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J wave is the bulge generated in the descending slope of the terminal portion of the QRS complex in the electrocardiogram. The presence of J wave may lead to sudden death. However, the diagnosis of J wave variation only depends on doctor’s clinical experiences at present and missed diagnosis is easy to occur. In this paper, a new method is proposed to realize the automatic detection of J wave. First, the synchrosqueezed wavelet transform is used to obtain the precise time-frequency information of the ECG. Then, the inverse transformation of SST is computed to get the intrinsic mode function of the ECG. At last, the time-frequency features and SST-based and the entropy features based on modes are fed to Random forest to realize the automatic detection of J wave. As the experimental results shown, the proposed method has achieved the highest accuracy, sensitivity, and specificity compared with existing techniques.

J wave is the bulge or ectrosis generated in the descending slope of the terminal portion of the QRS complex in the electrocardiogram (ECG). The morphologic pattern, amplitude, and the duration of J wave are various; besides, it always hides in the ST segment [

In 1936, Shipley and Hallaran discovered J wave in the ECG of patients with premature repolarization syndrome for the first time [

At present, there are very few people who do this work. To the best of our knowledge, in 2014, Clack et al. analyzed the ECG with the help of computer for the first time. They set up a breakpoint at the descending slope of the QRS wave. As a result, they achieved the sensitivity of 89.5%, the specificity of 94.5%, and the accuracy of 91.3% [

Wavelet transform (WT) is a good time-frequency analysis method, while it is restricted to the Heisenberg time-frequency uncertainty principle [

In this paper, a new methodology based on SST and Random forest (RF) is proposed to realize the automatic detection of J wave. We computed the time-frequency feature based on SST as the first feature. Through the inverse transformation of SST we obtained five modes of the ECG episodes and we have evaluated Renyi entropy, approximate entropy, and sample entropy as the nonlinear features. Then, the RF is utilized to achieve the detection and classification of J wave-positive and J wave-negative from ECGs. The flow chart of the proposed method for the automatic detection of J wave is provided in Figure

Block diagram of the proposed method.

In our work, the ECG signals were collected from the Shanxi Dayi Hospital, which is the cooperating partner of our project. Infiniti digital twelve-channel ECG SE_1200-Express was applied and the ECG data were sampled at 500 Hz. The database consisted of 30 normal ECG recordings (20 males and 10 females), which come from the health checkup, and 25 abnormal ECG recordings (23 males and 2 females), which come form the patients with J wave related diseases, and all human beings enrolled in the study were signed informed consent. We choose 20-minute duration of Holter monitoring for each ECG record. It is to say that we intercepted 1200 heart beats of each ECG recording in our research. In this paper, the normal ECG patter is defined as J wave-negative and the abnormal ECG patter is defined as J wave-positive. We divided the data into training sets and testing sets. Among them, the training sets contain 18 J wave-negative data and 15 J wave-positive data, while the testing sets are comprised of 12 J wave negative data and 10 J wave-positive data.

Denoising of the ECG signal is carried by eight level Daubechies wavelet 6 (db6) in this preprocessing stage [

The number of beats used in the work.

Set | J wave-negative | J wave-positive |
---|---|---|

Training set | 21600 | 18000 |

Testing set | 14400 | 12000 |

Total | 36000 | 30000 |

SST is a powerful and promising tool to analyze the time-frequency (TF) information of nonstationary signals, which is based on WT and reallocation methods [

The Continuous Wavelet Transform (CWT) of a signal is [

According to Plancherel’s theory, equation (

When

The process of the SST is as follows [

Calculate the frequency domain form of the results of WT, just as (

Calculate the instantaneous frequency (IF) of the signal.

Discretize scaling factor

Compress and rearrange the coefficients of WT. The information can be transformed from the time-scale plane to the time-frequency plane; moreover, the IF can be extracted in this step.

Equation (

SST is an improvement based on CWT. The choice of wavelet basis and the setting of wavelet base parameter make great differences to the results of CWT. In [

The time-frequency curve of the ECG fragment when the center frequency is 25hz. (a) The TF-plane WT-based of J wave-positive. (b) The TF-plane WT-based of J wave-negative. (c) The TF-plane SST-based of J wave-positive. (d) The TF-plane SST-based of J wave-negative.

The time-frequency curve of the ECG fragment when the center frequency is 35hz. (a) The TF-plane WT-based of J wave-positive. (b) The TF-plane WT-based of J wave-negative. (c) The TF-plane SST-based of J wave-positive. (d) The TF-plane SST-based of J wave-negative.

The time-frequency curve of the ECG fragment when the center frequency is 45hz. (a) The TF-plane WT-based of J wave-positive. (b) The TF-plane WT-based of J wave-negative. (c) The TF-plane SST-based of J wave-positive. (d) The TF-plane SST-based of J wave-negative.

The TF-plane WT-based is obtained by (

For any signal

When

(3) The discretized result of

The intrinsic mode of J wave-positive and J wave-negative (a) mode 1, (b) mode 2, (c) mode 3, (d) mode 4, and (e) mode 5. The red lines stand for J wave-positive and the blue lines stand for J wave-negative.

It can be seen from Figure

The entropy features extracted in this paper are resulted from these intrinsic mode functions. It is discussed in the next subsection.

Due to the nonlinear properties of biological signals, researchers tend to choose the theory of nonlinear dynamics, which are effective methods, to analyze them. When studying biological signals, entropy, as a kind of nonlinear feature, often makes a good performance. Renyi entropy (RE), approximate entropy (ApEn), and sample entropy (SampEn), for this reason, are used in this study to implement J wave automatic detection.

In [

ApEn is a kind of nonnegative quantitative description of the complexity of nonlinear time series. The more complex time series correspond to the greater value of ApEn [

The performance of the ApEn is related to the values of

Proposed by Richman and Moornan, SampEn is similar to the ApEn but with higher precision to measure the complexity of the time series. For the sake of the value of SampEn, continuous matching of points inside the threshold

Combining with his Bagging Integrated Learning Theory proposed in 1996 and the random subspace method proposed by Ho in 1998, Leo Breiman introduced Random forest (RF) in 2001. RF is always regard as an excellent ensemble classifier [

RF is selected as the classifier to realize J wave automatic detection in this paper, since it has the following excellent properties compared to other classifiers:

In this subsection, we have analyzed the entropy features from the statistical perspective. The within-class variation of RE feature for J wave-negative and J wave-positive class from mode 1 to mode 5 is shown in Figures

The t-value and the p-value of RE from mode 1 to mode 5.

Features | RE M1 | RE M2 | RE M3 | RE M4 | RE M5 |

t-value | 20.82 | 19.95 | 18.64 | 19.89 | 17.96 |

p-value | <0.001 | <0.001 | <0.001 | <0.001 | <0.001 |

(a) The within-class variation of RE feature for J wave-negative from mode 1 to mode 5. (b) The within-class variation of RE feature for J wave-positive from mode 1 to mode 5.

(a) The mean of RE from mode 1 to mode 5; (b) the standard deviation values of RE from mode 1 to mode 5.

The within-class variation of ApEn and SampEn feature for J wave-negative and J wave-positive class from mode 1 to mode 5 is shown in Figures

The t-value and the p-value of ApEn from mode 1 to mode 5.

Features | ApEn M1 | ApEn M2 | ApEn M3 | ApEn M4 | ApEn M5 |

t-value | 8.07 | 6.54 | 13.75 | 12.69 | 9.32 |

p-value | 0.003 | 0.007 | <0.001 | <0.001 | 0.002 |

The t-value and the p-value of SampEn from mode 1 to mode 5.

Features | SampEn M1 | SampEn M2 | SampEn M3 | SampEn M4 | SampEn M5 |

t-value | 26.89 | 25.78 | 28.37 | 24.56 | 27.53 |

p-value | <0.001 | <0.001 | <0.001 | <0.001 | <0.001 |

(a) The within-class variation of ApEn feature for J wave-negative from mode 1 to mode 5. (b) The within-class variation of ApEn feature for J wave-positive from mode 1 to mode 5.

(a) The mean of ApEn from mode 1 to mode 5; (b) the standard deviation values of ApEn from mode 1 to mode 5.

(a) The within-class variation of SampEn feature for J wave-negative from mode 1 to mode 5; (b) the within-class variation of SampEn feature for J wave-positive from mode 1 to mode 5.

(a) The mean of SampEn from mode 1 to mode 5; (b) the standard deviation values of SampEn from mode 1 to mode 5.

The following five types of performance evaluation indicators are used to evaluate the effect of the proposed method for ECG J wave detection [

Firstly, we compared the presented method in this paper with some existing techniques and the results are listed in Table

The results of existing techniques.

Method | ACC (%) | Se (%) | Sp (%) | MCC | AUC |

Clark et al. [ | 91.3 | 89.5 | 94.5 | 0.840 | 0.893 |

Wang et al. [ | 89.6 | 88.5 | 87.8 | 0.760 | 0.852 |

The proposed method | 96.9 | 96.5 | 95.8 | 0.923 | 0.957 |

Table

Secondly, the previous method we have reported in [

The results of the the previous method we have reported using the latest data.

Method | ACC (%) | Se (%) | Sp (%) | MCC | AUC |

Li and Liu et al. [ | 92.6 | 93.2 | 93.9 | 0.870 | 0.928 |

Li and Bai et al. [ | 93.4 | 91.3 | 92.2 | 0.850 | 0.899 |

The proposed method | 96.9 | 96.5 | 95.8 | 0.923 | 0.957 |

Table

In this subsection, the effect of different features on the classification results has been discussed firstly. RF can rank features according to the importance of the features; this is one of the superiorities of the RF. Figure

The ranking results of features extracted in this paper.

The ROC curve of RF classifier for various features.

In addition, the computational efficiency and detection results of different classifiers are discussed in this subsection. Table

The ACC, MCC, AUC, and training and testing time (in seconds) of different classifiers.

Classifier | ACC | MCC | AUC | Training time | Testing time | Total time | |
---|---|---|---|---|---|---|---|

RF | 75 | 90.9% | 0.819 | 0.875 | 28.583 | 2.735 | 31.318 |

150 | 96.9% | 0.923 | 0.957 | 56.879 | 5.625 | 62.504 | |

300 | 94.1% | 0.896 | 0.913 | 113.427 | 9.673 | 123.100 | |

KNN (K=2) | 87.63% | 0.712 | 0.846 | 0.953 | 45.797 | 46.750 | |

DT | 85.6% | 0.672 | 0.823 | 2.9041 | 0.052 | 2.993 | |

SVM | 95.0% | 0.908 | 0.935 | 84.475 | 45.539 | 130.014 |

It can be seen from Table

A new method is proposed in this paper to achieve the automatic detection of J wave. The experimental results have proved that the proposed method can detect the J wave automatically and accurately. What is more, it provides a reliable foundation for the clinical diagnosis. We introduced time-frequency domain features and nonlinear entropy features (RE, ApEn, and SampEn) in the process of the feature extraction, after that, the RF is utilized in the stage of classification. The entropy features are computed by the modes of the ECG, which are evaluated by the inverse transformation of SST.

Compared with the existing techniques, the advantages of the proposed method are as follows. It is the first time to obtain the intrinsic mode function of ECG though SST. The good time-frequency characteristics and the perfect reconstruction ability of SST make it a powerful tool to discriminate J wave-negative and J wave-positive from ECGs. Combined with RF, which is a kind of ensemble classifiers with great performance, we obtain the best results to realize the automatic detection of J wave.

In the future, the work can be extended in two aspects:

All data used and analyzed during the current study are available from the corresponding author on reasonable request.

The authors declare that they have no conflicts of interest.

This project is supported by the National High Technology Research and Development Program (“863” Program ) of China (2015AA016901), High Linearity Laser Diode Array and High Saturation Power Photodiode Array; National Natural Science Foundation of China (Grant no. 61371062), Research on the Theory and Key Technology of J Wave Extraction in ECG signal; International Cooperation Project of Shanxi Province (Grant no. 201603D421014), Three-Dimensional Reconstruction Research of Quantitative Multiple Sclerosis Demyelination; the General Object of National Natural Science Foundation (61772358), Research on the Key Technology of BDS Precision Positioning in Complex Landform.