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CHAPTER 4
CLASSIFICATION OF HEART MURMURS USING
WAVELETS AND NEURAL NETWORKS
4.1
INTRODUCTION
Heart auscultation is the process of interpreting sounds produced by
the turbulent flow of blood into and out of the heart and the movement of
mechanical structures that control this flow. This non-invasive, low-cost
screening technique is used as a primary tool in the diagnosis of certain heart
disorders, especially valvular problems. The conventional method of
auscultation with a stethoscope has many limitations. The skills required for
interpretation are acquired by listening to the heart sounds of many different
patients. Therefore, it is a very subjective process that depends largely on the
physician’s experience and ability to differentiate between different sound
patterns. For an objective assessment of heart sounds for diagnosis of certain
cardiac disorders, digital recording and subsequent analysis of these acoustic
signals is the only reliable method. Digital sounds can be analysed efficiently
using a computer.
4.2
LITERATURE SURVEY
Faizan et al (2006) have developed a heart murmur classification
system with features extracted using Spectrogram. Seven types of murmurs
are classified using a Multilayer Perceptron Neural Network based on their
timing within the cardiac cycle using Smoothed Pseudo Wigner-Ville
distribution. Zhou et al (2008) have proposed a heart sound recognition
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system based on features extracted from the normalized average Shannon
energy in wavelet domain. These features are used with Full Bayesian Neural
Networks to classify six types of heart sounds. Yadi et al (2008) report a
classification method based on statistical features extracted using wavelet
decomposition and MLP Neural Network to classify five murmurs. Many new
techniques have been introduced for efficient heart disease diagnosis.
However, they are expensive, require skilled technicians to operate the
equipment and experienced cardiologists to interpret the results (Faizan et al
2006). These facilities are usually available only in advanced hospitals and
not in rural and most urban hospitals. Furthermore, the wavelet transform has
demonstrated the ability to analyse the heart murmurs more accurately than
the techniques like STFT or Wigner Ville Distribution (WVD) cited in
literature. The WVD has the ability to separate signals in both time and
frequency. One advantage of the WVD over the STFT is that it does not
suffer from the time frequency trade-off problem. On the other hand, WVD
has a disadvantage since it shows cross terms in its response and attempts to
smooth these results in decreased resolution in both time and frequency
(Debbal and Bereksi-Reguig 2008). Considering these constraints, a new
approach based on wavelet transform and artificial neural networks has been
proposed for classifying heart murmurs into eight types, namely, normal,
early systolic, mid systolic, late systolic, holo systolic, early diastolic, mid
diastolic and late diastolic. Classification of heart murmurs into more number
of types leads to enhanced accuracy of diagnosis.
4.3
HEART MURMURS
4.3.1
Categories
In healthy adults, there are two normal heart sounds often described
as a lub and a dub, that occur in sequence with each heart beat. These are the
first heart sound (S1) and second heart sound (S2), produced by the turbulent
flow against the closed atrioventricular and semilunar valves respectively.
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The period between S1 and S2 is referred to as systole and the period between
S2 and subsequent S1 is diastole. Murmurs are abnormal sounds that occur
between S1 and S2 called systolic murmurs and between S2 and S1 called
diastolic murmurs. The former occurs during ventricular contraction (systole)
and the latter occur during ventricular filling (diastole). These heart sounds
and murmurs are shown in Figure 4.1.
(a) Normal heart sounds S1 and S2
(b) Systolic murmurs between S1 and S2
(c) Diastolic murmurs between S2 and S1
Figure 4.1 Heart sounds and murmurs
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The systolic murmurs are again sub classified into early, mid, late
and holo systolic murmurs depending on their position in the systolic period.
Similarly the diastolic murmurs are further sub classified into early, mid and
late diastolic murmurs. These pathological types of heart murmurs and their
associated abnormalities are shown in Table 4.1.
Table 4.1 Heart murmurs and associated abnormalities
Category
Systolic
Sub category
Early systolic
Mid systolic
Late systolic
Holo systolic
Early diastolic
Diastolic
Mid diastolic
Late diastolic
4.3.2
Associated abnormality
Mitral regurgitation
Aortic stenosis
Atrial septal defect
Mitral valve prolapse
Tricuspid valve prolapse
Papillary muscle dysfunction
Tricuspid insufficiency
Ventricular septal defect
Aortic regurgitation
Pulmonary regurgitation
Left anterior descending artery stenosis
Mitral stenosis
Tricuspid stenosis
Atrial myxoma
Complete heart block
Characteristics
Murmurs can be classified based on seven different characteristics :
timing, shape, location, radiation, intensity, pitch and quality. Timing refers to
whether the murmur is a systolic or diastolic murmur. Shape refers to the
intensity over time; murmurs can be crescendo, decrescendo or crescendodecrescendo. Location refers to where the heart murmur is auscultated best.
There are six places on the anterior chest to listen for heart murmurs; each of
these locations roughly corresponds to a specific part of the heart. Radiation
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refers to where the sound of the murmur radiates. The general rule of thumb is
that the sound radiates in the direction of the blood flow. Intensity refers to
the loudness of the murmur, and is graded on a scale from 0-6/6. The pitch of
the murmur is low, medium or high and is determined by whether it can be
auscultated best with the bell or diaphragm of a stethoscope. The quality of a
murmur may be blowing, harsh, rumbling and musical. In the proposed work,
classification is done with respect to the timing characteristic.
4.4
HEART MURMUR CLASSIFICATION
4.4.1
Data Collection and Pre-Processing
Heart murmur files, normal and pathological, collected from the
Johns Hopkins Cardiac Auscultatory Recording Database (CARD), an
excellent resource for research purposes, and other internet sites, were used in
this classification work (CARD 2006; Raymond 2006). The pathological
types include early systolic, mid systolic, late systolic, holo systolic, early
diastolic, mid diastolic and late diastolic murmurs. The murmur files obtained
in mp3 format were converted to wav format for further processing. The
sampling frequency chosen was 8000Hz in all cases to cover the range for
analysing murmurs (Zhou et al 2008). Signals, when contaminated with noise,
might lead to erroneous classification. To remove the noise that may overlap
with the heart sounds, SureShrink, the Discrete Wavelet Transform (DWT)
based wavelet shrinkage denoising technique was used (Donoho and
Johnstone 1995; Cai and Harrington 1998).
4.4.2
Feature Extraction
The main objective of feature extraction process is to derive a set of
features that best represents the signal. So, the selection of features is an
important criterion for proper classification of different heart murmurs. In this
work, a set of 15 statistical features were extracted from the murmur files. The
steps involved in the feature extraction process are illustrated in Figure 4.2.
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Digitized heart sound
sampled at 8000 Hz
16 bits/sample
Extraction of single cycle
of the heart murmur
Normalized to absolute
maximum
Wavelet decomposition
(db6 level 5)
3rd level
detail
500-1000
Hz
4th level
detail
250-500
Hz
5th level
detail
125-250
Hz
5th level
approximation
0-125
Hz
Determining mean of
absolute values of
coefficients in each sub band
Determining standard
deviation of wavelet
coefficients in each sub band
Determining average power
of wavelet coefficients in
each sub band
Determining ratio of
absolute mean values of
adjacent sub bands
Figure 4.2 Feature extraction process
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The denoised signal was segmented into cardiac cycles. A single
cycle containing first heart sound S1, systolic period, second heart sound S2
and diastolic period, was extracted for analysis. To nullify the effect of input
gain variations, the original signal was normalized to absolute maximum.
Heart murmurs are non-stationary signals exhibiting marked changes with
time and frequency (Debbal and Bereksi-Reguig 2008). Hence, Wavelet
Transform, a proven tool for time-frequency analysis, was used.
The most important aspect of feature extraction is the selection of a
suitable wavelet and the number of levels of decomposition. Usually, the
signal is visually inspected first and if they are kind of continuous, Haar or
other sharp wavelet functions are used; otherwise a smoother wavelet can be
employed. Another method is to perform tests with different types of wavelets
and the one which gives maximum efficiency can be selected for the
particular application. The number of levels decomposition is chosen based
on the dominant frequency components of the signal. The levels are chosen
such that those parts of the signal that correlate well with the frequencies
required for classification of the signal are retained in the wavelet
coefficients. Since the frequency range of heart murmurs is 0 to 1000Hz
(Zhou 2008), the number of levels was chosen to be 5. The normalized signal
was decomposed into five subbands using Daubechies db6 wavelet
decomposition. The DWT decomposition of the input signal x[n] is
schematically shown in Figure 4.3.
h[n]
h[n]
h[n]
x[n]
A2
2
g[n]
A
Level 2
2
D2
1
g[n]
…..
.
2
Level 5
Approximations
2
A5
g[n]
Level 5
Details
2
D5
Details
Level 1
2
Details
D1
Figure 4.3 Level-5 wavelet decomposition to obtain wavelet coefficients
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The decomposition of the signal into different frequency bands is
simply obtained by successive highpass and lowpass filtering of the signal
(Kandaswamy et al 2003; Sadik and Mustafa 2007).
The decomposed
subbands with their corresponding ranges of frequency are shown in
Table 4.2. The resulting wavelet coefficients provide a compact
representation of the energy distribution of the signal in each subband. As the
frequency spectrum of heart murmurs range from 0 to 1000 Hz and the values
of the observed wavelet coefficients in D1 and D2 were also very close to
zero, the higher subbands D1 and D2 were discarded from further processing.
Table 4.2 Frequency range of sub bands
Decomposed sub band
Frequency Range(Hz)
D1
2000-4000
D2
1000-2000
D3
500-1000
D4
250-500
D5
125-250
A5
0-125
The time domain representation of the subbands for a normal heart
sound file is shown in Figure 4.4.
From the wavelet coefficients in each subband (D3, D4, D5 and
A5), a set of 15 statistical parameters were derived in order to represent the
time-frequency characteristics of the heart murmurs. These are shown in
Table 4.3.
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Figure 4.4 Decomposition of normal heart sound with db6 wavelet
Table 4.3 Features derived for classification of heart murmurs
Sl
No
1
2
3
4
No.of
features
Mean of the absolute values of the coefficients in each sub band
4
Standard deviation of the wavelet coefficients in each sub band
4
Average power of the wavelet coefficients in each sub band
4
Ratio of the absolute mean values of adjacent sub bands
3
Description of feature
Total
15
In order to automate the whole feature extraction process, Matlab
was linked with Microsoft Excel. The features were then exported to the
worksheet directly. These 15 parameters along with the corresponding output
(type of murmur) forms the input feature vector for classification (Criley et al
2000; January and Zahra 2007). The dataset used in this work has 441 feature
vectors or instances.
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4.5
CLASSIFICATION USING ARTIFICIAL NEURAL
NETWORKS
4.5.1
Neural Network Classifier
Artificial Neural Networks (ANN) are computational models that
are patterned after the structure of the human brain. They have the ability to
‘learn’ mathematical relationships between a series of input (independent)
variables and the corresponding output (dependent) variables. This is
achieved by training the network with a training dataset consisting of input
variables and the known or associated outcomes. Networks are programmed
to adjust their internal weights based on the mathematical relationships
identified between the inputs and outputs in a dataset. The knowledge gained
by the learning experience through training is stored in the form of connection
weights, which are used to make decisions on test inputs. Once a network has
been trained, it can be used for classification tasks with a separate test data set
for validation (Rajendra et al 2003; Jack 1996).
H1
X1
Y1
O1
I1
H2
X2
Outputs
I2
Y8
Inputs
O8
X15
I15
Input Layer
Hn
Hidden Layer
Output Layer
Figure 4.5 Feedforward neural network to classify heart murmurs
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Among the several existing neural network architectures, the
feedforward neural network trained using supervised learning with
backpropagation algorithm has been chosen for this work. This model, which
is considered the most useful learning model, is being widely used in the
biomedical field (William 1995; Maurice and Donna 2006). The feedforward
neural network used in this classification work is shown in Figure 4.5. The
input layer has 15 nodes representing the 15 input features and the output
layer has 8 nodes representing normal and seven different classes of murmurs.
4.5.2
Encoding of Data for ANN
The classification scheme of 1-of-C coding has been used for
classifying the heart murmurs into one of the eight output types. For each type
of heart murmur, a corresponding output class is associated. The feature
vector set, x represents the ANN inputs and the corresponding class once
coded, constitutes the ANN outputs. In order to make the neural network
training more efficient, the input feature vectors were normalized so that all
the values fall in the range between 0 and 1 (Jack 1996; Richard and Michael
2005). The encoding of output is as shown in Table 4.4.
Table 4.4 Encoding of output for classification of heart murmurs
Sl No.
Output vector
Classification
1
1 0 0 0 0 0 0 0
Normal
2
0 1 0 0 0 0 0 0
Early systolic
3
0 0 1 0 0 0 0 0
Mid systolic
4
0 0 0 1 0 0 0 0
Late systolic
5
0 0 0 0 1 0 0 0
Holo systolic
6
0 0 0 0 0 1 0 0
Early diastolic
7
0 0 0 0 0 0 1 0
Mid diastolic.
8
0 0 0 0 0 0 0 1
Late diastolic
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The value corresponding to the correct class of output is entered as
1 and other values are entered as zero. The modified input vector is xk, with k
= 1, 2,…..K where K is the number of heart murmur signals. The output
vector associated with xk is denoted by yk.
4.5.3
Training with Backpropagation Learning
As inputs and desired outputs are known, the training is done in a
supervised fashion. In the basic back propagation (BP) training algorithm, the
weights are moved in the direction of the negative gradient. The BP learning
updates the network weights and biases in the direction in which the
performance function decreases most rapidly – the negative of the gradient. A
single iteration of this algorithm can be written as
wk+1 = wk – αk gk
(4.1)
where wk is a vector of current weights and biases, gk is the current gradient,
and αk is the learning rate. Convergence is sometimes faster if a momentum
term is added to the weight update formula. When using momentum, the net
is proceeding not in the direction of the gradient, but in the direction of a
combination of the current gradient and the previous direction of weight
correction. In backpropagation learning with momentum, the weights for
training step t+1 are based on the weights at training steps t and t-1. The newff
function in Matlab’s neural network toolbox was used for the generation of
feedforward backpropagation neural network architecture. This newff function
has ‘learngdm’ as the default learning function which chooses ‘initnw’
initialization function for initializing a layer’s weights and biases according to
the Nguyen-Widrow initialization algorithm. Learning occurs according to
learngdm’s learning parameters with their default values as 0.01 for learning
rate and 0.9 for momentum constant.
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4.5.4
Activation Function
There are different types of activation functions. The most
commonly used are : (i) hyperbolic tangent sigmoid (ii) log sigmoid and (iii)
linear. The first criterion of an activation function is that the function must
output values in the interval range [0,1]. A second criterion is that the
function should output a value close to 1 when sufficiently excited. The
sigmoid function meets both the criteria. The performance of these three
activation functions were experimented in the neural network models
constructed.
4.5.5
Stopping Criteria
Network training continues until a specific terminating condition is
satisfied. The terminating condition chosen for the network convergence is
the minimum mean squared error (MSE) as defined below :
MSE 
where
1 p
2
 (d  y )
m
m
p m 1
(4.2)
p = number of training instances
d = desired outputs
y = output obtained from the neural network
The target for mean squared error set in our work is 0.001. Training
stopped when the value of MSE dropped below 0.001.
4.6
EXPERIMENTAL RESULTS AND DISCUSSIONS
The training algorithm, activation function and the number of
neurons in the hidden layer that provide the best results were determined
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empirically. For this purpose, several feedforward backpropagation neural
networks were constructed using various combinations of training algorithms,
activation functions and different number of neurons in the hidden layer. The
training algorithms used are Levenberg-Marquardt (LM), Gradient Descent
with Adaptive learning rate (GDA), Resilient Backpropagation (RP) and
Scaled Conjugate Gradient Descent (SCG). The activation functions used are
logsigmoid, tansigmoid and purelin. Each network was trained with 331
instances (75% of the dataset with uniform distribution of all classes) and
tested with 110 instances (25% of the dataset with uniform distribution of all
classes). The performance of these neural network models was measured
through accuracy, sensitivity and specificity. The results obtained are
presented in Table 4.5.
Accuracy, sensitivity and specificity were calculated using the
following formulae (Sadik and Mustafa 2007) :
Accuracy 
where
TP  TN
Total
(4.3)
Sensitivity 
TP
TP  FN
(4.4)
Specificity 
TN
TN  FP
(4.5)
TP = True positive, positive cases classified as positive
TN = True negative, negative cases classified as negative
FN = False negative, positive cases classified as negative
FP = False positive, negative cases classified as positive
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Table 4.5 Performance of different neural network models
Model Training Activation Number
number Algorithm Function of Epochs
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
LM
LM
LM
LM
LM
LM
LM
LM
LM
LM
LM
LM
GDA
GDA
GDA
GDA
GDA
GDA
GDA
GDA
GDA
GDA
GDA
GDA
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
SCG
SCG
SCG
SCG
SCG
SCG
SCG
SCG
SCG
SCG
SCG
SCG
Logsig
Logsig
Logsig
Logsig
Purelin
Purelin
Purelin
Purelin
Tansig
Tansig
Tansig
Tansig
Logsig
Logsig
Logsig
Logsig
Purelin
Purelin
Purelin
Purelin
Tansig
Tansig
Tansig
Tansig
Logsig
Logsig
Logsig
Logsig
Purelin
Purelin
Purelin
Purelin
Tansig
Tansig
Tansig
Tansig
Logsig
Logsig
Logsig
Logsig
Purelin
Purelin
Purelin
Purelin
Tansig
Tansig
Tansig
Tansig
8
10
6
10
6
5
4
5
19
15
18
16
1734
1400
1472
1371
2000
2000
2000
2000
2000
2000
2000
2000
147
73
140
110
2000
2000
2000
2000
2000
2000
2000
2000
141
113
143
116
713
756
827
538
931
773
633
659
Number of
neurons in
hidden layer
21
26
31
35
21
26
31
35
21
26
31
35
21
26
31
35
21
26
31
35
21
26
31
35
21
26
31
35
21
26
31
35
21
26
31
35
21
26
31
35
21
26
31
35
21
26
31
35
Accuracy Sensitivity Specificity
%
%
%
91.4892
93.6419
97.9473
95.9768
85.0311
85.0311
85.0311
86.1174
97.9473
99.0236
99.0236
99.0943
94.7183
96.8710
94.7183
92.7117
88.2602
86.1075
85.0311
81.8838
95.7946
96.8710
95.7946
94.7916
95.7946
95.7946
94.7183
95.9117
85.0311
85.0311
85.0311
86.1025
99.0236
99.0236
99.0236
95.9419
97.9473
97.9473
88.2602
96.9502
85.0311
85.0311
85.0311
86.1234
97.9473
96.8710
99.0236
96.9289
91.7584
83.4166
91.7584
96.5837
75.0750
75.0750
75.0750
87.7788
91.7584
100.000
91.7584
100.000
75.0750
83.4166
91.7584
95.3390
75.0750
75.0750
75.0750
81.5821
75.0750
91.7584
91.7584
95.3834
83.4166
91.7584
91.7584
98.9725
75.0750
75.0750
75.0750
87.8596
91.7584
91.7584
91.7584
96.5213
91.7584
91.7584
91.7584
97.6854
75.0750
75.0750
75.0750
87.7144
83.4166
83.4166
91.7584
98.9593
91.4494
95.1568
98.8642
91.9587
86.5062
86.5062
86.5062
75.0898
98.8642
98.8642
100.000
91.8272
97.6284
98.8642
95.1568
75.1152
90.2136
87.7420
86.5062
83.3919
98.8642
97.6284
96.3926
91.8117
97.6284
96.3926
95.1568
75.2631
86.5062
86.5062
86.5062
75.2463
100.000
100.000
100.000
91.8808
98.8642
98.8642
87.7420
91.8179
86.5062
86.5062
86.5062
75.0984
100.000
98.8642
100.000
83.3982
67
The network models that performed best with each of the four
training algorithms were compared. The comparison results are presented in
Table 4.6 and illustrated in Figure 4.6.
Table 4.6 Performance comparison of training algorithms
No. of Number
Accuracy Sensitivity Specificity
Training Activation neurons in
of
algorithms function
hidden Epochs
%
%
%
layer
Tansig
26
15
99.02
100.00
98.86
LM
Tansig
31
633
99.02
91.76
100.00
GDA
Tansig
26
2000
96.87
91.76
97.63
RP
Tansig
21
2000
99.02
91.76
100.00
Percentage
SCG
102
100
98
96
94
92
90
88
86
Accuracy
Sensitivity
Specificity
LM
SCG
GDA
Training Algorithms
RP
Figure 4.6 Performance comparison of training algorithms
It was observed that the neural network model with LM training
algorithm and 26 neurons in the hidden layer showed better performance
when compared to the models with other training algorithms. It was also
noted that tansigmoid activation function outperforms the other two activation
functions. Also, given the speed of convergence of the network during
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training is indicated by the number of epochs, the networks trained with LM
algorithm were observed to converge faster than those with SCG, GDA and
RP. Hence, the neural network model (Sl. No.10 in Table 4.5) with 26
neurons in the hidden layer, trained with Levenberg-Marquardt (LM)
algorithm and tansigmoid activation function for both the hidden and output
layer was found to yield the best results for the dataset used. The performance
of the proposed neural network classifier is comparable with other classifiers
cited in literature and the comparison is presented in Table 4.7.
Table 4.7 Performance comparison of different classifiers
Reference
Classifier
No of
Average
types of Classification
murmurs Accuracy (%)
classified
7
86.40
Faizan et al (2006)
MLP-ANN
Zhou et al (2008)
FBNN
6
95.83
Yadi et al (2008)
MLP-ANN
5
92.00
Proposed
MLP-ANN
8
99.02
4.7
SUMMARY
In this chapter, the development of a heart murmur classifier was
presented.
Discrete Wavelet Transform was used to extract a set of 15
features from the heart murmur signals. Feedforward neural network models
with backpropagation learning were developed with different combinations of
training algorithms and activation functions to classify the heart murmurs into
one of the eight types namely normal, early systolic, mid systolic, late
systolic, holo systolic, early diastolic, mid diastolic and late diastolic. The
neural network model with Levenberg-Marquardt training algorithm and
tansigmoid activation function was found to yield the best performance. The
results demonstrate the capability of the developed system as a support tool
for physicians in the diagnosis of heart murmurs.