High Order Statistics and Time-Frequency Domain to Classify Heart Sounds for Subjects under Cardiac Stress Test

Abstract

This paper considers the problem of classification of the first and the second heart sounds (S1 and S2) under cardiac stress test. The main objective is to classify these sounds without electrocardiogram (ECG) reference and without taking into consideration the systolic and the diastolic time intervals criterion which can become problematic and useless in several real life settings as severe tachycardia and tachyarrhythmia or in the case of subjects being under cardiac stress activity. First, the heart sounds are segmented by using a modified time-frequency based envelope. Then, to distinguish between the first and the second heart sounds, new features, named α(opt), β, and γ, based on high order statistics and energy concentration measures of the Stockwell transform (S-transform) are proposed in this study. A study of the variation of the high frequency content of S1 and S2 over the HR (heart rate) is also discussed. The proposed features are validated on a database that contains 2636 S1 and S2 sounds corresponding to 62 heart signals and 8 subjects under cardiac stress test collected from healthy subjects. Results and comparisons with existing methods in the literature show a large superiority for our proposed features.

Figure 1

Synchronized ECG and PCG signals for a subject under cardiac stress test.

Figure 2

Normal heart sound with the HFS envelope and the magnitude of the S-Transform showing the higher frequency content in S1 compared to S2.

Figure 3

Segmented sound with the HFS envelope and the magnitude of the S-transform of the corresponding heart sound showing that HFS signature does not correspond necessarily to just one class.

Figure 4

The envelope of normalized signal for values of n = 1.5, 2, and 3.

Figure 5

The influence of the values of n in the SSE envelope for the detection of S2 sounds with very low intensities.

Figure 6

S1 and S2 signals (a) and optimized S-transform obtained with α = 0.8 for S1 and α = 0.5 for S2 (b).

Figure 7

S1 (left) and S2 (right) signals and their normalized SSE envelopes with the values of β (bottom).

Figure 8

S1 (left) and S2 (right) signals and their normalized SSE envelopes with the values of γ (bottom).

Figure 9

Receiver operation characteristic curves for feature α and for all subjects.

Figure 10

Receiver operation characteristic curves for feature β and for all subjects.

Figure 11

Receiver operation characteristic curves for feature γ and for all subjects.

Figure 12

Example of a segmented stress test heart sound for subject 4 and workload level 6 (HR = 181 bmp) with the values of α, β, and γ calculated for each located sound (S1 and S2).

Figure 13

Global receiver operation characteristic curves for α (Feature 1, AUC = 0.85), β (Feature 2, AUC = 0.87), γ (Feature 3, AUC = 0.96), and HFS (AUC = 0.6) features.

Figure 14

Example of a segmented stress test heart sounds with three different SNR ratios (12, 5, and 0 dB) with the values of γ calculated for each located sound (S1 and S2).

Figure 15

The variation of the high frequency content ratio (S2/S1) over the HR for all subjects. The red lines indicate the high frequency content of S2 becoming lower than that of S1.

Figure 16

The S-transform of two sounds corresponding to the same subject and two different heart rates ((a) HR = 80 bpm, (b) 142 bpm)) showing the high frequency content of S2 decreasing when the heart rate is higher.