. In this respect, results provided by all the tested wavelet families (presented in Table 5) can be considered as coherent and prove that the DWT translation variance has no effect in this application.

The results of \(y_{m_{\rm AA}}(k)\) organization analysis show that patients relapsing to AF present lower AA organization than those resulting in NSR after 4 weeks. This observation agrees with findings reported in other works, such as: (1) the higher the AA organization, the higher the success rates in AF cardioversion [36], (2) the higher the level of AA organization, the lower the energy required for successful cardioversion [7], and (3) paroxysmal AF requires lower energy for cardioversion than persistent AF [22]. Regarding the organization analysis of \({\bf C}_{m_{\rm AA}}(2^{m_{\rm AA}-1}k),\) the wavelet coefficients vector contains the similarity evolution through time between the analyzed signal and the scaled mother wavelet. A high regularity value in this time series indicates constant waveform 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 [30] 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.

With respect to the patients database, the leave-one-out cross validation showed that SampEn threshold variations were lower than 2% when each recording was excluded in the predictive capability evaluation. However, a wider database would be necessary for a deeper assessment of this new strategy and to evaluate the repeatability of these results which, on the other hand, are in agreement with those obtained through invasive recordings [7, 36], because they suggest that the lower the AA organization, the higher the likelihood of AF recurrence.

In previous works, several clinical, electrophysiological, and demographic features, such as the AF duration [10], the type of underlying disease [11], patient age [10], LAD [11, 17], left ventricular function, and the continuation of therapy with antiarrhythmic drugs [28], have been proposed as predictors of successful AF cardioversion and sinus rhythm maintenance. But the predictive value of these parameters is far from optimal. In fact, in this study, the LAD analysis did not show significative differences between patients who relapsed to AF and resulted in NSR. Regarding the DAF, its results showed a limited ability to identify patients who will relapse to AF. These outcomes disagree with the obtained by Bollman et al. [5] and Holmqvist et al. [19], but are in agreement with those reported by Meurling et al. [26], although in this last work, patients without anti-arrhythmic drugs were studied.

Regarding the explicit analysis of AF organization, Holmqvist et al. [18] evaluated a parameter obtained from time–frequency analysis of the atrial signals, such as harmonic decay. This parameter was designed to be an index of the waveform shape (and indirectly organization) of the atrial component in the ECG, but a low number of patients relapsing to AF were correctly identified (47%, 14 out of 30). In [4], ventricular rhythm was analyzed using 3-D RR intervals plots, quantifying clustering of 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 out of 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. [39] examined a variety of wavelet transform-based statistical markers as potential candidates to predict the post-cardioversion patient status after 1 month following ECV, and 88% (15 out of 17) sensitivity and 100% (13 out of 13) specificity was obtained. Zohar et al. [40] 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. [23] 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 was obtained after the first 2 weeks following ECV.

Finally, this study also presents some limitations. First, the number of analyzed cardioversions was not very large and, therefore, the presented results must be considered with caution. A wider data set allowing a more rigorous statistical analysis should be required in order to provide confidence in the robustness of the method. Second, only lead V 1 was analyzed, thus rejecting the possible information contained in the remaining leads. However, for this type of studies, lead V 1 seems to be the most suitable because Husser et al. [20] showed, with persistent AF patients, a significative correlation between the atrial frequency obtained from this lead and those obtained from atrial electrograms. Finally, although AF recurrence is common during the first 2 weeks following ECV, 40–60% of cardioverted patients revert back to AF within 3 months and around 60–80% within 1 year [24]. Therefore, a wider database containing patients who resulted in NSR and relapsed to AF after 3, 6, and 12 months following ECV, would be necessary.

5 Conclusions

The presented results show that organization analysis, both in time and wavelet domains, together with their suitable combination, are promising candidates in the prediction of successful cardioversion and NSR maintenance in cardioverted AF patients. The prediction accuracy of these techniques has been superior to previously described non-invasive studies. Additionally, the dominant atrial frequency and the left atrium diameter were also studied, and their discriminatory ability was lower than those obtained with the proposed organization analysis. Nevertheless, further studies are required to reliably determine the robustness of these analysis and the repeatability of the obtained results on wider databases.