Heart Sound Segmentation using Empirical Mode Decomposition

Heart sound segmentation method detects and extracts first (S1) and second (S2) sounds from phonocardiogram. Heart sounds are processed using Empirical Mode Decomposition (EMD). Intrinsic Mode functions (IMFs) obtained from EMD is selected based on energy, frequency and kurtosis based criterion. These select IMFs are analyzed by its kurtosis features. Kurtosis estimate of IMFs that lie outside of Gaussian distribution are selected for reconstruction of heart sounds. S1, S2 systolic and diastolic murmurs components are grouped separately. Keywords—Empirical Mode Decomposition, Estimator Intrerval I(N,q), First heart sound (S1), Gaussian distribution, Intrinsic Mode Function, Kurtosis, Second heart sound (S2).


INTRODUCTION
Heart sounds heard through stethoscope are essential for medical diagnosis of patient and provide heart rate and rhythm, valve functioning, and anatomical defects of heart [1]. This process called as heart auscultation. Now electronic stethoscopes are developed which captures heart sounds and convert them into electronic signal. These sounds can be processed with signal processing algorithm. This will help doctors for diagnosis instead going for ECG result which are large hardware. Developing such algorithm which will help in diagnose based on heart sounds features is done here.
Functioning of heart is periodic by repeating cycles of systole and diastole. Systole represents ejection of blood from heart and diastole represents filling of heart chambers with blood. First heart sound (S1) represents beginning of systole and second heart sound represents (S2) beginning of diastole [1]. This periodic functioning produces vibration which are propagated through chest walls and become audible. Only presence of S1 and S2 means normal functioning of heart. In abnormal conditions sounds present between S1 and S2 are called murmurs. These murmurs represent dysfunctions of heart valves. Murmurs loudness, its location in PCG wave, frequency decides dysfunction. Aortic stenosis and mitral regurgitation are well known murmurs. PCG is visual representation of heart sounds. In Fig 1 PCG wave of normal, aortic stenosis and mitral regurgitation is shown. S1, S2 and murmurs locations are shown in figure 1. In heart sound segmentation S1, S2 and murmurs are extracted using Empirical Mode Decomposition (EMD). EMD decomposes signal into oscillations that are present in signals [6]. These oscillations are called Intrinsic Mode Functions (IMF). These IMF are analyzed based on kurtosis which indicates changes in signal. Among IMFs some corresponds to S1 S2, others correspond to murmurs. These IMFs are separated as per requirement of desire segments. The rest paper is structured as Mathematical Background, proposed approach and obtained results.

A. Empirical Mode Decomposition
Empirical mode decomposition (EMD) decomposes signal into fast oscillation and slow oscillation [2]. It is iterative process until all oscillations are extracted. These finite numbers of oscillation are called as Intrinsic Mode Function (IMF). IMFs are obtained from signal by algorithm called as sifting algorithm sown in fig 2 [3]. Sifting algorithm is based on two constraints: each IMF has same number of zero-crossing and extremes, and also has symmetric envelope defined by the local maxima, and minima respectively. Furthermore it assumes that the signal has at least two extremes [2]. So, for any 1-D discrete signal I ori , EMD can be represented with following representation: Where IMF (j) is the j th mode (or IMF) of the signal, and I res is residual trend. The sifting procedure generates a finite number of IMFs that are nearly orthogonal to each other [3].

B. Intrinsic Mode function
EMD decomposes signal into zero mean band limited oscillatory components, simply called IMFs. Each IMF satisfies two basic conditions [4]: i) In whole data set the number of extreme and number of zero crossings must be same or differ at most by one ii) At any point, the mean value of the envelope defined by the local maxima and envelope defined by local minima is zero. IMF defined by first condition ensures instantaneous frequency will not have redundant fluctuations. IMF defined by the zero oscillations involves one mode of oscillations, no complex riding waves are allowed. IMF is not restricted to narrow band signal; it can be both amplitude and frequency modulated, also it can be non-stationary [2].
The idea of finding IMFs relies on subtracting the highest oscillations from signal step by step process, which is called the sifting process.

C. Kurtosis[2]
Kurtosis of a fourth-order stationary, zero-mean, stochastic process x(t) is defined as the fourth order cumulant for zerolag. Kurtosis is signal length dependent. Thus, the kurtosis estimate exists in a confidence interval, which is determined by the probability properties of the estimator. Estimator is having probabilistic lower and upper bound depends on the first statistics of estimator. For the X random process (X ∈ x t ) of mean μ and standard deviation σ. Chebyshev inequality gives this interval using equation (2) [2].
Where,q = 1 − (σ 2 /ϵ 2 ), ε >0, and  q) )) . . . (6) It states that if the kurtosis estimate of N-sample observation x(n) lies outside I(N,q), then it does not lie in Gaussian distribution. It could be hypothesized that heart sounds do not follow Gaussian distribution. This hypothesis is applied to heart sounds [1]; parts of PCG which lies outside Gaussian distribution correspond to heart sound. The IMFs which lies outside Gaussian distribution are used to reconstruct heart sounds. This is main concept behind EMD for heart sound segmentation. Extracting IMF from original signal, then applying kurtosis hypothesis and reconstructing oscillations correspond to heart sound.

A. Preprocessing
Heart sound segmentation is based on statistics parameter kurtosis so it necessary to make zero-mean signal, then signal is filtered using third order median and followed by tenth order butterworth filter with cutoff frequency 250 Hz. As major part of heart sound lies between 20-250 Hz. This filtered signal x f [n] is analyzed using EMD. Before filtration signal is down sampled to 12 kHz. iii) Kurtosis Based criterion [1] As previously discussed probabilistic interval in (6) is Gaussian distribution. Calculate kurtosis of each IMF based on Bootstrap concept. If it lies outside Gaussian distribution means IMF correspond to heart sound. In such way on three criterion IMFs are selected. IMF which does not follow one of them is rejected. Selected IMF are noted as sIMFλ[n].

B. EMD and Selection of IMFs
C. S1 and S2 Detection sIMF are processed using windowing followed by kurtosis estimate. This is done to locate S1 and S2 in heart sound. lw (w = 1, 2 . . W) = Fs/50: Fs/50: Fs/10 where Fs is samplingfrequency of signal. As each signal down sampled to 12 kHz i.e. Fs.
Each IMF undergoes windowing with different windows and one sample shifting. Kurtosis of each windowed section is estimated using (8). Start and ends of S1 and S2 are determined usingλ 4,j m ,lw .
Kurtosis can detect sudden changes in signal, so S1 and S2 suddenly rises at point where it starts. Stating points are STARTS find using (9).

IV. RESULTS
Empirical mode decomposition gives IMFs as shown in fig 3. Four IMFs are shown here for systolic murmur signal. Actually total seven IMFs are obtained. Number of IMFs also depends on sampling frequency of signal. For 12 kHz 7 IMFs and for 44.1 kHz 57 IMFs obtained.
While selection of IMFs energy criteria gives first IMF to Mn means its reject last IMFs while frequency based criterion reject initial IMFs as contains higher frequency oscillation. Selection of IMFs is as shown in fig 5. While estimating Gaussian interval using (6) q = 0.9999 [1], higher q value ensures Gaussian distribution curve. q is adjusted such that at least one IMFs must be selected by kurtosiscriterion. lw = Fs/50: Fs/50: Fs/10 is used such that smaller window will look at fast oscillation and larger window will look at slower oscillation. Detection of S1 and S2 is shown in fig 4. Segments of signal after complete process are sown in fig 6. Different S1, S2 and murmurs are separated from signal.