International Journal of Cardiovascular ResearchISSN: 2324-8602

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Research Article, Int J Cardiovasc Res Vol: 4 Issue: 5

A Novel Approach to Detect Congestive Heart Failure using Dispersion Entropy

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Chandrakar Kamath*
Chandrakar Kamath, ShanthaNilaya, 107, Ananthnagar, Manipal- 576104,India
Corresponding author : Chandrakar Kamath
ShanthaNilaya, 107, Ananthnagar, Manipal- 576104, India
Tel: +91 0820 4294139
E-mail: [email protected]
Received: March 30, 2015 Accepted: June 08, 2015 Published: June 10, 2015
Citation: Kamath C (2015) A Novel Approach to Detect Congestive Heart Failure using Dispersion Entropy. Int J Cardiovasc Res 4:6. doi:10.4172/2324-8602.1000232

Abstract

A Novel Approach to Detect Congestive Heart Failure using Dispersion Entropy

Background: Congestive heart failure (CHF) being difficult to manage in clinical practice, has been the subject of intensive research.

Methods: A novel chaotic analysis which is a combination of graphical (second-order difference, SOD) plot and numerical (Dispersion entropy, DispEn) method to detect CHF is presented. Instead of central tendency measure which is commonly used together with SOD, DispEn, a quantifier adapted from nonlinear dynamics and deterministic chaos theory which has some advantages is used. DispEn quantifies degree of complex variability/chaos in a signal over time. This approach permits not only classification of HRV time series, but also assessment of cardiac sympathetic and parasympathetic activities. Hypothesizing that CHF patient will experience an altered cardiac rhythm, with changes in the magnitude of the beat-to-beat HR fluctuations and perturbations in the HR fluctuation dynamics, the HRV of CHF patients is compared with those of healthy subjects using DispEn and two other measures, an entropy related to parasympathetic and sympathetic activities, CDispEn13 and an entropy ratio associated with low-frequency to high-frequency ratio of the variations in the RR intervals, CDispEn13/CDispEn24.

Keywords: Cardiac autonomic regulation; Chaotic analysis; Congestive heart failure; Heart rate variability; Parasympathetic activity; Secondorder difference plot; Sympathetic activity

Keywords

Cardiac autonomic regulation; Chaotic analysis; Congestive heart failure; Heart rate variability; Parasympathetic activity; Secondorder difference plot; Sympathetic activity

Introduction

Heart rate variability (HRV) reflects the complex interaction of the control loops of the cardiovascular system and its nonlinear response to perturbations. HRV has been widely studied in patients suffering from congestive heart failure (CHF) [1-10]. CHF is a major health problem with a large associated economic burden. CHF is chronic, degenerative, and age related. Despite numerous medical advances, CHF has been difficult to manage in clinical practice [11,12]. Moreover, heart failure (HF) is asymptomatic in its initial stages and therefore early detection is crucial to avoid clinical complications, which may increase social costs. Therefore, new non-invasive, fast, and low-cost techniques which are amenable to reliable analysis, classification, and automation of large amount of HRV data and for early assessment of HF severity could contribute to containing the number of patients and related costs. Cardiac diseases, including CHF, often manifest themselves in characteristic changes in the HRV fluctuations magnitude and fluctuation dynamics. Fluctuations magnitude provides independent information beyond average values. Fluctuation dynamics evaluates how the beat interval changes from one beat to the next, independent of the variance. Several researchers have been working on the analysis of HRV for the diagnosis of CHF disorders. In the literature, different linear and nonlinear theory tools have been used to measure HRV parameters in healthy subjects and CHF patients. Analysis of linear statistics, however, does not directly address the complexity of the HRV time series and thus may potentially miss important inherent information. Nonlinear methods of assessing HRV and its dynamics may provide additional information regarding cardiac autonomic fluctuations that cannot be detected by linear methods. Guzzetti et al., Poon et al., Cohen et al., Wagner et al., and Radojicic et al. have found through quantitative analysis that chaotic properties of HRV series would be altered during the progression of the CHF disease [13-17]. Chaotic is the term used to represent a deterministic process, which because of its extreme sensitivity to initial conditions and system’s parameters, appears to behave completely randomly. Unlike random processes, deterministic chaos may be rather easily controlled [18]. Though different methods have been tried in this direction, little has been done to classify healthy and CHF patient groups with high diagnostic accuracy.
There are two approaches to chaotic analysis: graphical and numerical. Graphical techniques include strange attractors, Poincare plots, and second-order difference plots. Numerical techniques include the fractal dimension, the Lyapunov exponent, and the central tendency measure [19]. The earlier studies using CTM made an attempt to classify normal and CHF subjects [19,20]. However, those studies could not assess cardiovascular regulation. In this study, we employ a combination of graphical and numerical representations to take the advantage of either. The improved approach based on SOD in conjunction with dispersion entropy (DispEn) [21] permits assessment of cardiac autonomic fluctuations.
Hypothesizing that CHF patient will experience an altered cardiac rhythm, with changes in the magnitude of the beat-to-beat HR fluctuations and perturbations in the HR fluctuation dynamics, the HRV of CHF patients is compared with those of healthy subjects using a recently defined quantifier adapted from nonlinear dynamics and deterministic chaos theory: dispersion entropy (DispEn) [21]. DispEn quantifies degree of complex variability/chaos in a signal over time. In this context, low entropy values indicate too periodic and predictable HRV series while high values indicate too random and irregular time series. In either case, it implies inability of the HRV in the subject to adapt to changing tasks. Medium values suggest optimal complexity which is a balance between predictability and complexity that implies ability of the HRV of the subject to adapt to changing tasks. The prime advantages of the DispEn quantifier are: (1) it can be used to characterize a signal irrespective of the nature of the underlying dynamics, i.e. whether the signal is chaotic, deterministic, or stochastic. (2) Since it is derived from second-order difference plot, the measure is independent of the stationarity of the signal. (3) It is also found that the degree of complex variability of the HRV time series changes depending on the physiological/pathological state and this measure of rate of change of variability can serve as a stand-alone indicator for medical diagnosis. (4) DispEn has the advantage of easy implementation and fast computation. Further, we show that the different combinations of component/quadrant DispEns (CDispEns) provide us additional information regarding cardiac autonomic fluctuations.

Materials and Methods

HRV database and pre-processing
The interbeat (RR) interval database used in this study is obtained from MIT-BIH normal sinus rhythm (NSR database-nsrdb) and BIDMC CHF database (chfdb) database available at htpp://www. physionet.org [22]. The NSR database includes beat annotation files of long term ECG records of 18 subjects including 13 women (aged 20–50 years) and 5 men (aged 26–45 years). The sampling frequency for normal sinus rhythm data is Fs=128 Hz. The BIDMC CHF database includes beat annotation files of long term ECG records of 15 subjects (11 men, aged 22 to 71, and 4 women, aged 54 to 63) with severe congestive heart failure (NYHA classes 3-4). ECG signals in this database are sampled at 250 samples per second (Fs=250 Hz). For validation of the proposed method we use CHF data from CHF database-chf2db. This database includes beat annotation files of long term ECG records of 29 subjects (aged 34-79 years) from CHF database (NYHA classes 1, 2, and 3). The sampling frequency for this CHF data is Fs=128 Hz. The beat annotations in all the databases have been obtained by automated analysis with careful manual review and correction by the experts. A rhythmic pattern of the heart rate may be destroyed by the presence of non-sinus beats and artefacts which usually appear very early or very late. We pre-process the RR interval time series of both the normal and the two CHF groups to remove such potential artefacts, trends, ectopic beats and post-ectopic compensatory pauses. We use annotation filter combined with square filter and a filter to remove haemo-dynamics for certain types of beats [23,24]. For construction of second-order difference plots we use normal beats only as annotated in the PhysioNet database resource. On an average about 10-12% of the RR intervals are eliminated during RR interval rejection operation.
Measures of fluctuation magnitude of beat-to-beat variability
It is often difficult to use the usual standard deviation to compare measurements from different populations. To circumvent this problem, two measures are used to evaluate the magnitude of beatto- beat variability and HR fluctuations; 1) coefficient of variation (CV) original HRV time series and 2) standard deviation of the detrended HRV time series (SDdetrended). It is important to note that both of these measures are not sensitive to changes in the ordering of the RR intervals or HRV dynamics. That is to say, randomly ordering the time series will not affect these measures.
The CV expresses the standard deviation as a percentage of what is being measured relative to the sample or population mean. CV is a normalized measure of beat-to-beat variability. It is defined as the ratio of the standard deviation (SD) σ to mean μ as, CV=σ /μ. It shows the extent of variability in relation to mean of the population. It provides a measure of relative variability.
The standard deviation of a time series, in general, provides a measure of overall variations in the RR interval with respect to mean. It is a metric for absolute variability. This measure may be influenced by the trend in the data and may fail to differentiate between beats with large changes from one beat to next and those in which the changes are small. To minimize effects of local changes in the mean the time series is detrended. The detrended HRV time series refers to time series from which the trend is removed. Detrending can be carried out by computing the first difference of the time series or removing the least-squares-fit straight line. In this study, the former method is used for detrending. SDdetrended is a measure of variability which minimizes the effects of the local changes in the mean.
Measure of fluctuation dynamics of beat-to-beat variability
Unlike linear measures which are not affected by random ordering of the time series, nonlinear measures of complexity are explicitly concerned with the temporal structures of data values [25- 27]. Fluctuation dynamics is about how the RR interval changes from one beat to the next, independent of the variance. To quantify how the HRV dynamics fluctuates over time, we employed dispersion entropy [21], which is explained in detail below.
Second-order difference plot (SOD) and Dispersion entropy (DispEn)
Chaotic equations are occasionally used to generate graphs. If s(n) represents a time series, a graph of [s(n+2) - s(n+1)] plotted against [s(n+1) - s(n)] produces a scatter plot of first differences of the data, which many times, is called a second-order difference (SOD) plot of s(n) [19,28]. The purpose of these plots is to remove the dominant characteristic (high correlation between one interval and next). Thus these plots reveal serial dependencies of cardiac accelerations and decelerations. Such a SOD plot, which is centered about the origin, can be useful tool to physicians, who can make a preliminary diagnosis by the visual inspection of these scatter diagrams. SOD has been shown to be useful in the study of chaotic systems, like hemodynamic systems, brain interface systems, and in classification problems, like distinguishing between congestive heart failure patients and normal subjects [20,29,30]. The most commonly used measure in conjunction with SOD plot is the central tendency measure (CTM), which quantifies the degree of variability in a scatter plot. We propose in this study, application of Dispersion entropy (DispEn) [21] which is adapted from nonlinear dynamics and deterministic chaos theory. In fact, it is also computed from secondorder difference (SOD) plot. It can replace the earlier measure of degree of variability, i.e. CTM, with some additional advantages: (1) Computation of Central tendency measure (CTM) requires an optimal radius, r. The performance of this method highly depends upon the chosen value of r, which in turn depends on the character of the data. However, there are no specific rules to arrive at an optimum value of r. On the other hand, Dispersion entropy (DispEn) does not require the computation of an optimum r. (2) CTM computed with optimum radius, being a fractional measure, accounts for dispersion of points inside the selected radius and does not account for the dispersion of all the points in the SOD. However, DispEn accounts for complete distribution (and hence, complex variability) of the points in the SOD plot. As an implication it permits to assess cardiovascular autonomic regulation. (3) CTM and variability of the time series are negatively correlated, which is due to the own nature of the method. As a consequence, small values of CTM imply high variability and vice versa. DispEn, on the other hand, is positively correlated with variability and hence, high values of DispEn imply high variability and vice versa.
Cohen et al. had proposed CTM which quantifies the degree of variability in a scatter plot of the first difference of the series [19]. Given a circular region of radius r, about the origin, the CTM is defined as the ratio of the number of points that fall within this radius r, to the total number of points in the entire plot. This count involves the number of successive rates that include all sign combinations or quadrant regions within radius r. The performance of this method highly depends upon the chosen value of r, which in turn depends on the character of the data. However, there are no specific rules to arrive at an optimum value of r. Hence, we employ DispEn [21], which does not require the computation of an optimum r, as shown below.
If R corresponds to the radius of the most extreme point among all the scatter plots and there are N points in the scatter plot, then a good approximation for the number of annular rings is M=√N. Hence the width of each annular ring is ΔR=R/M. Then we divide the SOD plot into annular rings using M concentric circles defined as
(1)
Each annular ring represents a partition in concentric space. For example, the first annular ring extends over the range 0 ≤ r ≤ r1; the second annular ring extends over the range r1 ≤ r ≤ r2; the last annular ring extends over the range rM-1 ≤ r ≤ rM. For all the scatter plots the same ΔR and M are maintained. We first count the number of points that fall within each of these annular rings. Then we compute the probability distribution for the entire SOD plot as the ratio of the number of points that fall within each annular ring to the total number of points in the entire plot. If p1, p2, p3., ..., pM represent the probability densities in the different annular rings/partitions of the SOD, then applying Shannon entropy to this distribution, the dispersion entropy is obtained as
(2)
The DispEn is a measure of the dispersion of points in the scatter plot. A larger value of DispEn indicates a higher spread of points, while a smaller value indicates more concentration of points near the centre. Dispersion of points is closely associated with degree of variability of the time series. The higher the dispersion is the more is the degree of complex variability/chaos. The complex variability seen in the SOD plot is reflected in the DispEn. Increased (decreased) DispEn implies an increased (decreased) degree of variability/chaos of the time series. In the context of HRV, low entropy values indicate too periodic and predictable HRV series and high values indicate too random and irregular time series. In either case, it implies inability of the HRV of the subject to adapt to changing tasks due to loss of HRV control mechanism. Medium values suggest optimal complexity that implies ability of the HRV of the subject to adapt to changing tasks.
Quadrant counts and Component Dispersion entropies (CDispEns)
The points in the SOD plot are dispersed in an area which is defined by four quadrants. Each quadrant represents a pattern which corresponds to the direction and amount of change in the RR interval length from one beat to the next and the successive increase or decrease in the interval length. Thus, four patterns can be identified: +/+ represents parasympathetic activity (I-quadrant, a lengthening sequence corresponding to cardiac deceleration); -/- represents sympathetic activity (III-quadrant, a shortening sequence corresponding to cardiac acceleration); -/+ or +/- represent balanced sequences activity (II-quadrant or IV-quadrant, corresponding to balanced sequences). Patterns of each type can be counted by a quadrant (Hanratty et al.). Points in quadrants I and III correspond to low frequency variations in RR intervals while points in quadrants II and IV correspond to high frequency variations in RR intervals.
Based on quadrant count Thuraisingham et al. proposed component CTMs (CCTMs) [20]. On similar lines, based on quadrant count distribution we propose component DispEns (CDispEns), which quantify dispersion of points in the four quadrants of the scatter plot. We first count the number of points that fall within each of the annular rings confined to each quadrant. Then we compute the probability distribution function for the each quadrant in the SOD plot as the ratio of the number of points that fall within each annular ring confined to that quadrant to the total number of points in that quadrant.
If p1k, p2k, p3k, ..., pMk represent the probability densities in the different annular rings/partitions in the kth quadrant of the SOD plot, then applying Shannon entropy to this distribution, the component dispersion entropy is obtained as
(3)
The CDispEn is a measure of the dispersion of points in a specific quadrant of the scatter plot. The complex variability seen in the particular quadrant of the SOD plot is reflected in the corresponding CDispEn. A larger value of CDispEn indicates a higher spread of points in that quadrant, while a smaller value indicates more concentration of points near the centre in that quadrant. The higher the dispersion is the more is the degree of variability.
The physiological significance of the CDispEns in the four quadrants is as below. CDispEn1 represents entropy as a marker of parasympathetic activity; CDispEn3 represents entropy as a marker of sympathetic activity; CDispEn2 and CDispEn4 represent entropy markers of balanced sequences activity. CDispEn1 and CDispEn3 together symbolize the entropy of LF variation in RR intervals as seen in the SOD plane and we designate it as CDispEn13 while CDispEn2 and CDispEn4 together symbolize the entropy of HF variation in RR intervals and we designate it as CDispEn24.
In this work, we investigate the diagnostic ability of dispersion entropy under the following categories: (1) Total DispEn which accounts for all the four quadrants or entire SOD plane, (2) CDispEn13 and CDispEn24 which account for LF and HF variations in RR intervals as manifested in SOD plots, and (3) Ratio of CDispEn13 and CDispEn24which corresponds to LF/HF in the SOD domain.
Receiver Operating Characteristic (ROC) analysis
Independent-samples significance tests (Student’s t-tests) are used to evaluate the statistical differences between the DispEn and related measures of normal and CHF classes. Statistical significance was set at p<0.01 for all pair-wise comparisons. If significant differences between classes are found, then the ability of the nonlinear analysis method to discriminate normal and CHF states is evaluated using receiver operating characteristic (ROC) plots in terms of area under ROC curve (AUC) [31]. ROC curves are obtained by plotting sensitivity values (which represent that proportion of states identified as CHF) along the y axis against the corresponding (1-specificity) values (which represent the proportion of the correctly identified normal states) for all the available cutoff points along the x axis. Accuracy is a related parameter that quantifies the total number of states (both normal and CHF states) precisely classified. The AUC measures this discrimination, which is, the ability of the test to correctly classify normal and CHF classes and is regarded as an index of diagnostic accuracy. The optimum threshold is the cut-off point in which the highest accuracy (minimal false negative and false positive results) is obtained. This can be determined from the ROC curve as the closet value to the left top point (corresponding to 100% sensitivity and 100% specificity). An AUC value of 0.5 indicates that the test results are better than those obtained by chance, where as a value of 1.0 indicates a perfectly sensitive and specific test.

Results and Discussion

A linear measure focuses on the magnitude of variation in a distribution irrespective of the order in which data points accumulate. However, a nonlinear measure is specifically concerned with the temporal evolution of structure of the data variability and hence, may contain more meaningful information. In this study, first we investigate the linear statistics of RR interval time series of normal and CHF (BIDMC) group subjects. Then, we examine the suitability of the novel approach employing DispEn in discerning the normal and pathological CHF groups. Representative examples of RR interval time series, over consecutive 500 beats, for the two groups are illustrated in Figure 1. Higher variability is found in the case of normal group and lower is found in the case of CHF group. Before the application of the proposed methods, it is necessary to pre-process the RR interval time series of the two groups as discussed in Section 2.1. Each RR interval record, in each group, is divided into segments, with 2500 beats per segment. A thumb rule to select segment length is that it must be long enough to reliably estimate the measure of interest, while it must be short enough to accurately capture local activities. For each segment the variability measures are computed and the results of a particular group are averaged. Table 1 shows the linear measures of fluctuation magnitude of beat-to-beat variability characteristic of normal and BIDMC CHF group RR interval time series. All the variability measures are expressed as mean ± SD. It is found that the average RR interval time is longer in the normal group (0.741) compared to that of the CHF (0.639) group. The two measures of fluctuation magnitude, CV and SDdetrend, are also considerably decreased in the CHF (6.14 and 0.038, respectively) disorder group compared to that of the normal (11.91 and 0.085, respectively) group. The CV of patients with CHF was nearly half as that observed in normal subjects while the SDdetrend in CHF disease group was less than half as that of normal group. These results indicate that the magnitude of beat-to-beat variability in CHF patients is significantly decreased by the cardiovascular morbidity. It is important to note that the higher fluctuations of RR interval time series and their variability is a typical feature of healthy cardiac system. This is necessary to accommodate some adaptability to physical activity and perturbations/influences (e.g. posture, sleep, exercise, walking speed, stress, aging, etc.). The same, however, is not true in regard to patients from CHF disorder groups. This conclusion is in agreement with those of the earlier studies [5]. Independent t-tests are performed to evaluate the statistical differences between the different measures of the two groups. The tests detected significant group differences with all the three linear variability measures.
Figure 1: HRV of a normal subject contrasted with that of a CHF patient (500 beats only shown).
Table 1: Fluctuation magnitude of beat-to-beat variability of normal control (MITBIH) and CHF (BIDMC) groups. Values are presented as mean ± SD.
It is important to stress that the fluctuation magnitude of HRV variability provides vital information, as reported above. Likewise, investigation of fluctuation dynamics of HRV variability offers additional insights as shown below. Next, for the same RR interval segments from each group (normal and BIDMC CHF), the nonlinear beat-to-beat variability entropy measure DispEn, CDispEn13, and the CDispEn13/CDispEn24 ratio are computed and averaged. Graphical representative examples of SOD plot to compute DispEn for the two groups are depicted in Figure 2. While Figure 2a for normal subject shows more dispersion of points around the centre, Figure 2b for CHF patient shows concentration of points near the centre. It is also found that the SOD plot is almost a circle for the case of normal control while it is an ellipse with the major axis extended in II and IV quadrants, for the case of CHF patient. This suggests that the LF and HF variations in RR intervals are almost equal in the case of normal while HF variations dominate over LF variations in the RR intervals in the case of CHF subjects. As an implication we show below that a comparison of LF and HF variations in the RR intervals as manifested in the SOD plots can unravel the complexity of the HRV time series and facilitate classification into normal and CHF. Thus visual inspection shows more variability in normal subject as compared to that in CHF patient. The descriptive results of distribution of DispEn, CDispEns, CDispEn13, CDispEn24, and the CDispEn13/CDispEn24 ratio for the normal and CHF RR interval data (all values expressed as mean ± SD) are reported in Table 2. The first point to note is that the normal group shows medium values (optimal variability state) of entropy for the DispEn. This implies that medium entropy values (optimal variability state) reflect the physiological adaptation of HRV in the healthy subjects to different activities. Unlike normal group, the CHF disorder group exhibits lower DispEn values. The low values of DispEn in CHF patients indicate their inability to adapt to changing tasks. In fact, the low values have been attributed to impaired parasympathetic modulation of the heart rate in the CHF group. This is the reason why CDispEn1 is significantly diminished in CHF group as compared to the corresponding CDispEn1 in normal group. Further, despite the presence of enhanced sympathetic activity in advanced CHF (NYHA classes 3 and 4) its manifestation is either suppressed or absent. One possible reason is that the sympathetic component loses its characteristic oscillations due to central autonomic regulatory impairment under CHF conditions [7]. Other possible explanations include the following: (i) impaired β-adrenergic receptor responsiveness [32] and (ii) increased chemoreceptor sensitivity [33]. As a consequence CDispEn3 is also significantly reduced in the used CHF group as compared to the corresponding CDispEn3 in normal group. But note that the reduction in sympathetic activity in is not as much as that in parasympathetic activity.
Figure 2a: Second-order difference plot to compute DispEn of a MIT-BIH normal control.
Figure 2b: Second-order difference plot to compute DispEn of a BIDMC CHF patient.
Table 2: Descriptive results of distribution of DispEn and different CDispEns for the normal control (MIT-BIH) and CHF (BIDMC) RR interval data (all values expressed as mean ± SD).
The graphical distribution of the total DispEn, CDispEn13, and the CDispEn13/CDispEn24 ratio corresponding to normal and CHF (BIDMC) groups using box-whiskers plots (without outliers) are illustrated in Figure 3a, 3b, and 3c respectively. The independent t-tests are used to evaluate the statistical differences between the respective entropy measures of the two groups. The results are tabulated in the first and last three rows of Table 2. Since the tests showed significant group differences, we evaluated the diagnostic ability of DispEn, CDispEn13, and the CDispEn13/CDispEn24 ratio in discriminating the normal and CHF (BIDMC) groups using ROC analysis. The corresponding ROC plots are shown in Figure 4 for all the three cases. The results of evaluation of diagnostic quality of these entropy measures in separating normal and CHF RR interval time series is summarized in Table 3. It is found that the DispEn, CDispEn13, and the CDispEn13/CDispEn24 ratio perform extremely well in their diagnostic ability. In discerning normal control and CHF (BIDMC), DispEn as well as CDispEn13 yielded the following diagnostic parameters: accuracy=94.7%, specificity=100.0%, sensitivity=90.0%, and precision=100.0%. In the case of CDispEn13/CDispEn24 ratio the following diagnostic parameters were seen: accuracy=91.2%, specificity=92.6%, sensitivity=90.0%, and precision=93.1% .
Figure 3a: Box-whisker plots for the distribution of total DispEn in the entire SOD plane.
Figure 3b: Box-whisker plots for the distribution of CDispEn13.
Figure 3c: Box-whisker plots for the distribution of CDispEn13/ CDispEn24 ratio in the MIT-BIH normal control and BIDMC CHF groups.
Figure 4: ROC plots for classification between MIT-BIH normal control and BIDMC CHF groups using (i) total DispEn in the entire SOD plane, (ii) CDispEn13, and (iii) CDispEn13/ CDispEn24 ratio.
Table 3: Results of diagnostic parameters using ROC analysis for DispEn anddifferent CDispEns in discerning the normal control (MIT-BIH) and CHF (BIDMC)RR interval data.
As mentioned earlier, we validate our approach conducting another case study by comparing normal database with CHF subjects from chf2db database. The corresponding descriptive results of distribution of total DispEn, CDispEns, CDispEn13, and the CDispEn13/CDispEn24 ratio for the normal and CHF (chf2db) RR interval data (all values expressed as mean ± SD) are reported in Table 4. The first thing to note is that all the conclusions drawn with the previous case study are very well applicable to this case study as well. Unlike normal group which exhibits medium entropy values (optimal variability state), the CHF (chf2db) disorder group exhibits lower DispEn values. Again, the low values of DispEn in CHF patients indicate their inability to adapt to changing tasks due to impaired parasympathetic modulation of the heart rate. The results of the independent t-tests used to evaluate the statistical differences between the respective entropy measures of the two groups are tabulated in the first and last three rows of Table 4. Since the tests showed significant group differences, we evaluated the diagnostic ability of DispEn, CDispEn13, and the CDispEn13/CDispEn24 ratio on normal and CHF (chf2db) database using ROC analysis. The results of evaluation of diagnostic quality of the dispersion entropies in separating normal and CHF (chf2db) RR interval time series is summarized in Table 5. Like before, it is seen that the DispEn, CDispEn13, and the CDispEn13/CDispEn24 ratio perform extremely well in their diagnostic ability.
Table 4: Descriptive results of distribution of DispEn and CDispEns for the normal (MIT-BIH) and CHF (chf2db) RR interval data (all values expressed as mean ± SD).
Table 5: Results of diagnostic parameters using ROC analysis for DispEn and CDispEns in discerning the normal (MIT-BIH) and CHF (chf2db) RR interval data.
In this study of HRV dynamics of healthy controls and CHF disordered patients, we summarize the following key findings: (1) the average RR interval is shorter in the CHF group compared to that of normal group. (2) The two measures of fluctuation magnitude, CV and SDdetrend, are considerably decreased in the CHF group compared to those of the normal group. (3) Since DispEn accounts for complete distribution (and hence, complex variability) of the points in the SOD plot it permits assessment of cardiovascular autonomic regulation. (4) CDispEn1 represents entropy as a marker of parasympathetic activity; CDispEn3 represents entropy as a marker of sympathetic activity; CDispEn2 and CDispEn4 represent entropy markers of balanced sequences activity. (5) In discerning healthy control subjects and patients with CHF disorders, DispEn, CDispEn13, and the CDispEn13/CDispEn24 ratio exhibited excellent performance in both the case studies. (6) The normal group shows medium values (optimal variability state) for the DispEn, compared to those of CHF groups which exhibit lower DispEn values. This optimal range of DispEn is important for the physiological adaptation of HRV in healthy subjects to different activities. The low values of DispEn in CHF patients indicate their inability to adapt to changing tasks due to impaired parasympathetic modulation of the heart rate. Due to central autonomic regulatory impairment, under CHF conditions, the chronic sympathetic activity is also suppressed as shown by CDispEn3. Results suggest that total DispEn has independent prognostic value in patients with CHF.
We wind up saying that the medium values of total DispEn are crucial for being healthy. Neither low nor high values of DispEn are admissible for a healthy heart. DispEn and related entropy measures can be considered as a promising tool for screening, diagnosing, and automated classification of CHF.

Conclusion

A chaotic analysis which is a combination of graphical (SOD) and numerical (DispEn) methods is presented. This novel approach permits classification of HRV time series, as well as assessment of cardiac sympathetic and parasympathetic activities. It is found that the medium values of total DispEn are crucial for being healthy. The proposed classification algorithm meets all our requirements because it is fully noninvasive, fast, low-cost and high accuracy method that provides an objective classification and hence is most suitable for automated classification of CHF.

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