**5.2. HRV analysis during AF**

In order to characterize the chaos degree in the ventricular response during AF, Stein et al. [68] implemented an algorithm that uses nonlinear predictive forecasting for the RR-interval series, predicting its future behavior for a few beats by observing other sufficiently similar trajectories in the phase space [69]. Thus, given a RR-interval, the next interval is predicted as the weighed mean of the RR intervals following the three nearest neighbors (found according to Euclidean distance). Results showed that some patients had RR interval series during AF significantly (although weakly) predictable on very short-term scale. This weak predictability, according to the authors, may represent the effect of cyclic oscillations in vagal and/or sympathetic tone at the level of the AV node.

The aforementioned regularity index presented by Mainardi et al [24] has also been applied to the evaluation of exercise effect on ECG recordings from patients with persistent AF [70]. As the autonomic nervous system plays an important role among the factors influencing ventricular response by modulating refractoriness of the AV node, that is mainly dependent on vagal tone, the purpose of the study was to characterize ventricular response during AF to changes of the autonomic balance induced by exercise. The index, reflecting nonlinear series predictability, tended to increase during exercise. It was found that regularity values were very low compared to SR [71], thus the predictability degree of ventricular response is very small during AF. Nevertheless, taking linear and nonlinear dynamics into account, the index succeeded in underlining the increased predictability of ventricular response during exercise. The results highlighted the relevant activity played by the autonomic nervous system in patients with AF, as time domain parameters decreased and predictability indices increased. On the other hand, note that the same regularity index has also been used in order to assess different characteristics in spontaneous paroxysmal AF termination [71]. Thus, the index tried to discriminate between paroxysmal AF episodes that terminate immediately (within 1 second) and others that were not observed to terminate for the duration of the long-term recording, at least for an hour. Results showed higher regularity values for non-terminating than terminating paroxysmal AF episodes, suggesting in agreement with aforementioned works a decrease in the HRV complexity prior to the SR restoration [58, 59, 61].

Sun and Wang have also presented two different alternatives from the HRV analysis to predict spontaneous termination of paroxysmal AF. Thus, in a first way [72], they characterized RR-interval series and its PP extracting eleven features from statistical and geometric viewpoints, respectively. A sequential forward search algorithm was utilized for feature selection and a fuzzy SVM was applied for AF termination prediction. The second alternative [73] was based on the sign sequence of differences of RR intervals. More precisely, this sequence of differences was transformed into the sign sequence based on a threshold. Next, the complexity of the sign sequence and ShEn of probability distribution of substring length were taken as the features of AF signals. Finally, a fuzzy SVM was used to predict AF termination. Although a notably high diagnostic accuracy was reached by both algorithms, the complex combination of multiple parameters in both cases makes difficult the clinical interpretation of the results. In this sense, clinical meaning of each individual parameter is blurred within the classification approach.

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 al [74].

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].

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

14 Atrial Fibrillation

the development of post-surgery AF [67].

blurred within the classification approach.

**5.2. HRV analysis during AF**

coronary artery bypass graft surgery, larger values of HRV complexity being associated with

In order to characterize the chaos degree in the ventricular response during AF, Stein et al. [68] implemented an algorithm that uses nonlinear predictive forecasting for the RR-interval series, predicting its future behavior for a few beats by observing other sufficiently similar trajectories in the phase space [69]. Thus, given a RR-interval, the next interval is predicted as the weighed mean of the RR intervals following the three nearest neighbors (found according to Euclidean distance). Results showed that some patients had RR interval series during AF significantly (although weakly) predictable on very short-term scale. This weak predictability, according to the authors, may represent the effect of cyclic

The aforementioned regularity index presented by Mainardi et al [24] has also been applied to the evaluation of exercise effect on ECG recordings from patients with persistent AF [70]. As the autonomic nervous system plays an important role among the factors influencing ventricular response by modulating refractoriness of the AV node, that is mainly dependent on vagal tone, the purpose of the study was to characterize ventricular response during AF to changes of the autonomic balance induced by exercise. The index, reflecting nonlinear series predictability, tended to increase during exercise. It was found that regularity values were very low compared to SR [71], thus the predictability degree of ventricular response is very small during AF. Nevertheless, taking linear and nonlinear dynamics into account, the index succeeded in underlining the increased predictability of ventricular response during exercise. The results highlighted the relevant activity played by the autonomic nervous system in patients with AF, as time domain parameters decreased and predictability indices increased. On the other hand, note that the same regularity index has also been used in order to assess different characteristics in spontaneous paroxysmal AF termination [71]. Thus, the index tried to discriminate between paroxysmal AF episodes that terminate immediately (within 1 second) and others that were not observed to terminate for the duration of the long-term recording, at least for an hour. Results showed higher regularity values for non-terminating than terminating paroxysmal AF episodes, suggesting in agreement with aforementioned

oscillations in vagal and/or sympathetic tone at the level of the AV node.

works a decrease in the HRV complexity prior to the SR restoration [58, 59, 61].

Sun and Wang have also presented two different alternatives from the HRV analysis to predict spontaneous termination of paroxysmal AF. Thus, in a first way [72], they characterized RR-interval series and its PP extracting eleven features from statistical and geometric viewpoints, respectively. A sequential forward search algorithm was utilized for feature selection and a fuzzy SVM was applied for AF termination prediction. The second alternative [73] was based on the sign sequence of differences of RR intervals. More precisely, this sequence of differences was transformed into the sign sequence based on a threshold. Next, the complexity of the sign sequence and ShEn of probability distribution of substring length were taken as the features of AF signals. Finally, a fuzzy SVM was used to predict AF termination. Although a notably high diagnostic accuracy was reached by both algorithms, the complex combination of multiple parameters in both cases makes difficult the clinical interpretation of the results. In this sense, clinical meaning of each individual parameter is 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.

Although previous algorithms reached a high classification ability in long heart rate records, their performance was notably reduced for sort data sets. Similar behavior was appreciated for MSE measures [23]. Thus, in long RR time series, when matches abound, entropy metrics can distinguish AF well from SR [23]. However, there is a challenge, though, in assuring a sufficient number of matches when the data sets are short [82]. Thereby, Lake and Moorman [82] optimized the SampEn, developing general methods for the rational selection of the template length *m* and the tolerance matching *r*. The major innovation was to allow *r* to vary so that sufficient matches are found for confident entropy estimation, with conversion of the final probability to a density by dividing by the matching region volume, 2*rm*. The optimized SampEn estimate and the mean heart beat interval each contributed to accurate detection of AF in as few as 12 heartbeats. The final algorithm, called the coefficient of SampEn (COSEn), provided high degrees of accuracy in distinguishing AF from SR in 12-beat calculations performed hourly. The most common errors were atrial or ventricular ectopy, which increased entropy despite SR, and atrial flutter, which can have low or high entropy states depending on dynamics of atrioventricular conduction.

10.5772/53407

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http://dx.doi.org/10.5772/53407

however, that these RR-interval histograms were not stratified for different average heart rates. Nonetheless, authors suggest that PPs with two sectors could hold information of the functional refractory periods of each of the two conduction routes that can present the AV node [87]. Interestingly, the circadian variability of the fast pathway functional refractoriness was more pronounced than that of the slow pathway. More recently, Climent et at [88] have presented a method to automatically detect and quantify preferential clusters of RR-intervals. This method, named Poincaré surface profile (PSP), uses the information of histographic PPs to filter part of the AV node memory effects. PSP detected all RR populations present in RR interval histograms in 55 patients with persistent AF and also 67% additional RR populations. In addition, a reduction of beat-to-beat dependencies allowed a more accurate location of RR populations. This novel PP-based analysis also allowed monitoring of short-term variations of preferential conductions, which was illustrated by evaluating the effects of rate control

The Contribution of Nonlinear Methods in the Understanding of Atrial Fibrillation

Different pathophysiologic processes control heart's behavior during AF in opposite directions, making difficult the understanding of the mechanisms provoking onset, maintenance and termination of this arrhythmia. Nonetheless, the state of the art summarized in the present work suggests that the use of modern methods of nonlinear analysis can facilitate the understanding of cardiovascular function during AF, in a complementary way to the traditional linear techniques. Thus, nonlinear indices have provided robust estimates of AF organization able to reveal information about several aspects of the arrhythmia. In this respect, clinically relevant information related to the arrhythmia state and its progression after pharmacological and electrical cardioversion has been shown by different researches. In addition, nonlinear analysis has shown to play an important role in the analysis of the ventricular response provoked by the arrhythmia, thus being able to reflect cardiovascular autonomic regulation changes before, during and after AF onset.

This work was supported by the projects TEC2010–20633 from the Spanish Ministry of Science and Innovation and PPII11–0194–8121 and PII1C09–0036–3237 from Junta de

1Innovation in Bioengineering Research Group, University of Castilla-La Mancha, Cuenca,

2Biomedical Synergy, Universidad Politécnica de Valencia, Gandía, Spain

drugs on each preferential conduction.

**6. Conclusions**

**7. Acknowledgements**

**Author details**

Spain

Comunidades de Castilla-La Mancha.

Raúl Alcaraz1,<sup>⋆</sup> and José Joaquín Rieta2

<sup>⋆</sup> Address all correspondence to: raul.alcaraz@uclm.es

Finally, Segerson et al [83] showed that measures of short-term HRV during SR correlate with measures of cycle length entropy during paroxysms of AF. More precisely, two measures of short-term HRV in SR, such as the root mean square of the differences between consecutive normal intervals (RMSSD) and the inter-beat correlation coefficient (ICC), correlated with well-established measurements of entropy during AF, such as ShEn and ApEn. Recognizing that RMSSD and ICC are known measures of parasympathetic function in SR, authors' claimed that their results suggest a role for vagal regulation of cycle length entropy during AF.

### **5.4. HRV analysis to characterize the AV node**

During AF, the fibrillatory impulses continuously bombard and penetrate the AV node to varying degrees (concealed conduction), creating appreciable variability on the AV nodal refractoriness [84]. Since the AV node is the structure responsible for the conduction of atrial impulses to the ventricles, the strategy of rate control during AF deals with efforts to utilize and adjust the propagation properties of the node [84]. Characteristics of AV conduction have been widely investigated during the last years by using different techniques and, especially, PP analysis. In this graph, it is possible to identify the lower envelope, which have been used to characterize the functional refractory period and the rate dependence of AV node conduction [85, 86]. In addition, the degree of scatter of the PP, calculated as the root mean square difference of each RR-interval and the lower envelope, has been presented as a measure of concealed conduction in the AV node [86].

By applying PP analysis to 24-h Holter recordings of 48 patients with chronic AF, it was suggested that both AV node refractoriness and the degree of concealed AV conduction during AF may show a circadian rhythm, but also that circadian rhythms may be attenuated in patients with heart failure [86]. These findings point to the possibility of obtaining information concerning altered autonomic control of the RR intervals in patients with AF (and heart failure or other disease) with this simple technique.

On the other hand, Oka et al [87] showed that for some PPs computed from 24-h recordings exhibited two separate sectors of RR intervals. When this occurred, the RR-interval histogram disclosed a bimodal distribution in approximately 40% of patients. It should be noted, however, that these RR-interval histograms were not stratified for different average heart rates. Nonetheless, authors suggest that PPs with two sectors could hold information of the functional refractory periods of each of the two conduction routes that can present the AV node [87]. Interestingly, the circadian variability of the fast pathway functional refractoriness was more pronounced than that of the slow pathway. More recently, Climent et at [88] have presented a method to automatically detect and quantify preferential clusters of RR-intervals. This method, named Poincaré surface profile (PSP), uses the information of histographic PPs to filter part of the AV node memory effects. PSP detected all RR populations present in RR interval histograms in 55 patients with persistent AF and also 67% additional RR populations. In addition, a reduction of beat-to-beat dependencies allowed a more accurate location of RR populations. This novel PP-based analysis also allowed monitoring of short-term variations of preferential conductions, which was illustrated by evaluating the effects of rate control drugs on each preferential conduction.
