**4.1. Invasive organization methods**

The observation that some degree of organization is present during AF has motivated many investigators to develop algorithms quantifying this degree of organization. Nevertheless, the term *organization* is ambiguous, because of the lack of a standard and common definition within the context of AF. As a consequence, several methods have been proposed to quantify different aspects of AF organization, which are related to different electrophysiological properties or AF mechanisms [49]. According to the number of endocardial recording places involved in the analysis, single-site measurements [50, 51] provide information on the local electrical activity of specific atrial areas, while multi-site algorithms [52–54] introduce the concept of spatial coordination between different regions.

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Hoekstra et al. [57]. They analyzed epicardial mapping data obtained from atrial fibrillation patients undergoing surgical correction of an accessory pathway. The nonlinear applied techniques were correlation dimension and correlation entropy on the epicardial signals. It was found that these measures discriminated between the various types of electrograms as defined by Wells, thus suggesting that nonlinear dynamics plays a relevant role in atrial

Finally, one interesting work quantifying AF organization from single-site measurements was introduced by Faes et al. [9] and relied on wave morphology similarity. The algorithm quantified the regularity of an atrial electrogram by measuring the extent of repetitiveness over time of its consecutive activation waves. Since the analysis was focused on the shape of the waveforms occurring in correspondence to the local activations of the atrial tissue, the morphology of the atrial activations was the element by which the algorithm differentiated among various degrees of AF organization. As an example, Figure 13 plots the local activation waves associated to three different AF episodes with different complexity. As can be seen, the method is able to generate a pattern which, later, can be quantified following the organization criteria. The same team introduced an automatic organization estimation method based on features extraction, selection and classification of the AF patterns [58].

With respect to multi-site measurements, this viewpoint would imply that activity at one site should be judged in relation to the activity at another site. Furthermore, when distances between the recording sites are known, and especially when more than two sites are used to compute the organization, spatial organization concepts are also incorporated into these measures [11]. One interesting comparison of methods for estimating AF synchronization between two atrial sites was published by Sih et al. [53]. In this study, after filtering and scaling short segments (300 ms) of atrial fibrillation, the electrograms were passed through two parallel linear adaptive filters, as shown in Figure 14. One way of interpreting an adaptive filter is that it attempts to predict one electrogram through linear filtering of a second electrogram. If the two electrograms are linearly related, then the prediction process would theoretically be perfect. However, if there are non-linearities between the electrograms, the adaptive filter would yield a prediction error. This algorithm defines organization according to the prediction errors from the parallel adaptive filters. The algorithm was theoretically extensible to account for non-linear relationships between electrograms by simply altering the nature of the adaptive filters. This group used the algorithm to quantify organization differences between acute and chronic models of atrial

Other works have quantified AF organization between two different atrial sites making use of nonlinear techniques. In this way, Censi et al. [60] quantified the duration of stable recurrence patterns through the use of recurrent plots as well as a measure of entropy in the recurrence plots. The authors suggested that there may exist nonlinear relationships between electrograms from the right versus the left atrium that would otherwise be missed

Finally, cardiac mapping tools have brought a wealth of information to cardiac electrophysiology, where the concept of a combined spatial and temporal organization is most easily realized. Within this context, the concept of coupling between several endocardial signal has been introduced. In this respect a two-dimensional analysis by evaluating the simultaneous presence of morphological similarity in two endocardial signals, in order

fibrillation and can also be used to quantify AF organization.

fibrillation [59].

by algorithms relying on linear analyses.

**Figure 13.** Analysis of the local activation waves for AF episodes with different complexity class. From top to bottom, bipolar electrograms of type I, type II, and type III AF following Wells classification. Filled triangles indicate the time of local activation waves detection. On the right panels, superposition of the normalized activation times obtained from the signals of the left panels [9].

Regarding single-site measurements, Wells et al. [55] published one of the earliest studies examining relative differences in atrial fibrillation electrograms. From right atrial bipolar electrograms after open-heart surgery, Wells classified atrial fibrillation recordings into four categories based on the discreteness of the electrograms and the stability of the baseline. However, the greatest weakness of this method is its subjectivity because it requires manual interpretation and over-reading of the epicardial recordings. Nonetheless, later works have implemented automated methods based on these criteria [56]. In this case, the method was based on comparing diverse features of the parameters describing the dynamic, morphological and spectral properties of intraatrial bipolar electrograms during AF. Next, by making use of that parameters an algorithm was designed for automated AF classification.

On the other hand, organization has also been used in the frequency domain. Given that the AF waveform can be effectively analyzed in the frequency domain, as described in Section § 3, some authors have hypothesized that analysis of the spectra of short segments of an interatrial electrogram during AF would show a correlation of the variance of the signal and the amplitude of harmonic peaks with defibrillation efficacy [51]. Furthermore, the same authors hypothesized that the spatiotemporal organization of AF would vary over time and tried to determine the optimal sampling window to optimize defibrillation predictability.

Nonlinear analysis has also been used to evaluate single-site AF electrograms. In this respect one of the first works specifically applied to atrial fibrillation electrograms was introduced by Hoekstra et al. [57]. They analyzed epicardial mapping data obtained from atrial fibrillation patients undergoing surgical correction of an accessory pathway. The nonlinear applied techniques were correlation dimension and correlation entropy on the epicardial signals. It was found that these measures discriminated between the various types of electrograms as defined by Wells, thus suggesting that nonlinear dynamics plays a relevant role in atrial fibrillation and can also be used to quantify AF organization.

16 Atrial Fibrillation

panels [9].

**Figure 13.** Analysis of the local activation waves for AF episodes with different complexity class. From top to bottom, bipolar electrograms of type I, type II, and type III AF following Wells classification. Filled triangles indicate the time of local activation waves detection. On the right panels, superposition of the normalized activation times obtained from the signals of the left

Regarding single-site measurements, Wells et al. [55] published one of the earliest studies examining relative differences in atrial fibrillation electrograms. From right atrial bipolar electrograms after open-heart surgery, Wells classified atrial fibrillation recordings into four categories based on the discreteness of the electrograms and the stability of the baseline. However, the greatest weakness of this method is its subjectivity because it requires manual interpretation and over-reading of the epicardial recordings. Nonetheless, later works have implemented automated methods based on these criteria [56]. In this case, the method was based on comparing diverse features of the parameters describing the dynamic, morphological and spectral properties of intraatrial bipolar electrograms during AF. Next, by making use of that parameters an algorithm was designed for automated AF classification. On the other hand, organization has also been used in the frequency domain. Given that the AF waveform can be effectively analyzed in the frequency domain, as described in Section § 3, some authors have hypothesized that analysis of the spectra of short segments of an interatrial electrogram during AF would show a correlation of the variance of the signal and the amplitude of harmonic peaks with defibrillation efficacy [51]. Furthermore, the same authors hypothesized that the spatiotemporal organization of AF would vary over time and tried to determine the optimal sampling window to optimize defibrillation predictability. Nonlinear analysis has also been used to evaluate single-site AF electrograms. In this respect one of the first works specifically applied to atrial fibrillation electrograms was introduced by Finally, one interesting work quantifying AF organization from single-site measurements was introduced by Faes et al. [9] and relied on wave morphology similarity. The algorithm quantified the regularity of an atrial electrogram by measuring the extent of repetitiveness over time of its consecutive activation waves. Since the analysis was focused on the shape of the waveforms occurring in correspondence to the local activations of the atrial tissue, the morphology of the atrial activations was the element by which the algorithm differentiated among various degrees of AF organization. As an example, Figure 13 plots the local activation waves associated to three different AF episodes with different complexity. As can be seen, the method is able to generate a pattern which, later, can be quantified following the organization criteria. The same team introduced an automatic organization estimation method based on features extraction, selection and classification of the AF patterns [58].

With respect to multi-site measurements, this viewpoint would imply that activity at one site should be judged in relation to the activity at another site. Furthermore, when distances between the recording sites are known, and especially when more than two sites are used to compute the organization, spatial organization concepts are also incorporated into these measures [11]. One interesting comparison of methods for estimating AF synchronization between two atrial sites was published by Sih et al. [53]. In this study, after filtering and scaling short segments (300 ms) of atrial fibrillation, the electrograms were passed through two parallel linear adaptive filters, as shown in Figure 14. One way of interpreting an adaptive filter is that it attempts to predict one electrogram through linear filtering of a second electrogram. If the two electrograms are linearly related, then the prediction process would theoretically be perfect. However, if there are non-linearities between the electrograms, the adaptive filter would yield a prediction error. This algorithm defines organization according to the prediction errors from the parallel adaptive filters. The algorithm was theoretically extensible to account for non-linear relationships between electrograms by simply altering the nature of the adaptive filters. This group used the algorithm to quantify organization differences between acute and chronic models of atrial fibrillation [59].

Other works have quantified AF organization between two different atrial sites making use of nonlinear techniques. In this way, Censi et al. [60] quantified the duration of stable recurrence patterns through the use of recurrent plots as well as a measure of entropy in the recurrence plots. The authors suggested that there may exist nonlinear relationships between electrograms from the right versus the left atrium that would otherwise be missed by algorithms relying on linear analyses.

Finally, cardiac mapping tools have brought a wealth of information to cardiac electrophysiology, where the concept of a combined spatial and temporal organization is most easily realized. Within this context, the concept of coupling between several endocardial signal has been introduced. In this respect a two-dimensional analysis by evaluating the simultaneous presence of morphological similarity in two endocardial signals, in order

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Auricula

Tricuspid Valve

Anterior

1

2

3

4

Antero-Lateral Postero-Lateral Postero-Septal

ρ1 = 0.10

ρ2 = 0.72 ρ3 = 0.65 ρ4 = 0.82

**4.2. Surface organization methods**

Posterior Antero-Septal

and the coupling (*χ*) between pairs of signals recorded on adjacent sites are indicated [49].

episode or the outcome of electrical cardioversion in persistent AF [10].

Septal

χ12 = 0.11 χ23 = 0.72 χ34 = 0.70 Anterior

)a( )b(

**Figure 15.** Example of regularity and coupling indices obtained for endocardial signals recorded by a multipolar basket catheter in the human right atrium during AF. (a) Schematic representation of the internal surface of the right atrium with the position of the sites of bipolar signal acquisition. (b) Endocardial recordings taken during AF, from the four electrodes placed in the postero-lateral wall along with the detected activation times (circles). The regularity index (*ρ*) associated with the four signals

From a clinical point of view, the assessment of AF organization from the standard surface ECG would be very interesting, because it can be easily and cheaply obtained and could avoid the risks associated to invasive procedures [12]. However, only few indirect non-invasive AF organization estimates from this recording have been proposed in the literature. Firstly, the DAF, which has been described in Section § 3. Its inverse has been directly related to atrial refractoriness [64] and, hence, to atrial cycle length [5]. Moreover, it has been suggested that the DAF is directly related to the number of simultaneous wavelets [65]. On the other hand, the second way to get a non-invasive estimate of AF organization has been based on a nonlinear regularity index, such as sample entropy [66]. This index has been proposed to estimate the amount of repetitive patterns existing in the fibrillatory waves from the fundamental waveform of the atrial activity signal, which have been named as main atrial wave (MAW) in the literature. Through the application of sample entropy to the MAW, it has been possible to predict a number of AF-reated events. For example, the onset of paroxysmal AF, its spontaneous termination, its time course from the beginning up to the end of the

Obviously, the drawback of non-invasive organization estimation is the lack of strict accuracy in the process, given that both sample entropy and DAF are only able to assess fibrillatory waves regularity indirectly. However they have been recently validated by comparison with

Coronary Sinus Ostium

Fossa Ovalis

1

2

3

4

1 s

Lateral

**Figure 14.** Example of a multi-site AF organization method based on the application of adaptive filtering to the electrograms under study. If there are nonlinearities between the two electrograms, the adaptive filters would yield a concrete prediction error, thus allowing to quantify the degree of synchronization between the electrograms [53].

to quantify their degree of coupling has been introduced [49]. The method considers the atrial activation times on every recording place and estimates the cross-probability of finding similar local activation waves between the considered recordings places, as shown in Figure 15. On the other hand, Mainardi et al. [54] introduced a comparative study for the analysis among atrial electrical activities in different sites during AF. They characterized the properties of pairs between atrial signals making use of a linear parameter obtained from the cross-correlation function and by a nonlinear association estimator. Furthermore, they also studied synchronization through the application of an index based on the corrected cross-conditional entropy [61]. The most recent advances in the study of propagation patterns in AF have been introduced by Richter and co-workers. They investigated propagation patterns in intracardiac signals using a approach based on partial directed coherence, which evaluated directional coupling between multiple signals in the frequency domain [62]. Furthermore, the same team recently presented an improvement in propagation pattern analysis based on sparse modeling through the use of the partial directed coherence function derived from fitting a multivariate autoregresive model to the observed signal [63].

**Figure 15.** Example of regularity and coupling indices obtained for endocardial signals recorded by a multipolar basket catheter in the human right atrium during AF. (a) Schematic representation of the internal surface of the right atrium with the position of the sites of bipolar signal acquisition. (b) Endocardial recordings taken during AF, from the four electrodes placed in the postero-lateral wall along with the detected activation times (circles). The regularity index (*ρ*) associated with the four signals and the coupling (*χ*) between pairs of signals recorded on adjacent sites are indicated [49].

#### **4.2. Surface organization methods**

18 Atrial Fibrillation

0 300 ms

500


500

500

500

X Y

retliF retliF

Resample Resample

Xfilt Yfilt

XL YL

**Figure 14.** Example of a multi-site AF organization method based on the application of adaptive filtering to the electrograms under study. If there are nonlinearities between the two electrograms, the adaptive filters would yield a concrete prediction

to quantify their degree of coupling has been introduced [49]. The method considers the atrial activation times on every recording place and estimates the cross-probability of finding similar local activation waves between the considered recordings places, as shown in Figure 15. On the other hand, Mainardi et al. [54] introduced a comparative study for the analysis among atrial electrical activities in different sites during AF. They characterized the properties of pairs between atrial signals making use of a linear parameter obtained from the cross-correlation function and by a nonlinear association estimator. Furthermore, they also studied synchronization through the application of an index based on the corrected cross-conditional entropy [61]. The most recent advances in the study of propagation patterns in AF have been introduced by Richter and co-workers. They investigated propagation patterns in intracardiac signals using a approach based on partial directed coherence, which evaluated directional coupling between multiple signals in the frequency domain [62]. Furthermore, the same team recently presented an improvement in propagation pattern analysis based on sparse modeling through the use of the partial directed coherence function

derived from fitting a multivariate autoregresive model to the observed signal [63].

Detrend & Scale

Hanning window

> Linear filter

error, thus allowing to quantify the degree of synchronization between the electrograms [53].

0 300 ms


Linear filter

Hanning window

Detrend & Scale



From a clinical point of view, the assessment of AF organization from the standard surface ECG would be very interesting, because it can be easily and cheaply obtained and could avoid the risks associated to invasive procedures [12]. However, only few indirect non-invasive AF organization estimates from this recording have been proposed in the literature. Firstly, the DAF, which has been described in Section § 3. Its inverse has been directly related to atrial refractoriness [64] and, hence, to atrial cycle length [5]. Moreover, it has been suggested that the DAF is directly related to the number of simultaneous wavelets [65]. On the other hand, the second way to get a non-invasive estimate of AF organization has been based on a nonlinear regularity index, such as sample entropy [66]. This index has been proposed to estimate the amount of repetitive patterns existing in the fibrillatory waves from the fundamental waveform of the atrial activity signal, which have been named as main atrial wave (MAW) in the literature. Through the application of sample entropy to the MAW, it has been possible to predict a number of AF-reated events. For example, the onset of paroxysmal AF, its spontaneous termination, its time course from the beginning up to the end of the episode or the outcome of electrical cardioversion in persistent AF [10].

Obviously, the drawback of non-invasive organization estimation is the lack of strict accuracy in the process, given that both sample entropy and DAF are only able to assess fibrillatory waves regularity indirectly. However they have been recently validated by comparison with

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in Figure 16 where several recordings and the corresponding delineation result have been plotted. As can be observed, the method is able to provide precise and automatic fibrillatory waves delineation, making it possible to quantify non-invasively AF organization in short

The recent advances in signal analysis and processing have provided powerful solutions for the improved knowledge of atrial fibrillation. In this respect, intensive research has been carried out to separate atrial activity from ventricular activity in the ECG and invasive recordings. Furthermore, the proper extraction of an atrial signal has opened the possibilities of developing advanced analysis techniques to gain as much information as possible on the fibrillatory waves. Within this context, relevant information, like the atrial fibrillatory frequency or arrhythmia organization, have been reliably assessed from surface and invasive

This work was supported by projects TEC2010–20633 from the Spanish Ministry of Science and Innovation and PPII11–0194–8121 from Junta de Comunidades de Castilla-La Mancha.

1Biomedical Synergy, Electronic Engineering Department, Universidad Politécnica de

2Innovation in Bioengineering Research Group, University of Castilla-La Mancha, Cuenca,

[1] Andreas Bollmann, Daniela Husser, Luca Mainardi, Federico Lombardi, Philip Langley, Alan Murray, José Joaquín Rieta, José Millet, S. Bertil Olsson, Martin Stridh, and Leif Sörnmo. Analysis of surface electrocardiograms in atrial fibrillation: Techniques,

[2] Leif Sörnmo, Martin Stridh, Daniela Husser, Andreas Bollmann, and S Bertil Olsson. Analysis of atrial fibrillation: from electrocardiogram signal processing to clinical

[3] J Slocum, E Byrom, L McCarthy, A Sahakian, and S Swiryn. Computer detection of atrioventricular dissociation from surface electrocardiograms during wide qrs complex

management. *Philos Transact A Math Phys Eng Sci*, 367(1887):235–53, Jan 2009.

research, and clinical applications. *Europace*, 8(11):911–926, Nov 2006.

tachycardias. *Circulation*, 72(5):1028–1036, 1985.

time.

**5. Conclusions**

**Acknowledgements**

José Joaquín Rieta1,<sup>⋆</sup> and Raúl Alcaraz2

<sup>⋆</sup> Address all correspondence to: jjrieta@upv.es

**Author details**

Valencia, Gandia, Spain

Spain

**References**

recordings using digital signal processing methods.

**Figure 16.** Delineation of the fibrillatory waves for typical 4 second segments corresponding to (a) type I, (b) type II and (c) type III AF episodes, respectively. For each segment, the ECG and atrial activity, after QRST cancellation, are displayed. The upper black circles mark the maximum associated to each activation, whereas lower gray circles indicate their boundaries [70].

invasive recordings [67]. On the other hand, an additional disadvantage of these estimators is that the proper DAF identification in the AA spectral content, computed via the fast Fourier transform, depends significantly on the analyzed segment length, because it determines the spectral resolution [68]. It is advisable that segment length is chosen to be, at least, several seconds for an appropriate DAF identification and to produce an acceptable variance of the frequency estimate [69]. On the other hand, although AF organization could be successfully estimated by analyzing a segment as short as 1 second with sample entropy, the proper MAW obtention depends on an adequate DAF computation [10]. Thereby, it could be considered that the two aforesaid estimators can only yield an average AF organization assessment, thus blurring the possible information carried by each single activation.

One solution to the aforementioned limitations has been recently proposed which is able to quantify directly and in short-time AF organization from the surface ECG. The method quantifies every single fibrillatory wave regularity by measuring how repetitive its morphology is along onward atrial activations [70]. Basically, the atrial activity was delineated through mathematical morphology operators [71]. A combination of erosion and dilation operations was applied to the atrial activity with two structuring elements. The first one was adapted to the fibrillatory waves by an even triangular shape with duration proportional to the DAF. The second was designed as a rectangular shape of length larger to the DAF to suppress the drift between atrial cycles [70]. Finally, the resulting impulsive signal was used to extract atrial activations by peak detection [70]. An example of the potential applications offered by this method, able to work from the surface ECG, is shown in Figure 16 where several recordings and the corresponding delineation result have been plotted. As can be observed, the method is able to provide precise and automatic fibrillatory waves delineation, making it possible to quantify non-invasively AF organization in short time.
