A Time-Frequency Approach for Discrimination of Heart Murmurs

doi:10.4236/jsip.2011.23032

Paper Menu >>

Journal Menu >>

Journal of Signal and Information Processing, 2011, 2, 232-237

doi:10.4236/jsip.2011.23032 Published Online August 2011 (http://www.SciRP.org/journal/jsip)

A Time-Frequency Approach for Discrimination of

Heart Murmurs

Sepideh Jabbari, Hassan Ghassemian

School of Electrical and Computer Engineering, Tarbiat Modares University, Tehran, Iran.

Email: [email protected]

Received May 29th, 2011; revised July 18th, 2011; accepted July 26th, 2011.

ABSTRACT

In this paper, a novel fram ework based on a time-frequ ency (TF) approach is proposed for detection of murmurs from

heart sound signal. First, a high-resolution TF algorithm, matching pursuit, was used to decompose each heart beat

into a series of TF atoms selected from a redundant dictionary. Next, representative components of murmurs were iden-

tified by clustering the selected a toms of all th e beats into a finite numb er of clusters. Then, Wign er-Ville distrib ution of

the representative components was used to generate a set of 8 features which were fed to a classifier. Experiments with

a dataset consisting of heart sounds from 35 normal and 35 pathological subjects showed a classification accuracy of

95.71% in dist i ng ui shing murmur s fr o m n or mal heart sounds.

Keywords: Phonocardiogram (PCG), Murmur, Matching Pursuit (MP), Time-Frequency Atom, Clustering

1. Introduction

Mechanical activity of the heart is evaluated by ausculta-

tion and analysis of phonocardiogram (PCG) signal,

which is a recording of heart sounds. PCG provides val-

uable information on the structural integrity and function

of heart valves. Heart sounds normally consist of two

regularly repeated thuds, known as S1 and S2 for every

heat beat. An underlying pathology such as diseased

valves produces some additional and abnormal sounds

which are called murmurs. The automatic detection of

murmurs has been widely considered for several decades

because of the human auditory limitations in distin-

guishing them from normal heart sounds [1].

PCG is highly nonstationary signal with multicompo-

nent nature and identification of its components can be

performed by a nonstationary signal analysis tool such as

time-frequency (TF) analysis methods [2]. Short-time

Fourier transform (STFT) is one of the existing tech-

niques that tackles the nonstationarity of the PCG signal

by segmenting it into stationary parts [3,4]. Wavelet

transform (WT) was used to obtain TF decomposition of

PCG signals in previous studies [5,6]. It does not require

the fixed data window needed for STFT; however, even

wavelet bases are not well suited to exact TF representa-

tion of PCG components whose localizations in time and

frequency vary widely. Some researchers performed

analysis of PCG by using Wigner-Ville distribution (WV-

D) [7]. A major drawback of the WVD is presence of

cross-term artifacts caused by aliasing when analyzing

multicomponent signals such as PCG. A true nonstation-

ary TF technique would be one that can give an accurate

parametric display of PCG characteristics with satisfac-

tory TF resolution, cross-term suppression, and without

segmentation requirements. The parameters of decom-

posed components could be later used to extract crucial

features for identification of murmurs. In this paper, we

achieve this goal using a cross-term free high-resolution

method, matching pursuit (MP) algorithm. MP is a signal

decomposition method whereby a signal is decomposed

into a linear combination of TF components (atoms) that

are selected from a redundant dictionary [8].

Figure 1 represents the architecture of our proposed

framework for heart murmur detection. PCG signal from

an electronic stethoscope is processed along with a si-

multaneously recorded electrocardiogram (ECG) stream

as a reference signal. First, preprocessing stage is carried

out consisting of filtering, down sampling, and beat seg-

mentation. Next, all the beats are decomposed into a se-

ries of TF atoms using the MP algorithm and a redundant

Gabor-type dictionary. Each selected atom is described

by a set of parameters including the amplitude, position

in time, scale, frequency, and phase. Groups of atoms

with similar morphology of parameters are then isolated

into clusters. For each cluster, atoms are merged together

A Time-Frequency Approach for Discrimination of Heart Murmurs233

Figure 1. Block diagram of the propose d schem e .

based on the mean values of their parameters to create a

single representative atom. Also, a prototypical beat cor-

responding to the beats of the analyzed PCG can be con-

structed by synthesizing these representative atoms. MP-

based TF decomposition (MPTFD) of the PCG signal is

obtained by taking the WVD of the resulted atoms. Fea-

tures are derived from the MPTFD followed by classifi-

cation using a MLP-based classifier.

The paper is organized as follows. In Section 2, theory

of the utilized method for murmurs detection is intro-

duced and our data set of typical murmurs is described.

The obtained results on murmurs detection are presented

in Section 3 and conclusion in Section 4 is the final part

of this paper.

2. Materials and Methods

2.1. Matching Pursuit

In the MP method, a discrete-time signal



n is de-

composed into a sum of TF atoms selected from a re-

dundant dictionary

 

nagne





n

(1)

where



πcos 2π

np s

gn efnp

















 (2)

and



n is a Gabor-type TF atom which has good

time-frequency localization. The scale factor m

is used

to control the width of the th atom, and the latency

parameter controls the temporal placement. The

parameters m

and m



are frequency and phase, re-

spectively and the amplitude factor m is the expansion

coefficient. The collection of atoms with all possible

combinations of scaling, translations, modulations, and

phase-shifting, forms a redundant dictionary. The first

part in (1) denotes the sum of TF atoms till

itera-

tions of the MP algorithm, and the second part is the re-

sidue to be decomposed in the subsequent iterations. At

first iteration the signal is projected over the dictionary of

atoms and the best correlated atom that can model the

maximum possible function of the signal energy is se-

lected. The selected atom is then subtracted from the

signal to form a residue signal that will be decomposed

in the subsequent iterations [8].

2.2. K-Means Clustering

We next analyzed all the TF atoms decomposed from

different beats of a subject’s PCG to group the atoms into

a finite number of clusters, that each cluster contains

atoms with similar parameters. Clustering of the atoms

was carried out by the K-means method. K-means at-

tempts to find a user-specified number of clusters (

which are represented by their centroids. One of the

common initialization methods for the K-means algo-

rithm can be performed by determining the local maxima

of the joint probability density function (PDF) of the

samples and placing a cluster centroid at each peak [9].

After detecting these maxima, their locations were used

as the initial centroids for the K-means clustering. For

each cluster, a representative TF atom was created by

merging all the atoms of that cluster.

2.3. MP-Based TF Decomposition (MPTFD)

A MPTFD was obtained by taking the WVD of the rep-

resentative TF atoms of the previous stage by

 

representative

Wta Wt







 (3)

where





representative ,W



is the WVD of the th rep-

resentative atom, k is its coefficient, and is the

number of clusters. This cross-term-free decomposition

has very good readability and is appropriate for analysis

of nonstationary, multicomponent signals [10].

2.4. Feature Extraction

The four TF parameters of the MPTFD are the energy

parameter (), energy spread parameter (), fre-

quency parameter (

EP ESP

P) and frequency spread parameter

SP , as described by (4)-(7), respectively

A Time-Frequency Approach for Discrimination of Heart Murmurs

234

 

EP t







(4)

  

Wt EPt

ESP t























(5)

 



FP t









(6)

  



FP tWt

FSP t





























(7)

where m



is the maximum frequency present in the

signal [10]. The average (, ,

mEP mESP m

P, m

SP )

and standard deviation values (s,s,EPESP s

P,s

SP )

of each parameter, described above, were used as the

features of the input vector for the classifier.

2.5. Data Collection and Preprocessing

Heart sound and ECG data of 70 patients have been col-

lected under the supervision of Dr. Sepehri’s group.

From 70 PCGs, 35 signals are from children with patho-

logical murmurs. The remaining 35 signals are from

children with normal heart valves. The PCG signals in

this da set have been labeled by a cardiologist using

echocdiography. All PCG and ECG signals have been

recorded over a time-interval of 10 seconds. For data

acquisition, a WelchAllyn Meditron stethoscope, the

ECG, and a 1.8 GHz ACER notebook with a 16 bit stereo

soundcard and sampling rate of 44.1 kHz have been used.

Preprocessing of the heart sound recordings is neces-

sary to withhold unrepresentative data and separate indi-

vidual heart beats. First, an 8th-order Butterworth low-

pass IIR filter (at 1 kHz) was used to remove the high

frequency noise from the PCG signal. Then, down sam-

pling to 2 kHz was performed prior to any processing

block. Segmentation of the raw PCG into intervals cor-

responding to different cardiac beats is done to perform

the analysis on each of the individual beats. S1 occurs

shortly before R peak in ECG, thus detecting properly

the R peaks one can pick up the beginning and end points

of every heart beat. Therefore, the automatic segmenta-

tion of a recording PCG into separate heart beats was

carried out by means of ECG’s R peaks and a method

similar to what was proposed in [1]. A sample segmented

normal PCG and an abnormal PCG with systolic murmur

(SM) are shown in Figure 2. Synchronization of PCG

and ECG is obvious.

3. Results and Discussions

For the sake of illustration, the mentioned PCG with SM

is considered here. We applied the MP algorithm to de-

compose each individual beat of this PCG. The MP algo-

rithm was allowed to proceed until the iteration reached a

preset number

as a stopping criterion. For the ap-

plication in hand,

was set to 50, because the se-

lected atoms after this iteration have negligible correla-

tion with the original signal. At this stage, the MP algo-

rithm has selected 50 Gabor atoms from the dictionary

for decomposing each of 11 beats of the analyzed PCG.

500 100015002000 2500

-0.05

0.05

Samples

500 1000 1500 2000 2500

-0.05

0.05

Samples

Normal

Amplitude Amplitude

5001000 1500 20002500

-0.05

0.05

Samples

500 100015002000 2500

-0.05

0.05

Samples

Abnormal

Amplitude Amplitude

Figure 2. Segmented ECG & PCG of a normal subject & an abnormal subject with systolic murmur (SM).

A Time-Frequency Approach for Discrimination of Heart Murmurs235

Therefore, a total of 550 TF atoms were selected for fur-

ther clustering and analysis. Each Gabor atom is charac-

terized by a 5-D parameter vector



,,,, T

upfas





3PC

Since clustering in a 5-D space was difficult, principle

component analysis (PCA) was applied to reduce the

dimension of the parameter vectors to three

(). The joint PDF of the new pa-

rameter vectors in the



1,2,3 T

vPCPCPC



12PC PC



space was

used to obtain initial points of clusters. The local peaks

of PDF with values larger than 50% of the maximum

PDF value were selected as initial centroids of clusters

which were 20 peaks. After the clustering procedure, the

550 TF atoms were categorized into twenty clusters,

named as CC . We examined statistical

properties of the parameters including their mean and

standard deviation for each cluster, which are illustrated

in Table 1. Based on the mean values of parameters, a

representative atom was created for each cluster and by

synthesizing these atoms a prototypical beat was con-

structed (Figure 3(a)). This prototypical beat provides a

robust, compact representation of the PCG signal. The

MPTFD of the representative atoms is shown in Figure

3(b). High-frequency activates have been represented

with good TF localization in this distribution. The ,

1, 2,,

ESP

20C

P, and

SP waveforms were obtained from

the MPTFD and their mean and standard deviation were

calculated to form feature vectors.

The classification of PCGs as normal or pathological

was achieved using a three-layer feed-forward multilayer

perceptron (MLP). The input layer consisted of 8 nodes

indicating the input feature vectors. After some prelimi-

nary simulations, it turned out that 11 nodes in the hidden

layer showed a satisfactory performance. A tan-sigmoid

transfer function was applied to each neuron of the hid-

den layer. The output layer consisted of one neuron with

a linear transfer function in which 0 represented a normal

case and 1 represented a pathological case. The neural net-

work was trained using back propagation error method

and its training was conducted until the maximum itera-

tion limit of 30 was reached. The classification accuracy

was estimated using the leave-one-out method, which

one sample is excluded from the dataset and the classifier

is trained with the remaining samples. Then the excluded

signal is used as the test data and the classification accu-

racy is determined. This is repeated for all samples of the

dataset and the performance was calculated averaging the

classification results.

For comparison purposes, another method which per-

forms beat-to-beat detection of murmur was also exe-

cuted. Unlike our proposed framework that simply ex-

amines the prototypical beat, the second technique inves-

tigates each individual beat of the PCG and classifies the

subject as having murmur if the majority of the beats are

00.1 0.2 0.3 0.4 0.5

-0.05

0.05

Time (s)

Amplitude

(a)

Time (s)

0.1 0.2 0.3 0.40.5

100

150

200

250

300

350

400

Frequency (Hz)

(b)

Figure 3. (a) Prototypical beat (b) MPTFD of the proto-

typical beat.

labeled as showing murmur. First, each beat of the PCG

was decomposed into a series of atoms by the MP algo-

rithm. Then, the TF features corresponding to that beat

were extracted from the WVD of the selected atoms.

Next, presence of murmur was diagnosed by applying the

features into the MLP classifier. Finally, identification of

subject as normal or abnormal was done based on the

labels of majority of beats.

Results are shown in Tables 2 and 3 in the form of a

confusion matrix with percentage classification accuracy.

The use of prototypical beat results higher classification

accuracy of 95.71% compared to the beat-to-beat classi-

fication accuracy of 90.01%. From the table it can be

seen that out of 35 normal signals, 34 were correctly

classified as normal, and 1 was misclassified as patho-

logical. Similarly, out of 35 pathological signals, 33 were

correctly classified as pathological and 2 were misclassi-

fied as normal. The misclassified signals were analyzed

in detail, and we observed tat they were perceptually h

A Time-Frequency Approach for Discrimination of Heart Murmurs

236

Table 1. Statistical values of parameters of first five clusters (mean ± SD).

Cluster C1 C2 C3 C4 C5

Amplitude 0.182 ± 0.1 0.124 ± 0.075 0.117 ± 0.062 0.088 ± 0.043 0.075 ± 0.032

Time position (ms) 29.45 ± 9.12 301 ± 4.55 297 ± 2.93 127.5 ± 12.41 159 ± 8.26

Scale (ms) 51.5 ± 10.73 36 ± 6.41 60 ± 4.33 14 ± 8.92 25 ± 4.27

Frequency (Hz) 21.65 ± 4.27 33.46 ± 7.77 78.74 ± 12.23 147.6 ± 6.54 139.8 ± 5.43

Phase (rad) 0.6792 ± 0.281 –1.9342 ± 0.961 –1.2938 ± 0.629 –2.0339 ± 0.876 0.777 ± 0.265

Table 2. Classification results of prototypical beat in identification of valvular disorders. Cross-validation: MLP with

leave-one-out method, %: Percentage of classification.

Method Groups Normal Pathological Total

Cross-validation Normal

Pathological

% Normal

Pathological

97.14

5.71

2.86

94.29 100

100

Table 3. Classification results of individual beats in identification of valvular disorders. Cross-validation: MLP with

leave-one-out method, %: Percentage of classification.

Method Groups Normal Pathological Total

Cross-validation Normal

Pathological

% Normal

Pathological

91.43

11.40

8.57

88.60 100

100

similar to normal and that they could be hardly classified

as pathological by an untrained listener.

4. Conclusions

In this paper, the TF features of PCG signal were ex-

tracted by using the MP algorithm, K-means clustering

method, and WVD for detection of murmurs. The MP

algorithm first decomposed signal into a set of TF atoms,

and a clustering was followed to group these atoms into

several clusters. The representative atom for each cluster

was calculated and MPTFD was obtained by taking the

WVD of these atoms. The TF features of PCG were ex-

tracted from MPTFD followed by classification using a

MLP-based classifier. The proposed method showed

good potential for the noninvasive diagnosis of murmurs.

REFERENCES

[1] Z. Syed, D. Leeds, D. Curtis, F. Nesta, R. A. Levine and J.

Guttag, “A Framework for the Analysis of Acoustical

Cardiac Signals,” IEEE Transactions on Biomedical En-

gineering, Vol. 54, No. 4, 2007, pp. 651-662.

doi:10.1109/TBME.2006.889189

[2] X. Zhang, L. G. Durand, L. Senhadji, H. C. Lee and J. L.

Coatrieux, “Analysis-Synthesis of the Phonocardiogram

Based on the Matching Pursuit Method,” IEEE Transac-

tions on Biomedical Engineering, Vol. 45, No. 8, 1998, pp.

962-972. doi:10.1109/10.704865

[3] B. Ergen and Y. Tatar, “Time-Frequency Analysis of

Phonocardiogram,” Proceedings of the 4th Conference on

Measurement, Bratislava, 2003, pp. 222-225.

[4] S. M. Debbal and F. Bereksi, “Time-Frequency Analysis

of the First and Second Heart Beat Sounds,” Applied Ma-

thematics and Computation, Vol. 184, No. 2, 2007, pp.

1041-1052. doi:10.1016/j.amc.2006.07.005

[5] W. Thompson, C. Hayek, C. Tuchinda and J. Telford,

“Automated Cardiac Auscultation for Detection of Patho-

logical Heart Murmurs,” Pediatric Cardiology, Vol. 22,

No. 5, 2001, pp. 373-379.

[6] S. M. Debbal and F. Bereksi, “Analysis of the Second

Cardiac Sound Using the Fast Fourier and the Continuous

Wavelet Transforms,” Internet Journal of Medical Tech-

nology, Vol. 3, No. 1, 2006.

http://www.ispub.com/ostia/index.php?xmlFilePath=jour

nals/ijmt/vol3n1/cardiac.xml

[7] S. Daliman and A. Z. Shaameri, “Time-Frequency Analy-

sis of Heart Sounds Using Windowed and Smooth Win-

dowed Wigner-Ville Distribution,” 2003.

http://eprints.utm.my/2002/1/article177.pdf

[8] S. G. Mallat and Z. Zhang, “Matching Pursuit with Time-

Frequency Dictionaries,” IEEE Transactions on Signal

A Time-Frequency Approach for Discrimination of Heart Murmurs237

Processing, Vol. 41, No. 12, 1993, pp. 3397-3415.

doi:10.1109/78.258082

[9] P. S. Bradley and U. M. Fayyad, “Refining Initial Points

for K-Means Clustering,” Proceedings of the 15th Con-

ference on Machine Learning, Wisconsin, 24-27 July

1998, pp. 91-99.

[10] S. Krishnan and R. Rangaraj, “Adaptive Time-Frequency

Analysis of Knee Joint Vibroarthrographic Signals for

Noninvasive Screening of Articular Cartilage Pathology,”

IEEE Transactions on Biomedical Engineering, Vol. 47,

No. 6, 2000, pp. 773-783. doi:10.1109/10.844228