In this study, we devised animal experiments to collect real-world data using living canine subjects with cholinergic AF model. The canine heart was exposed after thoracotomy and suspension of the pericardium. 8 flexible patches containing a total of 128 unipolar electrodes were carefully attached to right atrium, left atrium and the root of pulmonary veins. AF was induced by rapid pacing (with a frequency of 20 Hz) at the atrial appendages of the canine heart with an intravenous injection of acetylcholine (see details of experimental procedures and mapping sites in [21] and [22]). Then real data were recorded at a sampling frequency of 2 kHz from the 128-channel unipolar epicardial mapping system developed by the Electrophysiology Laboratory in Fudan University [21, 22]. The hardware of our mapping system included amplifying and filtering, and the hardware filters were a notch filter at 50 Hz and a band pass filter (BPF) at 3–500 Hz. The software which contain signal processing and analyzing were implemented with MATLAB (Mathworks Inc.). 8 dogs (weight 13.4 ± 2.9 kg) was used, all these data formed a signal database in the Electrophysiology Laboratory of Fudan University, and all the AF data used in this study were randomly selected from this database.

### Dominant frequency and Botteron’s approach

Figure 1 shows a unipolar epicardial AF signal and its spectrum. DF is an important frequency domain index, which often detected as the frequency with the maximum power in the power spectrum. Preprocessing may be needed for a more accurate DF result. Botteron’s approach is just the classic preprocessing method, its preprocessing steps are: (1) band-pass filtering at 40–250 Hz, (2) absolute value, and (3) low-pass filtering at 20 Hz.

Figure 2 shows each step of Botteron’s approach and the signal’s spectrum after each step. The spectrum is based on fast Fourier transform (FFT). A Hamming window is used before FFT.

Each of the above three steps has its specific role. But considering the reason that this preprocessing algorithm was not for DF analysis, but for the correlation calculation when Botteron first proposed it in 1995, these three steps could be adjusted if used in seeking for DF, especially during AF.

### Adjust the parameters of band-pass filter

Band-pass filter (BPF) is often used to eliminate noise and interference, such as baseline drift (caused by breathing or beating of the heart) and high frequency noise [23]. Botteron first used this preprocessing step to calculate the cross-correlation of signals, especially for the activation pattern, since the components between two activation intervals may influence the results [14, 15] and the spectral content of those components are below 40 Hz [17]. Nevertheless, due to the fact that DF is within 20 Hz, such “interference” has smaller impact on DF than on cross-correlation and therefore the selection of pass band may vary with the actual situation.

In order to get an effective BPF, we firstly analyze the energy distribution of epicardial mapping signals during AF in frequency domain. As Fig. 1 shows, the energy of epicardial AF signal is concentrated in 10–100 Hz, which is different from some previous studies [24, 25]. To improve the performance, we could make an appropriate adjustment for the range of 40–250 Hz.

In this study, all the band pass filters are FIR filter and we adjusted the cutoff frequency of the filter and then compared the DF results. The statistical analysis of DF results was also done with different pass band.

### Taking absolute value

Taking absolute value in Botteron’s approach is also known as the rectification to restore the low frequency components after band-pass filtering [17]. During this process, the DF which reflects the main rhythm of signal will appear and be highlighted. After taking absolute value, the amplitude of the direct current (DC) component is the largest and the maximum peak will appear at 0 Hz. Then, DF is shown as the second maximum peak. For the theoretical explanation of the effect by taking absolute, you could also see the article [17], which is to find out the changes in the spectrum area by the analysis of phase change. Here we will illustrate the role of absolute value from another perspective.

Due to myocardial cells’ fast depolarization, the epicardial ECG signal will have a steeper slope when the tissue is exciting. The shape of a single ECG after taking the absolute value is similar to that of waveform *f*(*t*) in graph (a) or (b) of Fig. 3, some may also be similar to the waveform shape in graph (f). From a theoretical point of view, one episode of epicardial ECG signal can also be obtained (mainly superposition) by the linear combination of waveforms in (a), (b), (c), (d) and (f). The spectrum of these five waveforms all decreases their amplitude when frequency increasing from 0 Hz as the red box in Fig. 3 shows. In case the waveform occurs periodically, the spectrum becomes discrete spectrum, as shown in Fig. 3f. The decreasing envelope shape, combined with discrete spectral line appears at every other *f*
_{0} (*f*
_{0} = 1/*T*). We can clearly see that, except 0 Hz, the first line has the maximum peak and is corresponding to the frequency of any periodical signal. This is the reason why the DF could reflect signal’s rhythm (period or frequency) and accords with the largest peak in the spectrum.

The role of taking absolute value is very important. When a signal has both positive part and negative part (before taking absolute value), as graph (e) shows in Fig. 3 [e.g. the ECG waveform in Fig. 6 is close to (c) plus (e) in Fig. 3], its spectrum would not show a single reduction trend from 0 Hz. Thus when the first spectral line falls into the decreasing area, it is still the largest peak, which can accurately correspond to the DF. Otherwise, when the first discrete line falls into the area before the maximum peak (the blue box in Fig. 3e), the maximum peak line may no longer corresponding to *f*
_{0}.

### Low-pass filtering at 20 Hz

Botteron proposed the preprocessing at first (1995) for the correlation algorithm [14, 15]. In fact, after 20 Hz low-pass filtering all kinds of excited waveforms become similar with each other [9]. This could get rid of different waveforms’ effect caused by different atrial positions [14]. The effect of this low-pass filter (LPF) is just filtering out the components beyond 20 Hz, so that the waveform in the time domain would be more similar to the sine wave shape. However, as for seeking DF, low-pass filtering at 20 Hz is actually not necessary because the rhythm of atrial signal is within 20 Hz.

In general, after the previous two steps: band-pass filtering and rectification, the DC component of the signal is increased, the maximum peak in the frequency domain is at 0 Hz and the frequency at the second largest peak is the DF, which is within 0–20 Hz.

### Without Botteron’s preprocessing steps

Some researchers do DF analysis not in accordance with the three steps of Botteron’s approach [12, 19, 20]. Their method is just directly doing spectral analysis based on FFT.

To illustrate and compare the DF result of the direct FFT method and Botteron’s approach, we marked the two methods as: method 1-directly do spectral analysis (FFT) and the DF result is denoted by DF_{1}; method 2-first 20–100 Hz band-pass filtering, subsequently taking absolute value, finally do spectral analysis (FFT) and getting the DF result DF_{2}. Then the relative ratio R was defined as:

$$R = \frac{{\left| {DF_{1} - DF_{2}} \right|}}{DF_{2}}$$

If R < 0.1, the results of these two methods were regarded identical. On the other hand if R > 1, we think the results were completely different from each other.

### Evaluating the effect of sampling frequency on DF

Down-sampling is known as the decimation in digital signal processing [26]. Before decimation, LPF is needed to mitigate aliasing distortion. *M*-times decimation to the original discrete-time signal (sampling frequency *f*
_{1}) is just taking one data after every *M*-*1* data and getting the sampling frequency of *f*
_{1}/*M* [27, 28]. After down-sampling the signal could lose high-frequency components and the maximum frequency *f*
_{
max
} < *f*
_{1}/(2 *M*). Therefore, after down-sampling high-frequency components are removed but low-frequency components are kept.

Different acquisition system may have different sampling frequency. Low sampling frequency could benefit the real-time performance of DF mapping. Here we used the down-sampling method on our 128-channel epicardial signals to construct different sampling frequency and evaluated the influence of sampling frequency on DF.

### The influence of ventricular far-field depolarization on DF

The crosstalk from the far-field ventricular potential is also apparent when collecting the atrial signal and we can call it ventricular artifact. Removing the crosstalk from ventricle may often take away a portion of the atrial activation information and lead to a distorted signal. So, whether it is necessary to remove the ventricular artifact when doing the DF analysis during AF is worth considering.

Ng et al. has especially analyzed the impact of the ventricular far-field depolarizations (VFDs) and found VFDs significantly affected DFs [8]. However, they ignored the fact that the impact on dominant atrial frequency was limited when the ventricular amplitude was small. During endocardial and epicardial mapping, the electrodes are directly attached to the atrial tissue to collect signal and the amplitude of atrial signal is much larger than the amplitude of VFDs (only in the area near ventricle the amplitude will be larger).

In this study, we employed the ventricular reference signals from the apex of the heart, and introduced a least mean square adaptive filter with noise canceller model to remove the VFDs [29]. Then we did DF analysis and compared it with the DF which from the same signal but with VFDs.