Identification of Pulmonary Hypertension Using Entropy Measure Analysis of Heart Sound Signal
Abstract
:1. Introduction
2. Materials and Methods
2.1. Data Collection
2.2. Feature Extraction
2.3. Entropy
2.3.1. Sample Entropy
2.3.2. Fuzzy Entropy
2.3.3. Fuzzy Measure Entropy
2.4. Statistical Tests
2.5. Probability Density Function of an Entropy Measure Fitted by Kernel Density Estimation
2.6. Identification of a PH Patient from a Healthy Subject Using the pdf Based on the Bayes’ Decision Rule
3. Results and Discussions
3.1. Significance of the Features and Reduction of the Age Confounding Factor
3.2. Identification Performance of a Single Entropy Measure
3.3. Identification Performance of Two Joint-Entropy Measures
3.4. Identification Performance of the Joint pdf of Multiple Entropy Measures
3.5. Summary and Discussions
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
Ethical statement
Data availability
References
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Item | Value | Range |
---|---|---|
Number (M/F) | 50 (26/24) | - |
Age (year) | 69.4 ± 12.3 | 33–89 |
Height (cm) | 164.0 ± 8.4 | 148–177 |
Weight (kg) | 64.5 ± 12.6 | 32–90 |
BMI (kg/m2) | 23.9 ± 4.3 | 14.2–35.3 |
PSBP (mmHg) | 38.4 ± 11.8 | 20.4–68.0 |
Item | Value | Range |
---|---|---|
Number (M/F) | 54 (47/7) | - |
Age (year) | 32.6 ± 14.9 | 22–67 |
Height (cm) | 172.5 ± 7.0 | 155–184 |
Weight (kg) | 64.3 ± 7.8 | 43–76 |
BMI (kg/m2) | 21.6 ± 2.3 | 17.6–26.9 |
PSBP (mmHg) | <25 | - |
No. | Name | Physical Meaning |
---|---|---|
1 | Int_s1 | Time interval of S1 |
2 | Int_s2 | Time interval of S2 |
3 | Car_cycle | Cardiac cycle |
4 | Max_pow_s1 | Maximum magnitude of the power spectral density of S1 |
5 | Max_f_s1 | The frequency value corresponding to “Max_pow_s1” |
6 | Max_pow_s2 | Maximum magnitude of the power spectral density of S2 |
7 | Max_f_s2 | The frequency value corresponding to “Max_pow_s2” |
8 | Ener_s1 | Average energy of S1 |
9 | Ener_s2 | Average energy of S2 |
10 | ShanEner_s1 | Average Shannon energy of S1 |
11 | ShanEner_s2 | Average Shannon energy of S2 |
Algorithm 1: identification using a single entropy measure |
Let be the pdf of an entropy measure of the PH patient group and be the pdf of the entropy measure of the health control group. The entropy measure of an unknown subject is . If then the unknown subject is judged as a PH patient else the unknown subject is judged as a healthy subject |
Algorithm 2: identification using joint entropy measures |
Let be the pdf of joint entropy measures of the PH patient group and be the joint pdf of the entropy measures of the health control group. The entropy measure vector of an unknown subject is . If then the unknown subject is judged as a PH patient else the unknown subject is judged as a healthy subject |
No. | Entropy Measure | p Value | CC. | No. | Entropy Measure | p Value | CC. |
---|---|---|---|---|---|---|---|
1 | SampEn_Ener_s1 | 1.49 × 10−5 | −0.30 | 18 | SampEn_ShanEner_s1 | 9.79 × 10−7 | −0.37 |
2 | FuzzyEn_Ener_s1 | 2.12 × 10−5 | −0.29 | 19 | FuzzyEn_ShanEner_s1 | 3.67 × 10−6 | −0.35 |
3 | FMEn_Ener_s1 | 6.42 × 10−6 | −0.33 | 20 | FMEn_ShanEner_s1 | 1.60 × 10−6 | −0.38 |
4 | SampEn_ShanEner_s2 | 5.88 × 10−5 | −0.28 | 21 | FMEn_max_f_s2 | 1.52 × 10−6 | 0.41 |
5 | FuzzyEn_ShanEner_s2 | 6.57 × 10−5 | −0.27 | 22 | SampEn_Ener_s2 | 1.11 × 10−5 | −0.31 |
6 | FMEn_ShanEner_s2 | 1.29 × 10−4 | −0.26 | 23 | FuzzyEn_Ener_s2 | 1.76 × 10−5 | −0.31 |
7 | SampEn_max_f_s1 | 7.25 × 10−4 | 0.21 | 24 | FMEn_Ener_s2 | 3.36 × 10−5 | −0.31 |
8 | FuzzyEn_max_f_s1 | 3.52 × 10−3 | 0.14 | 25 | SampEn_max_pow_s1 | 1.58 × 10−5 | −0.40 |
9 | FMEn_max_f_s1 | 6.47 × 10−3 | 0.16 | 26 | FuzzyEn__max_pow_s1 | 1.14 × 10−5 | −0.40 |
10 | SampEn_Car_cycle | 4.90 × 10−3 | −0.31 | 27 | FMEn_max_pow_s1 | 3.91 × 10−6 | −0.40 |
11 | FuzzyEn_Car_cycle | 3.99 × 10−3 | −0.30 | 28 | SampEn_Int_s2 | 5.38 × 10−4 | 0.39 |
12 | FMEn_Car_cycle | 1.89 × 10−3 | −0.33 | 29 | FuzzyEn_Int_s2 | 5.06 × 10−4 | 0.42 |
13 | SampEn_max_pow_s2 | 1.20 × 10−9 | −0.41 | 30 | FMEn_Int_s2 | 9.26 × 10−3 | 0.37 |
14 | FuzzyEn__max_pow_s2 | 2.69 × 10−9 | −0.39 | 31 | SampEn_Int_s1 | 4.22 × 10−1 | 0.21 |
15 | FMEn_max_pow_s2 | 6.13 × 10−9 | −0.39 | 32 | FuzzyEn_Int_s1 | 2.35 × 10−1 | 0.22 |
16 | SampEn_max_f_s2 | 8.02 × 10−7 | 0.43 | 33 | FMEn_Int_s1 | 3.92 × 10−1 | 0.19 |
17 | FuzzyEn_max_f_s2 | 4.27 × 10−5 | 0.39 |
No. | Entropy Measure | Sen. | Spe. | Acc. | AUC | Corresponding pdf Pair and ROC Curve |
---|---|---|---|---|---|---|
1 | SampEn_Ener_s1 | 0.720 | 0.648 | 0.683 | 0.720 | Figure 6a1 and Figure 7a1 |
2 | FuzzyEn_Ener_s1 | 0.680 | 0.648 | 0.663 | 0.714 | Figure 6a2 and Figure 7a2 |
3 | FuzzyEn_Car_cycle | 0.600 | 0.852 | 0.731 | 0.709 | Figure 6a3 and Figure 7a3 |
4 | SampEn_ShanEner_s2 | 0.580 | 0.796 | 0.692 | 0.667 | Figure 6b1 and Figure 7b1 |
5 | FuzzyEn_ShanEner_s2 | 0.480 | 0.778 | 0.635 | 0.681 | Figure 6b2 and Figure 7b2 |
6 | FMEn_ShanEner_s2 | 0.500 | 0.796 | 0.654 | 0.670 | Figure 6b3 and Figure 7b3 |
7 | SampEn_Max_f_s1 | 0.540 | 0.759 | 0.654 | 0.629 | Figure 6c1 and Figure 7c1 |
8 | FuzzyEn_Max_f_s1 | 0.660 | 0.648 | 0.654 | 0.646 | Figure 6c2 and Figure 7c2 |
9 | FMEn_Max_f_s1 | 0.580 | 0.667 | 0.625 | 0.584 | Figure 6c3 and Figure 7c3 |
No. | Joint Two Entropy Measures | Sen. | Spe. | Acc. | AUC | Corresponding pdfs |
---|---|---|---|---|---|---|
1 | SampEn_Ener_s1/SampEn_ShanEner_s2 | 0.680 | 0.796 | 0.740 | 0.770 | Figure 8a |
2 | SampEn_Ener_s1/FuzzyEn_ShanEner_s2 | 0.680 | 0.796 | 0.740 | 0.759 | Figure 8b |
3 | SampEn_Ener_s1/FMEn_ShanEner_s2 | 0.640 | 0.778 | 0.712 | 0.756 | Figure 8c |
4 | FuzzyEn_Ener_s1/SampEn_ShanEner_s2 | 0.640 | 0.778 | 0.712 | 0.759 | Figure 8d |
5 | FuzzyEn_Ener_s1/FuzzyEn_ShanEner_s2 | 0.640 | 0.759 | 0.702 | 0.748 | Figure 8e |
6 | FuzzyEn_Ener_s1/FMEn_ShanEner_s2 | 0.620 | 0.778 | 0.702 | 0.741 | Figure 8f |
7 | FMEn_ShanEner_s2/SampEn_Max_f_s1 | 0.540 | 0.704 | 0.625 | 0.680 | Figure 8g |
8 | FMEn_ShanEner_s2/FuzzyEn_Max_f_s1 | 0.580 | 0.648 | 0.615 | 0.680 | Figure 8h |
9 | FMEn_ShanEner_s2/FMEn_Max_f_s1 | 0.520 | 0.722 | 0.625 | 0.666 | Figure 8i |
No. | Joint Entropy Measures | Number of Joint Measures | Sen. | Spe. | Acc. | AUC |
---|---|---|---|---|---|---|
1 | SampEn_Ener_s1/FuzzyEn_Ener_s1/SampEn_Max_f_s1/FuzzyEn_Car_cycle/FMEn_Max_f_s1 | 5 | 0.740 | 0.870 | 0.808 | 0.829 |
2 | SampEn_Ener_s1/SampEn_Max_f_s1/FuzzyEn_Max_f_s1/FuzzyEn_Car_cycle | 4 | 0.740 | 0.870 | 0.808 | 0.814 |
3 | SampEn_Ener_s1/SampEn_Max_f_s1/FuzzyEn_Car_cycle/FMEn_Max_f_s1 | 4 | 0.740 | 0.870 | 0.808 | 0.813 |
4 | SampEn_Ener_s1/FuzzyEn_Ener_s1/SampEn_Max_f_s1/FuzzyEn_Car_cycle | 4 | 0.720 | 0.870 | 0.798 | 0.839 |
5 | SampEn_Ener_s1/FuzzyEn_Ener_s1/SampEn_Max_f_s1/FuzzyEn_Max_f_s1/FuzzyEn_Car_cycle/FMEn_Max_f_s1 | 6 | 0.740 | 0.852 | 0.798 | 0.810 |
6 | SampEn_Ener_s1/FuzzyEn_Car_cycle/FMEn_Max_f_s1 | 3 | 0.720 | 0.870 | 0.798 | 0.798 |
7 | SampEn_Ener_s1/SampEn_Max_f_s1/FuzzyEn_Car_cycle | 3 | 0.720 | 0.852 | 0.788 | 0.821 |
8 | SampEn_Ener_s1/FuzzyEn_Ener_s1/SampEn_Max_f_s1/FuzzyEn_Max_f_s1/FuzzyEn_Car_cycle | 5 | 0.760 | 0.815 | 0.788 | 0.818 |
9 | SampEn_Ener_s1/SampEn_Max_f_s1/FuzzyEn_Max_f_s1/FuzzyEn_Car_cycle/FMEn_Max_f_s1 | 5 | 0.720 | 0.833 | 0.779 | 0.801 |
10 | FuzzyEn_Ener_s1/SampEn_Max_f_s1/FuzzyEn_Car_cycle | 3 | 0.680 | 0.852 | 0.769 | 0.815 |
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Tang, H.; Jiang, Y.; Li, T.; Wang, X. Identification of Pulmonary Hypertension Using Entropy Measure Analysis of Heart Sound Signal. Entropy 2018, 20, 389. https://doi.org/10.3390/e20050389
Tang H, Jiang Y, Li T, Wang X. Identification of Pulmonary Hypertension Using Entropy Measure Analysis of Heart Sound Signal. Entropy. 2018; 20(5):389. https://doi.org/10.3390/e20050389
Chicago/Turabian StyleTang, Hong, Yuanlin Jiang, Ting Li, and Xinpei Wang. 2018. "Identification of Pulmonary Hypertension Using Entropy Measure Analysis of Heart Sound Signal" Entropy 20, no. 5: 389. https://doi.org/10.3390/e20050389
APA StyleTang, H., Jiang, Y., Li, T., & Wang, X. (2018). Identification of Pulmonary Hypertension Using Entropy Measure Analysis of Heart Sound Signal. Entropy, 20(5), 389. https://doi.org/10.3390/e20050389