Stochastic- and Neuro-Fuzzy-Analysis-based characterization and classification of 4-Channel Phonocardiograms for Cardiac Murmur Detection

Abstract

[...]a relevance analysis is carried out using Fuzzy Rough Feature Selection. The valve lesion severity was evaluated by cardiologists according to a clinical routine. 55 patients were labeled as normal, while 88 had evidence of cardiac murmurs (aortic stenosis, mitral regurgitation, etc). [...]400 individual beats were chosen, 200 normal and 200 with evidence of cardiac murmur. [...]the following two different combinations of IMF were selected:

Headnote

Abstract: Cardiac murmurs (CMs) are the most common hearts diseases that are typically diagnosed from phonocardiogram (PCG) and echocardiogram tests -often supported by computerized systems. Research works have traditionally addressed the automatic CM diagnosis with no distinctively use of the four auscultation areas (one of each cardiac valve), resulting -most probably- in a constrained, nonimpartial diagnostic procedure. This study presents a comparison among four different CM detection systems from a 4-channel PCG. We first evaluate the acoustic characteristics derived from Mel-Frequency Cepstral Coefficients, Empirical Mode Decomposition (EMD), and statistical measures. Secondly, a relevance analysis is carried out using Fuzzy Rough Feature Selection. Thirdly, Hidden Markov Models (HMM), Adaptative Neuro-Fuzzy Inference System (ANFIS), Naive Bayes, and Gaussian Mixture Model were applied for classification and validated using a 50fold cross-validation procedure with a 70/30 split demonstrating the functionality and capability of EMD, Hidden Markov Model and ANFIS for CM classification.

Keywords: ANFIS, cardiac murmur, empirical mode decomposition, hidden markov models, phonocardiogram.

(ProQuest: ... denotes formulae omitted.)

1.Introduction

Cardiovascular diseases (CVDs) are the main cause of mortality in the world (Dwivedi et al., 2019) (World Health Organization, 2020), as well as of perioperative morbidity and mortality (Lee et al., 2019), and the numbers are still increasing. CVDs are generated when the blood flow becomeses turbulent and damages valves, being cardiac murmurs (CMs) one of most common mechanical CVD. Heart mechanical activity can be appraised by auscultation recordings, i.e., phonocardiographic (PCG) signals (Dwivedi et al., 2019) (Ismail et al., 2018), which is an inexpensive and non-invasive clinical procedure (Becerra et al., 2012). These heart sounds are commonly analyzed at 4-Standard Auscultation Areas (4-SAA), one for each cardiac valve, in order to thoroughly examine the state of the cardiac valves, as there are invisible murmurs for systems based on auscultation signals acquired from a single area (Karnath & Thornton, 2002). Besides, the PCG signals could be used patient identification (Becerra et al., 2018).

By taking advantage of the morphological changes in the signal shape caused by heart murmurs, some studies have addressed the CM detection following approaches based on energy and temporal measurements (Ahlstrom et al., 2006). Notwithstanding, CMs have a nonstationary nature and exhibit sudden frequency changes and transients (Becerra et al., 2012) making then the morphological features non-sufficient. Other studies have considered the nonlinear nature of physiological signals by means of the analysis of fractal features and the optimization of the embedding parameters in order to improve the training and classification stages(Ahlstrom et al., 2006) (Kumar et al., 2010), although the increment in processing time becomes a big problem for real-time applications. On the other hand, several approaches based on wavelets have been proposed taking into account the time-frequency disturbances associated with cardiac murmurs (Ergen et al., 2012)(Ismail et al., 2018). However, in contrast to approaches based on wavelets, other decomposition methods, such as Empirical Mode Decomposition (EMD), and Hilbert-Huang Transform (HHT) (Ismail et al., 2018) , express the signal as an expansion of functions which are signal-dependent (Kopsinis & McLaughlin, 2009). Another interesting field is related to the acoustical disturbances caused by heart murmurs, which can be analyzed using Mel-Frequency Cepstral Coefficients (MFCC) (Vepa, 2009), but these procedures are very sensitive to artifacts or noises frequently involved in the acquisition stage (Becerra et al., 2012).For this reason, the combination between MFCC and statistical moments of HHT with appropriate EMD components would be suitable. Additionally, the learning capability of Adaptive NeuroFuzzy Inference Systems (ANFIS) (Fahad et al., 2018) (Uǧuz, 2012) can improve the classification. The use of Linear Discriminant Analysis (LDA) and ANFIS to detect heart valve disorders was studied in (Sengur, 2008) with promising results. In (Chourasia et al., 2012), an ANFIS model for evaluation of foetal health status using PCG signals was implemented effectively and provided high accuracy for antepartum antenatal care. Besides, a biomedical-based decision support system was developed in (Uǧuz, 2012) for heart sound signal classification, where the reduced features of three types of heartbeat sounds were used as input patterns of an ANFIS classifier. Likewise, the inclusion of stochastic models, such as Hidden Markov Models (HMM), have successfully complemented procedures for cardiac murmur detection (Uǧuz, 2012) (Kotb et al., 2019). However, all these studies have been developed using a single auscultation signal, and fail when a murmur is missing or attenuated in the standard single derivation.

In this study, we present a classification approach, which is based on a MFCC-HHTHMM optimized by means of Genetic Algorithms and compared with another based on MFCC-HHT-ANFIS hybrid technique, which are applied on the combination of different IMFs of 4-channel PCG. As well, a relevance analysis is used to reduce the number of features. This comparison is presented to structure an objective and accurate mechanism for generating a more reliable CM diagnosis.

2.Materials and methods

A robust murmur detection system from 4 SAA PCG signals was developed. The Figure 1 shows the methodology carried out in this work. Broadly, it consists of six phases: i) Data Base, ii) preprocessing, iii) signal decomposition analysis, iv) feature extraction, v) relevance analysis and vi) Inference. The workflow of proposed methodology is described in the following subsections.

2.1. Database

The database is made up of 143 de-identified adult subjects, who gave their formal consent, and underwent a medical examination with the approval of the ethical committee. The valve lesion severity was evaluated by cardiologists according to a clinical routine. 55 patients were labeled as normal, while 88 had evidence of cardiac murmurs (aortic stenosis, mitral regurgitation, etc). From each patient, 8 recordings were recorded according to the four standard auscultation areas (4-SAA), i.e., mitral, tricuspid, aortic and pulmonic areas, in the phase of post-expiratory and post-inspiratory apnea. Each recording lasts 8 s and was obtained with the patient standing in dorsal decubitus position. The signals were acquired at 44.1 kHz with 16-bits per sample with an electronic stethoscope (WelchAllynr Meditron model). Finally, 400 individual beats were chosen, 200 normal and 200 with evidence of cardiac murmur. The individual beats picked out were the best from each cardiac sound signal, according to a visual and audible inspection by a cardiologists.

2.2. Preprocessing

According to Figure 1, the 4-SAA PCG recordings were resampled from 44.1 kHz to 4410 Hz applying a FIR low-pass antialiasing filter in order to reduce the computational cost. Next, the signals were normalized in [-1,1] and 200 normal heartbeats and 200 with murmurs were segmented for each channel.

2.3.Signal decomposition analysis

In order to obtain relevant features, a decomposition analysis was carried out on PCG signals using the EMD method. Seven Intrinsic Mode Functions (IMFs) were estimated for each signal using the Sifting algorithm, with the following parameters: resolution 40 dB, residual energy 40 dB and the gradient step size 0.01. Next, several constructions based on different IMFs were made in order to highlight the murmur and attenuate the noise. Finally, the following two different combinations of IMF were selected: IMF-C1= {3, 5, 7} and IMF-C2= {1, 3, 5, 7} as result of adding to odd and even IMF respectively. The technique EMD applied is describes as follow.

Empirical Mode Decomposition - This method, reported in (N. E. Huang et al., 1998), adaptively decomposes a multicomponent signal x(t) into a number L of IMFs, h(i) (t ), 1 < i < L,

... (1)

where d(t) is a remainder which is a non zero-mean slowly varying function with only few extrema. Each one of the IMFs, say the ith one h(i) (t), is estimated with the aid of an iterative process, called sifting, applied to the residual multi-component signal.

... (2)

According to this, during the (n +1) th sifting iteration, the temporary IMF estimate (t) is improved according to the following steps [10]: 1) Find the local maxima and minima of ?) (t) 2) Interpolate, using natural cubic splines, along the points of ?) (t) previously estimated, in order to form an upper and a lower envelope. 3) Compute the mean of the two envelopes. 4) Obtain the refined estimate hП+ (t) of the IMF by subtracting the mean found in the previous step from the current IMF estimate ?) (t) 5) Proceed from step 1 again unless a stopping criterion has been fulfilled. For the first iteration, x1'1) (t) is used as temporary IMF estimate h1 (t).

2.4.Characterization

The MFCC were calculated to signals without decomposition and to the two constructs IMF-C1 and IMF-C2. Particularly, a Mel-scaled filter bank was used to calculate the Melwarped spectrum, so the first 8 and 12 MFCC were estimated using 24 Hamming shaped filters and sliding hamming windows (50% overlap) over different combinations of EMD components derived from the whole beats. Additionally, 10 statistical measures were obtained from instantaneous parameters calculated of the result achieved by the HHT applied to constructs. These measures are shown in Table 1.

Mel-Frequency Cepstral Coefficients (MFCC)- Studies have shown that human perception of the frequency content of audio sounds does not follow a linear scale but as a Mel-warped frequency, which spaces linearly for low-frequency contents and logarithmical at high frequencies (Becerra et al., 2012). So, MFCC are a family of parameters that are estimated as (X. Huang et al., 2001):

... (3)

Where, XF [m] = ln(^N_ 1 X[г]|2 Hm [г]). Here, X[i] is the Fourier transform of an input random sequence x[n] and Hm[i] is a triangular band-pass filter with central frequency in f [m]. Thus, in order to simplify the signal spectrum without any significant loss of data, a set of M triangular band-pass filters must be used, which are nonuniform in the original spectrum and uniformly distributed at the Melwarped spectrum. Each filter is multiplied by the spectrum so that only a single value of magnitude is returned per filter.

Hilbert-Huang Transform (HHT) - Instantaneous frequency and its magnitude of heart sound signals can be extracted by HHT, which is used to adaptively decompose non-stationary and nonlinear signals and extract the instantaneous frequency. In general, HHT consists of two steps: Empirical Mode Decomposition (EMD) and Hilbert transform (HT). EMD is used to adaptively decompose the signal into a series of IMFs. HT is then carried out to acquire the instantaneous frequency and amplitude of each IMF and constitute the time-frequency-energy distribution in the Hilbert-Huang spectrum of the signal (Y. Tseng et al., 2012).

This transform is a simple method for analyzing the frequency and amplitude changes of signals into the time, which can only be applied to mono-component signals. The HT of a real function x (t) is calculated from convolution between x (t) and the inverse of the time , using (4) which highlight local properties of the function (Y.-L. Tseng et al., 2012).

... (4)

The HHT carried out the construction of one analytics complex signal Z(t) where its imaginary part is the HHT of x(t) and the real part is the original signal x(t) and its espectral frequency is null for negative frequencies. This function is described by (5).

... (5)

... (6)

... (7)

... (8)

... (9)

Where, a(t) Instantaneous amplitude, 6(t): Instantaneous phase, w(t): Instantaneous angular frequency [rad/s] and f (t) Instantaneous frequency [Hz].

2.5.Relevance Analysis

Following the steps of the Figure 1, the relevance analysis was carried out using Fuzzy Rough Set with entropy (FRFS) with the aim of obtaining a minimal feature subset. The algorithm FRFS was implemented and its parameters associated to the neighbor distance tolerance (d) and the inclusion rate (b) were adjusted according to procedure presented in (Orrego et al., 2012).

Fuzzy-Rough Feature Selection (FRFS): Fuzzy-rough sets encapsulate the related but distinct concepts of vagueness and indiscernibility, both of which occur as a result of uncertainty in knowledge (Hu et al., 2006). Fuzzy-rough feature selection (FRFS) provides a means by which discrete or real-valued noisy data (or a mixture of both) can be effectively reduced without the need for user-supplied information.

Let Ube a non-empty set of finite objects (the universe of discourse) where x,y e U and A is a non-empty finite set of features where a is a feature in A, P ç A and Г is a set of decision features. The fuzzy lower and upper approximations can be defined using a r-transitive fuzzy similarity relation to approximate a fuzzy equivalence class X (Radzikowska & Kerre, 2002):

... (10)

... (11)

where W is a fuzzy implication and r a t-norm. Rp is the fuzzy similarity relation induced by the subset of features P:

... (12)

... is the degree to which objects x and y are similar for feature a. The crisp positive region in traditional rough set theory is defined as the union of the lower approximations. By the extension principle (Zadeh, 1975), the membership of an object x e U, belonging to the fuzzy positive region can be defined by (MacParthalain & Jensen, 2009):

... (13)

An important issue in data analysis is discovering dependencies between attributes. The fuzzy-rough degree of dependency of H on the attribute subset P can be defined

... (15)

A fuzzy-rough reduct R can be defined as a minimal subset of features of the initial attribute set C such that for a given set of attributes Г preserves the dependency degree of the entire dataset, i.e., угл ?) = y'z 0е) У Ýa_?3 0е) ~ у'я ?) for all а в R.

2.6.Classification and validation

In this study four classifiers were implemented: i) Gaussian Mixture Model (GMM), ii) Naive Bayes, iii) HMM, and iv) ANFIS. The GMM and Naive Bayes classifiers were used in order to select the better combination of IMF (IMF-C1 and IMF-C2) together with the MFCC coefficients due to their simplicity. GMM and Naive bayes techniques are widely known and described in different medical applications (Al-Aidaroo et al., 2012) (Farsaie Alaie et al., 20i6)(Mannepalli et al., 20i5)(Reynolds & Rose, 1995). On the other hand, the HMM classifier (Fahad et al., 2018) (Jimenez et al., 2014) is compared with an ANFIS classifier in order to obtain the higher accuracy in murmur detection for which the arquitecture (number of states and Gaussian functions) of HMM classifier was optimized using Genetic Algorithm.

The HMM classifier (with unoptimized arquitecture) implemented for stochastic analysis of the feature space, in order to recognize the beat samples is type ergodic with 16 Gaussian functions and 5 states. The training stage was developed using an EM algorithm in order to estimate the maximum likelihood parameters with a convergence at loe-6. The classification stage was carried out by a 30- fold cross-validation procedure using a 70/30 split, where consistency and representation capability of the feature space were analyzed. The optimization of the architecture of this classifier was carried out implementing a genetic algorithm with uniform and geometric distributions for mutation and selection respectively, and Bounds of Gaussians with domain [1 40] and states with domain [2 40]. The genetic algorithm are widely described by (Bartz-Beielstein et al., 2014). The last classifier implemented was the ANFIS with training parameters described in Table 2 for the classification of heartbeat sounds, i.e., normal or murmur, where the reduced feature set was used as the input vector and this classification stage was carried out by a 50- fold cross-validation procedure using a 70/30 split, where consistency and representation capability of the feature space were analyzed.

Hidden Markov Models (HMM) - HMM is an extension of Markov chains, where each state does not correspond to an observable event, but is connected to a group of probability distributions of the state. In some applications, the states may have a certain physical meaning attached to the states or the sets of states (Uǧuz et al., 2007). There are several well-known training criteria, such as Maximum Likelihood Estimation (MLE), Maximum Mutual Information (MMI), among others, however, this study has focused on applications based on the MLE criterion, given its good performance in previous studies (Becerra et al., 2012). Let X = Irp°'Pr:r = 1.r} a training set of R samples, with categories C = {c" ^r: r = 1.Rj for M different classes, i.e., c1 e {cm: m = 1,..., M}. Also, each sample is represented by a sequence of feature vectors of length ncpr, so, = {tprt:t = 1.гмрг}. The total set of parameters of the HMM is denoted by 0 and is composed of M models, i.e., 0 = {Xm}, where Xm denotes the set of parameters of the HMM corresponding to class cm. The training procedure based on MLE criterion is carried out taking into account the following objective function:

... (16)

The optimization of (4) is achieved by adjusting the parameters of each model separately, relying on the training observation data, so that expression (4) gets a maximum value. This procedure includes the Expectation Maximization (EM) algorithm which is a wellknown method for finding the maximum-likelihood estimate of the parameters of an underlying distribution from a data set when the data are incomplete or have hidden parameters (Fink, 2007).

Adaptive Neuro-Fuzzy Inference System (ANFIS): It is a simple data learning technique that uses Fuzzy Logic to transform given inputs into a desired output through highly interconnected Neural Network processing elements and information connections, which are weighted to map the numerical inputs into an output (Jang, 1993). For simplicity, it is assumed in the ANFIS architecture, two fuzzy IF-THEN rules based on a first order Sugeno model (Becerra et al., 2013):

... (17)

... (18)

Where, x and y are inputs, A. and B. are fuzzy sets, f are outputs within the fuzzy region specified by the fuzzy rule, and p,, q,, r. are design parameters which are adjusted during the training process. In Figure 2, these two rules are implemented by means of a fivelayer ANFIS architecture, where П is an AND operator to fuzzify the inputs, the N-nodes indicate a normalization to the firing strengths from the previous layer. In the 4th layer, the nodes are adaptive and the output of each node is the product of the normalized firing strength with a first order polynomial (for a first order Sugeno model). The overall output f of the model is given by one single fixed S-node, i.e., f = S, w/J.

3.Results and discussion

Table 3 shows the dimensionality reduction results of the technique implemented in this study. FRS-E means Fuzzy Rough Set Algorithm using entropy estimation, its parameters associated to the neighbor distance tolerance (8) and the inclusion rate (ß) were adjusted by heuristic routines comparing the difference in the classification accuracy corresponding to the cross-validation 70-30 with the algorithms k-NN and Naive Bayes which are widely known by their simplicity. The best average results are achieved with 8=0.05 for the accuracy and ß=0.5 for percentege reduction. The best accuracy was obtained with 8=0.05 and ß=0.5 which was used for final selection of characteristic with FRS-E.

The Table 4 shows the results in terms of accuracy of murmur detection by area of the Naive Bayes and GMM classifiers, in order to select relevance coefficient MFCC of constructs IMF-C1 and IMF-C2, obtaining the best results with 12 MFCC of IMF-C2 for both classifiers.

Table 5 presents the average accuracy of classification of two cardiac murmur detection systems for PCG signals the first based on HMM and second using ANFIS tested with the same feature sets shown in table 5 and obtaining the same feature set as the best but the more accuracy. These results show that MFCC 9, 10, 11 and 12 of the IMF 1 contain relevant acoustical information related to heart valve damages.

Table 6 presents statistical measures of the HMM, ANFIS and HMM-AG classification performance for MFCC-HHT features over EMD components IMF-C2, considering each auscultation area.

Finally, these classification approaches are compared with other HMM-based classifiers trained with features of single auscultation signals (see Table 7) and support vector machine (SVM), where a greater performance is evidenced by ANFIS.

4.Conclusions

The interpretation of heart sounds depends on the physician's ability and experience. Such limitations can be reduced by developing biomedical-based decision support systems. In this study a comparison between two objective and accurate mechanisms of 4-SAA PCG signal classification carried out.

The first system is based on HMM and second in ANFIS. One system reliable cardiac murmur detection, in terms of sensitivity and specificity, was obtained. The representation capability of the EMD technique applied to 4-SAA PCG signals and stochastic analysis performed by an ergodic HMM of acoustic features derived from MFCC and statistical moments of HHT offered a high performance in the detection of heart murmurs.

These features substantially outperformed the traditional MFCC applied directly on the signal. The EMD representation enhanced the acoustical content associated with cardiac murmurs and reduced the acoustical components related to normal heart sounds or noises included in the acquisition stage. The relevance analysis based on FRFS allowed a reduced feature space to be found with low complexity and high representation capability, which is related to a high learning capability. The MFCC 9, 10, 11 and 12 of the IMF-C2 contain relevant acoustical information in terms of the detection of heart murmurs. Although this stochastic classifier demonstrated to be highly dependent on the signal representation and parameter initialization for the model optimization.

The combination of different EMD components enhances the acoustical content associated with cardiac murmurs and reduces the acoustical components related to the normal heart sounds or noises included in the acquisition stage. However, the ANFIS demostred a similar performance with respect to HMM, but HMM optimized with AG achieved an increase in the accuracy of 0.14% which showed high discriminatory power of the feature sets obtained from EMD-MFCC and low dependence on the performance of the classifier. However, and regarding the ANFIS results, a high performance in terms of accuracy, sensitivity and specificity was achieved, and the fuzzy rules played an important role in the detection procedure. Nevertheless, the operation parameters and the type of fuzzy functions were not optimized by a criterion function. In this sense, the automatic tuning of ANFIS parameters is an issue to be dealt with in future works.

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