**3.3. The spectral profile**

The aforementioned spectral analysis techniques had the limitation of only considering the fundamental spectral peak of the atrial activity, but its harmonics have not been put under consideration. However, harmonics could improve DAF estimation and, furthermore, their pattern may be of clinical interest [45]. To alleviate this problem the spectral profile has been proposed [44], its block diagram being depicted in Figure 10. Its main idea is to obtain a time-frequency distribution of successive short segments from the atrial signal. Next, the distribution is decomposed into a spectral profile and a number of parameters

12 Atrial Fibrillation

has been improved notably [39].

STFT analysis [39].

**Figure 9.** Cross Wigner-Ville distribution of the same atrial activity signal presented in Fig. 8. As shown, frequency resolution

that are long compared to the window length [43], but also because it reflected precisely the variations in the DAF [39]. In order to illustrate how the XWVD is able to improve time-frequency analysis in AF, Figure 9 shows the same analyzed lead as in Fig. 8 but, this time, computed via the XWVD. As can be observed, frequency resolution has been improved notably, thus allowing to follow subtle changes in the DAF that would remain masked under

cancellation

**Figure 10.** Block diagram of the spectral profile method for time-frequency analysis of atrial signals. Each new time slice, the time-frequency distribution is aligned to the spectral profile in order to find estimates of the frequency and amplitude. The

The aforementioned spectral analysis techniques had the limitation of only considering the fundamental spectral peak of the atrial activity, but its harmonics have not been put under consideration. However, harmonics could improve DAF estimation and, furthermore, their pattern may be of clinical interest [45]. To alleviate this problem the spectral profile has been proposed [44], its block diagram being depicted in Figure 10. Its main idea is to obtain a time-frequency distribution of successive short segments from the atrial signal. Next, the distribution is decomposed into a spectral profile and a number of parameters

Parameterization profile

of the spectral

Atrial characterization

> Update of the spectral profile

Preprocessing QRST

For every signal segment: Frequency and amplitude trend estimation

Time-frequency analysis

spectral profile is then parameterized and updated [44].

**3.3. The spectral profile**

**Figure 11.** Illustration of the spectral profile technique for three one-minute recordings of atrial fibrillation. The left panel shows the logarithmic time-frequency distribution of the atrial signals. The middle panel shows the spectral profile in solid thick line, the conventional magnitude power spectrum in solid thin line and the fitted spectral line model in dashed line. Finally, the DAF trend is shown in the right panel.(a) Spectral profile for a rather organized AF. (b) Similar to (a) but with notably larger DAF variations. (c) A noisy case with a very high DAF together with a large trend variation [44].

able to describe variations in the DAF as well as in the fibrillatory waves morphology are extracted. Hence, each spectrum is modeled as a frequency-shifted and amplitude-scaled version of the spectral profile. The transformation to the frequency domain is performed by using a nonuniform discrete-time Fourier transform with a logarithmic frequency scale. This particular scale allows for two spectra to be matched by shifting, even though they have different fundamental frequencies and related harmonics [44].

The spectral profile is dynamically updated from previous spectra, which are matched to each new spectrum using weighted least squares estimation. The frequency shift needed to achieve optimal matching then yields a measure on instantaneous fibrillatory rate and

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http://dx.doi.org/10.5772/54199

rate, making it less sensitive to single noisy segments, a short sequence of bad segments causes the spectral profile to lose its structure, and thus, the frequency estimates become incorrect. Furthermore, once the spectral profile has lost its structure, the recovery time until the frequency estimates are valid again becomes unacceptably long, even if the segments

Unfortunately, there are clinical situations in which sequences of noisy segments are common, e.g., during stress testing and ambulatory monitoring and, accordingly, the spectral profile is bound to become corrupt. Therefore, an improved spectral profile method has been proposed able to test the spectrum of each data segment before entering the spectral profile update [46]. A model defined by a superimposition of Gaussian functions, which represent the peaks of the fundamental and harmonics of the AF spectrum, has been proposed (see Fig. 12). These parameters are used to decide whether a new spectrum should be included in the spectral profile or not. The parameters are descriptors of the spectrum and designed so as to verify if a spectrum exhibits the typical harmonic pattern of AF, i.e., a fundamental

Finally, a recently presented approach to improve AF spectral estimation is to use a hidden Markov model (HMM) to enhance noise robustness when tracking the DAF. With a HMM, short-time frequency estimates that differ significantly from the frequency trend can be detected and excluded or replaced by estimates based on adjacent frequencies [47]. A Markov model consists of a finite number of states with predefined state transition probabilities [48]. Based on the observed state sequence, the Viterbi algorithm retrieves the optimal sequence by exploiting the state transition matrix, incorporating knowledge of AF characteristics, and the observation matrix, incorporating knowledge of the frequency estimation method and

During last years several methods to estimate the degree of AF organization have been presented. Primarily, organization estimation was introduced making use of invasive recordings, in which the atrial signal is of notably higher amplitude. However, in recent years, new methods have emerged in the estimation of organization from surface recordings, thus been able to provide clinical useful information through very cheap procedures. The next subsections will describe some of the most recent and extended methods to estimate

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

have an harmonic structure.

signal-to-noise ratio [47].

**4. Arrhythmia organization**

atrial fibrillation organization.

**4.1. Invasive organization methods**

concept of spatial coordination between different regions.

component and, possibly, few harmonics [46].

**Figure 12.** Spectral profile of different atrial signals (dashed line) and the corrected spectral profile obtained by spectral modeling applying the exclusion criteria (solid line). (a) and (b) atrial activity signals with a considerable amount of QRS residua. (c) and (d) atrial activities without noise contamination [46].

is trended as a function of time. An important feature of this approach is that, due to the alignment procedure, the peaks of the spectral profile become more prominent than the corresponding peaks of the conventional power spectrum. As a result, the spectral profile lends itself much better to analysis of the harmonics whose amplitudes reflect the shape of the fibrillatory waveforms and are related with AF organization [44].

Three different examples of the spectral profile technique are shown in Figure 11. Firstly, Fig. 11.a shows the results of a rather organized case of atrial fibrillation, with a DAF of about 6 Hz and a variation within 5–7 Hz. The high degree of organization in the signal is reflected in the presence of two harmonics in the spectral profile (thick solid line in the middle panel). Comparing the spectral profile to the magnitude spectrum (thin solid line), it is evident that the fundamental peak of the former spectrum is narrower and that its harmonics are much more easily discerned. Such a behavior is, of course, expected since the spectral profile represents an average of spectra from successive signal intervals where each individual spectrum, prior to averaging, has been shifted such that the fundamental is optimally aligned to the fundamental frequency of the spectral profile [44]. The example in Fig. 11.b has a DAF of about 7 Hz with a relatively large variation and one harmonic. Finally, Fig. 11.c presents a much more disorganized atrial activity, with a DAF around 8.5 Hz and lack of harmonic behavior. As can be appreciated in the three examples, the spectral profile notably improves DAF and harmonics estimation, specially in the presence of noisy signals.

#### **3.4. Improved spectral estimation**

A drawback of the spectral profile-based method is its lack of control of what goes into the spectral profile: a spectrum reflecting large QRS residuals is just as influential as a spectrum reflecting clear atrial activity. Although the spectral profile has a slow adaptation rate, making it less sensitive to single noisy segments, a short sequence of bad segments causes the spectral profile to lose its structure, and thus, the frequency estimates become incorrect. Furthermore, once the spectral profile has lost its structure, the recovery time until the frequency estimates are valid again becomes unacceptably long, even if the segments have an harmonic structure.

Unfortunately, there are clinical situations in which sequences of noisy segments are common, e.g., during stress testing and ambulatory monitoring and, accordingly, the spectral profile is bound to become corrupt. Therefore, an improved spectral profile method has been proposed able to test the spectrum of each data segment before entering the spectral profile update [46]. A model defined by a superimposition of Gaussian functions, which represent the peaks of the fundamental and harmonics of the AF spectrum, has been proposed (see Fig. 12). These parameters are used to decide whether a new spectrum should be included in the spectral profile or not. The parameters are descriptors of the spectrum and designed so as to verify if a spectrum exhibits the typical harmonic pattern of AF, i.e., a fundamental component and, possibly, few harmonics [46].

Finally, a recently presented approach to improve AF spectral estimation is to use a hidden Markov model (HMM) to enhance noise robustness when tracking the DAF. With a HMM, short-time frequency estimates that differ significantly from the frequency trend can be detected and excluded or replaced by estimates based on adjacent frequencies [47]. A Markov model consists of a finite number of states with predefined state transition probabilities [48]. Based on the observed state sequence, the Viterbi algorithm retrieves the optimal sequence by exploiting the state transition matrix, incorporating knowledge of AF characteristics, and the observation matrix, incorporating knowledge of the frequency estimation method and signal-to-noise ratio [47].
