**5. Ventricular activity analysis**

Ventricular response during AF has been widely characterized making use of the heart rate variability (HRV) analysis. Although how the autonomic nervous system exactly modulates the heart rate remains an open question, HRV can be used to quantify several aspects of the autonomic heart rate modulation [56]. Standard time and frequency domain methods of HRV are well described by the Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology [57], but they fail to show the dynamic properties of the fluctuations. Therefore, nonlinear methods have been typically applied to the HRV for assessing its variability, scaling and correlation properties, thus providing complementary information to the standard HRV metrics [9]. Within this context, the next subsections summarize how nonlinear indices has been applied to HRV analysis in an attempt to understand cardiovascular autonomic regulation before, during and after AF onset and behavior of the AV node during the arrhythmia.

## **5.1. HRV analysis during SR**

The mechanisms leading to the initiation of AF have been under intensive investigation within the last decade. It has been proposed that the autonomic nervous system might have a role in the initiation of this arrhythmia. Precisely, increased vagal tone can predispose to the development of AF [58]. Thereby, several measures of entropy, such as SampEn and ApEn, together with the DFA have been applied to study the HRV complexity evolution in the minutes preceding spontaneous paroxysmal AF onset. To this respect, Vikman et al [59] studied the DFA and ApEn in 20-minutes intervals before 92 episodes of paroxysmal AF in 22 patients without structural heart disease. A progressive decrease in complexity was observed by both indices before the AF episodes. In addition, they also noticed lower complexity values before the onset of AF compared with values obtained from matched healthy control subjects. In a similar way, Tuzcu et al [58] studied via SampEn the HRV complexity of 30 minutes-length segments containing the ECG immediately preceding a paroxysmal AF episode and 30 minutes-length segments of ECG during a period distant, at least 45 minutes, from any episode of AF. Complexity of the HRV was found to be significantly reduced in the segments preceding AF compared with those distant from any AF occurrence. The same study was repeated, but premature atrial complexes were previously removed. In this case, a less pronounced difference was provided. The authors considered that decreased heart rate complexity, for both cases, reflects a change in cardiovascular autonomic regulation that preconditions AF onset. Additionally, the segments preceding AF onset were divided into three successive 10 minutes periods and analyzed with SampEn in order to show the presence of a possible trend. A decreasing complexity trend towards the onset of AF was observed independently on the presence or absence of ectopics, although in the later case the tendency was less pronounced. According to the authors, the decrease in complexity via SampEn before the onset of AF resulted mainly from 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 [60].

12 Atrial Fibrillation

shown to discriminate among different AF types and to elicit spatial heterogeneities in the synchronization between different atrial sites. Moreover, a comparison of the real data with simulation results linked the different shapes of the time delay distribution, and thus the

Finally, CauEn has been recently used to monitor coupling between temporal variations from two atrial EGMs for paroxysmal and persistent AF episodes [50]. Results showed differences between both atrial chambers with a higher disorganization in the LA than RA in paroxysmal AF patients and a more homogenous behavior along the atria in persistent AF patients. These findings were in strong agreement with the hypothesis that high-frequency periodic sources located in the LA drive AF [55]. Nonetheless, the result may also support the multiple

Ventricular response during AF has been widely characterized making use of the heart rate variability (HRV) analysis. Although how the autonomic nervous system exactly modulates the heart rate remains an open question, HRV can be used to quantify several aspects of the autonomic heart rate modulation [56]. Standard time and frequency domain methods of HRV are well described by the Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology [57], but they fail to show the dynamic properties of the fluctuations. Therefore, nonlinear methods have been typically applied to the HRV for assessing its variability, scaling and correlation properties, thus providing complementary information to the standard HRV metrics [9]. Within this context, the next subsections summarize how nonlinear indices has been applied to HRV analysis in an attempt to understand cardiovascular autonomic regulation before, during and after AF

The mechanisms leading to the initiation of AF have been under intensive investigation within the last decade. It has been proposed that the autonomic nervous system might have a role in the initiation of this arrhythmia. Precisely, increased vagal tone can predispose to the development of AF [58]. Thereby, several measures of entropy, such as SampEn and ApEn, together with the DFA have been applied to study the HRV complexity evolution in the minutes preceding spontaneous paroxysmal AF onset. To this respect, Vikman et al [59] studied the DFA and ApEn in 20-minutes intervals before 92 episodes of paroxysmal AF in 22 patients without structural heart disease. A progressive decrease in complexity was observed by both indices before the AF episodes. In addition, they also noticed lower complexity values before the onset of AF compared with values obtained from matched healthy control subjects. In a similar way, Tuzcu et al [58] studied via SampEn the HRV complexity of 30 minutes-length segments containing the ECG immediately preceding a paroxysmal AF episode and 30 minutes-length segments of ECG during a period distant, at least 45 minutes, from any episode of AF. Complexity of the HRV was found to be significantly reduced in the segments preceding AF compared with those distant from any AF occurrence. The same study was repeated, but premature atrial complexes were previously removed. In this case, a less pronounced difference was provided. The authors considered that decreased heart rate complexity, for both cases, reflects a change in cardiovascular autonomic regulation that

proposed index, to different underlying electrophysiological propagation patterns.

wavelet hypothesis, which have a random movement throughout the atria [5].

**5. Ventricular activity analysis**

**5.1. HRV analysis during SR**

onset and behavior of the AV node during the arrhythmia.

On the other hand, because of paroxysmal AF has been classified into vagally-mediated and sympathetically-mediated types, based on the autonomic profile and the clinical history, Shin et al [61] analyzed the 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 minutes segment of normal sinus rhythm preceding AF onset was divided into 6 periods of 10 minutes. The DFA showed a poor tendency to decrease before the onset of AF and the change of this parameter was divergent according to the AF type. In contrast, ApEn and SampEn revealed a linear decrease of complexity irrespective of AF type. In addition, this result in both ApEn and SampEn before AF onset was not affected whether excluding the ectopic beats or not. In the authors' opinion, the meaning of this progressive entropy 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.

It is interesting note that although nonlinear indices, especially SampEn, have provided to be better predictors than standard HRV measures, their diagnostic ability in paroxysmal AF prediction is far from clinically optimal. Thus, in order to improve their discriminant capability, these nonlinear indices have been combined with other HRV metrics making use of different classification approaches. In this respect, Chesnokov [62] analyzed the combination of spectral features, SampEn and MSE of the HRV by using different artificial intelligent methods. More recently, Mohebbi and Ghassemian have proposed two different combinations of parameters to reach a diagnostic accuracy higher than 95%. Thus, in a first way, they computed a RP of the RR-interval series together with five statistically significant features: recurrence rate, length of longest diagonal segments, average length of the diagonal lines, entropy and trapping time. These parameters were combined making use of a support vector machine (SVM)-based classifier [63]. In the second alternative, a SVM-based classifier was also used to combine spectrum and bispectrum features with SampEn and PP-extracted parameters from the HRV [64].

Finally, several studies have applied nonlinear indices to the HRV after coronary artery bypass graft surgery, i.e. before the onset of AF. Thus, Hogue et al [65] showed that patients who developed AF presented reduced heart rate complexity through ApEn and that standard measures of HRV did not distinguish between these two groups. Logistic regression analysis indicated that only lower complexity via ApEn and higher heart rate were independently associated with AF. In addition, ApEn did not correlate with any other HRV variable, so that the data provide little evidence for a direct relationship between the magnitude of ApEn and the level of autonomic modulation of heart rate. In a similar way, Chamchad et al showed that ApEn provides little complexity in predicting AF after off-pump coronary artery bypass graft surgery [66] and that the CD was independently associated with AF after coronary artery bypass graft surgery, larger values of HRV complexity being associated with the development of post-surgery AF [67].

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On the other hand, Yamada et al [74] analyzed the prognostic significance of ApEn by quantifying intrinsic unpredictability of the RR patterns and found reduced entropy of beat-to-beat fluctuations being predictive of cardiac mortality after adjustment for left ventricular ejection fraction and ischemic etiology of AF. In a similar way, Platonov et al [75] examined the regularity via ApEn of the RR-interval series during AF using short ECG tracings in a subgroup of patients enrolled in the MADIT-II study. However, contrary to the previously mentioned work, ApEn was not predictive of clinical outcome in the MADIT-II subgroup. Nonetheless, there were important differences in the clinical profile of the ischemic patients with congestive heart failure enrolled in the MADIT-II study and the patients with permanent AF with mostly preserved left ventricular ejection fraction studied by Yamada et

The Contribution of Nonlinear Methods in the Understanding of Atrial Fibrillation

Finally, PPs were used to determine the ventricular response to AF and quinidine-induced changes in its variability in an in vivo study in horses [76]. Results showed a distinct shape in the RR-interval series distribution, suggesting that each RR-interval is determined by the previous one. This, together with the demonstration that there was a negative correlation between consecutive RR intervals and that the standard deviation of the mean of RR intervals was reduced as the AF frequency decreases in the course of quinidine administration, supported the suggestion that, although in the long-term the ventricular response may seem unpredictable, in the short term, the beat-to-beat changes in RR intervals follow deterministic laws established by the frequency-dependent conduction properties of the AV node. On the other hand, by adding the number of occurrences of RR-interval pairs, a 3-D PP can be constructed in which clusters of RR intervals can be identified. Interestingly, in AF patients with clustering of RR intervals, ECV was more effective to restore SR, and, of greater clinical

interest, SR persisted for a longer period than in patients without clustering [77].

Automated detection of AF in heart beat interval time series is useful in patients with cardiac implantable electronic devices that record only from the ventricle. To this respect, PPs have been widely applied to the RR-interval series. Thus, Kikillus et al [78] estimated density of points in each segment of PP and calculated an indicator of AF from standard deviation of temporal differences of the consecutive inter-beat intervals. Thuraisingham [79] used a wavelet method to obtain a filtered time series from the input ECG. He calculated the standard deviation of the time series and the standard deviation of successive differences, and the length of the ellipse that characterized the PP. These indicators were used to discriminate AF from SR. Esperer et al [80] analyzed PP of 2700 patients with atrial and/or ventricular tachyarrhythmias and 200 controls with pure SR. Each plot obtained was categorized according to its shape and basic geometric parameters. Thus, results provided that different shapes were associated with AF and SR, both rhythms being accurately distinguished. Finally, Park et al [81] extracted three measures from PP characterizing AF and SR: the number of clusters, mean stepping increment of inter-beat intervals and dispersion of the points around a diagonal line in the plot. They divided distribution of the number of clusters into two, calculated mean value of the lower part by *k*-means clustering method and classified data whose number of clusters was more than one and less than this mean value as SR data. In the other case, they tried to discriminate AF from SR using SVM with the other feature measures: the mean stepping increment and dispersion of the points in the PP.

**5.3. HRV analysis to distinguish between AF and SR**

al [74].
