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Abstract
Heart rate variability 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 is important because it provides a window 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. Parameters are extracted from the heart rate signals and analysed using computers for diagnostics. This paper describes the analysis of normal and seven types of cardiac abnormal signals using approximate entropy (ApEn), sample entropy (SampEn), recurrence plots and Poincare plot patterns. Ranges of these parameters for various cardiac abnormalities are presented with an accuracy of more than 95%. Among the two entropies, ApEn showed better performance for all the cardiac abnormalities. Typical Poincare and recurrence plots are shown for various cardiac abnormalities.
1. Introduction
Heart rate variability (HRV) study refers to the characterization and measurement of changes in heart rate. Disease and ill health influence heart rate, and therefore the pattern and the range of HRV contain important information about the robustness of health and disease type, etc. Classification based on the spread and pattern of this parameter can provide useful insights into 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 ANS controls 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 HR provides information about the functioning of nervous control of HR and the heart's ability to respond.
There are two main approaches for analysis: time domain analysis of HRV for standard deviation of normal-to-normal intervals (SDNN); and frequency domain analysis for power spectrum density (PSD). The latter provides high frequency (parasympathetic activity), low frequency (sympathetic 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 because the heart is not a periodic oscillator under normal physiologic conditions. Recent studies have also stressed the importance of nonlinear techniques for studying HRV in both healthy and diseased states, because the commonly employed moment statistics of HRV may not be able to detect subtle but important changes in heart rate time series.
The nonlinear dynamic techniques based on the concept of chaos have been applied to many areas of medicine and biology. The theory of chaos has been used to detect some cardiac arrhythmias such as ventricular fibrillation [3]. Nonlinear parameters, such as the fractal dimension for pathological signals have been found to be useful indicators of pathologies. Methods based on chaos theory have been applied in tracking HRV signals and predicting onset events such as ventricular tachycardia, detecting congestive heart failure situations [4]. A novel method based on phase space technique to distinguish normal and abnormal cases has been proposed for cardiovascular signals [5]. The technique has been extended here to identify the abnormalities of different types. Mohamed et al. [6] used nonlinear dynamic modelling in ECG arrhythmia detection and classification. The approximate entropy and Poincare plots were earlier studied in normal subjects [7],[8].
Recurrence plots (RPs) were introduced by Eckmann et al. in 1987 [9] to visualize the behaviour of trajectories of dynamic systems in phase space. Later, this tool of data analysis proved to be useful not only as a visualization technique, but also motivated quantification measures for the local rate of divergence, even for datasets with just few hundred values [10]. Furthermore, a set of measures, constituting what is now known as recurrence quantification analysis (RQA) was proposed to quantify systematically the different structures found in RPs [11]. The applications of RPs include study of different sleep stages [12], analysis of epileptic EEG signals [13],[14], study of the non-stationary nature of cardiac signals [15], and study of variation in the electromyocardiogram (EMG) during exercise [16].
Approximate entropy (ApEn) [17] and sample entropy (SampEn) [18] are nonlinear measures obtained through direct signal estimation, capable of quantifying the complexity (or the regularity) of a signal. ApEn was first proposed by Pincus [17] to estimate the entropy of a system represented by a time series signal of short and noisy data, such as bio-signals. Richman et al. [18] developed and characterized SampEn to measure the complexity and regularity of clinical and experimental time series data. They compared its performance with ApEn.
Acharya et al. [19] analysed ApEn for normal and seven other cardiac states. Its value is high in the case of normal and sick sinus syndrome (SSS) subjects and falls as the RR variation decreases. Hence, ApEn will have a smaller value for cardiac abnormal cases, indicating smaller variability in the beat to beat. But for SSS this RR variation will be higher than for normal subjects.
SampEn statistics [18] provide an improved evaluation of time series regularity and could be a more useful tool in studies of the dynamics of human cardiovascular physiology than ApEn. In this work, we have compared the performances of ApEn with SampEn. We also propose the use of unique patterns using recurrence and Poincare plots and Poincare plots for identifying different cardiac disorders. The complexity of the heart rate signals is analysed using the approximate entropy, sample entropies and Poincare geometries, i.e. short range correlation (SD1) and long range correlation (SD2).
The layout of this paper is as follows: §2 presents the data acquisition process and preprocessing of the raw cardiac signals; §3 deals with the parameters, i.e. approximate entropy (ApEn), sample entropy (SampEn), recurrence plot and Poincare geometry; and §4 presents the results of the study. A discussion of the data analysis is presented in §5, and finally the paper concludes in §6.
2 Materials and methods
ECG data for the analysis were 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 ECG R peaks 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 (tRR) and the heart rate (beats per minute) is given as:
Table 1. ECG data for different cardiac health states.
In this work, an effort is made to characterize and classify eight different classes depending on their morphological features [22]:
normal sinus rhythm (NSR);
preventricular contraction (PVC);
complete heart block (CHB);
sick sinus syndrome (SSS);
atrial fibrillation (AF);
ischaemic/dilated (ISC);
left bundle branch block (LBBB); and
ventricular fibrillation (VF).
3 Analysis
The cardiac signal is analysed using different entropies, Poincare plot and recurrent plots.
3.1 Approximate entropy (ApEn)
ApEn is defined as the logarithmic likelihood that the patterns of the data that are close to each other will remain close for the next comparison with a longer pattern. It is a simple index for the overall ‘complexity’ and ‘predictability’ of each time series. In our study ApEn quantifies the regularity of the RR interval. The more regular and predictable the RR interval series, the lower will be the value of ApEn. This method quantifies the unpredictability of fluctuations in a time series such as an instantaneous RR interval time series, RR(i).
To compute the ApEn of each dataset, m-dimensional vector sequences x(n) were constructed from the RR interval time series:
where the index n can take on values ranging from 1 to N – m+ 1 and N is the total number of data points in the RR interval time series. If the distance between two vectors x(i) and x(j) is defined as d(x(i), x(j)), then we have:
Where N is a sequence of 1000 consecutive instantaneous RR intervals; m specifies the pattern length, which is 2 in this study; r defines the criterion of similarity, which has been set at 15% of the standard deviation of 1000 RR intervals, and
.
The criterion of similarity, r, was chosen such that it was larger than most of the noise but at the same time not so large that detailed information about the system dynamics would be lost. On the basis of the work of Pincus and Goldberger [23], for m = 2, N = 1000 and r = 15% of the standard deviation of the data, reasonable statistical validity of ApEn would be produced.
3.2 Sample entropy (SampEn)
SampEn agreed with theory much more closely than ApEn over a broad range of conditions. The improved accuracy of SampEn statistics make them useful in the study of experimental clinical cardiovascular and other biological time series.
The basic idea of SampEn is very similar to ApEn, but there is a small computational difference. For the calculation of SampEn we first take the original time series x(i), i = 1, … , N, and construct vector sequences of size m, u(1) to u(N – m+ 1), defined by u(i) = (x(i), … , x(i+m – 1)). The vector length m is known as the embedded dimension. The constructed vectors represent m consecutive x values commencing with the ith point. The distance d(u(i), u(j)) between vectors u(i) and u(j) is defined as d(u(i), u(j) = max(|u(I+k) –u(j+k)|, 0 ≤k≤m – 1), where k accounts for the vector component index. The probability of finding another vector within distance r from the template vector u(i) is estimated by:
Now we can determine:
and
3.3 Recurrence plots (RP)
The dynamic analysis of an experimental time series requires it to be drawn from a stationary process. To satisfy this requirement, the recurrence plot can be used [9]. This is a graphical tool for the diagnosis of drift and hidden periodicities in the time evolution of dynamic systems, which are unnoticeable otherwise.
Let s(i) be the ith point on the orbit describing a dynamic system in dE – dimensional space. The recurrence plot is an N×N square, where a dot is placed at (i, j) whenever s(j) is sufficiently close to s(i). To obtain a recurrence plot from time series s(i), an embedding dimension dE is chosen and the dimensional orbit of s(i) is constructed by method of delays [24]. Next, we choose r(i) such that the ball of radius r(i) centred at s(i) in RdE contains a reasonable number of other points s(j) of the orbit. Finally, we plot at each point (i, j) for which s(j) is in the ball of radius r(i) centred at s(j). The resulting plot is the recurrence plot.
Recurrence plots are graphical devices specially suited to detect hidden dynamic patterns and nonlinearities in data. They are used in visualization techniques to detect the recurrence or correlations in the data, and are graphs showing all the times at which a state of the dynamic system recurs. In other words, the RP reveals all the times when the phase space trajectory visits roughly the same area in the phase space.
3.4 Poincare geometry
The Poincare plot, a technique taken from nonlinear dynamics, portrays the nature of RR interval fluctuations. Each RR interval is plotted as a function of the previous RR interval. Poincare plot analysis is an emerging quantitative-visual technique whereby the shape of the plot is categorized into functional classes that indicate the degree of the heart failure in a subject [25]. The plot provides summary information as well as detailed beat-to-beat information on the behaviour of the heart [26]. This plot may be analysed quantitatively by calculating the standard deviations of the distances of the RR(i) to the lines y = x and y = –x+ 2 × RRm, where RRm is the mean of all RR(i) [27]. The standard deviations are referred to as SD1 and SD2, respectively. SD1 related to the fast beat-to-beat variability in the data, while SD2 describes the longer-term variability of RR(i) [27]. The ratio SD1/SD2 may also be computed to describe the relationship between these components. Figure 1(b) shows the Poincare plot of a normal young subject.
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Figure 1. Recurrence (a) and Poincare (b) plots of normal heart rate.
3.5 Quantitative analysis
The p-value can be obtained using ANOVA (analysis of variance between groups) test. ANOVA uses variances to decide whether the means are different. This test uses the variation (variance) within the groups and translates into variation (i.e. differences) between the groups, taking into account how many subjects there are in the groups. If the observed differences are high then it is considered to be statistical significant.
In this work, the parameters ApEn, SampEn, SD1 and SD2 of the Poincare plots were used for the analysis of cardiac health. The results of these were subjected to t-tests with more than 95% confidence interval giving excellent p-values in all cases (table 2).
Table 2. Results of entropies and SD1 and SD2 for different cardiac abnormalities.
4 Results
The resulting recurrence plots for various types of disease are shown in parts (a) of figures 1–8 and the Poincare plots are shown in parts (b) of figures 2–8. The results of the entropies for various types of subjects are listed in table 2.
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Figure 2. Recurrence (a) and Poincare (b) plots of heart rate with ectopic beat.
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Figure 3. Recurrence (a) and Poincare (b) plots of heart rate with AF.
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Figure 4. Recurrence (a) and Poincare (b) plots of heart rate with CHB.
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Figure 5. Recurrence (a) and Poincare (b) plots of heart rate with SSS-III.
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09 July 2009Figure 6. Recurrence (a) and Poincare (b) plots of heart rate with ischaemic/dilated cardiomyopathy.
![]({"type":"image","src":"/na101/home/literatum/publisher/tandf/journals/content/ijmt20/2008/ijmt20.v032.i04/03091900600863794/20150515/images/medium/ijmt_a_186307_f0006_b.jpg"})
Figure 6. Recurrence (a) and Poincare (b) plots of heart rate with ischaemic/dilated cardiomyopathy.
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Figure 7. Recurrence (a) and Poincare (b) plots of heart rate with LBBB.
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Figure 8. Recurrence (a) and Poincare (b) plots of heart rate with VF.
For normal cases, the RP has diagonal lines and fewer squares, indicating more variation (figure 1(a)). The Poincare pattern appears to be ellipse-shaped, aligned at the centre (figure 1(b)), with SD2 longer than SD1, indicating more long term correlation in the data. The plot will be aligned at the centre of the quadrant. ApEn = 1.993 ± 0.292 and SampEn = 1.323 ± 0.253. This value is high due to the high variation in the heart rate.
In the ectopic beat abnormality there is a sudden impulsive jump in the heart rate. This may be due to a pre-ventricular beat in the ECG signal. Figure 2(a) shows the RP, and the stripes in the plot shows the ectopic beat. The shape of the Poincare plot is almost circular and is aligned at a small area (figure 2(b)) with SD2 comparable with SD1 (correlation exists in the short and long duration data) at the fourth quadrant. ApEn = 1.543 ± 0.272 and SampEn = 1.025 ± 0.428. This value is high due to the presence of the ectopic beat in the heart rate signal.
In atrial fibrillation (AF), the heart rate signal records highly erratic variability; this is depicted as sudden changes in colour in the plot (figure 3(a)). The high beat-to-beat variation in the heart rate is shown by the yellow colour and many fewer squares in the plot. This variation is depicted as a spread of RR interval values in the plot (figure 3(b)) with SD2 longer than SD1 (correlation is more in the long interval than the short interval data) and the plot is placed in the fourth quadrant. The entropies are low (ApEn = 1.241 ± 0.315 and SampEn = 0.947 ± 0.281), indicating the inherent periodicity in the heart rate data.
In complete heart block (CHB), as the AV node fails to send electrical signals rhythmically to the ventricles, the heart rate remains low. There are more squares in the plot, indicating the inherent periodicity, and the low heart rate is shown by the maroon colour in the RP (figure 4(a)). The pattern of the Poincare plot is predominantly a small ellipse (figure 4(b)) with SD2 longer than the SD1 (correlation is more in the long interval than the short interval data) and the plot is at the second quadrant. The ApEn is 1.380 ± 0.419 and SampEn = 0.923 ± 0.248: slightly low values, as compared to normal heart rate signals, indicating low variation in the heart rate data.
In sick sinus syndrome III (SSS-III, bradycardia-tachycardia) there is a continuous variation of heart rate between bradycardia and tachycardia, which shows up by way of alternating patches of maroon (brady) and yellow coloured (tachy) patterns in the RP (figure 5(a)). In the Poincare plot (figure 5(b)), the SD2 is longer than SD1 (correlation is more in the long interval than the short interval data) and the plot is more towards the fourth quadrant. In this case, ApEn = 1.453 ± 0.223 and SampEn = 0.826 ± 0.302. The values are higher due to high variation in consecutive heart rate values.
In the case of ischaemic/dilated cardiomyopathy, the ventricles are unable to pump out blood to the normal degree. Here the heart rate variation is very small. Correspondingly, the colour variation in the RP too is gradual and periodic (figure 6(a)). In this plot there are many squares, indicating the similarity in the heart rate. The yellow colour indicates the presence of high heart rate in dilated cardiomyopathy. The Poincare plot resembles an ellipse and is aligned in the fourth quadrant with SD1 smaller than SD2 (figure 6(b)). The variation between the consecutive heart rates is low, resulting in lower entropy values (ApEn = 1.486 ± 0.414 and SampEn = 1.017 ± 0.397).
Heart rate variation in left bundle branch block (LBBB) is high, like normal subjects. Hence, the plot of RP (figure 7(a)) resembles that of the normal plot. However, the plot is coarse due to the small length of the heart rate data and it resembles that of normal subjects. The diagonal line indicates a high variation in the heart rate. The Poincare plot is aligned at the centre with SD2 being longer than SD1 (figure 7(b)). The variation of the heart rate in VF is high and rhythmic. The entropy values (ApEn = 1.475 ± 0.138; SampEn = 1.453 ± 0.543) for the subjects with LBBB are slightly lower than normal subjects due to the reduced RR variation.
The RP of ventricular fibrillation (VF) (figure 8(a)) resembles that of ischaemic/dilated cardiomyopathy, indicating rhythm in the heart rate. There are many small squares indicating the inherent similarity in the heart rate, and the yellow colour indicates the high heart rate. The diagonal line indicates the high variation in the heart rate. The Poincare plot is aligned at the centre and SD1 is slightly longer than the SD2 (figure 8(b)). The entropies (ApEn = 1.128 ± 0.186; SampEn = 0.985 ± 0.171) for subjects with VF are lower due to the presence of inherent rhythm.
5 Discussion
The importance of ApEn lies in the fact that it is measure of the disorder in the heart rate signal. It is a measure quantifying the regularity and complexity of time series. It has a higher value in the case of normal subjects and lower values for abnormal (SSS, CHB, ischaemic/dilated cardiomyopathy, VF, etc) subjects, indicating lower variability in the beat to beat. Our results show that ApEn shows a better range of values (lower p-values) for different cardiac classes as compared to SampEn (table 2). Hence, ApEn can be used to determine disorder in the cardiac signal.
The Poincare plots are aligned to the centre of the quadrant. This position will shift depending on the cardiac abnormality, and also the values of SD1 and SD2. As can be seen from our results, for highly varying heart rate signals such as PVC, SSS and AF, the Poincare plot is oriented towards the third quadrant of the Cartesian quadrant. For the slowly varying cardiac abnormalities such as CHB and ischaemic cardiomyopathy the plot is shifted to the first quadrant.
The results of SD1 (small range correlation) and SD2 (long range correlation) show that for normal subjects these values are small. This indicates that normal heart rate is highly random. These values in CHB and ischaemic/dilated cardiomyopathy subjects are almost comparable. This is because in these subjects the heart rate variation is very small. In highly varying data (AF, PVC, SSS and VF), we can find very high correlation in small range data and also in long range data (SD1 and SD2 are high).
As can be seen from the RPs in the previous section, the different abnormalities are clearly indicated by unique patterns. Slowly varying heart rate diseases such as CHB and ischaemic/dilated cardiomyopathy have a higher number of squares in the RP. This is due to the inherent periodicity of the time series. The RP shows more patches of colours in cardiac diseases, where the heart rate signal is highly varying (SSS, VF and AF).
Censi et al. [28] performed a quantitative study of coupling patterns between respiration and spontaneous rhythms of heart rate and blood pressure variability signals by using recurrence quantification analysis (RQA). They applied RQA to both simulated and experimental data obtained in control breathing at three different frequencies (0.25, 0.20 and 0.13 Hz) from 10 normal subjects.
The RP concept was used to detect life threatening arrhythmias such as ventricular tachycardias [29]. In this work, we have proposed the RPs for normal and seven different cardiac arrhythmias.
This work can also be extended for more abnormalities, such as ventricular tachycardia, pause and atria-ventricular block, etc. These parameters and patterns can be used as tool for the identification of the cardiac diseases. Also, the features from the Poincare plot and recurrence plot can be fed in to the neural network for the classification of these diseases. Presently, authors are working on this part.
7 Conclusion
Heart rate variability (HRV) signal can be used as a reliable indicator of heart diseases. In this work, we have compared the performances of ApEn with SampEn. The ApEn can be used to identify the disorder in the cardiac signal (as compared to SampEn). We also proposed the use of unique patterns using recurrence and Poincare plots for identifying different cardiac disorders. The complexity of the heart rate signals can also be is analysed using short range correlation (SD1), long range correlation (SD2) of the Poincare plots.
| Type | NSR | PVC | CHB | SSS | ISC | AF | VF | LBBB |
|---|---|---|---|---|---|---|---|---|
| Number of datasets | 60 | 60 | 20 | 20 | 20 | 35 | 45 | 40 |
| Class | Normal | PVC | LBBB | AF | VF | SSS | ISC | CHB | p-value |
|---|---|---|---|---|---|---|---|---|---|
| ApEn | 1.993 ± 0.292 | 1.543 ± 0.272 | 1.475 ± 0.138 | 1.241 ± 0.315 | 1.128 ± 0.186 | 1.453 ± 0.223 | 1.486 ± 0.414 | 1.380 ± 0.419 | 0.0001 |
| SampEn | 1.323 ± 0.253 | 1.025 ± 0.428 | 1.453 ± 0.543 | 0.947 ± 0.281 | 0.985 ± 0.171 | 0.826 ± 0.302 | 1.017 ± 0.397 | 0.923 ± 0.248 | 0.0190 |
| SD1 | 1.928 ± 0.740 | 12.240 ± 7.948 | 3.000 ± 0.781 | 55.880 ± 9.696 | 16.120 ± 12.670 | 35.780 ± 15.280 | 3.663 ± 4.576 | 1.314 ± 0.727 | 0.0001 |
| SD2 | 5.317 ± 2.121 | 12.220 ± 6.970 | 5.800 ± 2.771 | 40.020 ± 25.000 | 23.460 ± 24.430 | 40.480 ± 14.560 | 5.413 ± 5.144 | 1.771 ± 0.869 | 0.0100 |
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