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Selection of wavelet packet measures for insufficiency murmur identification
Expert Systems with Applications 38 (2011) 4264–4271
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Selection of wavelet packet measures for insufficiency murmur identification Samjin Choi a, Youngkyun Shin b, Hun-Kuk Park a,c,⇑ a
Department of Biomedical Engineering & Healthcare Industry Research Institute, College of Medicine, Kyung Hee University, 1 Hoegi-dong, Dongdaemun-gu, Seoul 130-701, Republic of Korea b Department of Electrical Engineering, Yuhan University, 636 Gyeongin-ro, Sosa-gu, Bucheon-si, Gyeonggi-do 422-749, Republic of Korea c Program of Medical Engineering, Kyung Hee University, Seoul 130-701, Republic of Korea
a r t i c l e
i n f o
Keywords: Wavelet packet Insufficiency murmur Heart sound Wavelet packet coefficient Energy and entropy
a b s t r a c t This paper presents a new analysis method for aortic and mitral insufficiency murmurs using wavelet packet (WP) decomposition. We proposed four diagnostic features including the maximum peak frequency, the position index of the WP coefficient corresponding to the maximum peak frequency, and the ratios of the wavelet energy and entropy information to achieve greater accuracy for detection of heart murmurs. The proposed WP-based insufficiency murmur analysis method was validated by some case studies. We employed a thresholding scheme to discriminate between insufficiency murmurs and control sounds. Three hundred and thirty-two heart sounds with 126 control and 206 murmur cases were acquired from four healthy volunteers and 47 patients who suffered from heart defects. Control sounds were recorded by applying a wireless electric stethoscope system to subjects with no history of other heart complications. Insufficiency murmurs were grouped into two valvular heart defect categories, aortic and mitral. These murmur subjects had no other coexistent valvular defects. The proposed insufficiency murmur detection method yielded a high classification efficiency of 99.78% specificity and 99.43% sensitivity. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Cardiac auscultation is the process of recording the sounds produced by the mechanical actions of the heart. Commonly, heart sounds (HS) are comprised of four sounds including two major sounds (S1, S2) and two minor sounds (S3, S4). S1 and S2 (S1nS2) are always audible and appear at very high amplitudes in normal subjects and are easily detected through conventional auscultation procedures, whereas S3 and S4 (S3nS4) appear at very low amplitudes with low frequency components and are difficult to detect routinely (Choi & Jiang, 2008; Jiang & Choi, 2006). Valvular defects usually belong to one of two groups, stenosis or insufficiency. Stenosis occurs when valves is do not open completely and is also referred to as narrowing. Insufficiency occurs when valves do not close completely and is also referred to as regurgitation. In auscultation, these conditions are heard as murmurs and can appear in different phases of the cardiac cycle. Most of the murmurs occurring during systole are cases of ventricular systole, during which the aortic valve should be opened and mitral valve should be closed, and therefore systolic murmurs (SMs) in⇑ Corresponding author at: Department of Biomedical Engineering, College of Medicine, Kyung Hee University, 1 Hoegi-dong, Dongdaemun-gu, Seoul 130-701, Republic of Korea. Tel.: +82 2 961 0290; fax: +82 2 6008 5535. E-mail address: [email protected] (H.-K. Park). 0957-4174/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2010.09.094
clude aortic stenosis (AS) and mitral insufficiency (MI). Most murmurs occurring during diastole are cases of ventricular diastole, during which the aortic valve should be closed and mitral valve should be opened, and therefore diastolic murmurs (DMs) include aortic insufficiency (AI) and mitral stenosis (MS) (Criley, Criley, & Criley, 2000; Choi & Jiang, 2008; Jiang & Choi, 2006). Wavelet transform (WT) has received attention in recent years for the analysis of non-stationary signals. The main advantage of the WT approach is that it has a varying window size that is wide for slow frequency components and narrow for fast ones; thus, it provides good resolution in both the time and frequency domains. In medical applications (Ceylan & Ozbay, 2007; Figliola, Rosso, & Serrano, 2003; Kara & Dirgenali, 2007; Liang & Hartimo, 1998; Reed, Reed, & Fritzson, 2004; Subasi, 2007; Tirtom, Engin, & Engin, 2008; Turkoglu, Arslan, & Ilkay, 2002, 2003), it has become a powerful alternative to the Fourier approach, which is not suitable for the analysis of transients. WT provides good frequency resolution for the low frequency components of a signal, but poor frequency resolution for the high frequency components of a signal. This property results in a logarithmic splitting of bandwidth. To allow fine and adjustable frequency resolutions at low frequencies, the wavelet packet (WP) approach was developed by Coifman, Meyer, and Wickerhauser (1992) and Coifman and Wickerhauser (1992). The WP approach splits both the low-pass (LP) band and high-pass (HP) band at all stages instead of decomposing only the low
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frequency components. Thus, it is possible to subdivide the whole time-frequency (TF) plane into different TF pieces and to carry out more elaborate investigations on the piecewise variations of features in the signal spectrum (Burrus, Gopinath, & Guo, 1998; Goswami & Chan, 1999). Turkoglu et al. (2003, 2002) presented a WP neural network intelligent system for diagnosing heart valvular diseases using WP entropy of Doppler heart sounds. Liang and Hartimo. (1998) implemented a HS segmentation method based on WT decomposition using the Shannon envelope. Their results yielded low performance. Reed et al. (2004) used seventh level WT decomposition for HS analysis, but only to reduce data size. In this paper, we introduce the development of a new wavelet system-based cardiac sound analysis algorithm. We first targeted regurgitation mur-
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murs, which are well-known heart valvular defects. We present the time and frequency characteristics of heart sounds to aid in the discrimination between normal and insufficiency murmurs (IMs) using WP decomposition. This paper is organized into four sections. Section 2 presents a brief review of methods to extract WP-based features. The results and discussions of the case studies using the considered WP features are presented in Section 3. The conclusions are summarized in Section 4. 2. Materials and methods 2.1. Data preparation A data set with 332 sounds consisting of 126 normal and 206 IM samples was prepared for this study. There were three experimental groups including four healthy subjects (control group) and 47 patients with 23 AI and 24 MI murmurs. The control group sounds were recorded from healthy subjects with no history of heart complications using a self-produced wireless electric stethoscope system (Jiang & Choi, 2005). Neither of the two IM groups included other coexistent heart valvular disorders. For the training task, we selected 50 samples from the control group and 75 samples from the two IM groups. The remaining data were used for classification. In order to utilize HS for medical diagnoses, noise cancellation techniques were used to filter the HS signal. A one-dimensional model of a signal x(t) with additive noises can be approximated as follows:
xðtÞ ¼ smðtÞ þ eðtÞ
ð1Þ
where x(t) is the raw HS, sm(t) is the de-noised HS and e(t) are the additive noises. The linear phase finite impulse response notch filter (60 Hz pass-band and filter order 4) and band-pass filter (15–750 Hz pass-band and filter order 4), which provided zerophase digital filtering by processing the input data in both the forward and reverse directions, were applied to the signal x(t) with an 8 kHz sample rate at 16-bit resolution (Rabiner & Gold, 1975). Then, the resulting signal had precisely zero-phase distortion and there was no time delay. The normalization was applied by setting the variance of the signal to a value of one. Fig. 1. Equivalent models of representative heart sounds including normal (a), aortic insufficiency (b) and mitral insufficiency (c). We found that normal sounds were sufficient to represent the normal condition of the heart. Insufficiency murmurs appeared during either systole or diastole with diamond-shaped or rectangular patterns. S1 = first heart sound; S2 = second heart sound; EDM = early diastolic murmur; SM = systolic murmur.
2.2. Separation of S1nS2 and murmurs Since S1nS2 is always audible and appears at very high amplitudes in control samples, the control can be represented by
Fig. 2. The binary tree structure of wavelet packet decomposition. C sp or C(s, p) denotes the pth wavelet packet coefficient at the sth scale. In sm(t) = C(0, p) as shown in Eq. (2), the frequency ranges of wavelet packet coefficients C(s + 2, p) to C(s + 2, p + 3) were 0–Fs/2s+3 Hz (0–1 kHz), Fs/2s+3–2 Fs/2s+3 Hz (1–2 kHz), 2 Fs/2s+3–3 Fs/2s+3 Hz (2–3 kHz), and 3 Fs/2s+3–4 Fs/2s+3 Hz (3–4 kHz), respectively, where the sampling frequency Fs was 8 kHz. The shaded nodes indicated the bands not to be obtained by a conventional wavelet transform method.
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S1nS2 as shown in Fig. 1(a). S1nS2 was sufficient to describe the normal heart condition (Choi & Jiang, 2008; Jiang & Choi, 2006). Fig. 1(b) and (c) represents two IM models. Heart defects including early DM (EDM) and SM mostly appeared as either S1–S2 or S2–S1 with different noise patterns like diamond and/or rectangular shapes (Choi & Jiang, 2008; Gaskin, Owens, Talner, Sanders, & Li, 2000; Jiang & Choi, 2006). The noise-cancelled HS signal sm(t) can be decomposed by
smðtÞ ¼ S þ M
ð2Þ
where S is S1nS2 and M is IM. It is difficult to decompose the signal sm(t) into S and M, particularly in the case where they occupy similar regions in the frequency domain, i.e., in an MS murmur.
2.3. Wavelet packet coefficient In general, WT decomposes only the lower frequency band so that it leads to a logarithmic binary tree structure, while WP decomposes the lower as well as the higher frequency bands and leads to a balanced binary tree structure, as shown in Fig. 2. It was evident from Fig. 2 that the bands with the position indices p + 2 to p + 3 at a scale s + 2 and the position indices p + 2 to p + 7 at a scale s + 3 could not be extracted by the conventional WT. WP makes it possible to subdivide the whole TF plane into different TF pieces, instead of just decomposing the low frequency components. The node (lobe) as shown in Fig. 2 is called the WP coefficient (WPC). The WPC at different scales and positions of a signal can be calculated efficiently as follows:
WPsf;p ¼
X k
Table 1 Definitions of the proposed wavelet packet-based feature set.a Feature
Definition
MPF pWPC-MPF SMR-WEG SMR-WET
Maximum peak frequency Position index of WPC with MPF SMR of relative wavelet energy SMR of Shannon wavelet entropy
a WPC = wavelet packet coefficient; SMR = S1nS2 to murmur ratio; WEG = wavelet energy; WET = wavelet entropy.
hðp 2kÞ WPs1 2f ;p þ
X
gðp 2kÞ WPs1 2f þ1;p ;
ð3Þ
k
where s is the scale (level) index, f is the frequency index, p is the position index, and [h(k), g(k)] are the LP and HP filters with g(k) = (1)kh(1k) (Burrus et al., 1998; Goswami & Chan, 1999). WP was implemented using the Daubechies DB10 function (Daubechies, 1988) with scale s = 8 as a mother wavelet function. Therefore, we obtained 256 WPCs with a frequency resolution of 15.62 Hz, in which the sampling frequency was 8 kHz and WP decomposition level was eight. In order to decompose HS, we selected the frequency range of 20–700 Hz. Therefore, WPCs from C(8, 1) to C(8, 44) were selected; WPC at C(8, 1) to cut off the low
Fig. 3. Normalized heart sound time waveforms (left panels) and their normalized power spectral densities (right panels) in the control sound (a), aortic insufficiency murmur (b) and mitral insufficiency murmur (c). As compared to the control sound, time waveforms of the insufficiency murmurs clearly indicated the occurrence of EDM when the aortic valve was incapable of preventing the back flow of blood from the aorta into the left ventricle during ventricular diastole, and the occurrence of SM when the mitral valve was incapable of preventing the back flow of blood from the left ventricle into the left atrium during ventricular systole. The maximum peak of heart sounds should exist in the frequency range of 0–200 Hz whether the subjects were normal or had murmurs.
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frequency components less than 15.62 Hz and WPC C(8, 44) to cut off the high frequency components greater than 703.12 Hz, where C sp or C(s, p) is the pth WPC at the sth scale. Then, Eq. (2) can be expressed as:
2007). We used Shannon entropy to measure the entropy of HS. Thus, the Shannon wavelet entropy (WET) can be calculated as follows:
smðtÞ ¼ C 00 ðC 80 C 845 C 8255 Þ
WETp ¼
S1nS2
h i ðC sp ðkÞÞ2 ln ðC sp ðkÞÞ2 ;
ð7Þ
k¼1
¼ ðC 80 C 8255 Þ ðC 80 C 845 C 8255 Þ ¼ ðC 81 C 812 Þ ðC 813 C 844 Þ; |fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
N X
ð4Þ
where k is the time window of WPC. From Eq. (7), it is obvious that the more erratic the observations of WPC, the higher the entropy.
murmur
where and are WP operators.
2.6. Feature extraction
2.4. Wavelet energy
Feature extraction is the key to HS analysis, as it is the most important procedure in designing the classification system since even the best classifier will perform poorly if features are not chosen well. A high-dimensional feature might cause an increase in computational complexity. Commonly, in the statistical information, the maximum criterion can be used to detect a singularity or sharp transition in a signal and the mean criterion can be used to measure the central location and the spread in a signal. Therefore, we proposed four features, including the maximum peak frequency (MPF), to observe singularity in the HS signal; the position index of WPC corresponding to MPF (pWPC-MPF) to observe singularity in the HS signal on the wavelet space; and the S1nS2 to murmur ratios (SMRs, Eq. (8)) of energy and entropy to observe the spread in the HS signal. These feature sets are summarized in Table 1.
Energy provides useful information for signal analysis (Bhatikar, DeGroff, & Mahajan, 2005; Choi & Jiang, 2008; Nygaard, Thuesen, Hasenkam, Pedersen, & Paulsen, 1992; Zunino, Perez, Garavaglia, & Rosso, 2007). With WPC, the wavelet energy corresponding to the position indices at the sth scale can be calculated as:
Energyp ¼ jC sp j2 ;
ð5Þ s
where the position index p = 0, . . . , 2 1. This study used the relaP tive wavelet energy (WEG, Eq. (6)) and the total energy p WEGp was 1 (100%).
Energyp WEGp ¼ P : p Energyp
ð6Þ
2.5. Wavelet entropy Entropy is an ideal tool for quantifying ordered non-stationary signals. There are various entropy types including norm, Shannon, threshold, log energy, and sure (Choi & Jiang, 2008; Coifman & Wickerhauser, 1992; Turkoglu et al., 2002, 2003; Zunino et al.,
SMR-WEG=WET ¼
PI J WEGi or WETi 1 PJ i¼1 ; a I j¼Iþ1 WEGi or WETi 1
ð8Þ
where i = 1, 2, . . . , I is the position index of WPCs at 15.62– 203.12 Hz, j = I + 1, . . . , J is the position index of WPCs at 203.12– 703.12 Hz and a is the weighting parameter. These parameters were set to be I = 11, J = 44 and a = 3, in this study.
Fig. 4. Statistical results of the wavelet packet features such as MPF (a), position in WPC of MPF (b), WEG (c), and WET (d) for the three groups. MPF and position in WPC of MPF were calculated in the frequency range of 20–200 Hz while WEG and WET were calculated in the frequency range of 200–500 Hz. MPF = maximum peak frequency; WPC = wavelet packet coefficient; WEG = wavelet energy; WET = wavelet entropy. *P < 0.0001 vs. control.
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2.7. Statistics The results for WP-based features for the identification of IM were expressed as mean ± standard deviation (SD). Statistical analyses were performed to observe the differences between control and IM data using the two-tailed Student’s t-test. P-values less than 0.05 were regarded as statistically significant. 3. Results and discussions 3.1. Time waveform and power spectral density Fig. 3 represents the noise-cancelled and normalized HS signals observed during one cycle, and the corresponding normalized power spectral densities (NPSDs). Panel (a) shows the control sound. Panels (b) and (c) show AI with EDM and MI with SM, respectively. In the control sound samples, the basic HS pattern was sufficient to describe heart condition and its NPSD had a narrow distribution concentrated on a low frequency range of less than 200 Hz. However, IM showed different patterns compared to the control sound. In the case of an AI murmur, the time waveform clearly showed the occurrence of EDM when the aortic valve was incapable of preventing the back flow of blood from the aorta into the left ventricle during ventricular diastole. Also, its NPSD showed different patterns compared to the control NPSD. In the frequency range of 200–500 Hz, AI cases showed an increase in NPSD while control cases showed a flat NPSD. The increased NPSD in the presence of AI murmurs is likely to be responsible for the presence of EDM. In the case of an MI murmur, the time waveform clearly showed the occurrence of SM when the mitral valve was incapable of preventing the back flow of blood from the left ventricle into the left atrium during ventricular systole. The MI murmur showed an increase in NPSD compared to the control in the frequency range of 200–600 Hz. An increase in NPSD of MI is related to the presence of a murmur, an SM. Therefore, it was evident that the time patterns and frequency distributions of the control and IM were completely different in both the time and frequency domains. 3.2. Maximum peak frequency Furthermore, from Fig. 3, IMs in the frequency range of 0– 200 Hz showed similar frequency distributions to the control sound, but the MPF in AI and MI murmurs was significantly higher than that in the control group (p < 0.0001 vs. control). This phenomenon (Fig. 4a) was caused by a frequency characteristic of S1nS2. Commonly, most of the HSs always had S1nS2, whether they were control or IM cases. The MPF of HSs in the frequency domain, therefore, might exist in the frequency ranges of 0–200 Hz whether the subjects are normal or IM (Travel & Katz, 2005). This phenomenon was seen in our study in 98.99% of the cases. 3.3. Wavelet packet coefficients Fig. 5 represents the time waveforms and their WPCs in the position indices p = 1, 3, 7, 14, 23, and 31, corresponding to control (a), AI murmur (b), and MI murmur (c). The heart cycle of the control sound had a systolic period of 0.26 s and a diastolic period of 0.46 s. Heart cycles of the two IM types had systolic periods of 0.29 and 0.34 s, diastolic periods of 0.46 and 0.67 s, and [EDM, SM] durations of 0.35 and 0.67 s in the AI and MI groups, respectively. Three WPCs, C(8, 1), C(8, 3) and C(8, 7), were selected as the signals of S1nS2 and three WPCs, C(8, 14), C(8, 23) and C(8, 31), were selected as the signals of IM. S1nS2 had the largest amplitude and the widest spectrum, and therefore these peaks were visible at all WPCs. However, they were most prominent at
Fig. 5. Time waveforms and their WPCs at the position indices [1, 3, 8] as a frequency range of S1 and S2, and [14, 23, 31] as a frequency range of murmur in control sound (a), aortic insufficiency (b) and mitral insufficiency (c). S1 and S2 had the largest amplitudes and the widest spectra, and were visible at all WPCs. The insufficiency murmurs had high frequency and low amplitude waves compared to the control sound, and were concentrated in the high frequency bandwidth.
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Fig. 6. The distributions of wavelet energy (top panels) and entropy (bottom panels) in control sound (a), aortic insufficiency murmur (b) and mitral insufficiency murmur (c). Most energy and entropy existed in the low frequency bands regardless of heart sounds due to S1 and S2 peaks. Energy and entropy information related to valve malfunctions was stronger in high frequency bandwidths than in low frequency bandwidths.
Table 2 Results of wavelet packet-based feature sets in three groups.a
a
Group
Control
AI
MI
THV
P-value
Sens (%)
Spec (%)
MPF (Hz) pWPC-MPF SMR-WEG (dB) SMR-WET (dB)
38.3 ± 4.5 1.9 ± 0.2 36.4 ± 7.9 32.9 ± 6.0
138.5 ± 27.7 8.4 ± 1.9 5.4 ± 4.5 0.6 ± 8.1
153.0 ± 78.2 9.4 ± 4.9 2.8 ± 7.4 1.2 ± 10.3
55 3 23 18
<0.0001 <0.0001 <0.0001 <0.0001
100 100 100 95.1
100 97.7 100 100
AI = aortic insufficiency; MI = mitral insufficiency; THV = threshold value; Sens = sensitivity; Spec = specificity.
less than 200 Hz. In contrast, IM resulted in high frequency and low amplitude waves compared to the control sound. Thus, IM energies were concentrated in the high frequency range. S1nS2 was significantly decreased at about 200–700 Hz while murmurs were significantly increased. In addition, the results of pWPC-MPF are shown in Fig. 4(b). The pWPC-MPFs in the IM groups were significantly higher than that in the control group (p < 0.0001 vs. control). Therefore, it is evident that the advantage of the WP technique is that it makes it possible to carry out more elaborate investigations on the piecewise variations of measures in the signal spectrum. In addition, WPC and pWPC-MPF could be used as powerful indicators for the presence of IM. 3.4. Wavelet energy The top panels of Fig. 6 represent the distributions of WEGs in the three frequency ranges, with respect to the control and the two IM groups. Panel (a) shows the WEG distributions for less than 200 Hz. Panels (b) and (c) show the WEG distributions in the frequency ranges of 203–500 and 500–703 Hz, respectively. It can be observed that most of the WEGs caused by S1nS2 existed in the low frequency bands regardless of HSs, but their maximum energies were different, i.e., 37% at 46.87–62.5 Hz in the control vs. 25.93% and 23.51% at 109.37–125 Hz in the AI and MI groups, respectively. Also, WEGs caused by the valve malfunctions reflected just the high frequency bands. Specifically, the WEGs of
the IM groups at about 300–500 Hz, WPCs C(8, 19) to C(8, 31), were significantly greater than that of the control group (p < 0.0001 vs. control). It was evident that the WEGs in IM cases differed from the controls. Therefore, we conclude that S1nS2 appeared most prominent in the frequency range of less than 200 Hz and that the energy information at 300–500 Hz might have potential for discriminating between control and IM groups. 3.5. Wavelet entropy The bottom panels of Fig. 6 represent the distributions of WET in control (a) and IM (b and c) groups. The experimental results showed that the patterns of WET were similar to those of WEG. That is, most of the entropy regardless of HSs existed in the 20– 200 Hz range, i.e., 98.59% in the control group, 89.85% in the AI group and 87.48% in the MI group. Also, we observed that the entropy of S1nS2 at less than 200 Hz was stronger than its energy. In the 203–500 Hz range, WET showed different patterns compared to WEG, and the WETs in the IM group were about 10 times bigger than those in the control group (p < 0.0001 vs. control). However, the relationship between entropy and energy at 500–703 Hz showed a significant positive correlation, with R = 0.9941 (p < 0.0001) in MI and R = 0.9989 (p < 0.0001) in AI, where R is the Pearson correlation coefficient. Therefore, we conclude that the entropy information at 300–500 Hz also has potential for identification of the AI and MI cases.
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Fig. 7. Notched box plots of the classification results of four feature sets, MPF, pWPC-MPF, SMR-WEG and SMR-WET, with marked threshold values. THV = threshold value.
3.6. Identification
4. Conclusions
Based on the present dataset, the quantitative results of the feature sets MPF, pWPC-MPF, SMR-WEG and SMR-WET are summarized in Table 2. The diagnostic value of each feature was evaluated experimentally using a threshold value (THV) to achieve high accuracy. To facilitate easy interpretation, the classification results based on the training dataset are graphically illustrated in Fig. 7. The plots indicate that a THV for MPF could best classify the IM with a high significance level (p < 0.0001). Also, the corresponding feature pMPF could classify them using the third WPC. In case of the two SMR features, SMR-RWE and SMR-SWE, THVs of 23 and 5 dB could discriminate between IM and the control with significance (p < 0.0001), as presented in Table 2. Finally, each of the derived THVs was applied to the corresponding testing dataset to assess its sensitivity and specificity. The THVs yielded high sensitivity (95–100%) and specificity (97–100%). Some research on HS signal analysis has been reported in the literature. van Vollenhoven, van Rotterdan, Dorenbos, and Schlesinger (1969) presented a method to improve the detection of AI in the presence of MS using energy measurements performed through frequency analysis. A combined MS and AI rather than pure MS (no AI) clearly showed more components in the higher frequencies, that is, the combined MS and AI showed in the 0–700 Hz range and pure MS showed in the 0–350 Hz range. Additionally, AI murmurs occupied the frequency range of about 350–700 Hz. In our study, the energy and entropy information at 300–500 Hz showed good possibilities for discrimination between control and IM groups. Syed et al. (2006) reported that S1nS2 had the largest amplitude and the widest spectrum, so that this peak could be visible over all frequency ranges. However, MI murmurs were significantly increased at about 350–850 Hz, compared to S1nS2. This same phenomenon was also observed in our study. Nygaard et al. (1992) tried to access the severity of AS using the SM energy ratio between 100–500 and 20–500 Hz. Travel and Katz (2005) demonstrated the HS spectral averaging technique to discriminate between innocent SM and AS sounds using the peak frequency and time duration at 200 Hz. In order to access the presence and severity of AS, Kim and Travel (2003) used the duration of the spectra of >300 Hz. Iwata, Ishii, Suzumura, and Ikegaya (1980) reported an algorithm to detect S1nS2 using spectral tracking by linear prediction at 50–250 Hz with a 50 Hz step. Therefore, we conclude that MPF and pWPC-MPF features at less than 200 Hz and SMR-WEG and SMR-WET features in the 300–500 Hz range were well established for distinguishing between normal and insufficiency murmurs. Also, WP decomposition was shown to be a viable method to carry out more elaborate investigations in the signal spectrum.
This study presented four WP features that are useful for the detection of AI and MI. To quantitatively observe IM in the wavelet space, four features including MPF, pWPC-MPF, WET, and WEG were proposed and observed. MPF and pWPC-MPF features were proposed and evaluated for discriminating between the control and IM groups in less than 200 Hz. To identify the presence of IM, the relative amount of S1nS2 and murmurs in a one-dimensional model of an HS signal was quantified by an SMR corresponding to the energy and entropy in WP space. S1nS2 peaks in the IM groups were significantly greater than those in the control case. Also, SMR in the control sound was significantly lower than that in the IM groups. Our results suggest that the four features constitute efficient indicators for identifying heart disorders, thereby making our novel IM identification method applicable to clinical environments.
Acknowledgement This study was supported by a grant from the Health and Medical Technology Research and Development Project of the Ministry for Health, Welfare and Family Affair (#A084152).
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S. Choi et al. / Expert Systems with Applications 38 (2011) 4264–4271 Goswami, J. C., & Chan, A. K. (1999). Fundamentals of wavelets – theory, algorithms, and applications. New York: John Wiley & Sons. Iwata, A., Ishii, N., Suzumura, N., & Ikegaya, K. (1980). Algorithm for detecting the first and the second heart sounds by spectral tracking. Medical and Biological Engineering and Computing, 18, 19–26. Jiang, Z., & Choi, S. (2005). Development of wireless electric stethoscope system and abnormal cardiac sound analysis method (Sound characteristic waveform analysis). Transactions of the Japan society of mechanical engineers series C (Vol. 71, pp. 3246–3253) [in Japanese with English abstract]. Jiang, Z., & Choi, S. (2006). A cardiac sound characteristic waveform method for inhome heart disorder monitoring with electric stethoscope. Expert Systems with Applications, 31, 286–298. Kara, S., & Dirgenali, F. (2007). A system to diagnose atherosclerosis via wavelet transforms, principal component analysis and artificial neural networks. Expert Systems with Applications, 32, 632–640. Kim, D., & Travel, M. E. (2003). Assessment of severity of aortic stenosis through time-frequency analysis of murmur. Chest, 124, 1638–1644. Liang, H., & Hartimo, I. (1998). A heart sound feature extraction algorithm based on wavelet decomposition and reconstruction. In Proceedings of 20th international IEEE/EMBS conference (pp. 1539–1542). Nygaard, H., Thuesen, L., Hasenkam, J. M., Pedersen, E. M., & Paulsen, P. K. (1992). Non-invasive evaluation of aortic valve stenosis by spectral analysis of heart murmurs. In Proceedings of the 14th annual international conference of the engineering medical and biological society (pp. 2584–2585). Rabiner, L. R., & Gold, B. (1975). Theory and application of digital signal processing. Englewood Cliffs: Prentice Hall.
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Contents lists available at ScienceDirect
Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa
Selection of wavelet packet measures for insufficiency murmur identification Samjin Choi a, Youngkyun Shin b, Hun-Kuk Park a,c,⇑ a
Department of Biomedical Engineering & Healthcare Industry Research Institute, College of Medicine, Kyung Hee University, 1 Hoegi-dong, Dongdaemun-gu, Seoul 130-701, Republic of Korea b Department of Electrical Engineering, Yuhan University, 636 Gyeongin-ro, Sosa-gu, Bucheon-si, Gyeonggi-do 422-749, Republic of Korea c Program of Medical Engineering, Kyung Hee University, Seoul 130-701, Republic of Korea
a r t i c l e
i n f o
Keywords: Wavelet packet Insufficiency murmur Heart sound Wavelet packet coefficient Energy and entropy
a b s t r a c t This paper presents a new analysis method for aortic and mitral insufficiency murmurs using wavelet packet (WP) decomposition. We proposed four diagnostic features including the maximum peak frequency, the position index of the WP coefficient corresponding to the maximum peak frequency, and the ratios of the wavelet energy and entropy information to achieve greater accuracy for detection of heart murmurs. The proposed WP-based insufficiency murmur analysis method was validated by some case studies. We employed a thresholding scheme to discriminate between insufficiency murmurs and control sounds. Three hundred and thirty-two heart sounds with 126 control and 206 murmur cases were acquired from four healthy volunteers and 47 patients who suffered from heart defects. Control sounds were recorded by applying a wireless electric stethoscope system to subjects with no history of other heart complications. Insufficiency murmurs were grouped into two valvular heart defect categories, aortic and mitral. These murmur subjects had no other coexistent valvular defects. The proposed insufficiency murmur detection method yielded a high classification efficiency of 99.78% specificity and 99.43% sensitivity. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Cardiac auscultation is the process of recording the sounds produced by the mechanical actions of the heart. Commonly, heart sounds (HS) are comprised of four sounds including two major sounds (S1, S2) and two minor sounds (S3, S4). S1 and S2 (S1nS2) are always audible and appear at very high amplitudes in normal subjects and are easily detected through conventional auscultation procedures, whereas S3 and S4 (S3nS4) appear at very low amplitudes with low frequency components and are difficult to detect routinely (Choi & Jiang, 2008; Jiang & Choi, 2006). Valvular defects usually belong to one of two groups, stenosis or insufficiency. Stenosis occurs when valves is do not open completely and is also referred to as narrowing. Insufficiency occurs when valves do not close completely and is also referred to as regurgitation. In auscultation, these conditions are heard as murmurs and can appear in different phases of the cardiac cycle. Most of the murmurs occurring during systole are cases of ventricular systole, during which the aortic valve should be opened and mitral valve should be closed, and therefore systolic murmurs (SMs) in⇑ Corresponding author at: Department of Biomedical Engineering, College of Medicine, Kyung Hee University, 1 Hoegi-dong, Dongdaemun-gu, Seoul 130-701, Republic of Korea. Tel.: +82 2 961 0290; fax: +82 2 6008 5535. E-mail address: [email protected] (H.-K. Park). 0957-4174/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2010.09.094
clude aortic stenosis (AS) and mitral insufficiency (MI). Most murmurs occurring during diastole are cases of ventricular diastole, during which the aortic valve should be closed and mitral valve should be opened, and therefore diastolic murmurs (DMs) include aortic insufficiency (AI) and mitral stenosis (MS) (Criley, Criley, & Criley, 2000; Choi & Jiang, 2008; Jiang & Choi, 2006). Wavelet transform (WT) has received attention in recent years for the analysis of non-stationary signals. The main advantage of the WT approach is that it has a varying window size that is wide for slow frequency components and narrow for fast ones; thus, it provides good resolution in both the time and frequency domains. In medical applications (Ceylan & Ozbay, 2007; Figliola, Rosso, & Serrano, 2003; Kara & Dirgenali, 2007; Liang & Hartimo, 1998; Reed, Reed, & Fritzson, 2004; Subasi, 2007; Tirtom, Engin, & Engin, 2008; Turkoglu, Arslan, & Ilkay, 2002, 2003), it has become a powerful alternative to the Fourier approach, which is not suitable for the analysis of transients. WT provides good frequency resolution for the low frequency components of a signal, but poor frequency resolution for the high frequency components of a signal. This property results in a logarithmic splitting of bandwidth. To allow fine and adjustable frequency resolutions at low frequencies, the wavelet packet (WP) approach was developed by Coifman, Meyer, and Wickerhauser (1992) and Coifman and Wickerhauser (1992). The WP approach splits both the low-pass (LP) band and high-pass (HP) band at all stages instead of decomposing only the low
S. Choi et al. / Expert Systems with Applications 38 (2011) 4264–4271
frequency components. Thus, it is possible to subdivide the whole time-frequency (TF) plane into different TF pieces and to carry out more elaborate investigations on the piecewise variations of features in the signal spectrum (Burrus, Gopinath, & Guo, 1998; Goswami & Chan, 1999). Turkoglu et al. (2003, 2002) presented a WP neural network intelligent system for diagnosing heart valvular diseases using WP entropy of Doppler heart sounds. Liang and Hartimo. (1998) implemented a HS segmentation method based on WT decomposition using the Shannon envelope. Their results yielded low performance. Reed et al. (2004) used seventh level WT decomposition for HS analysis, but only to reduce data size. In this paper, we introduce the development of a new wavelet system-based cardiac sound analysis algorithm. We first targeted regurgitation mur-
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murs, which are well-known heart valvular defects. We present the time and frequency characteristics of heart sounds to aid in the discrimination between normal and insufficiency murmurs (IMs) using WP decomposition. This paper is organized into four sections. Section 2 presents a brief review of methods to extract WP-based features. The results and discussions of the case studies using the considered WP features are presented in Section 3. The conclusions are summarized in Section 4. 2. Materials and methods 2.1. Data preparation A data set with 332 sounds consisting of 126 normal and 206 IM samples was prepared for this study. There were three experimental groups including four healthy subjects (control group) and 47 patients with 23 AI and 24 MI murmurs. The control group sounds were recorded from healthy subjects with no history of heart complications using a self-produced wireless electric stethoscope system (Jiang & Choi, 2005). Neither of the two IM groups included other coexistent heart valvular disorders. For the training task, we selected 50 samples from the control group and 75 samples from the two IM groups. The remaining data were used for classification. In order to utilize HS for medical diagnoses, noise cancellation techniques were used to filter the HS signal. A one-dimensional model of a signal x(t) with additive noises can be approximated as follows:
xðtÞ ¼ smðtÞ þ eðtÞ
ð1Þ
where x(t) is the raw HS, sm(t) is the de-noised HS and e(t) are the additive noises. The linear phase finite impulse response notch filter (60 Hz pass-band and filter order 4) and band-pass filter (15–750 Hz pass-band and filter order 4), which provided zerophase digital filtering by processing the input data in both the forward and reverse directions, were applied to the signal x(t) with an 8 kHz sample rate at 16-bit resolution (Rabiner & Gold, 1975). Then, the resulting signal had precisely zero-phase distortion and there was no time delay. The normalization was applied by setting the variance of the signal to a value of one. Fig. 1. Equivalent models of representative heart sounds including normal (a), aortic insufficiency (b) and mitral insufficiency (c). We found that normal sounds were sufficient to represent the normal condition of the heart. Insufficiency murmurs appeared during either systole or diastole with diamond-shaped or rectangular patterns. S1 = first heart sound; S2 = second heart sound; EDM = early diastolic murmur; SM = systolic murmur.
2.2. Separation of S1nS2 and murmurs Since S1nS2 is always audible and appears at very high amplitudes in control samples, the control can be represented by
Fig. 2. The binary tree structure of wavelet packet decomposition. C sp or C(s, p) denotes the pth wavelet packet coefficient at the sth scale. In sm(t) = C(0, p) as shown in Eq. (2), the frequency ranges of wavelet packet coefficients C(s + 2, p) to C(s + 2, p + 3) were 0–Fs/2s+3 Hz (0–1 kHz), Fs/2s+3–2 Fs/2s+3 Hz (1–2 kHz), 2 Fs/2s+3–3 Fs/2s+3 Hz (2–3 kHz), and 3 Fs/2s+3–4 Fs/2s+3 Hz (3–4 kHz), respectively, where the sampling frequency Fs was 8 kHz. The shaded nodes indicated the bands not to be obtained by a conventional wavelet transform method.
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S1nS2 as shown in Fig. 1(a). S1nS2 was sufficient to describe the normal heart condition (Choi & Jiang, 2008; Jiang & Choi, 2006). Fig. 1(b) and (c) represents two IM models. Heart defects including early DM (EDM) and SM mostly appeared as either S1–S2 or S2–S1 with different noise patterns like diamond and/or rectangular shapes (Choi & Jiang, 2008; Gaskin, Owens, Talner, Sanders, & Li, 2000; Jiang & Choi, 2006). The noise-cancelled HS signal sm(t) can be decomposed by
smðtÞ ¼ S þ M
ð2Þ
where S is S1nS2 and M is IM. It is difficult to decompose the signal sm(t) into S and M, particularly in the case where they occupy similar regions in the frequency domain, i.e., in an MS murmur.
2.3. Wavelet packet coefficient In general, WT decomposes only the lower frequency band so that it leads to a logarithmic binary tree structure, while WP decomposes the lower as well as the higher frequency bands and leads to a balanced binary tree structure, as shown in Fig. 2. It was evident from Fig. 2 that the bands with the position indices p + 2 to p + 3 at a scale s + 2 and the position indices p + 2 to p + 7 at a scale s + 3 could not be extracted by the conventional WT. WP makes it possible to subdivide the whole TF plane into different TF pieces, instead of just decomposing the low frequency components. The node (lobe) as shown in Fig. 2 is called the WP coefficient (WPC). The WPC at different scales and positions of a signal can be calculated efficiently as follows:
WPsf;p ¼
X k
Table 1 Definitions of the proposed wavelet packet-based feature set.a Feature
Definition
MPF pWPC-MPF SMR-WEG SMR-WET
Maximum peak frequency Position index of WPC with MPF SMR of relative wavelet energy SMR of Shannon wavelet entropy
a WPC = wavelet packet coefficient; SMR = S1nS2 to murmur ratio; WEG = wavelet energy; WET = wavelet entropy.
hðp 2kÞ WPs1 2f ;p þ
X
gðp 2kÞ WPs1 2f þ1;p ;
ð3Þ
k
where s is the scale (level) index, f is the frequency index, p is the position index, and [h(k), g(k)] are the LP and HP filters with g(k) = (1)kh(1k) (Burrus et al., 1998; Goswami & Chan, 1999). WP was implemented using the Daubechies DB10 function (Daubechies, 1988) with scale s = 8 as a mother wavelet function. Therefore, we obtained 256 WPCs with a frequency resolution of 15.62 Hz, in which the sampling frequency was 8 kHz and WP decomposition level was eight. In order to decompose HS, we selected the frequency range of 20–700 Hz. Therefore, WPCs from C(8, 1) to C(8, 44) were selected; WPC at C(8, 1) to cut off the low
Fig. 3. Normalized heart sound time waveforms (left panels) and their normalized power spectral densities (right panels) in the control sound (a), aortic insufficiency murmur (b) and mitral insufficiency murmur (c). As compared to the control sound, time waveforms of the insufficiency murmurs clearly indicated the occurrence of EDM when the aortic valve was incapable of preventing the back flow of blood from the aorta into the left ventricle during ventricular diastole, and the occurrence of SM when the mitral valve was incapable of preventing the back flow of blood from the left ventricle into the left atrium during ventricular systole. The maximum peak of heart sounds should exist in the frequency range of 0–200 Hz whether the subjects were normal or had murmurs.
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frequency components less than 15.62 Hz and WPC C(8, 44) to cut off the high frequency components greater than 703.12 Hz, where C sp or C(s, p) is the pth WPC at the sth scale. Then, Eq. (2) can be expressed as:
2007). We used Shannon entropy to measure the entropy of HS. Thus, the Shannon wavelet entropy (WET) can be calculated as follows:
smðtÞ ¼ C 00 ðC 80 C 845 C 8255 Þ
WETp ¼
S1nS2
h i ðC sp ðkÞÞ2 ln ðC sp ðkÞÞ2 ;
ð7Þ
k¼1
¼ ðC 80 C 8255 Þ ðC 80 C 845 C 8255 Þ ¼ ðC 81 C 812 Þ ðC 813 C 844 Þ; |fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
N X
ð4Þ
where k is the time window of WPC. From Eq. (7), it is obvious that the more erratic the observations of WPC, the higher the entropy.
murmur
where and are WP operators.
2.6. Feature extraction
2.4. Wavelet energy
Feature extraction is the key to HS analysis, as it is the most important procedure in designing the classification system since even the best classifier will perform poorly if features are not chosen well. A high-dimensional feature might cause an increase in computational complexity. Commonly, in the statistical information, the maximum criterion can be used to detect a singularity or sharp transition in a signal and the mean criterion can be used to measure the central location and the spread in a signal. Therefore, we proposed four features, including the maximum peak frequency (MPF), to observe singularity in the HS signal; the position index of WPC corresponding to MPF (pWPC-MPF) to observe singularity in the HS signal on the wavelet space; and the S1nS2 to murmur ratios (SMRs, Eq. (8)) of energy and entropy to observe the spread in the HS signal. These feature sets are summarized in Table 1.
Energy provides useful information for signal analysis (Bhatikar, DeGroff, & Mahajan, 2005; Choi & Jiang, 2008; Nygaard, Thuesen, Hasenkam, Pedersen, & Paulsen, 1992; Zunino, Perez, Garavaglia, & Rosso, 2007). With WPC, the wavelet energy corresponding to the position indices at the sth scale can be calculated as:
Energyp ¼ jC sp j2 ;
ð5Þ s
where the position index p = 0, . . . , 2 1. This study used the relaP tive wavelet energy (WEG, Eq. (6)) and the total energy p WEGp was 1 (100%).
Energyp WEGp ¼ P : p Energyp
ð6Þ
2.5. Wavelet entropy Entropy is an ideal tool for quantifying ordered non-stationary signals. There are various entropy types including norm, Shannon, threshold, log energy, and sure (Choi & Jiang, 2008; Coifman & Wickerhauser, 1992; Turkoglu et al., 2002, 2003; Zunino et al.,
SMR-WEG=WET ¼
PI J WEGi or WETi 1 PJ i¼1 ; a I j¼Iþ1 WEGi or WETi 1
ð8Þ
where i = 1, 2, . . . , I is the position index of WPCs at 15.62– 203.12 Hz, j = I + 1, . . . , J is the position index of WPCs at 203.12– 703.12 Hz and a is the weighting parameter. These parameters were set to be I = 11, J = 44 and a = 3, in this study.
Fig. 4. Statistical results of the wavelet packet features such as MPF (a), position in WPC of MPF (b), WEG (c), and WET (d) for the three groups. MPF and position in WPC of MPF were calculated in the frequency range of 20–200 Hz while WEG and WET were calculated in the frequency range of 200–500 Hz. MPF = maximum peak frequency; WPC = wavelet packet coefficient; WEG = wavelet energy; WET = wavelet entropy. *P < 0.0001 vs. control.
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2.7. Statistics The results for WP-based features for the identification of IM were expressed as mean ± standard deviation (SD). Statistical analyses were performed to observe the differences between control and IM data using the two-tailed Student’s t-test. P-values less than 0.05 were regarded as statistically significant. 3. Results and discussions 3.1. Time waveform and power spectral density Fig. 3 represents the noise-cancelled and normalized HS signals observed during one cycle, and the corresponding normalized power spectral densities (NPSDs). Panel (a) shows the control sound. Panels (b) and (c) show AI with EDM and MI with SM, respectively. In the control sound samples, the basic HS pattern was sufficient to describe heart condition and its NPSD had a narrow distribution concentrated on a low frequency range of less than 200 Hz. However, IM showed different patterns compared to the control sound. In the case of an AI murmur, the time waveform clearly showed the occurrence of EDM when the aortic valve was incapable of preventing the back flow of blood from the aorta into the left ventricle during ventricular diastole. Also, its NPSD showed different patterns compared to the control NPSD. In the frequency range of 200–500 Hz, AI cases showed an increase in NPSD while control cases showed a flat NPSD. The increased NPSD in the presence of AI murmurs is likely to be responsible for the presence of EDM. In the case of an MI murmur, the time waveform clearly showed the occurrence of SM when the mitral valve was incapable of preventing the back flow of blood from the left ventricle into the left atrium during ventricular systole. The MI murmur showed an increase in NPSD compared to the control in the frequency range of 200–600 Hz. An increase in NPSD of MI is related to the presence of a murmur, an SM. Therefore, it was evident that the time patterns and frequency distributions of the control and IM were completely different in both the time and frequency domains. 3.2. Maximum peak frequency Furthermore, from Fig. 3, IMs in the frequency range of 0– 200 Hz showed similar frequency distributions to the control sound, but the MPF in AI and MI murmurs was significantly higher than that in the control group (p < 0.0001 vs. control). This phenomenon (Fig. 4a) was caused by a frequency characteristic of S1nS2. Commonly, most of the HSs always had S1nS2, whether they were control or IM cases. The MPF of HSs in the frequency domain, therefore, might exist in the frequency ranges of 0–200 Hz whether the subjects are normal or IM (Travel & Katz, 2005). This phenomenon was seen in our study in 98.99% of the cases. 3.3. Wavelet packet coefficients Fig. 5 represents the time waveforms and their WPCs in the position indices p = 1, 3, 7, 14, 23, and 31, corresponding to control (a), AI murmur (b), and MI murmur (c). The heart cycle of the control sound had a systolic period of 0.26 s and a diastolic period of 0.46 s. Heart cycles of the two IM types had systolic periods of 0.29 and 0.34 s, diastolic periods of 0.46 and 0.67 s, and [EDM, SM] durations of 0.35 and 0.67 s in the AI and MI groups, respectively. Three WPCs, C(8, 1), C(8, 3) and C(8, 7), were selected as the signals of S1nS2 and three WPCs, C(8, 14), C(8, 23) and C(8, 31), were selected as the signals of IM. S1nS2 had the largest amplitude and the widest spectrum, and therefore these peaks were visible at all WPCs. However, they were most prominent at
Fig. 5. Time waveforms and their WPCs at the position indices [1, 3, 8] as a frequency range of S1 and S2, and [14, 23, 31] as a frequency range of murmur in control sound (a), aortic insufficiency (b) and mitral insufficiency (c). S1 and S2 had the largest amplitudes and the widest spectra, and were visible at all WPCs. The insufficiency murmurs had high frequency and low amplitude waves compared to the control sound, and were concentrated in the high frequency bandwidth.
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Fig. 6. The distributions of wavelet energy (top panels) and entropy (bottom panels) in control sound (a), aortic insufficiency murmur (b) and mitral insufficiency murmur (c). Most energy and entropy existed in the low frequency bands regardless of heart sounds due to S1 and S2 peaks. Energy and entropy information related to valve malfunctions was stronger in high frequency bandwidths than in low frequency bandwidths.
Table 2 Results of wavelet packet-based feature sets in three groups.a
a
Group
Control
AI
MI
THV
P-value
Sens (%)
Spec (%)
MPF (Hz) pWPC-MPF SMR-WEG (dB) SMR-WET (dB)
38.3 ± 4.5 1.9 ± 0.2 36.4 ± 7.9 32.9 ± 6.0
138.5 ± 27.7 8.4 ± 1.9 5.4 ± 4.5 0.6 ± 8.1
153.0 ± 78.2 9.4 ± 4.9 2.8 ± 7.4 1.2 ± 10.3
55 3 23 18
<0.0001 <0.0001 <0.0001 <0.0001
100 100 100 95.1
100 97.7 100 100
AI = aortic insufficiency; MI = mitral insufficiency; THV = threshold value; Sens = sensitivity; Spec = specificity.
less than 200 Hz. In contrast, IM resulted in high frequency and low amplitude waves compared to the control sound. Thus, IM energies were concentrated in the high frequency range. S1nS2 was significantly decreased at about 200–700 Hz while murmurs were significantly increased. In addition, the results of pWPC-MPF are shown in Fig. 4(b). The pWPC-MPFs in the IM groups were significantly higher than that in the control group (p < 0.0001 vs. control). Therefore, it is evident that the advantage of the WP technique is that it makes it possible to carry out more elaborate investigations on the piecewise variations of measures in the signal spectrum. In addition, WPC and pWPC-MPF could be used as powerful indicators for the presence of IM. 3.4. Wavelet energy The top panels of Fig. 6 represent the distributions of WEGs in the three frequency ranges, with respect to the control and the two IM groups. Panel (a) shows the WEG distributions for less than 200 Hz. Panels (b) and (c) show the WEG distributions in the frequency ranges of 203–500 and 500–703 Hz, respectively. It can be observed that most of the WEGs caused by S1nS2 existed in the low frequency bands regardless of HSs, but their maximum energies were different, i.e., 37% at 46.87–62.5 Hz in the control vs. 25.93% and 23.51% at 109.37–125 Hz in the AI and MI groups, respectively. Also, WEGs caused by the valve malfunctions reflected just the high frequency bands. Specifically, the WEGs of
the IM groups at about 300–500 Hz, WPCs C(8, 19) to C(8, 31), were significantly greater than that of the control group (p < 0.0001 vs. control). It was evident that the WEGs in IM cases differed from the controls. Therefore, we conclude that S1nS2 appeared most prominent in the frequency range of less than 200 Hz and that the energy information at 300–500 Hz might have potential for discriminating between control and IM groups. 3.5. Wavelet entropy The bottom panels of Fig. 6 represent the distributions of WET in control (a) and IM (b and c) groups. The experimental results showed that the patterns of WET were similar to those of WEG. That is, most of the entropy regardless of HSs existed in the 20– 200 Hz range, i.e., 98.59% in the control group, 89.85% in the AI group and 87.48% in the MI group. Also, we observed that the entropy of S1nS2 at less than 200 Hz was stronger than its energy. In the 203–500 Hz range, WET showed different patterns compared to WEG, and the WETs in the IM group were about 10 times bigger than those in the control group (p < 0.0001 vs. control). However, the relationship between entropy and energy at 500–703 Hz showed a significant positive correlation, with R = 0.9941 (p < 0.0001) in MI and R = 0.9989 (p < 0.0001) in AI, where R is the Pearson correlation coefficient. Therefore, we conclude that the entropy information at 300–500 Hz also has potential for identification of the AI and MI cases.
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Fig. 7. Notched box plots of the classification results of four feature sets, MPF, pWPC-MPF, SMR-WEG and SMR-WET, with marked threshold values. THV = threshold value.
3.6. Identification
4. Conclusions
Based on the present dataset, the quantitative results of the feature sets MPF, pWPC-MPF, SMR-WEG and SMR-WET are summarized in Table 2. The diagnostic value of each feature was evaluated experimentally using a threshold value (THV) to achieve high accuracy. To facilitate easy interpretation, the classification results based on the training dataset are graphically illustrated in Fig. 7. The plots indicate that a THV for MPF could best classify the IM with a high significance level (p < 0.0001). Also, the corresponding feature pMPF could classify them using the third WPC. In case of the two SMR features, SMR-RWE and SMR-SWE, THVs of 23 and 5 dB could discriminate between IM and the control with significance (p < 0.0001), as presented in Table 2. Finally, each of the derived THVs was applied to the corresponding testing dataset to assess its sensitivity and specificity. The THVs yielded high sensitivity (95–100%) and specificity (97–100%). Some research on HS signal analysis has been reported in the literature. van Vollenhoven, van Rotterdan, Dorenbos, and Schlesinger (1969) presented a method to improve the detection of AI in the presence of MS using energy measurements performed through frequency analysis. A combined MS and AI rather than pure MS (no AI) clearly showed more components in the higher frequencies, that is, the combined MS and AI showed in the 0–700 Hz range and pure MS showed in the 0–350 Hz range. Additionally, AI murmurs occupied the frequency range of about 350–700 Hz. In our study, the energy and entropy information at 300–500 Hz showed good possibilities for discrimination between control and IM groups. Syed et al. (2006) reported that S1nS2 had the largest amplitude and the widest spectrum, so that this peak could be visible over all frequency ranges. However, MI murmurs were significantly increased at about 350–850 Hz, compared to S1nS2. This same phenomenon was also observed in our study. Nygaard et al. (1992) tried to access the severity of AS using the SM energy ratio between 100–500 and 20–500 Hz. Travel and Katz (2005) demonstrated the HS spectral averaging technique to discriminate between innocent SM and AS sounds using the peak frequency and time duration at 200 Hz. In order to access the presence and severity of AS, Kim and Travel (2003) used the duration of the spectra of >300 Hz. Iwata, Ishii, Suzumura, and Ikegaya (1980) reported an algorithm to detect S1nS2 using spectral tracking by linear prediction at 50–250 Hz with a 50 Hz step. Therefore, we conclude that MPF and pWPC-MPF features at less than 200 Hz and SMR-WEG and SMR-WET features in the 300–500 Hz range were well established for distinguishing between normal and insufficiency murmurs. Also, WP decomposition was shown to be a viable method to carry out more elaborate investigations in the signal spectrum.
This study presented four WP features that are useful for the detection of AI and MI. To quantitatively observe IM in the wavelet space, four features including MPF, pWPC-MPF, WET, and WEG were proposed and observed. MPF and pWPC-MPF features were proposed and evaluated for discriminating between the control and IM groups in less than 200 Hz. To identify the presence of IM, the relative amount of S1nS2 and murmurs in a one-dimensional model of an HS signal was quantified by an SMR corresponding to the energy and entropy in WP space. S1nS2 peaks in the IM groups were significantly greater than those in the control case. Also, SMR in the control sound was significantly lower than that in the IM groups. Our results suggest that the four features constitute efficient indicators for identifying heart disorders, thereby making our novel IM identification method applicable to clinical environments.
Acknowledgement This study was supported by a grant from the Health and Medical Technology Research and Development Project of the Ministry for Health, Welfare and Family Affair (#A084152).
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