**3. Time course of the P-wave variability**

#### **3.1. Time characterization of the P-wave**

The variability of features from the P-wave time course before the onset of PAF has started to be studied very recently through a new alternative able to assess time diversity of the P-wave features from single-lead ECG recordings [25]. The method has demonstrated that the P-wave features presented an increasing variability as PAF onset approximates, thus suggesting intermittently disturbed conduction in the atrial tissue. Indeed, it is able to assess the risk of arrhythmia one hour before its onset, thus being a significant advance in the early prediction of the risk of PAF with clinical usefulness [25].

The method can be decomposed in various steps. Firstly, because no standard definition of the P-wave fiducial points can be found in the literature, the P-wave onset and offset were determined by an automatic delineator [37]. It is important to note that the delineator had the ability to deal also with ectopic beats in the same way as with normal beats [37]. Therefore, Pwave fiducial points that originated from APCs were automatically detected without any additional requirement.

After its delineation, several P-wave time features were defined as potential indicators that might be of interest for PAF onset prognosis in a beat-to-beat way, as shown in Fig. 3. To this respect, the P-wave duration was defined as the distance between its offset and onset, i.e.,

Recent Advances in the Noninvasive Study of Atrial Conduction Defects Preceding Atrial Fibrillation http://dx.doi.org/10.5772/60729 33

$$\mathbf{P}\_{\text{dur}} = \mathbf{P}\_{\text{off}} - \mathbf{P}\_{\text{on}}.\tag{1}$$

**Figure 3.** Visual description of the chosen parameters to characterize P-wave time features and assess its time course variation.

Previous works have demonstrated that increased P-wave duration can be considered as an indicator of increased risk of AF [11, 38, 39, 40]. In a similar way, the P-wave morphology measured from lead V1 has also shown ability to stratify the AF risk [41]. Hence, the duration of the P-wave initial and terminal portions was considered as the distances between its peak and the P-wave onset (Pini) and offset (Pter), respectively. Therefore, these features were defined as

$$\mathbf{P}\_{\rm lin} = \mathbf{P}\_{\rm k} - \mathbf{P}\_{\rm on} \tag{2}$$

and

were considered as atrial, whereas those altering more than ±30% of that value were considered as ventricular. In [35], a morphological comparison among potential ectopic and normal beat was also considered. Finally, ectopic beats were considered as those with a QRS morphology similar to normal beats. In a similar line, Schreier et al. [36] considered that those beats with a very different morphology compared to their neighbors could cause the onset of PAF. On the other hand, symbolic analysis was applied to the RR series to identify acceleration and decelerations in the heart rate and associate them with the onset of PAF. Finally, Hickey et al. [32] identified APCs by using an algorithm based on two steps. First, a beat was flagged as a suspected APC if the RR interval preceding it was 15% shorter than a defined local moving average of the surrounding RR intervals. In the second stage, the area, width, and amplitude of the QRS were computed. If all these parameters differed more than 10% from a normal beat, they were confirmed as APCs. The first 100 beats from a regular sinus rhythm were used to compute the parameters associated with normal beats. This algorithm is based on the fact that ventricular ectopics present morphologies very different from normal beats. Although the accuracy of this algorithm to identify ECG intervals immediately before the onset of PAF was slightly lower than those presented by Thong et al.'s algorithm, its combination with infor‐ mation obtained from the RR series spectral analysis yielded a better outcome (i.e., an accuracy around 98%) [32]. Indeed, subjects with imminent PAF showed to have highly correlated lowfrequency and high-frequency components in their heart rate. Thus, the authors suggested that sympathetic and parasympathetic autonomic activity may be coupled in these subjects [32].

The variability of features from the P-wave time course before the onset of PAF has started to be studied very recently through a new alternative able to assess time diversity of the P-wave features from single-lead ECG recordings [25]. The method has demonstrated that the P-wave features presented an increasing variability as PAF onset approximates, thus suggesting intermittently disturbed conduction in the atrial tissue. Indeed, it is able to assess the risk of arrhythmia one hour before its onset, thus being a significant advance in the early prediction

The method can be decomposed in various steps. Firstly, because no standard definition of the P-wave fiducial points can be found in the literature, the P-wave onset and offset were determined by an automatic delineator [37]. It is important to note that the delineator had the ability to deal also with ectopic beats in the same way as with normal beats [37]. Therefore, Pwave fiducial points that originated from APCs were automatically detected without any

After its delineation, several P-wave time features were defined as potential indicators that might be of interest for PAF onset prognosis in a beat-to-beat way, as shown in Fig. 3. To this respect, the P-wave duration was defined as the distance between its offset and onset, i.e.,

**3. Time course of the P-wave variability**

**3.1. Time characterization of the P-wave**

32 Abnormal Heart Rhythms

of the risk of PAF with clinical usefulness [25].

additional requirement.

$$\mathbf{P}\_{\text{tor}} = \mathbf{P}\_{\text{off}} - \mathbf{P}\_{\text{k}} \,. \tag{3}$$

Moreover, the P-wave asymmetry was estimated by computing the ratio between the duration of its initial and terminal portions [42], i.e.,

$$\mathbf{P}\_{\rm asy} = \frac{\mathbf{P}\_{\rm ter}}{\mathbf{P}\_{\rm ind}}.\tag{4}$$

On the other hand, conduction time from the sinus node to the ventricles defines the PR interval. Thus, this interval contains information about different specific places of the atria [43]. In fact, prolongation of the PR interval has been associated with increased risk of AF in the Framingham Heart Study [43, 44]. This fact motivated the measurement of this interval from three different ways, considering the time from the onset, the peak, and the offset of the Pwave up to the R peak. This can be mathematically defined as

$$\mathbf{PR}\_{\text{on}} = \mathbf{R} - \mathbf{P}\_{\text{on}} \,\prime \tag{5}$$

$$\mathbf{PR}\_{\mathbf{k}} = \mathbf{R} - \mathbf{P}\_{\mathbf{k}'} \tag{6}$$

$$\mathbf{PR}\_{\rm off} = \mathbf{R} - \mathbf{P}\_{\rm off}.\tag{7}$$

Finally, differences between successive P-waves were considered to estimate the P-wave location variability. In this case, three data series were also calculated. Thus, the distances among onset, peak, and offset from the *i* th and *i* + 1 th waves were computed as

$$\mathbf{PP}\_{\rm on} = \mathbf{P}\_{\rm on}^{(l \times 1)} - \mathbf{P}\_{\rm on}^{(l)} \tag{8}$$

$$\mathbf{P} \mathbf{P}\_{\mathbf{k}} = \mathbf{P}\_{\mathbf{k}}^{(\!\!\times 1)} - \mathbf{P}\_{\mathbf{k}}^{(\!\!\times 1)} \tag{9}$$

$$\mathbf{PP}\_{\rm off} = \mathbf{P}\_{\rm off}^{(l+1)} - \mathbf{P}\_{\rm off}^{(l)}.\tag{10}$$

Once all the P-wave time features were defined, they were applied on a database of 24 patients with 24-h Holter ECG recordings. The 120 minutes preceding the onset of PAF from the longest sinus rhythm interval of every patient were extracted and divided into two 60-minute-length intervals. Moreover, a third set of 28 healthy individuals without statistically significant differences in terms of age and gender compared to the PAF patients was also analyzed. Subjects in this control group did not present any previous history of AF or structural heart disease. From each individual, a one-hour-length segment was randomly chosen.

Given the relatively low amplitude of the P-wave in the ECG, to minimize the impulsive noise in results, 10 sample-length blocks from data series for each P-wave metric were considered [25]. In each block, the variability was obtained as the difference between the 90- and 10 quantiles. On the other hand, the electrophysiological alterations occurring in the atria prior to the onset of PAF [39] provoke a great deal of scatter in the variability of the aforementioned P-wave features. To this respect, Pdur variability over time for a healthy subject and intervals far from PAF and close to PAF from a diseased patient are shown in Fig. 4. Then, to reduce the effect of this variability, the expected P-wave feature trend was estimated by means of a linear fitting also shown in Fig. 4. Obviously, the slope *α* of this fitting line provides information about the P-wave variability over time. Whereas positive *α* values indicate an increasing variability, a lower dispersion in the data can be indicative of negative values. Finally, *α* values near zero could be indicative of very reduced variability in the P-wave over time.

on on PR = R P , - (5)

k k PR = R P , - (6)

off off PR = R P . - (7)

on on on PP = P P , <sup>+</sup> - (8)

kk k PP = P P , <sup>+</sup> - (9)

off off off PP = P P . <sup>+</sup> - (10)

Finally, differences between successive P-waves were considered to estimate the P-wave location variability. In this case, three data series were also calculated. Thus, the distances

(i 1) (i)

(i 1) (i)

(i 1) (i)

Once all the P-wave time features were defined, they were applied on a database of 24 patients with 24-h Holter ECG recordings. The 120 minutes preceding the onset of PAF from the longest sinus rhythm interval of every patient were extracted and divided into two 60-minute-length intervals. Moreover, a third set of 28 healthy individuals without statistically significant differences in terms of age and gender compared to the PAF patients was also analyzed. Subjects in this control group did not present any previous history of AF or structural heart

Given the relatively low amplitude of the P-wave in the ECG, to minimize the impulsive noise in results, 10 sample-length blocks from data series for each P-wave metric were considered [25]. In each block, the variability was obtained as the difference between the 90- and 10 quantiles. On the other hand, the electrophysiological alterations occurring in the atria prior to the onset of PAF [39] provoke a great deal of scatter in the variability of the aforementioned P-wave features. To this respect, Pdur variability over time for a healthy subject and intervals far from PAF and close to PAF from a diseased patient are shown in Fig. 4. Then, to reduce the effect of this variability, the expected P-wave feature trend was estimated by means of a linear fitting also shown in Fig. 4. Obviously, the slope *α* of this fitting line provides information about the P-wave variability over time. Whereas positive *α* values indicate an increasing variability, a lower dispersion in the data can be indicative of negative values. Finally, *α* values

disease. From each individual, a one-hour-length segment was randomly chosen.

near zero could be indicative of very reduced variability in the P-wave over time.

among onset, peak, and offset from the *i* th and *i* + 1 th waves were computed as

34 Abnormal Heart Rhythms

**Figure 4.** Typical P-wave duration variability over time from (a) a healthy individual and from ECG intervals (b) close to PAF and (c) far from PAF for a diseased patient.

Receiver operating characteristic (ROC) curves were used to obtain discriminative thresholds between the patient groups. For each P-wave feature, optimal thresholds were selected as those values of *α* minimizing the classification error. In the end, a stepwise discriminant analysis (SDA) was performed with the objective of improving the patient group classification.

Interestingly, for all the studied metrics, significant differences among sets were noticed, although the features measuring P-wave duration showed the most remarkable trends. Regarding the classification performance, apart from Pter, metrics associated with the P-wave duration reported a higher predictive ability than the other single parameters (see Table 1). Indeed, 84.21% of all the analyzed patients were correctly identified by Pdur, providing among healthy subjects and PAF patients and among ECG intervals far from PAF and close to PAF accuracy values of 90.79% and 83.33%, respectively (see Fig. 5). The metric estimating the PP rhythm constituted a second set of predictive power. A global accuracy around 70% was

**Figure 5.** Classification into healthy subjects (group C), patients far from PAF (group B), and patients close to PAF (group A) making use of the P-wave duration time course.

provided by all of them, with more than 65% of the cross-validated grouped cases appropri‐ ately classified. Moreover, the RR series variability showed a classification performance very similar to PPk and also it provided almost identical statistical differences among patients. In fact, for the three studied groups, correlation between these metrics was 0.98, 0.92, and 0.84, respectively. Finally, the most reduced ability to identify patient groups was provided by the metrics associated with the PR interval. Nevertheless, PRon provided an accuracy close to the metrics computed from the PP series.


**Table 1.** Percentage of ECG segments correctly classified for each group from the slope *α* obtained for each studied time P-wave feature. The table also shows the global accuracy (GAcc) and cross-validation (CV) results.

On the other hand, the SDA revealed an improved classification among patients from a discriminant model constructed by the combination of Pdur and PPk. To this respect, as can be seen in Table 1 and Fig. 6, 92.10% of the analyzed patients were properly classified, 90.79% of cross-validated grouped cases being correctly discerned. Therefore, an increase of around 8% in the accuracy was reached in comparison with Pdur. Moreover, this model was also able to discern 96.05% of healthy subjects from patients suffering from PAF with a false-positive rate lower than 4%, such as can be observed in Fig. 6.

provided by all of them, with more than 65% of the cross-validated grouped cases appropri‐ ately classified. Moreover, the RR series variability showed a classification performance very similar to PPk and also it provided almost identical statistical differences among patients. In fact, for the three studied groups, correlation between these metrics was 0.98, 0.92, and 0.84, respectively. Finally, the most reduced ability to identify patient groups was provided by the metrics associated with the PR interval. Nevertheless, PRon provided an accuracy close to the

**Figure 5.** Classification into healthy subjects (group C), patients far from PAF (group B), and patients close to PAF

C B A Patient Group

Pdur 100.0% (28/28) 70.83% (17/24) 79.17% (19/24) 84.21% (64/76) 82.89% (63/76) Pini 67.86% (19/28) 70.83% (17/24) 79.17% (19/24) 72.37% (55/76) 72.37% (55/76) Pter 89.29% (25/28) 16.67% (4/24) 83.33% (20/24) 64.47% (49/76) 61.84% (47/76) Pasy 96.43% (27/28) 66.67% (16/24) 75.00% (18/24) 80.26% (61/76) 78.94% (60/76) PRk 89.29% (25/28) 45.83% (11/24) 50.00% (12/24) 63.16% (48/76) 60.53% (46/76) PRon 85.71% (24/28) 58.33% (14/24) 62.50% (15/24) 69.74% (53/76) 68.42% (52/76) PRoff 78.57% (22/28) 37.50% (9/24) 58.33% (14/24) 59.21% (45/76) 60.53% (46/76) PPk 82.14% (23/28) 58.33% (14/24) 70.83% (17/24) 71.05% (54/76) 69.74% (53/76) PPon 82.14% (23/28) 45.83% (11/24) 75.00% (18/24) 68.42% (52/76) 67.11% (51/76) PPoff 89.29% (25/28) 33.33% (8/24) 87.50% (21/24) 71.05% (54/76) 69.74% (53/76) RR 82.14% (23/28) 45.83% (11/24) 70.83% (17/24) 67.11% (51/76) 65.79% (50/76) SDA (Pdur, PPk) 100.0% (28/28) 83.33% (20/24) 91.67% (22/24) 92.10% (70/76) 90.79% (69/76)

**Table 1.** Percentage of ECG segments correctly classified for each group from the slope *α* obtained for each studied

time P-wave feature. The table also shows the global accuracy (GAcc) and cross-validation (CV) results.

**ECGs close to PAF GAcc** CV

metrics computed from the PP series.

**Feature Healthy Subjects ECGs far from**

0.15

36 Abnormal Heart Rhythms

0.10

for Pdur

0.05

0

(group A) making use of the P-wave duration time course.

Th1=0.0091

Th2=0.0398

**PAF**

**Figure 6.** Classification into healthy subjects, patients far from PAF, and patients close to PAF making use of the dis‐ criminant model based on the parameters Pdur and PPk. Each dotted line represents optimal discrimination thresh‐ olds between groups.

These outcomes agree with previous findings showing that prolongation of the P-wave duration is associated with history of AF [15, 38, 45, 46, 47]. Moreover, it is also worth noting that a relevant correlation between P-wave duration variability and the longest duration of the right atrial activation registered on electrograms has been previously documented [48]. Nonetheless, both for discerning among healthy subjects and PAF patients [49] and among ECG segments far from PAF and close to PAF, the beat-to-beat P-wave variability analysis over time has revealed higher discriminant ability than previous works.

The P-wave duration reflected on the ECG can be considered as the overlapped result of two effects [42]: (i) its prolongation due to the decrease in atrial conduction velocity and (ii) its shortening due to overlapping between atrial depolarization and possible premature atrial repolarization, as a result of decreased refractory period. Given that the patients prone to AF manifest a heterogeneous combination of both effects [42, 2], the observed higher P-wave duration variability preceding the onset of PAF can be considered as a natural consequence feasible to be expected. A similar behavior could also be expected for the PR interval variability over time, because that variability could reflect alterations in atrial depolarization and delays in atrioventricular node conduction. Anyway, although both parameters showed the same behavior, it has to be remarked that the P-wave duration variability was a better predictive marker. Moreover, any of the three estimates of the PR interval reported a classification higher than 70%. Nonetheless, statistically significant differences among groups were revealed by the three metrics, thus agreeing with previous works which have addressed the susceptibility to spontaneous AF [50] and post-coronary bypass surgery AF [51].

On the other hand, the notable correlation between the series of RR and PP merits special attention. This result suggests that similar information is provided by both series. However, in comparison with healthy subjects, the correlation for PAF patients was lower, thus sug‐ gesting that some information differences are revealed in this case. These differences between PP and RR series may be related to the P-wave variability before the onset of PAF, such as the aforementioned. As a consequence, the assessment of the PP series instead of the RR series is recommended to estimate the risk of PAF onset.

In recent years, a wide variety of previous works have analyzed the RR series preceding the onset of PAF to predict this event [52, 32, 53, 54, 55, 56, 57]. Whereas typical time and frequency measurements on the RR time series provided not to be relevant markers of the onset of PAF, the identification of a decreased heart rate complexity has proven ability to identify that event [52, 53, 54]. Entropy metrics such as approximate entropy and sample entropy have been mainly used to analyze RR complexity. However, the result provided by these metrics is in contrast with the previously presented increasing trend in the PP series variability. This contradictory outcomes could be justified by an incorrect use of the entropy metrics. In previous works, a notable effect of spikes on entropy metrics has been reported [58], and the increasing presence of APCs before the onset of PAF is a notable source of spikes in RR series [53]. Anyway, additional studies are required to validate this hypothesis.

On the other hand, although many studies quantifying RR complexity have presented a higher ability to predict the onset of PAF than the metrics based on PP series, they had to combine a wide variety of different indices by using very complex classifiers. To this respect, artificial neural networks, self-organization maps, support vector machines, or linear discriminant classifiers have been introduced in different studies [32, 55, 56, 57]. Obviously this kind of metrics combination hinders the direct and clinical interpretation of the results, thus obstruct‐ ing the possibility to be used in daily clinical routine. On the contrary, the beat-to-beat P-wave variability analysis has revealed a simple discriminant model based on the combination of two clearly interpretable metrics such as Pdur and PPk [25]. Indeed, the discriminant model suggests that the presence of a high P-wave duration and rhythm variability over time is indicative of a high risk of the onset of PAF.

#### **3.2. Morphological characterization of the P-wave**

Factors such as right and left atrial depolarization as well as the shape and size of atrial chambers determine the P-wave morphology [9]. Therefore, alterations in the P-wave mor‐ phology can be indicative of a disrupting atrial conduction [11]. Within this context, recent works have focused on quantifying the P-wave morphological variability during the two hours preceding the onset of PAF [26]. In this case, a wider database composed of 48 Holter record‐ ings from PAF patients and 53 healthy individuals, age and gender matched, has been considered [26]. As in [25], the longest sinus rhythm interval in the recording from each patient was selected and the two-hour segment preceding the onset of PAF was analyzed. The interval under study was divided into two one-hour-length segments. Additionally, an ECG segment of one hour in length was randomly chosen from the Holter recording of each healthy subject.

feasible to be expected. A similar behavior could also be expected for the PR interval variability over time, because that variability could reflect alterations in atrial depolarization and delays in atrioventricular node conduction. Anyway, although both parameters showed the same behavior, it has to be remarked that the P-wave duration variability was a better predictive marker. Moreover, any of the three estimates of the PR interval reported a classification higher than 70%. Nonetheless, statistically significant differences among groups were revealed by the three metrics, thus agreeing with previous works which have addressed the susceptibility to

On the other hand, the notable correlation between the series of RR and PP merits special attention. This result suggests that similar information is provided by both series. However, in comparison with healthy subjects, the correlation for PAF patients was lower, thus sug‐ gesting that some information differences are revealed in this case. These differences between PP and RR series may be related to the P-wave variability before the onset of PAF, such as the aforementioned. As a consequence, the assessment of the PP series instead of the RR series is

In recent years, a wide variety of previous works have analyzed the RR series preceding the onset of PAF to predict this event [52, 32, 53, 54, 55, 56, 57]. Whereas typical time and frequency measurements on the RR time series provided not to be relevant markers of the onset of PAF, the identification of a decreased heart rate complexity has proven ability to identify that event [52, 53, 54]. Entropy metrics such as approximate entropy and sample entropy have been mainly used to analyze RR complexity. However, the result provided by these metrics is in contrast with the previously presented increasing trend in the PP series variability. This contradictory outcomes could be justified by an incorrect use of the entropy metrics. In previous works, a notable effect of spikes on entropy metrics has been reported [58], and the increasing presence of APCs before the onset of PAF is a notable source of spikes in RR series

On the other hand, although many studies quantifying RR complexity have presented a higher ability to predict the onset of PAF than the metrics based on PP series, they had to combine a wide variety of different indices by using very complex classifiers. To this respect, artificial neural networks, self-organization maps, support vector machines, or linear discriminant classifiers have been introduced in different studies [32, 55, 56, 57]. Obviously this kind of metrics combination hinders the direct and clinical interpretation of the results, thus obstruct‐ ing the possibility to be used in daily clinical routine. On the contrary, the beat-to-beat P-wave variability analysis has revealed a simple discriminant model based on the combination of two clearly interpretable metrics such as Pdur and PPk [25]. Indeed, the discriminant model suggests that the presence of a high P-wave duration and rhythm variability over time is indicative of

Factors such as right and left atrial depolarization as well as the shape and size of atrial chambers determine the P-wave morphology [9]. Therefore, alterations in the P-wave mor‐

[53]. Anyway, additional studies are required to validate this hypothesis.

spontaneous AF [50] and post-coronary bypass surgery AF [51].

recommended to estimate the risk of PAF onset.

38 Abnormal Heart Rhythms

a high risk of the onset of PAF.

**3.2. Morphological characterization of the P-wave**

In order to define the morphological features able to characterize the P-waves, it has to be considered that previous works have suggested that inhomogeneous intra-atrial and intera‐ trial electrical conduction predisposes to the development of AF [42, 16]; therefore, maximum and minimum conduction velocities during the atrial depolarization were estimated as [42]

$$\nu\_{\text{max}} = \max\_{n=2,3,\dots,L} \left( \tilde{w}\left\lceil n \right\rceil - \tilde{w}\left\lceil n-1 \right\rceil \right) \qquad \text{and} \tag{11}$$

$$\nu\_{\text{min}} = \min\_{u=2,3,\dots,L} \left( \tilde{w}\left[ \boldsymbol{n} \right] - \tilde{w}\left[ \boldsymbol{n} - 1 \right] \right),\tag{12}$$

respectively, *w*˜ *<sup>n</sup>* being each individual sample of the P-wave. Moreover, the dispersion in the propagation velocity during the depolarization process was also obtained as

$$
\nu\_{\text{disp}} = \nu\_{\text{max}} - \nu\_{\text{min}}.\tag{13}
$$

On the other hand, altered and fractionated atrial activity seems to be reflected as the appear‐ ance of bumps in the P-wave normal gaussian shape [15], which could provoke even phase changes in lead V1 [41]. This morphology change was computed by means of the arc length of each P-wave (Pal), i.e.,

$$P\_{\rm al} = \sum\_{n=2}^{L} \sqrt{1 + \left(\tilde{w}\left[\left.n\right] - \tilde{w}\left[\left.n-1\right]\right]\right)^2} \,. \tag{14}$$

This metric is able to discern between two waves with the same duration but different morphologies (see Fig. 7), because it computes the rectified P-wave length. In fact, in this figure, a notably longer arc length can be observed for the wave with abnormal morphology than for those with a normal waveform.

On the other hand, the P-wave amplitude has been widely analyzed in previous works. Indeed, various authors have suggested a relationship between this metric and the electrical mass depolarized in each atrial beat, thus showing a significant decrease after pulmonary vein ablation [59] and external electrical cardioversion [14]. Overall, several metrics to quantify this

**Figure 7.** Representative P-waves showing different morphologies but similar lengths. As can be observed, the P-wave arc length is able to discern between the two different morphologies.

amplitude have been proposed in the literature [26]. To this respect, two robust parameters are based on computing the normalized root mean square value and the area of the P-wave as

$$\mathbf{P}\_{\text{nrms}} = \sqrt{\frac{1}{L} \sum\_{n=1}^{L} \tilde{w} \left[ n \right]^2} \quad \text{and} \tag{15}$$

$$P\_{\text{area}} = \sum\_{n=1}^{L} \left| \tilde{w} \left[ \begin{array}{c} n \\ \end{array} \right] \right| \tag{16}$$

respectively. Finally, to avoid the effect of the P-wave duration on its amplitude, both param‐ eters have been also normalized as follows:

$$\mathbf{P\_{n energy}} = \frac{\mathbf{P\_{n rms}}^2}{\mathbf{P\_{al}}}, \quad \mathbf{P\_{narea}} = \frac{\mathbf{P\_{area}}}{\mathbf{P\_{al}}} \tag{17}$$

The variability of these parameters over the one-hour-length recordings was estimated in the same way as in the previous subsection. However, the performance of each single-parameter variability to discriminate between ECG segments far from and close to PAF and healthy subjects was evaluated by means of a stratified 2-fold cross-validation. The results are summarized in Table 2. In this case, more than 82% of the healthy subjects were identified by all the metrics. Additionally, Pal and Parea discerned between ECG intervals far from PAF and close to PAF with a accuracy greater than 60% and 70%, respectively. Thus, the greatest global accuracy around 80% was reached by the P-wave arc length, also presenting accuracy values of 94.48% and 86.96% among healthy individuals and PAF patients and among ECG intervals far from PAF and close to PAF, respectively. The second highest discriminant ability was presented by the P-wave area, which reported a global accuracy slightly higher than 75% in the test sets.


**Table 2.** Percentage of ECG segments correctly classified for each group from the slope *α* obtained for each studied morphological P-wave feature.

amplitude have been proposed in the literature [26]. To this respect, two robust parameters are based on computing the normalized root mean square value and the area of the P-wave as

**Figure 7.** Representative P-waves showing different morphologies but similar lengths. As can be observed, the P-wave

2

é ù å ë û % (15)

Pal = 109 ms Pal = 176 ms

Duration = 108 ms

*w n*é ù å ë û % (16)

P = ,P = P P (17)

=1 <sup>1</sup> P = and *L n w n*

> =1 P= , *L n*

> > 2

nenergy narea

respectively. Finally, to avoid the effect of the P-wave duration on its amplitude, both param‐

nrms area

P P

al al

The variability of these parameters over the one-hour-length recordings was estimated in the same way as in the previous subsection. However, the performance of each single-parameter variability to discriminate between ECG segments far from and close to PAF and healthy subjects was evaluated by means of a stratified 2-fold cross-validation. The results are summarized in Table 2. In this case, more than 82% of the healthy subjects were identified by all the metrics. Additionally, Pal and Parea discerned between ECG intervals far from PAF and close to PAF with a accuracy greater than 60% and 70%, respectively. Thus, the greatest global accuracy around 80% was reached by the P-wave arc length, also presenting accuracy values of 94.48% and 86.96% among healthy individuals and PAF patients and among ECG intervals far from PAF and close to PAF, respectively. The second highest discriminant ability was presented by the P-wave area, which reported a global accuracy slightly higher than 75% in

*L*

area

nrms

Pal = 97 ms Pal = 182 ms

arc length is able to discern between the two different morphologies.

40 Abnormal Heart Rhythms

Duration = 96 ms

eters have been also normalized as follows:

the test sets.

Moreover, a decision tree was assembled to investigate non-monotonic relationships among single parameters, thus improving group classification. This tree showed that the optimal combination of parameters was also achieved by the P-wave arc length and area. Figure 8 shows the obtained decision tree. As can be observed, low P-wave area variability identified healthy individuals. On the contrary, increasing variability in P-wave area and arc length over time was observed when the onset of PAF approximated. Thus, a classification improvement around 6% and 10% was reached by this classifier, respectively. In fact, the three considered patient groups were classified with accuracies of 95.42%, 79.29%, and 83.98%, respectively, the global accuracy being around 86%. Additionally, healthy subjects and PAF patients were discerned with an accuracy of 95.42% and false-positive rate around 5%.

**Figure 8.** Decision tree generated from the learning sets to classify ECG segments from healthy subjects, far from PAF and close to PAF.

By considering these results, the analysis of the P-wave morphological variability over time could be considered as a useful tool to anticipate PAF. More concretely, the rectified Pwave length variability over time provided the highest statistical differences between groups of ECG segments and the best classification results from all the analyzed P-wave morpho‐ logical features. As for the time P-wave features, higher morphological variability was observed when the onset of PAF approximated. This finding is in line with the atrial alterations preceding the onset of PAF, which eventually will provoke an intermittently disrupted electrical conduction [39].

Other authors have also suggested a greater P-wave morphology alteration when AF onset approximates. Thus, by using a P-wave modeling based on the addition of gaussian functions, more fragmented atrial depolarizations have been observed in patients with greater risk of AF development [15]. Similarly, the P-wave modeling based on singular value decomposition [60] or wavelet analysis [61] has also reported a higher P-wave complexity in patients developing AF after coronary artery bypass grafting compared to those who maintained normal sinus rhythm. Finally, making use of the P-wave spectral turbulence analysis, Barbosa et al. [62] have found a direct relationship between the probability of AF recurrence after electrical cardio‐ version and the P-wave fragmentation. However, it has to be remarked that such a kind of analysis was not proposed to study the beat-to-beat P-wave morphological alterations.

Regarding the P-wave energy, other works have reported higher energy values for PAF patients than for healthy subjects in the signal-averaged P-wave [17]. Similarly, within PAF patients, higher energy values have been observed in those patients with an increased number of episodes [16]. Moreover, a P-wave energy reduction after pharmacological treatment with antiarrhythmic drugs has also been corroborated by several authors [14]. Because these drugs can enlarge the refractory period without altering conduction velocity, this metric has been proposed as a noninvasive marker of atrial refractoriness [14]. According to this finding, parameters such as Parea, Pnrms, Pnenergy, and Pnarea reported high variability over time. However, it is noteworthy that the P-wave energy has been computed in frequency [17] or wavelet [16] domains in the aforementioned previous work.

On the other hand, it is interesting to note that only the number of gaussian functions to appropriately fit this model to the signal-averaged P-wave was studied in [15]. Moreover, only spatial diversity between the acquired 32 leads was considered by comparing the obtained results from each other. Nonetheless, a similar P-wave modeling in a wave-to-wave fashion with a single gaussian function has also been proposed to analyze P-wave variability over time [27]. In order to quantify their morphology, each P-wave was modeled by a gaussian function defined as

$$\hat{w}\left[\boldsymbol{n}\right] = \boldsymbol{A} \cdot \boldsymbol{e}^{-\left(\frac{\boldsymbol{n}-\boldsymbol{C}}{\boldsymbol{W}}\right)^{2}}\,,\tag{18}$$

where the constants *A*, *C*, and *W* represent its amplitude, time position, and width, respec‐ tively. To compute these parameters, the gaussian function *w* ^ *<sup>n</sup>* was fitted to every single Pwave by a nonlinear least squares approach [27].

On the other hand, previous works have proved that a normal P-wave resembles a gaussian shape [63]. However, altered and fractionated atrial electrical activity seems to be reflected in the appearance of bumps in the P-wave [15]. Therefore, higher differences between the real P- wave and its gaussian model could be expected when PAF onset approximates. This P-wave alteration can be assessed by the normalized root mean square error (*ε*) between the real and the gaussian modeled P-wave [27]. As an example, Fig. 9 shows typical cases of P-waves coming from healthy and diseased PAF patients together with their corresponding gaussian modeling. Observe how *ε* is able to represent quite robustly the differences between real and modeled P-waves.

logical features. As for the time P-wave features, higher morphological variability was observed when the onset of PAF approximated. This finding is in line with the atrial alterations preceding the onset of PAF, which eventually will provoke an intermittently

Other authors have also suggested a greater P-wave morphology alteration when AF onset approximates. Thus, by using a P-wave modeling based on the addition of gaussian functions, more fragmented atrial depolarizations have been observed in patients with greater risk of AF development [15]. Similarly, the P-wave modeling based on singular value decomposition [60] or wavelet analysis [61] has also reported a higher P-wave complexity in patients developing AF after coronary artery bypass grafting compared to those who maintained normal sinus rhythm. Finally, making use of the P-wave spectral turbulence analysis, Barbosa et al. [62] have found a direct relationship between the probability of AF recurrence after electrical cardio‐ version and the P-wave fragmentation. However, it has to be remarked that such a kind of analysis was not proposed to study the beat-to-beat P-wave morphological alterations.

Regarding the P-wave energy, other works have reported higher energy values for PAF patients than for healthy subjects in the signal-averaged P-wave [17]. Similarly, within PAF patients, higher energy values have been observed in those patients with an increased number of episodes [16]. Moreover, a P-wave energy reduction after pharmacological treatment with antiarrhythmic drugs has also been corroborated by several authors [14]. Because these drugs can enlarge the refractory period without altering conduction velocity, this metric has been proposed as a noninvasive marker of atrial refractoriness [14]. According to this finding, parameters such as Parea, Pnrms, Pnenergy, and Pnarea reported high variability over time. However, it is noteworthy that the P-wave energy has been computed in frequency [17] or wavelet [16]

On the other hand, it is interesting to note that only the number of gaussian functions to appropriately fit this model to the signal-averaged P-wave was studied in [15]. Moreover, only spatial diversity between the acquired 32 leads was considered by comparing the obtained results from each other. Nonetheless, a similar P-wave modeling in a wave-to-wave fashion with a single gaussian function has also been proposed to analyze P-wave variability over time [27]. In order to quantify their morphology, each P-wave was modeled by a gaussian function

2

è ø é ù <sup>×</sup> ë û (18)

^ *<sup>n</sup>* was fitted to every single P-

*n C*

æ ö - -ç ÷

where the constants *A*, *C*, and *W* represent its amplitude, time position, and width, respec‐

On the other hand, previous works have proved that a normal P-wave resembles a gaussian shape [63]. However, altered and fractionated atrial electrical activity seems to be reflected in the appearance of bumps in the P-wave [15]. Therefore, higher differences between the real P-

ˆ = ,

*<sup>W</sup> wn Ae*

tively. To compute these parameters, the gaussian function *w*

wave by a nonlinear least squares approach [27].

disrupted electrical conduction [39].

42 Abnormal Heart Rhythms

domains in the aforementioned previous work.

defined as

**Figure 9.** Comparison between the obtained gaussian models (dotted line) and representative P-waves (solid line) from typical (a) healthy subjects, (b) patients far from PAF, and (c) patients close to PAF. It has to be remarked that as PAF onset approximates, the root mean square error *ε* increases.

The variability of *A*, *C*, *W* , and *ε* over the one-hour-length recordings was estimated in the same way as before by fitting a linear model to the data in which the fitting slope (*α*) indicated the corresponding variability. The results obtained are summarized in Fig. 10. As was expected, an increased P-wave variability was shown by these parameters when the onset of PAF approximated. To this respect, the time course variability of *W* for typical ECG intervals from the studied groups is displayed in Fig. 11.

From a numerical point of view, the classification results are summarized in Table 3. As can be observed, parameters derived from the P-wave gaussian modeling did not improve the Pdur discriminant ability. However, the metric *W* only presented an accuracy slightly lower (around 3.5%) than the time course variability of the P-wave duration. In addition, a greater global accuracy than the feature PPk was reached by the remaining morphological P-wave features. Thus, improvements around 3.5, 9, and 6% in the global accuracy were obtained from the metrics *A*, *C*, and *ε*, respectively, compared with the PPk. Moreover, it is also interesting to note that a stepwise discriminant analysis provided a global accuracy increase of around 6 and 9% compared with the features Pdur and *W* , respectively. As expected, given that these metrics provided the highest single accuracy, they were combined to produce the optimal discriminant model.

**Figure 10.** Boxplots showing the distribution of the fitting line slope associated to each analyzed parameter from the gaussian modeling of the P-wave for healthy subjects, patients far from PAF, and patients close to PAF.

**Figure 11.** Typical P-wave width *W* variability over time from representative ECG intervals from (a) a healthy subject, (b) patients far from PAF, and (c) patients close to PAF.

Finally, it has to be remarked that other attempts to quantify the P-wave morphology can also be found in the literature. To this respect, a classification rate higher than 90% among P-waves with different morphologies has been reached by means of systems identification in [64]. On the other hand, the AF risk after post-coronary artery bypass grafting has been successfully quantified by analyzing the singular value decomposition of the P-wave morphology [60]. Similarly, Clavier et al. [24] have presented an automatic method based on a hidden Markov model and wavelet transform to detect and delineate the P-wave. Moreover, they also proposed a polynomial characterization of this wave, thus noticing the need of higher orders to represent slight morphological details of the P-wave. Finally, the P-wave energy has also been analyzed by several authors from wavelet and frequency domains [16, 17], providing Pwaves with higher energy when the risk of AF development was increased.


**Table 3.** Percentage of ECG segments correctly classified for each group from the slope *α* obtained for each studied Pwave feature from its gaussian modeling.
