# Multiscale Entropy Analysis of the Differential RR Interval Time Series Signal and Its Application in Detecting Congestive Heart Failure

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Data

#### 2.2. Method Description

#### 2.3. Multiscale Entropy (MSE)

#### 2.4. Statistical Analysis

## 3. Results

#### 3.1. Statistical Differences of MSE_RR and MSE_dRR between the Two Groups

^{−}

^{8}whereas they were all larger than 10

^{−}

^{8}for MSE_RR.

#### 3.2. Classification Results Using ROC Curve Analysis

#### 3.3. Classification Results Using 5-Fold Cross Validation SVM Classifier

#### 3.4. Comparison of Different Editing Methods for Abnormal RR Intervals

## 4. Discussions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Block diagram of the proposed analytical procedure. Five steps are progressively connected. NSR: normal sinus rhythm; CHF: congestive heart failure; CI: confidence interval; MSE_RR: MSE results for the original RR segment; MSE_dRR: MSE results for the difference time series of RR segment.

**Figure 2.**Examples of RR segments ($N=\text{}500$) from: (

**A**) NSR subject (nsr008); (

**B**) CHF patient (chf203). In each sub-figure, the upper panel shows the original RR segment and the lower panel shows the corresponding differential signal.

**Figure 3.**Dependence of MSE results (mean ± SDs) on the scale factor $\tau $ for the NSR and CHF groups when applied to the time series with length of $N=\text{}500$: (

**A**) MSE_RR results for the original RR interval time series; (

**B**) MSE_dRR results for its difference time series. NSR: normal sinus rhythm group; CHF: congestive heart failure group. The other parameters setting for MSE are: $m=\text{}2$ and $r=\text{}0.1$.

**Figure 4.**Dependence of MSE results (mean ± SDs) on the scale factor $\tau $ for the NSR and CHF groups when applied to the time series with length of $N=\text{}1000$: (

**A**) MSE_RR results for the original RR interval time series; (

**B**) MSE_dRR results for its difference time series. NSR: normal sinus rhythm group; CHF: congestive heart failure group. The other parameters setting for MSE are: $m=\text{}2$ and $r=\text{}0.1$.

**Figure 5.**Dependence of MSE results (mean ± SDs) on the scale factor $\tau $ for the NSR and CHF groups when applied to the time series with length of $N=\text{}2000$: (

**A**) MSE_RR results for the original RR interval time series; (

**B**) MSE_dRR results for its difference time series. NSR: normal sinus rhythm group; CHF: congestive heart failure group. The other parameters setting for MSE are: $m=\text{}2$ and $r=\text{}0.1$.

**Figure 6.**Dependence of MSE results (mean ± SDs) on the scale factor $\tau $ for the NSR and CHF groups when applied to the time series with length of $N=\text{}5000$: (

**A**) MSE_RR results for the original RR interval time series; (

**B**) MSE_dRR results for its difference time series. NSR: normal sinus rhythm group; CHF: congestive heart failure group. The other parameters setting for MSE are: $m=\text{}2$ and $r=\text{}0.1$.

**Figure 7.**Examples of ROC curve plots with AUC values for the MSE_RR and MSE_dRR for classifying NSR and CHF groups under four RR segment length types: (

**A**) $N=\text{}500$; (

**B**) $N=\text{}1000$; (

**C**) $N=\text{}2000$; (

**D**) $N=\text{}5000$. Herein, Scale 4 was used.

**Figure 8.**Examples of original RR time series from the CHF patient (chf201). Normal RR intervals are marked as blue circles and the abnormal ones are marked as red circles. The interpolated RR time series are shown in black dots. (

**a**) The original RR time series; (

**b**) the interpolated RR time series.

**Figure 9.**Dependence of MSE results (mean ± SDs) on the scale factor $\tau $ for the NSR and CHF groups when applied to the RR time series ($N=\text{}1000$) using two editing methods for the abnormal RR intervals, i.e., the direct deletion method and the interpolation method: (

**A**) MSE_RR results; (

**B**) MSE_dRR results. NSR: normal sinus rhythm group; CHF: congestive heart failure group. The other parameters setting for MSE are: $m=\text{}2$ and $r=\text{}0.1$.

**Table 1.**Statistical results of the numbers of RR interval recordings, RR intervals and RR segments from the 54 normal sinus rhythm (NSR) and 29 congestive heart failure (CHF) RR Interval Databases.

Variables | NSR Group | CHF Group |
---|---|---|

Name of RR interval recordings | nsr001–nsr054 | chf201–chf229 |

No. of RR interval recordings | 54 | 29 |

No. of RR intervals | 5,790,504 | 3,312,195 |

No. of RR intervals after removing greater than 2 s | 5,780,148 | 3,306,394 |

No. of RR intervals after removing abnormal heartbeats | 5,738,937 | 3,102,120 |

No. of RR segments when setting N = 500 | 11,452 | 6192 |

No. of RR segments when setting N = 1000 | 5711 | 3089 |

No. of RR segments when setting N = 2000 | 2843 | 1540 |

No. of RR segments when setting N = 5000 | 1123 | 607 |

**Table 2.**Statistical results of Multiscale entropy (MSE) for the NSR and CHF groups by analyzing MSE_RR and MSE_dRR respectively. The RR segment lengths were set as $N=\text{}500$, $N=\text{}1000$, $N=\text{}2000$ and $N=\text{}5000$, respectively. Scales 1–10 were used. The other parameters setting for MSE are: $m=\text{}2$ and $r=0.1$. (The shadows mean there are no significant differences between the two groups).

Length of RR Segment $\mathit{N}$ | Scale Factor $\mathit{\tau}$ | MSE_RR (Original RR Segment) | MSE_dRR (Difference Time Series) | ||||
---|---|---|---|---|---|---|---|

NSR | CHF | p-Value | NSR | CHF | p-Value | ||

500 | 1 | 1.84 ± 0.16 | 1.53 ± 0.30 | 4 × 10^{−8} | 2.00 ± 0.22 | 1.58 ± 0.35 | 1 × 10^{−9} |

2 | 1.99 ± 0.15 | 1.78 ± 0.27 | 2 × 10^{−5} | 2.22 ± 0.26 | 1.69 ± 0.40 | 2 × 10^{−10} | |

3 | 2.04 ± 0.15 | 1.90 ± 0.23 | 9 × 10^{−4} | 2.35 ± 0.21 | 1.81 ± 0.42 | 2 × 10^{−11} | |

4 | 2.09 ± 0.16 | 1.94 ± 0.22 | 8 × 10^{−4} | 2.33 ± 0.14 | 1.85 ± 0.41 | 1 × 10^{−11} | |

5 | 2.10 ± 0.13 | 1.97 ± 0.17 | 2 × 10^{−4} | 2.29 ± 0.08 | 1.89 ± 0.37 | 3 × 10^{−11} | |

6 | 2.03 ± 0.09 | 1.95 ± 0.13 | 9 × 10^{−4} | 2.20 ± 0.07 | 1.88 ± 0.33 | 2 × 10^{−8} | |

7 | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{1.93 \xb1 0.07}$}$ | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{1.88 \xb1 0.12}$}$ | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{0.01}$}$ | 2.11 ± 0.09 | 1.85 ± 0.29 | 7 × 10^{−5} | |

8 | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{1.83 \xb1 0.06}$}$ | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{1.81 \xb1 0.09}$}$ | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{0.3}$}$ | 2.04 ± 0.07 | 1.80 ± 0.26 | 0.003 | |

9 | 1.76 ± 0.05 | 1.68 ± 0.06 | 5 × 10^{−4} | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{1.98 \xb1 0.09}$}$ | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{1.81 \xb1 0.24}$}$ | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{0.1}$}$ | |

10 | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{1.63 \xb1 0.05}$}$ | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{1.63 \xb1 0.08}$}$ | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{0.98}$}$ | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{1.89 \xb1 0.07}$}$ | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{1.77 \xb1 0.21}$}$ | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{0.4}$}$ | |

1000 | 1 | 1.80 ± 0.15 | 1.53 ± 0.29 | 3 × 10^{−7} | 2.00 ± 0.22 | 1.58 ± 0.35 | 2 × 10^{−9} |

2 | 1.86 ± 0.16 | 1.72 ± 0.24 | 0.002 | 2.20 ± 0.25 | 1.68 ± 0.39 | 2 × 10^{−10} | |

3 | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{1.90 \xb1 0.17}$}$ | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{1.79 \xb1 0.21}$}$ | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{0.02}$}$ | 2.34 ± 0.24 | 1.79 ± 0.42 | 9 × 10^{−11} | |

4 | 1.99 ± 0.18 | 1.85 ± 0.23 | 0.003 | 2.43 ± 0.24 | 1.85 ± 0.45 | 4 × 10^{−11} | |

5 | 2.09 ± 0.18 | 1.93 ± 0.23 | 8 × 10^{−4} | 2.49 ± 0.21 | 1.92 ± 0.45 | 2 × 10^{−11} | |

6 | 2.15 ± 0.17 | 1.97 ± 0.19 | 6 × 10^{−5} | 2.50 ± 0.16 | 1.98 ± 0.44 | 1 × 10^{−11} | |

7 | 2.18 ± 0.16 | 2.02 ± 0.20 | 1 × 10^{−4} | 2.48 ± 0.12 | 2.00 ± 0.43 | 4 × 10^{−11} | |

8 | 2.19 ± 0.14 | 2.05 ± 0.17 | 1 × 10^{−4} | 2.45 ± 0.09 | 2.03 ± 0.41 | 3 × 10^{−10} | |

9 | 2.17 ± 0.13 | 2.06 ± 0.18 | 0.002 | 2.40 ± 0.08 | 2.03 ± 0.38 | 9 × 10^{−10} | |

10 | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{2.13 \xb1 0.12}$}$ | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{2.08 \xb1 0.15}$}$ | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{0.1}$}$ | 2.32 ± 0.08 | 2.02 ± 0.33 | 7 × 10^{−9} | |

2000 | 1 | 1.75 ± 0.15 | 1.52 ± 0.27 | 4 × 10^{−6} | 2.00 ± 0.22 | 1.58 ± 0.35 | 3 × 10^{−9} |

2 | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{1.72 \xb1 0.17}$}$ | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{1.64 \xb1 0.21}$}$ | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{0.1}$}$ | 2.19 ± 0.25 | 1.68 ± 0.39 | 3 × 10^{−10} | |

3 | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{1.76 \xb1 0.19}$}$ | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{1.67 \xb1 0.22}$}$ | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{0.1}$}$ | 2.32 ± 0.24 | 1.78 ± 0.41 | 6 × 10^{−11} | |

4 | 1.83 ± 0.20 | 1.68 ± 0.25 | 0.003 | 2.39 ± 0.23 | 1.84 ± 0.44 | 6 × 10^{−11} | |

5 | 1.92 ± 0.19 | 1.75 ± 0.24 | 8 × 10^{−4} | 2.47 ± 0.21 | 1.92 ± 0.47 | 2 × 10^{−10} | |

6 | 1.98 ± 0.19 | 1.79 ± 0.23 | 2 × 10^{−4} | 2.53 ± 0.20 | 1.98 ± 0.47 | 1 × 10^{−10} | |

7 | 2.02 ± 0.18 | 1.84 ± 0.23 | 2 × 10^{−4} | 2.56 ± 0.19 | 2.02 ± 0.47 | 8 × 10^{−11} | |

8 | 2.04 ± 0.18 | 1.88 ± 0.22 | 6 × 10^{−4} | 2.59 ± 0.19 | 2.05 ± 0.47 | 1 × 10^{−10} | |

9 | 2.06 ± 0.17 | 1.91 ± 0.22 | 8 × 10^{−4} | 2.60 ± 0.18 | 2.08 ± 0.45 | 5 × 10^{−11} | |

10 | 2.09 ± 0.17 | 1.94 ± 0.22 | 5 × 10^{−4} | 2.59 ± 0.15 | 2.09 ± 0.44 | 4 × 10^{−11} | |

5000 | 1 | 1.64 ± 0.19 | 1.50 ± 0.25 | 0.004 | 2.00 ± 0.22 | 1.58 ± 0.35 | 3 × 10^{−9} |

2 | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{1.55 \xb1 0.19}$}$ | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{1.53 \xb1 0.20}$}$ | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{0.7}$}$ | 2.17 ± 0.25 | 1.68 ± 0.39 | 4 × 10^{−10} | |

3 | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{1.59 \xb1 0.21}$}$ | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{1.49 \xb1 0.25}$}$ | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{0.1}$}$ | 2.30 ± 0.23 | 1.78 ± 0.41 | 9 × 10^{−11} | |

4 | 1.67 ± 0.22 | 1.50 ± 0.26 | 0.003 | 2.36 ± 0.23 | 1.82 ± 0.42 | 4 × 10^{−11} | |

5 | 1.74 ± 0.22 | 1.56 ± 0.24 | 0.001 | 2.43 ± 0.21 | 1.90 ± 0.45 | 2 × 10^{−10} | |

6 | 1.79 ± 0.21 | 1.59 ± 0.23 | 2 × 10^{−4} | 2.47 ± 0.19 | 1.96 ± 0.46 | 3 × 10^{−10} | |

7 | 1.82 ± 0.20 | 1.62 ± 0.24 | 9 × 10^{−5} | 2.50 ± 0.18 | 2.00 ± 0.45 | 3 × 10^{−10} | |

8 | 1.83 ± 0.19 | 1.65 ± 0.24 | 3 × 10^{−4} | 2.53 ± 0.18 | 2.03 ± 0.45 | 2 × 10^{−10} | |

9 | 1.84 ± 0.19 | 1.68 ± 0.24 | 0.001 | 2.56 ± 0.18 | 2.05 ± 0.44 | 1 × 10^{−10} | |

10 | 1.86 ± 0.18 | 1.71 ± 0.25 | 0.002 | 2.57 ± 0.17 | 2.07 ± 0.44 | 2 × 10^{−10} |

**Table 3.**Results of AUC values (%) for MSE_RR and MSE_dRR for classifying the NSR and CHF groups. Four RR segment length types ($N=\text{}500$,$\text{}N=\text{}1000$, $N=\text{}2000$ and $N=\text{}5000$) were evaluated. Scales 1–10 were used. The other parameters setting for MSE are: $m=\text{}2$ and $r=\text{}0.1$.

Scale Factor $\mathsf{\tau}$ | $\mathit{N}=500$ | $\mathit{N}=1000$ | $\mathit{N}=2000$ | $\mathit{N}=5000$ | ||||
---|---|---|---|---|---|---|---|---|

MSE_RR | MSE_dRR | MSE_RR | MSE_dRR | MSE_RR | MSE_dRR | MSE_RR | MSE_dRR | |

1 | 79.7 | 82.8 | 78.9 | 82.4 | 77.4 | 82.5 | 69.1 | 82.5 |

2 | 75.2 | 84.4 | 67.3 | 84.4 | 61.0 | 83.9 | 52.7 | 83.6 |

3 | 69.0 | 84.9 | 64.3 | 84.6 | 62.5 | 84.9 | 64.4 | 84.9 |

4 | 70.3 | 82.7 | 68.6 | 84.7 | 68.9 | 84.3 | 68.3 | 85.0 |

5 | 71.4 | 84.1 | 71.9 | 85.9 | 71.5 | 83.5 | 69.8 | 83.5 |

6 | 70.0 | 80.0 | 74.5 | 83.7 | 73.1 | 82.8 | 71.1 | 82.1 |

7 | 63.9 | 80.5 | 71.9 | 83.8 | 72.2 | 83.7 | 72.1 | 81.9 |

8 | 55.7 | 80.4 | 71.7 | 81.0 | 69.5 | 83.2 | 69.8 | 82.7 |

9 | 84.0 | 73.7 | 66.9 | 79.1 | 69.1 | 83.1 | 66.8 | 83.4 |

10 | 46.7 | 61.5 | 61.6 | 81.1 | 70.6 | 83.0 | 66.8 | 81.7 |

Mean | 68.6 | 79.5 | 69.8 | 83.1 | 69.6 | 83.5 | 67.1 | 83.1 |

SD | 11.0 | 7.1 | 5.1 | 2.1 | 4.8 | 0.7 | 5.5 | 1.2 |

**Table 4.**Results of five-fold cross validation for MSE_RR and MSE_dRR using the default SVM parameter setting. Three RR segment length types ($N=\text{}1000$, $N=\text{}2000$ and $N=\text{}5000$) were evaluated. The other parameters setting for MSE are: $m=\text{}2$ and $r=\text{}0.1$.

Length of RR Segment $\mathit{N}$ | Fold | MSE_RR (Original RR Segment) | MSE_dRR (Difference Signal) | ||||
---|---|---|---|---|---|---|---|

$\mathit{S}\mathit{e}$ (%) | $\mathit{S}\mathit{p}$ (%) | $\mathit{A}\mathit{c}\mathit{c}$ (%) | $\mathit{S}\mathit{e}$ (%) | $\mathit{S}\mathit{p}$ (%) | $\mathit{A}\mathit{c}\mathit{c}$ (%) | ||

1000 | 1 | 71.4 | 66.7 | 68.8 | 80.0 | 90.9 | 87.5 |

2 | 80.0 | 75.0 | 76.5 | 100 | 76.9 | 81.3 | |

3 | 57.1 | 80.0 | 70.6 | 80.0 | 83.3 | 82.4 | |

4 | 66.7 | 81.8 | 76.5 | 80.0 | 91.7 | 88.2 | |

5 | 75.0 | 75.0 | 75.0 | 90.9 | 83.3 | 88.2 | |

Mean | 70.1 | 75.7 | 73.5 | 86.2 | 85.2 | 85.5 | |

SD | 8.7 | 5.9 | 3.6 | 9.1 | 6.1 | 3.4 | |

2000 | 1 | 71.4 | 66.7 | 68.8 | 80.0 | 90.9 | 87.5 |

2 | 80.0 | 83.3 | 82.4 | 100 | 84.6 | 87.5 | |

3 | 71.4 | 80.0 | 76.5 | 80.0 | 83.3 | 82.4 | |

4 | 66.7 | 72.7 | 70.6 | 80.0 | 91.7 | 88.2 | |

5 | 75.0 | 83.3 | 81.3 | 81.8 | 83.3 | 82.4 | |

Mean | 72.9 | 77.2 | 75.9 | 84.4 | 86.8 | 85.6 | |

SD | 5.0 | 7.3 | 6.1 | 8.8 | 4.2 | 3.0 | |

5000 | 1 | 71.4 | 55.6 | 62.5 | 80.0 | 90.9 | 87.5 |

2 | 80.0 | 83.3 | 82.4 | 100 | 84.6 | 87.5 | |

3 | 71.4 | 80.0 | 76.5 | 80.0 | 83.3 | 82.4 | |

4 | 66.7 | 72.7 | 70.6 | 80.0 | 91.7 | 88.2 | |

5 | 75.0 | 83.3 | 81.3 | 81.8 | 83.3 | 82.4 | |

Mean | 72.9 | 75.0 | 74.6 | 84.4 | 86.8 | 85.6 | |

SD | 5.0 | 11.7 | 8.2 | 8.8 | 4.2 | 3.0 |

**Table 5.**Statistical results of MSE (RR segment length $N=\text{}1000$) for the NSR and CHF groups by analyzing MSE_RR and MSE_dRR respectively. Herein, during the pre-processing for RR interval recording, the abnormal RR intervals were not deleted and were interpolated using the spline interpolation method. Scales 1–10 were used. The other parameters setting for MSE are: $m=\text{}2$ and $r=\text{}0.1$. (The shadows mean there are no significant differences between the two groups).

Length of RR Segment $\mathit{N}$ | Scale Factor $\mathit{\tau}$ | MSE_RR (Original RR Segment) | MSE_dRR (Difference Time Series) | ||||
---|---|---|---|---|---|---|---|

NSR | CHF | p-Value | NSR | CHF | p-Value | ||

1000 | 1 | 1.79 ± 0.15 | 1.51 ± 0.28 | 4 × 10^{−8} | 1.99 ± 0.22 | 1.57 ± 0.34 | 8 × 10^{−10} |

2 | 1.85 ± 0.17 | 1.72 ± 0.24 | 0.005 | 2.19 ± 0.25 | 1.71 ± 0.38 | 9 × 10^{−10} | |

3 | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{1.90 \xb1 0.18}$}$ | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{1.79 \xb1 0.22}$}$ | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{0.02}$}$ | 2.34 ± 0.24 | 1.83 ± 0.42 | 4 × 10^{−10} | |

4 | 1.98 ± 0.18 | 1.84 ± 0.23 | 0.003 | 2.42 ± 0.23 | 1.89 ± 0.43 | 1 × 10^{−10} | |

5 | 2.08 ± 0.18 | 1.92 ± 0.24 | 0.001 | 2.48 ± 0.20 | 1.96 ± 0.44 | 2 × 10^{−10} | |

6 | 2.15 ± 0.18 | 1.99 ± 0.22 | 4 × 10^{−4} | 2.49 ± 0.15 | 2.01 ± 0.44 | 2 × 10^{−10} | |

7 | 2.18 ± 0.16 | 2.03 ± 0.19 | 4 × 10^{−4} | 2.48 ± 0.12 | 2.05 ± 0.41 | 2 × 10^{−10} | |

8 | 2.18 ± 0.14 | 2.06 ± 0.19 | 0.002 | 2.44 ± 0.08 | 2.06 ± 0.38 | 4 × 10^{−10} | |

$\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{9}$}$ | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{2.15 \xb1 0.13}$}$ | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{2.07 \xb1 0.18}$}$ | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{0.02}$}$ | 2.40 ± 0.08 | 2.08 ± 0.36 | 9 × 10^{−9} | |

$\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{10}$}$ | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{2.13 \xb1 0.10}$}$ | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{2.06 \xb1 0.16}$}$ | $\colorbox[rgb]{0.850980392156863,0.850980392156863,0.850980392156863}{$\text{0.02}$}$ | 2.32 ± 0.07 | 2.05 ± 0.33 | 2 × 10^{−7} |

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**MDPI and ACS Style**

Liu, C.; Gao, R.
Multiscale Entropy Analysis of the Differential RR Interval Time Series Signal and Its Application in Detecting Congestive Heart Failure. *Entropy* **2017**, *19*, 251.
https://doi.org/10.3390/e19060251

**AMA Style**

Liu C, Gao R.
Multiscale Entropy Analysis of the Differential RR Interval Time Series Signal and Its Application in Detecting Congestive Heart Failure. *Entropy*. 2017; 19(6):251.
https://doi.org/10.3390/e19060251

**Chicago/Turabian Style**

Liu, Chengyu, and Rui Gao.
2017. "Multiscale Entropy Analysis of the Differential RR Interval Time Series Signal and Its Application in Detecting Congestive Heart Failure" *Entropy* 19, no. 6: 251.
https://doi.org/10.3390/e19060251