Research on Algorithm of Extracting PPG Signal for Detecting Atrial Fibrillation based on Probability Density Function

2.1. Extracting PPG Information

Previous studies have shown that PPG Information can be found by the smart phone`s camera. The method relies on fingertips images captured from the built-in smart phone camera. The pixel values in red channel can be calculated from the images.

In the paper, YUV420SP model was selected for previewing video [8], and was changed to RGB color model for extracting and calculating inter-pulse period.

Some experiments verified the red channel of RGB color model could accurately reflect PPG signals [9]. Thus, the red channel information was isolated as the inter-pulse period. Meanwhile, the adjacent pulse beat time could be found by adjacent pulse wave peaks.

Two peaks of PPG signals were then calculated as heart rate. Correctness of this method [10] was verified by comparing the calculated heart rate to the one obtained from standard pulse measuring instrument.

2.2. Phase Space Reconstruction

In prior work, phase space reconstruction was introduced into the kinetic [11]. With the phase space reconstruction, chaotic time series can be reconstructed to nonlinear dynamical system [12].

It is common knowledge that pulse waves contain copious information of human body, including waveform, amplitude, and velocity. These information can reflect many characteristics of the human cardiovascular system [13-15]. Inter-pulse period is one of the considerable measures of the pulse wave. According to Takens’ embed principles, the inter-pulse period is applied to reconstruct phase space, while system dynamics remain unchanged. Assuming x(n)，n=1,2,…N is the adjacent peaks time of the PPG signal, the m-dimensional vector can be constructed as

y(n)=(x(n),x(n+t),…x(n+(m-1)t)) (1)

In formula (1), m is embedded dimension, t is delay time. Phase space reconstruction y(n) of five-dimensional vector can be obtained by constructing x(n).

2.3. Probability Density Function (PDF)

Correlation function f(m,t,r) is constructed to calculate the probability for any two points whose distance in the phase space is less than r.

f(m,t,r) can be written as

Symbol is the Euclidean distance.Let the Unit step function be h:

The PDF can be obtained by the following formula:

2.4. Gaussian Fit

In this paper, PDF p was filtered, and Gaussian fit was then used for fitting function p. AF and normal sinus rhythm (NSR) could be separated based on Skewness of the fitting results.

3.1. Data Collection

In the paper, pulse data were collected by smart phone camera from fingertip information. The pulse data detection was compared with the standard ECG instrument simultaneously to ensure the accuracy of the extracted inter-pulse. Fig. (1) shows the results of PPG waveform and ECG waveform.

Table 1 shows one of the detecting information. The results of experiments proved that the accuracy of calculating inter-pulse time from collecting human pulse data by smart phones was more than 95%, and the average relative error was 0.0411.

Our study included 25 people of NSR in the University of Shanghai for Science and Technology, and 6 patients with persistent AF from community hospital.

It was found that the more human pulse data were collected, the easier it was to distinguish AF from NSR. Meanwhile, the more human pulse data were collected, the longer detecting time was needed. Considering these two factors, we collected 350 human pulse data in every experiment to ensure experiment accuracy while shortening the detection time.

3.2. PDF Distribution

We reconstructed different delay of the pulse data extracted in 5-dimensional based on the phase space reconstruction and PDF function, and then, we constructed the PDF by distance value of each data. Results are visually summarized in Fig. (2).

3.3. Filtering Result

In order to conveniently fit curve and ensure minimum loss of image information, the linear filter was used to make the curve more smooth as shown in Fig. (3).

It is obvious that PDF of NSR resembles lognormal distribution, while PDF of AF resembles normal distribution instead after filtering, as shown in Fig. (3) and Fig. (4).

In Fig. (4), the characteristic differences among different delay times were not very obvious in 5-dimension, and therefore, delay time t=1 was used for the next research.

With computer-aided technology [16], Gaussian curve fitting was used for the PDF curve with delay time t=1. As Fig. (5) shows, the fitting R-squared values are more than 0.95. The curve of NSR is shown as Fig. (5-1), and AF is shown as Fig. (5-2).

3.4. Comparison of Standard AF

To verify presented method ulteriorly, ECG signals taken from MITBIH database containing AF episodes were tested. The number of each AF segment data was selected as 350.

PDF curve was reconstructed from the AF segment data by phase space following the formula (2). The curve was then filtered by Gaussian fitting. Fig. (6) shows the filtering PDF curve.

Meanwhile, the curve with delay t=1 was fitted by Gaussian fitting. Fig. (7) was generated by plotting the time of delay t=1.

The new method was carried out exploiting the same number of date from MIT-BIH Fibrillation Database. Comparing Fig. (7) with PDF curve of AF in Fig. (5-2), it was obvious that they were all close to normal distribution.

3.5. P-P Plot

For evaluation of new method quality, the statistical regular pattern of PDF curve after fitting was analyzed by the P-P plot of NSR and AF normal distribution [17, 18].

Fig. (8-1) show the NSR P-P plots of normal distribution, and Fig. (8-2) show the AF P-P plots of normal distribution.

Fig. (9-1) show the NSR P-P plots of lognormal distribution, and Fig. (9-2) show the AF P-P plots of AF P-P plot.

It could be seen that results of NSR were more close to lognormal distribution and results of AF were more close to normal distribution.

Comparing with Zhang ChangLin, Fritz-Albert Popp’s study of human skin surface conductance measurement [19], we have obtained similar results. Their study found when a person was in a state of physiological disorders, skin surface conductance values were no longer close to lognormal distribution, but closer to normal distribution instead. This phenomenon was statistical self-similarity and was correspond with self-similar nested structure.

3.6. Skewness Analysis

As demonstrated in Fig. (8) and Fig. (9), PDF curves were close to normal distribution or lognormal distribution. Therefore, AF could be distinguished from NSR by the eigenvalues of normal distribution. The skewness of lognormal distribution was chosen to distinguish the curves [20, 21].

As shown in Tables 2 and 3, the skewness of data collected both from smart phones in experiment and MIT-BIH Fibrillation Database were calculated.

Results were visually presented in Tables 2 and 3. Skewness of AF data collected in experiment and MIT-BIH Fibrillation Database were all in range 0 to 1. Meanwhile, the skewness of NSR data were all out of range 0 to 1. Therefore, the skewness could be used to distinguish NSR and AF.