Original Article

Cardiac state diagnosis using higher order spectra of heart rate variability

K. C. Chua Division of Electronics and Computer Engineering, Ngee Ann Polytechnic, Singapore, 590011Correspondencejerry-petrofsky@sahp.llu.edu

V. Chandran School of Engineering Systems, Queensland University of Technology, Brisbane, Queensland, 4001, Australia

U. R. Acharya Division of Electronics and Computer Engineering, Ngee Ann Polytechnic, Singapore, 590011

C. M. Lim Division of Electronics and Computer Engineering, Ngee Ann Polytechnic, Singapore, 590011

Original Article

Cardiac state diagnosis using higher order spectra of heart rate variability

Abstract

Heart rate variability (HRV) refers to the regulation of the sinoatrial node, the natural pacemaker of the heart, by the sympathetic and parasympathetic branches of the autonomic nervous system. Heart rate variability analysis is an important tool to observe the heart's ability to respond to normal regulatory impulses that affect its rhythm. A computer-based intelligent system for analysis of cardiac states is very useful in diagnostics and disease management. Like many bio-signals, HRV signals are nonlinear in nature. Higher order spectral analysis (HOS) is known to be a good tool for the analysis of nonlinear systems and provides good noise immunity. In this work, we studied the HOS of the HRV signals of normal heartbeat and seven classes of arrhythmia. We present some general characteristics for each of these classes of HRV signals in the bispectrum and bicoherence plots. We also extracted features from the HOS and performed an analysis of variance (ANOVA) test. The results are very promising for cardiac arrhythmia classification with a number of features yielding a p-value <0.02 in the ANOVA test.

Keywords:

Heart rate Bispectrum Bicoherence Statistics Entropy

1. Introduction

Heart rate variability (HRV) study refers to the characterization and measurement of changes in heart rate. Disease and affliction influence the heart rate, and therefore, the pattern and range of heart rate variability (HRV) contain important information about the robustness of health and type of disease. Classification based on features that capture the spread and pattern of this parameter can provide useful insight about the type and intensity of the affliction.

HRV is a useful signal for understanding the status of the autonomic nervous system (ANS). HRV refers to the variations in the beat intervals or correspondingly in the instantaneous heart rate (HR). The normal variability in HR is due to autonomic neural regulation of the heart and the circulatory system [1]. The balancing action of the sympathetic nervous system (SNS) and parasympathetic nervous system (PNS) branches of the autonomic nervous system (ANS) controls the HR. Increased SNS or diminished PNS activity results in cardio-acceleration. Conversely, a low SNS activity or a high PNS activity causes cardio-deceleration. The degree of variability in the HR provides information about the functioning of the nervous control on the HR and the heart's ability to respond.

There are two main approaches to HRV analysis: time domain analysis such as standard deviation of normal-to-normal intervals (SDNN); and frequency domain analysis such as power spectral density (PSD). The latter provides high frequency (parasympathetic activity), low frequency (sympathetic activity and vagal activity) and total power (sympathetic/parasympathetic balance) values. Spectral analysis is the most popular linear technique used in the analysis of HRV signals [2]. Spectral power in the high frequency band (HF: 0.15 – 0.5 Hz) reflects respiratory sinus arrhythmia (RSA) and, thus, cardiac vagal activity. Low frequency (LF: 0.04 – 0.15 Hz) power is related to baroreceptor control and is mediated by both vagal and sympathetic systems. Very low frequency (VLF: 0.0033 – 0.04 Hz) power appears to be related to thermoregulatory and vascular mechanisms, and renin-angio tensin systems.

The human cardiovascular system is a nonlinear system and the heart is not a perfectly periodic oscillator under normal physiologic conditions. Recent HRV studies, in both health and disease, have also stressed the importance of nonlinear techniques because the commonly employed second order moment statistics of HRV may not be able to detect subtle but important changes in heart rate time series. Some of the nonlinear methods used for the study of HRV include recurrence plot [3,4], Poincare plot [5] and entropy analysis [6,7].

Higher order spectra (HOS) are spectral representations of moments and cumulants and can be defined for deterministic signals and random processes. They have been used to detect deviations from Gaussianity and identify nonlinear systems [8,9]. HOS-based features can be formulated to be rotation, translation and scaling invariant when applied to one and two dimensional pattern recognition [10]. Applications of HOS include detection of photomontage [11], mine detection [12], machine fault diagnosis [13], recognition of viruses from electron microscopic images [14], and the analysis of biosignals such as ECG [15] and EEG [16]. Although HOS have been used extensively in EEG analysis there has been relatively less research into their use in HRV analysis. Jamsek et al.[17] used bispectral analysis to study the coupling between cardiac and respiratory activity. Witte et al.[18] too studied the coupling between cardiac and respiratory activity but this research was on neonatal subjects. Pinhas et al.[19] used the bispectrum to analyse the coupling between blood pressure (BP) and HRV in heart transplant patients.

In this work, we have studied the HOS of the HRV signals of normal heartbeat and seven classes of arrhythmia. We present some general characteristics for each of these classes of HRV signals in bispectrum and bicoherence plots. We also extracted features from the HOS and performed an analysis of variance (ANOVA) test.

The layout of the paper is as follows: §2 presents the data acquisition process and preprocessing of the raw cardiac signals. §3 discusses the HOS analysis including the bispectrum, bicoherence and invariant features extracted from HOS, and §4 presents the results of the study. A discussion of the data analysis is presented in §5, and is followed by a conclusion in §6.

2 Data and classes

ECG data for the analysis was obtained from the MIT-BIH arrhythmia database [20]. Prior to recording, the ECG signals were processed to remove noise due to power line interference, respiration, muscle tremors, spikes, etc. The R peaks of ECG were detected using the Pan – Tompkins algorithm [21]. The number of datasets chosen for each of the eight classes is given in table 1. Each dataset consists of around 10 000 samples and the sampling frequency of the data is 360 Hz. The interval between two successive QRS complexes is defined as the RR interval (t_R-R) and the heart rate (beats per minute) is given as: As heart rate is a time series sequence of non-uniform RR intervals, this signal is further re-sampled at four samples per second each according to the algorithm of Berger et al. [22]. In this work, an effort is made to characterize and classify eight different classes depending on their morphological features [23]. These classes are: (i) normal sinus rhythm (NSR); (ii) preventricular contraction (PVC); (iii) complete heart block (CHB); (iv) sick sinus syndrome (SSS); (v) atrial fibrillation (AF); (vi) ischemic/dilated cardiomyopathy; (vii) left bundle branch block (LBBB); and (viii) ventricular fibrillation (VF).

Table 1. ECG data for different cardiac health states.

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3 Methods used for analysis

The HRV signal is analysed using different higher order spectra (also known as polyspectra) that are spectral representations of higher order moments or cumulants of a signal. In particular, this paper studies features related to the third order statistics of the signal, namely the bispectrum. The bispectrum is the Fourier transform of the third order correlation of the signal and is given by: where X(f) is the Fourier transform of the signal x(nT), n is an integer index, T is the sampling interval and E[.] stands for the expectation operation. It is a function of two frequencies unlike the power spectrum which is a function of one frequency variable. In practice, the expectation operation is replaced by an estimate that is an average over an ensemble of realizations of a random signal. For deterministic signals, the relationship in equation (2) holds without an expectation operation, along with the definition of the bispectrum as the Fourier transform of the third order correlation when the third order correlation refers to a time-average. For deterministic sampled signals, X(f) is the discrete-time Fourier transform and in practice is computed as the discrete Fourier transform (DFT) at frequency samples using the FFT algorithm. The frequency f may be normalized by the Nyquist frequency (one half of the sampling frequency) to be between 0 and 1.

The bispectrum may be normalized (by power spectra at component frequencies) such that it has a magnitude between 0 and 1, and indicates the degree of phase coupling between frequency components [8,9].

A normalized bispectrum by Haubrich [24] is given by: where P(f) is the power spectrum. Bicoherence, B_co(f₁, f₂), is defined as the squared-magnitude of the normalized bispectrum. If the Fourier components at the frequencies f₁, f₂ and f₁ + f₂ are perfectly phase-coupled in every realization (or block of data) the bicoherence will be 1. If they are completely random-phase the bicoherence would be 0, in theory. Since the power spectral values in the denominator are estimates in practice, this normalization does not ensure that the magnitude of the normalized bispectrum obtained from finite time series will be bounded by 1. An alternative normalization of the bispectrum by Kim and Powers [25] ensures that the magnitude of the normalized bispectrum will be bounded by 1, as has been proved using the Schwartz inequality. This is important only if we are interested in measuring the degree of phase coupling between frequency components reliably. In this work, the focus is on examining bispectral and bicoherence patterns and extracting features for classification, and the normalization in equation (3) was considered adequate. It is simpler to interpret because the denominator terms are all power spectral values.

In practice, we have only an estimate of the bispectrum or the bicoherence from a finite number of realizations and the estimate has a finite bias and variance. Values of bicoherence [26] and tricoherence [27] at various significance levels are known for Gaussian random noise. It is known that the bicoherence and tricoherence are asymptotically Chi-squared distributed [26,27]. If N realizations are averaged to compute the estimate, 95% of the bicoherence values should lie between 0 and (6/2N). Thus, if 100 independent blocks of data are averaged in the estimate, a bicoherence greater than 0.03 would be significant at the 95% confidence level to reject the hypothesis that the particular frequency components came from a Gaussian noise process. The case of a harmonic random process is discussed in [27]. For other processes, values for the random-phase hypothesis at different significance levels can be determined by randomizing the phases of the Fourier components while keeping the magnitude (and hence the power) spectrum the same and computing the distribution of bicoherence values. If the data blocks are short, the statistics of the bispectrum and the bicoherence can also be influenced by spectral leakage [28].

In this work, we are not trying to establish whether phase coupling exists between particular combinations of frequencies with quantitative statistical confidence; we have presented bispectrum magnitude and bicoherence plots from the different classes of signals to highlight differences in patterns in bifrequency space. If we look at the entire bifrequency space, the many different bifrequencies possible will not all be phase-coupled. Most of them are in fact not related harmonically or sub-harmonically to any significant peak in the power spectrum and would be random-phase except perhaps for spectral leakage. Therefore the large majority of the bicoherence values in the bifrequency space for each class gives a visual indication of the distribution for zero bicoherence. Peaks that are significantly higher than this background are highly likely to be phase-coupled. The actual value at any given significance level varies from plot to plot because the number of blocks averaged is different in each case (determined by the amount of data available). The average number of data blocks, N (512 data points each block) for each case is indicated in figures 2(a,b) to figures 9(a,b), along with significance levels at 95% for zero bicoherence. These significance levels are only approximate since the number of data blocks, N, is small in all the cases.

3.1 Higher order spectral features

One set of features in our experiments is based on the phases of the integrated bispectrum derived by Chandran and Elgar [10] and is described briefly below.

Assuming that there is no bispectral aliasing, the bispectrum of a real signal is uniquely defined with the triangle 0 ≤ f₂ ≤ f₁ ≤ f₁ + f₂ ≤ 1. Parameters are obtained by integrating along the straight lines passing through the origin in bifrequency space. The region of computation and the line of integration are depicted in figure 1. The bispectral invariant, P(a), is the phase of the integrated bispectrum along the radial line with the slope equal to a. This is defined by:

Figure 1. Non-redundant region of computation of the bispectrum for real signals. Features are calculated by integrating the bispectrum along the dashed line with slope = a. Frequencies are shown here normalized by the Nyquist frequency (one half the sampling frequency).

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where:

for 0 < a ≤ 1, and

. The variables I_r and I_i refer to the real and imaginary part of the integrated bispectrum, respectively.

These bispectral invariants contain information about the shape of the waveform within the window and are invariant to shift and amplification and robust to timescale changes. They are particularly sensitive to changes in the left – right asymmetry of the waveform. For windowed segments of a white Gaussian random process, these features will tend to be distributed symmetrically and uniformly about zero in the interval [−π, +π]. If the process is chaotic and exhibits a coloured spectrum with third order time-correlations or phase coupling between Fourier components, the mean value and the distribution of the invariant feature may be used to identify the process. In this work, only the mean and variance of the features are examined.

Another set of features are based on the work of Ng et al. [11]. These features are the mean magnitude and the phase entropy. However, unlike their work, we calculated these features within the region defined in figure 1. The formulae of these features are:

Mean magnitude of the bispectrum: Phase entropy: where L is the number of points within the region in figure 1, ϕ refers to the phase angle of the bispectrum, Ω refers to the space of the defined region in figure 1, and 1(.) is an indicator function which gives a value of 1 when the phase angle ϕ is within the range of bin ψ_n in equation (9).

We set each bin as 5-degree (with N = 36) and we compute the histogram as an estimate of the probability density function of the phase. The entropy used is the Shannon entropy [29]. The mean magnitude of the bispectrum can be useful in discriminating between processes with similar power spectra but different third order statistics. However, it is sensitive to amplitude changes. Thus if the HRV range changes, say from 30 – 50 beats per minute to 40 – 60 beats per minute, within the normal category, the power spectrum of the HRV and also the mean magnitude bispectrum will change. Normalization can easily take care of such variation. The phase entropy would be zero if the process were harmonic and perfectly periodic and predictable. As the process becomes more random, the entropy increases. Unlike Fourier phase, the bispectral phase does not change with a time shift.

In this work, in our attempt to characterize the regularity or irregularity of the HRV from bispectrum plots, we have defined two additional bispectral entropies similar to that of spectral entropy [30]. The formulae for these bispectral entropies are given as:

Normalized bispectral entropy (BE₁): where: and Ω = the region as in figure 1.

Normalized bispectral squared entropy (BE₂): where and Ω = the region as in figure 1.

The normalization in the equations above ensures that entropy is calculated for a parameter that lies between 0 and 1 (as required of a probability) and hence the entropies (P₁ and P₂) computed are also between 0 and 1.

Blocks of 512 samples, corresponding to 128 seconds at the re-sampled rate of four samples per second were used for computing the bispectrum and bicoherence. The bispectrum was computed using an indirect estimate as the Fourier transform of an estimate of the third cumulant of the time series using the higher order spectral analysis toolbox [31]. The mean value is removed from each block and a Hanning window is used. The default overlap of 50% between blocks was used and the estimate averages in the correlation domain over all blocks. The bicoherence was computed using the direct FFT method in the toolbox. In the direct method, the bispectrum is estimated as an averaged biperiodogram, as in equation (2), and normalized by the power spectral values, as in equation (3).

Bispectrum magnitude and bicoherence plots shown in figures 2 – 9 are obtained after examining the results over all examples of the particular category, and are typical of the class. However, it must be noted that the time series from any given class is quite non-stationary and some segments can yield considerably different results. The plots are useful in visually discriminating between the classes and to reveal what the source of information in the computed features may be. These plots cover the entire two-dimensional bifrequency plane and hence exhibit six-fold symmetry. The frequencies are normalized by the sampling frequency (4 Hz) in these plots. Features are computed from single blocks and only over the non-redundant region, and an analysis of variance is used to check if the mean values are different for the different classes.

Figure 2. Bispectrum (a) and bicoherence (b) plots of normal heart rate (average of 30 data blocks). b_95% = 0.1.

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Figure 3. Bispectrum (a) and bicoherence (b) plots of heart rate with ectopic beat (average of 20 data blocks). b_95% = 0.15.

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Figure 4. Bispectrum (a) and bicoherence (b) plots of heart rate with AF (average of 13 data blocks). b_95% = 0.23.

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Figure 5. Bispectrum (a) and bicoherence (b) plots of heart rate with CHB (average of 36 data blocks). b_95% = 0.083.

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Figure 6. Bispectrum (a) and bicoherence (b) plots of heart rate with SSS-III (average of 15 data blocks). b_95% = 0.2.

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Figure 7. Bispectrum (a) and bicoherence (b) plots of heart rate with ischemic/dilated cardiomyopathy (average of 12 data blocks). b_95% = 0.25.

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Figure 8. Bispectrum (a) and bicoherence (b) plots of heart rate with LBBB (average of 12 data blocks). b_95% = 0.25.

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Figure 9. Bispectrum (a) and bicoherence (b) plots of heart rate with VF (average of 10 data blocks). b_95% = 0.15.

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3.2 Statistical analysis

In this work, the parameters namely, the bispectral invariant features, P(a), the bispectrum mean magnitude, M_ave, and the phase entropy, P_e were obtained and tested with ANOVA test. For invariant feature we have selected a = 1/8, 1/2, 7/8 and 1 for testing. The plots of bispectrum and bicoherence are also presented as potential visual aids the analysis of cardiac health. The results of these were subjected to the t-test with more than 95% confidence interval giving excellent p values, far lower than 0.05 (with seven degrees of freedom), in all cases (table 2).

Table 2. Invariant features, mean bispectrum magnitude and phase entropy and bispectral entropy 1 and 2. Entries in columns other than the last two correspond to mean and standard deviation.

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4 Results

The resulting bispectrum magnitude plots for various types of disease are shown in figures 2(a) – 9(a) and the bicoherence plots are shown in figures 2(b) – 9(b). The results of ANOVA with features obtained from HOS for various kinds of cardiac diseases are listed in table 2.

For normal cases, the bispectrum magnitude plot exhibits peaks at lower frequencies (figure 2(a)). The heart rate is varying continuously between 60 and 80 bpm. The bicoherence plot is shown in figure 2(b). Bicoherence values appear to be scattered through out the bifrequency plane in a random manner, except for a few peaks that are narrowband. The entropies (P_e, P₁ and P₂) also appear to be high. The mean value of P₁ is 0.52 while that of P₂ is 0.25. We will examine features from the other categories with reference to these values. The bicoherence plot exhibits peaks around frequencies of 0.05 and 0.1 (the sampling frequency is 4 Hz and the plots extend from −0.5 to 0.5 in normalized frequency corresponding to −2 Hz and +2 Hz), which correspond to periods of 5 s and 2.5 s, respectively. In the normal case, we have averaged 30 blocks of data, and their 95% significance level for zero bicoherence is 0.1. The peaks are high compared to the significance level. It is quite possible that these values are related to the rate of breathing and its harmonics and there is some modulating effect on the heart rate variability owing to the breathing pattern. The fact that these peaks appear in the same vicinity in a number of the other plots strengthens this conjecture. However, without corresponding data on respiration, this cannot be verified. If this is true, any nonlinearity in the data from the nature of the disease must be considered in comparison with the effect of this nonlinearity. Potential respiratory confounds when estimating cardiac vagal control from high frequency HRV is reported [28] in laboratory data monitoring one channel of ECG, ventilation (via calibrated inductance plethysmography), and upper-torso motion (via two-dimensional accelerometry).

In the ectopic beat abnormality, there would be a sudden impulsive jump in the heart rate. This may be due to a pre-ventricular beat in the ECG signal. Figure 3(a) shows the bispectrum plot with multiple sets of peaks. The heart rate is varying continuously and there are ectopic beats inbetween the normal beats. The bicoherence plot (figure 3(b)) shows similar values scattered around frequencies of 0.05 and 0.1. There are multiple peaks around frequency of 0.1 probably due to the multiple beats. Entropies (P_e, P₁ and P₂) indicated in the table 2 are correspondingly higher than the normal case.

In atrial fibrillation (AF), the heart rate signal records highly erratic variability; there appears to be a frequency splitting or dual cycle type behaviour, as depicted in the plot in figure 4(a). The bicoherence plot of the AF is shown in figure 4(b) and the plot shows bicoherence indicates the several peaks around 0.1. Entropies (P_e, P₁ and P₂) indicated in table 2 are slightly higher than the normal case.

In complete heart block (CHB), as the A_V node fails to send electrical signals rhythmically to the ventricles, the heart rate remains low. The peaks seem to have moved to the lower frequency portion of the bispectrum plot, possibly indicating the inherent periodicity (figure 5(a)). Bicoherence plot of the CHB is shown in figure 5(b) and this plot indicates a spreading in the bifrequency plane with more peaks crowded at low frequency. The entropies (P_e, P₁ and P₂) indicated in table 2 are very high compared to the normal and similar to the ectopic beat case. Interestingly, the bicoherence plot still shows some isolated high bicoherence values (red) at locations similar to that in the normal, ectopic and AF cases.

In SSS-III (sick sinus syndrome-III, bradycardia-tachycardia) there is a continuous variation of heart rate between bradycardia and tachycardia, which shows up by the patches of red (Brady) or stronger and blue colored (Tachy) or weaker patterns in the bispectrum plot (figure 6(a)). The bicoherence plot (figure 6(b)) shows peaks at low frequencies and at high frequencies, corresponding to the bradycardia and tachycardia of the heart rate values. Entropies (P_e, P₁ and P₂) indicated in table 2 are also correspondingly higher than the normal case.

In the case of ischemic/dilated cardiomyopathy, the ventricles are unable to pump out blood to the normal degree. Here the heart rate variation is not very high. Correspondingly, the variation in the bispectrum is gradual (figure 7(a)). The heart rate (around 120 bpm) is high in dilated cardiomyopathy but does not fluctuate as much. The bicoherence plot shows less randomness (figure 7(b)) than the normal case and there are some significant low frequency bicoherence values and entropies (P_e, P₁ and P₂) indicated in table 2 are also slightly higher.

Heart rate variation in LBBB is high. Hence, the bispectrum plot of figure 8(a) shows higher peaks. But the plot is coarse in resolution because of the smaller length of the blocks of heart rate data used. The bicoherence plot (figure 8(b)) shows more structure than the normal case and the entropies (P_e, P₁ and P₂) indicated in table 2 are correspondingly lower.

Figure 9(a) shows the bispectrum plot of the VF. There are periodic strong peaks indicating some inherent periodicity similarity in the heart rate values. The bicoherence plot shown in figure 9(b) is very structured and the entropies (P_e, P₁ and P₂) indicated in table 2 are again correspondingly low.

Figure 10 shows the mean variation of bispectrum magnitude for various cardiac abnormalities. Mean value of bispectrum magnitude is related to magnitude the heart rate variation. In comparison to normal HRV, a patient with PVC will have a slightly higher heart rate, hence the mean bispectrum magnitude is also higher. On the other hand, the heart rate variations for the cases of CHB and ISC are relatively lower, so the corresponding mean bispectrum magnitudes are also lower. The heart rate variations in the case of AF, SSS, VF and LBBB are generally very high and it can be observed from figure 10 that their mean bispectrum magnitude too are much higher compared to the normal heart rate.

Figure 10. Mean magnitudes of the bispectrum and one standard deviation for each class.

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5 Discussion

The entropy quantifies the regularity and complexity of time series. It should have higher value in the case of normal subjects and this value will be smaller for abnormal (SSS, CHB, ischemic/dilated cardiomyopathy, VF, etc) subjects, indicating smaller variability (or inherent periodicity) in the beat-to-beat interval [32]. The phase entropy (P_e), bispectral entropy 1 (P₁) and bispectral entropy 2 (P₂) are evaluated from the bicoherence plots. They give a quantitative measure of this plot. Our results show that, these entropies show good range of values (lower p values) for different cardiac classes (table 1).

The bispectral invariant phase features computed from single blocks are suitable for deterministic signals and shapes [10],[33]. Their mean values are significantly different for the different categories. However, their variances are very high. For this application, they can serve as good features if we (a) reduce variance by averaging and (b) model the distribution of these features obtained from several blocks using a Gaussian mixture model and use multiple blocks to classify [14].

The bispectral entropies (P₁ and P₂) are low for the normal subjects and higher for the highly varying cardiac data, such as AF, PVC and SSS. The bicoherence plot of AF, SSS shows weaker bicoherence at low frequencies than the normal case; it also shows a more unique pattern (covering LF and HF) in the case of LBBB and VF.

Witte et al. analysed heart rate signals of human neonates during sleep, examining quadratic phase coupling between Fourier components by the higher order spectra technique [18]. They observed, in neonatal HRV, both a phase co-ordination between the 10-s rhythm and respiratory sinus arrhythmia (RSA), as well as nonlinear coupling between these HRV components. Pinhas et al. analysed the HRV signals in heart transplanted subjects using statistical approach for bicoherence thresholding [19]. They developed several statistical tools in order to distinguish between ‘true’ bicoherence peaks (reflecting true phase coupling) and spurious peaks.

In our work, we have examined the statistical reliability of the mean bispectrum magnitude, bispectrum entropies, bispectrum phase entropies and invariant features for the classification of different cardiac abnormalities.

5.1 The scope of the study

This is a preliminary study which aims to explore the possibility of differentiating between different classes of cardiac arrhythmia with experiments on higher order spectral features using the MIT-BIH database. Our approach is to check the differences between the patterns in features space of different classes of arrhythmias and using statistical tools like bispectrum entropies to quantify the irregularity of these patterns. The parameters used in this study show significant differences between categories and are clinically, very significant (table 1). Recently, Rajendra et al.[34] classified the HRV signals using ANN and fuzzy equivalence relation into eight groups by using nonlinear parameters as input to the classifier. Dingfei et al. [35] classified cardiac arrhythmia into six classes using autoregressive modeling. In this paper, we have used higher order spectral features to analyse these classes.

The application of HOS for cardiac signals is new and we have proposed the use of bispectral and bicoherence patterns for identifying different cardiac arrhythmia. As can be seen from the proposed figures, each type of cardiac abnormality has a unique plot. These plots and parameters (table 1) can be better understood by understanding the causes of the underlying patterns, their relationship to breathing pattern and other bio-rhythms.

This work can be extended for other types of abnormalities, such as myocardial infarction (MI), complete heart failure, atrial premature contraction, etc. And these arrhythmias can be classified into different classes by feeding the features into the classifiers for automated classification. The authors are currently working towards these objectives.

7 Conclusion

Heart rate variability (HRV) signal can be used as an indicator of heart diseases. Higher order spectral analysis of the heart rate variability can yield patterns to visualize such indication or to extract it in features for automated classification. We have proposed the use of different bispectrum and bicoherence patterns for various cardiac abnormalities. We have also evaluated the effectiveness of bispectrum based features. Further work is required to fully understand the significance of the bispectral and bicoherence patterns and their relationship to any modulating effects on the heart rate variability from breathing pattern.

Type	NSR	PVC	CHB	SSS	Ischemic/dilated	AF	VF	LBBB
Number of datasets	60	60	20	20	20	35	45	40

Table 2. Invariant features, mean bispectrum magnitude and phase entropy and bispectral entropy 1 and 2. Entries in columns other than the last two correspond to mean and standard deviation.

Class	Normal	PVC	LBBB	AF	VF	SSS	ISC	CHB	p value	F value
P(1/8)	0.07 ± 1.49	−0.11 ± 1.61	−1.15 ± 2.14	0.41 ± 0.61	−0.01 ± 0.06	−0.96 ± 1.83	−0.47 ± 1.61	1.36 ± 1.14	0.024	2.454
P(1/2)	0.05 ± 1.40	0.54 ± 1.45	−1.66 ± 1.64	−0.97 ± 1.33	0.006 ± 0.02	−0.45 ± 0.92	0.24 ± 1.26	−0.73 ± 1.62	0.007	3.009
P(7/8)	0.38 ± 1.43	0.72 ± 1.26	−1.34 ± 2.22	0.09 ± 0.12	−0.01 ± 0.02	0.27 ± 0.11	−0.62 ± 1.20	−0.43 ± 2.19	0.022	2.485
P(1)	−0.41 ± 1.67	0.36 ± 1.52	−0.93 ± 2.23	0.23 ± 0.33	−0.01 ± 0.02	0.50 ± 0.12	0.29 ± 1.31	1.52 ± 2.04	0.030	2.357
M_ave	0.42e8 ± 0.74e8	0.11e9 ± 0.27e9	1.34e8 ± 0.84e8	5.45e8 ± 2.36e8	1.07e9 ± 0.63e9	2.67e8 ± 2.62e8	0.55e6 ± 0.96e6	0.63e5 ± 0.74e5	0.001	18.01
P_e	3.35 ± 0.39	3.36 ± 0.03	3.30 ± 0.11	3.56 ± 0.01	3.17 ± 0.31	3.58 ± 0.002	3.57 ± 0.01	3.58 ± 0.00	0.000	4.122
P₁	0.52 ± 0.18	0.74 ± 0.13	0.39 ± 0.14	0.64 ± 0.22	0.38 ± 0.13	0.83 ± 0.052	0.67 ± 0.09	0.71 ± 0.02	0.000	11.63
P₂	0.25 ± 0.18	0.41 ± 0.25	0.16 ± 0.14	0.33 ± 0.36	0.11 ± 0.08	0.53 ± 0.21	0.31 ± 0.21	0.41 ± 0.25	0.001	3.810

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Journal of Medical Engineering & Technology

Cardiac state diagnosis using higher order spectra of heart rate variability

Original Article

Cardiac state diagnosis using higher order spectra of heart rate variability

Abstract

1. Introduction

2 Data and classes

Published online:

Table 1. ECG data for different cardiac health states.