Time domain

Time related features can be extracted directly from the acoustic signal, represented in its temporal progression. In these cases, the signal does not undergo geometric or mathematical transformations; the phases of the cardiac cycle are still perfectly recognisable and identifiable. Features extracted with this approach are the time intervals between the various heart sounds, the amplitude (or intensity) and heart rate (table 1).

Frequency domain

A very large number of features can be extracted by exploring the signal in the frequency domain (table 1).16 ,17 ,27 ,28 Magnitude and phase characterise the frequency content; power spectrum is useful to characterise periodic signals; and energy spectrum is especially useful for time limited portions of the signal.

Analyses are usually performed with the FT and the wavelet transform (WT), often combined in the same algorithm.

1) FT: considers the signal as a sum of sinusoids. The short time FT (STFT) is obtained by calculating the FT of sequential portions of the time signal by applying a shifting window. The location of the window gives the time dimension to the frequency analysis. Window length is critical when using STFT because a wide window gives complete frequency information but does not follow the physiological signal short time variation. On the other hand, a small window reduces the frequency resolution. STFT allows distinguishing S1 and S2 because of their different frequency extent.17 The frequency domain also allows characterising the range of frequencies (bandwidth) of murmurs, which is usually larger for diastolic than for systolic ones.45 The SD of the duration of intervals from S1 and the point of maximum intensity within each cardiac cycle, the mean value of such intensity, and the distance between S1 and the beginning of the systolic murmur are three significant distinguishing features identified by El-Segaier et al.24 Information obtained in the frequency domain (envelopes of autocorrelation functions) may also allow for a method that does not require heart sound segmentation.30 A different approach based on cepstrum analysis (the result of taking the FT of the logarithm of the estimated spectrum of a signal)18 has been very successful as a feature vector for representing the human voice and musical signals. Unfortunately, there is too little literature on the implementation of this type of feature analysis of heart sounds, and so it is difficult to understand the reliability of this approach.

2) WT: This method of signal analysis allows obtaining high-resolution time and frequency information simultaneously. The main difference with the FT is that the wavelets are localised in both time and frequency whereas the standard FT is only localised in frequency. A WT plot is generally a 3D diagram in which the amplitude of each frequency of the signal is related to time.45 A high number of features can be extracted using a WT approach. Turkoglu et al35 extracted 13 coefficients using a wavelet decomposition method. Then, the STFT of wavelet coefficients, performed at seven different frequency intervals, was used to obtain 91 wavelet entropy features.35 Andrisevic et al33 used the wavelet techniques to de-noise and prefilter heart sounds. The WT plot of a whole cardiac cycle was then reorganised as a vector and taken as input of the classifier.33 Choi and Zhongwei32 presented a method in which only two features were extracted from the autoregressive spectral envelope after a wavelet-based analysis of the acoustic signal. In this case, the manipulation of the signal was minimal and easy, the features being simply extracted from the plot of the envelope. Starting from an initial set of 83 features obtained by decomposing a matrix of continuous WT values, Chen et al36 selected a final set of 26 features as input of the classifier by using the sequential floating forward selection. Yuenyong et al30 based their classification system on 35 features extracted with a WT approach (the values of the signal energy of 32 non-overlapping windows, the number of peaks detected, the mean distance between two consecutive peaks, and signal energy of the whole segment). It is now recognised that WT applications have a better performance than FT, regardless of the decisional instrument.

Non-linear and chaotic domain

Physiological signals often vary in a complex and irregular manner. Analysis of linear statistics such as mean values, variability measures and spectra of such signals generally does not address directly their complexity and useful information may be missed. Non-linear dynamics, of which Chaos Theory forms an important part, have been used to extract signal characteristics that are not time–frequency related. Ahlstrom et al37 combined ‘traditional’ parameters obtained in the time and frequency domains with other non-linear and chaotic features.37 Nigam and Priemer44 used a non-linear feature (simplicity index of the signal) to identify S1, S2 and murmurs in the cardiac cycle. The most used fractal parameters are the Lyapunov exponents (formally the quantity that characterises the rate of separation of infinitesimally close trajectories of a dynamical system). The maximum of these exponents determines a notion of predictability for a dynamical system. Using a database of 164 phonocardiographic recordings, Delgado-Trejos et al41 tested the accuracy of the system using several combinations of time-varying and time–frequency features, perceptual, and fractal features. Fractal type features were the most robust family of parameters (in the sense of accuracy vs computational load) for the automatic detection of murmurs, providing the best contribution to accuracy (97.17%), followed by time-varying and time–frequency (95.28%), and perceptual features (88.7%). Accuracy around 94% was reached just by using the two main features of the fractal family.41

Statistical model

The decision algorithm proposed by El-Segaier et al24 using a stepwise logistic regression analysis has 95% sensitivity and 72% specificity in distinguishing normal from pathological sounds. Other systems are based on fuzzy clustering, a process of assigning membership levels to assign data elements to one or more class. The system by Nigam and Priemer,44 based on a fuzzy clustering technique, had 73% sensitivity and 100% specificity in detection of presence of systolic murmur.44

Machine learning

The three main machine learning based algorithms used to classify heart sounds are K-nearest neighbour (K-nn), artificial neural network (ANN) and support vector machine (SVM).

These systems require a learning phase. The learning phase for K-nn and SVMs is a single step process where systems are fed with a set of known normal and pathological heart sounds (training set) to train the system to screen pathological (training phase). ANN requires a further step (test phase) on a different data set (test set) to verify that the training is unbiased and that the selected set of features is solid and fitting. When the data set is limited, the test phase can be iteratively performed by recruiting one observation each time for testing the ANN trained with the remaining set of data (Jack-Knifing method).27 ,28 At the end of the learning phase, the performance of the system can be assessed on the field.

1) K-nn classifier: The k-nn algorithm is one of the simplest machine learning algorithms—an object is assigned to the class most common among its k-nn values already correctly labelled (k is a positive integer, typically small). These classifiers are typically computationally simple. Performance (accuracy) of a K-nn classifier in the screening of cardiac valve disease (healthy/diseased) was 86% when the system was fed with WT features18 and 97% with non-linear features.41

2) ANN: ANN emulates the architecture and property of learning which characterise biological information systems, being a network of interconnected processing nodes (neurones) able to perform simple mathematical computation. A typical neurone receives inputs from the neurones feeding into it from which it generates an output. Its output is then disseminated to the neurones that it feeds into. The interconnections are weighted and modulate the inter-neuronal interactions. An ANN derives its property of emergent learning from the malleability of interconnection strengths.

ANN is the most used classifier in the automatic diagnosis of heart sounds. The system developed by DeGroff et al27 misclassified pathological cases (a case with pulmonary stenosis and a case with an atrial septal defect) belonging to pathological classes that were grossly under-represented in the training data. These results show that ANN generalisation would improve with better representation of all classes in the training data for which more data would have to be collected.

Bhatikar et al28 developed a classifier with 252 neurones input layer (corresponding to 252 bins in the discrete energy spectrum with a range of 0–252 Hz and a bin size of 1 Hz), 15 neurones hidden layer and one binary output neurone (0, innocent; 1, pathological),28 and high performance in the diagnosis of ventricular septal defect (88% sensitivity; 83% specificity).

Pretorius et al17 combined the results of a series of six ANNs. Each one of the six ANNs was designed to recognise the presence or the absence of a specific VHD (0, NO; 1, YES). The average sensitivity at the four auscultation sites was 60%. When using a subset of ANN combining registrations performed at the four auscultation sites, 91% sensitivity and 94% specificity were reached. Therefore, the number of auscultation sites is also important.

3) SVM: SVMs are supervised learning models with associated learning algorithms that analyse data and recognise patterns. Given a set of training examples, each marked as belonging to one of two categories, a training algorithm builds a model that predicts whether a new example falls into one category or the other. Multi-class classification follows a hierarchical structure. Choi and Zhongwei32 created a decision-making tree composed of six binary SVM modules classifiers having a set of the three features named above as input. The system recognised abnormal cardiac sound with 99.9% sensitivity and 99.5% specificity. As observed with other classifiers, performance reduces when the number of final decision classes increases so that these high performance standards were not reached in the diagnosis of the single valve disease (89.9% for aortic valve disorders, regurgitation or stenosis; 88% for mitral valve disorders, regurgitation or stenosis). Likewise, diagnostic performance of a sequential SVM-based decision tree16 using a wide feature set (100 features) was high at the first decisional step (healthy vs pathological) (sensitivity 87.5%; specificity 94.7%), and at each single decisional step (systolic vs diastolic 89.3% and 93.4%; aortic stenosis vs mitral regurgitation 91% and 93%; aortic regurgitation vs mitral regurgitation 94.7%, and 92.1%, respectively). However, the four steps were sequential so that the total accuracy of the system was 77% and 78% for systolic and diastolic murmurs, respectively.