Classification of heart sound signal using curve fitting and fractal dimension
Introduction
The heart is a vital organ of body and statistics show that the first cause of mortality in the world, which is equal to 29 percent of all deaths, is caused by cardiovascular disease [1]. According to the CDC3 in 2012, eleven percent of adults suffer from heart disease, which is the highest percentage compared to other diseases [2]. The sound of the heart can describe the mechanical activity of the heart. According to pathological conditions in heart, the characteristics of heart sound signal are changed. The changes in the PCG4 signal occur before their symptoms. So, the diagnosis will be in the early stages. Today, the diagnosis of heart disease is dependent on the advanced technologies such as echocardiography and cardiac MRI. These technologies are expensive and also they cannot be used as a portable device [3]. Traditionally, auscultation is a noninvasive, cheap and simple method for diagnosing diseases. Auscultation is the monitoring of sounds heard over the chest walls, which is usually done by the stethoscope. The heart sound can be measured by phonocardiography. In addition, the analog or digital stethoscope can be used for listening the heart sound signal. Stethoscope is a simple instrument to convey the heart sounds from the chest to the ear of examiner.
A healthy heart has two clear sounds called first sound (S1) and the second sound (S2). By closing the mitral and tricuspid valves, S1 is produced at the beginning of ventricular contraction. S2 is produced due to the closure of aortic and pulmonary valves. Murmurs sounds are heard because of return of blood back through leaky valve (regurgitation), ventricular septal defect or arterial venous connection, the forward flow through narrow or deformed heart valves (stenosis), or due to the high speed of blood flow through the normal or abnormal valve. Different diseases may cause the audible murmur in different parts of the cardiac cycle. In general, murmurs are divided into two categories called systolic and diastolic. Due to the human hearing limitation and transient and non-stationary nature of PCG signal, diagnosis based on heart sound through a stethoscope requires to experience and skill. Therefore providing a system that can properly do primary diagnosis with the lowest cost is desirable.
Two algorithms for feature extraction and classification of heart sound signal (PCG) are proposed in this paper. In the first proposed algorithm, the information of PCG signal sequence is obtained by using the curve fitting method. Coefficients calculated in this way are used as features.
Murmur is an obvious symptom of disease. Murmurs are high frequency sounds. This means that they are intensively changed. Simply, it can be said that signal is more crumpled in the location of murmur. In addition, the PCG signal is self-similar. In the second suggested method, the PCG signal is considered as a fractal signal where the fractal dimension is a measure of signal complexity. Previous studies have shown that MFCC as an audio processing technique has good results on the heart beat signal [4]. So, to provide the advantages of MFCC, the final feature vector in the second proposed method is obtained by merging the fractal and MFCC features. In the last section, the proposed methods are compared with previous studies [5], [6].
Section snippets
Material and methods
Extensive studies have been done on the PCG signal. They are looking for suitable features that can express the characteristics of the signals as well. Timing, morphology and frequency could determine PCG signal characteristics [7]. Heart sound signal can be considered as a type of time series. Time series are the consecutive sequence of points recorded at regular time intervals. There are several ways to describe time series: time methods, frequency methods and time-frequency methods. The
Curve fitting
The curve fitting method is traditionally used to obtain the mathematical relationship between the observed signal and the independent variables. A function is found for the data by using the curve fitting method. To this end, the distance between the data samples and is minimized by using the Least squares (LS) method:
where are the weights. Different curve fitting models such as polynomial, linear, spline, etc. can be used for
Datasets and preprocessing
In this study several datasets are used. The first data set with 4 classes contains 26 normal, 30 murmurs, 13 Extra heart sound and 40 artifacts. This data collection through mobile and public environments have been recorded. Sampling frequency is 1/44 KHZ. The lengths of signals are between 1–30 s. We removed signals with length less than 7 s. The first 7 s of remained signals were used to classify signals because we want to have the same length from each signal [1].
Other datasets are also used.
First proposed method
In the first proposed method, features were extracted by using the curve fitting method. This method has been used for classification of hyperspectral images previously [27]. For each pixel of a hyperspectral image with N spectral bands, the curve of the intensity values of N bands versus the band numbers is known as the spectral response curve or the spectral signature of pixel. The number of bands is about 100 or 200. Our study is done on PCG signal. Sampling
Classifier and performance parameters
In this study we used “K nearest neighbor” classifier with Euclidean distance. Classification is done based on distance of test points from the training points. Different criteria can be used to measure the distance between two points in input data space. Input matrix X with mx * n dimensions is given. This matrix can be considered as a set of row vectors: X1, X2, …, Xmx. Matrix Y with my * n dimensions also contains set of row vectors: Y1, Y2, …, Ymy. Euclidean distance between two vectors of X
Results
We compared the proposed methods with [5], [6] where features have been extracted using wavelet transform and filter banks. In Table 2, they have been named wavelet and Entropy, respectively. In addition to [5], [6], we have compared our methods with PCA and KPCA. The result of comparison is given in Table 2.
According to the filter bank algorithm, entropy curve determines how many filters are approximately required. So, the number of required features is determined. We implemented filter bank
Conclusion
The heart sound signal characteristics change according to type of pathological conditions in the heart. A problem in the activities of the heart can cause disturbances in heart sound signal. A cheap and efficient method for cardiac disorders diagnosing is interpreting of the heart sound.
In this paper two methods were proposed. The phonocardiogram signal is approximately periodic due to synchronization with a biological process which is a repeated cardiac cycle. In the first proposed method, we
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