# Association between Multiscale Entropy Characteristics of Heart Rate Variability and Ischemic Stroke Risk in Patients with Permanent Atrial Fibrillation

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## Abstract

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## 1. Introduction

## 2. Data and Methods

#### 2.1. Patients and HRV Time Series

#### 2.2. Multiscale Entropy (MSE) Analysis

**s**is represented in units of seconds and not beat number. In the calculation of ${S}_{E}$, we used the same values as in previous studies: $m=2$ and $r=0.15{\mathsf{\sigma}}_{x}$, where ${\sigma}_{x}$ is the standard deviation of the resampled HRV time series [2,7]. Note that ${\sigma}_{x}$ is not the standard deviation of coarse-grained time series {${y}_{j}^{\left(s\right)}$}.

#### 2.3. Multiscale Characterizations of Time Series

^{α}, where F(s) is a square root of mean-square deviations around a polynomial trend averaged over segments with length n of integrated time series. In our study, we analyzed the resampled HRV time series. Thus, the scale

**s**is represented in units of seconds.

#### 2.4. Statistical Analysis

## 3. Results

#### 3.1. Multiscale Characteristics of HRV in Patients with AFib

#### 3.2. Comparison of Predictive Performance for Ischemic Stroke

## 4. Discussion

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**RR interval {${x}_{i}$} and coarse-grained time series {${y}_{i}^{\left(s\right)}$} when s = 240 s. The left panels (

**a**) show a patient who did not develop ischemic strokes during the observation period, and the right panels (

**b**) show a patient who did. The coarse-grained time series is rescaled by subtracting its mean ${\mu}^{\left(s\right)}$ and dividing the differences by the standard deviation ${\sigma}_{x}$ of the resampled RR intervals.

**Figure 2.**Comparison between the groups that developed ischemic strokes (blue triangles) and did not develop ischemic strokes (red circles) during the observation period: (

**a**) Multiscale entropy (MSE) profiles of ${S}_{E}^{\left(s\right)}$; and (

**b**) fluctuation functions $F\left(s\right)$ estimated by detrended fluctuation analysis (DFA). Dashed lines indicate slopes with $\alpha =0.5$ and $\alpha =1.0$. The unit of s is seconds in both panels. Error bars indicate the standard deviation.

**Figure 3.**Comparison between the groups that developed (blue triangles) and did not develop (red circles) ischemic strokes during the observation period: (

**a**) autocorrelation coefficient at lag 1; (

**b**) variance ratio; and (

**c**) distribution-based entropy. The unit of s is seconds in all panels. Error bars indicate the standard deviation. No significant differences between the two groups were observed in the autocorrelation coefficient at lag 1 and the variance ratio.

**Figure 4.**Receiver operating characteristic (ROC) curves for the prediction of ischemic stroke occurrence during the observation period. The blue lines represent the ROC curve using the sample entropy ${S}_{E}^{\left(s\right)}$ when s = 240 s and the red lines represent the ROC curve using the distribution-based entropy ${H}_{D}^{\left(s\right)}$ when s = 2 s. The AUCs were 0.65 and 0.68, respectively.

**Figure 5.**Illustrative examples of the estimated probability density functions of coarse-grained time series {${y}_{i}^{\left(s\right)}$} at: (

**a**) s = 2 s; and (

**b**) s = 240 s. The coarse-grained time series is rescaled by the standard deviation ${\sigma}_{x}$ of the resampled RR intervals. Red bar charts represent a patient who did not develop ischemic strokes during the observation period, and blue bar charts represent a patient who did develop ischemic strokes.

**Figure 6.**(

**a**) Comparison of sample entropy ${S}_{E}^{\left(s\right)}$ between the original and randomly shuffled RR intervals. (

**b**) Comparison of distribution-based entropy ${H}_{D}^{\left(s\right)}$ between the original and randomly shuffled RR intervals. Blue triangles represent patients who developed ischemic strokes and red circles represent patients who did not develop ischemic stroke. The unit of s is seconds. (

**c**) The scale dependence of ${H}_{D}^{\left(s\right)}$ for Gaussian processes characterized by DFA scaling exponent $\alpha $. ${H}_{D}^{\left(s\right)}$ was estimated from the numerically generated time series. The unit of n is the number of data points.

Clinical Characteristics | Ischemic Stroke (n = 22) | Non-Ischemic Stroke (n = 151) | p-Value |
---|---|---|---|

Age | 71 ± 8 | 69 ± 11 | 0.35 |

Female, n (%) | 7 (32) | 43 (28) | 0.26 |

Underlying disease, n (%) | - | - | - |

Congestive heart failure | 9 (41) | 56 (37) | 0.72 |

Hypertension | 15 (68) | 88 (58) | 0.38 |

Diabetes | 1 (5) | 14 (9) | 0.46 |

Stroke or TIA | 9 (41) | 40 (26) | 0.16 |

Vascular disease | 2 (9) | 15 (10) | 0.90 |

Medications, n (%) | - | - | - |

Beta-blocker | 4 (18) | 24 (16) | 0.79 |

Digitalis | 8 (36) | 65 (43) | 0.55 |

Ca-channnel blocker | 7 (32) | 35 (23) | 0.38 |

ACE inhibitor | 9 (41) | 37 (25) | 0.47 |

Diuretics | 5 (23) | 56 (37) | 0.75 |

Warfarin | 10 (45) | 83 (55) | 0.40 |

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## Share and Cite

**MDPI and ACS Style**

Matsuoka, R.; Yoshino, K.; Watanabe, E.; Kiyono, K.
Association between Multiscale Entropy Characteristics of Heart Rate Variability and Ischemic Stroke Risk in Patients with Permanent Atrial Fibrillation. *Entropy* **2017**, *19*, 672.
https://doi.org/10.3390/e19120672

**AMA Style**

Matsuoka R, Yoshino K, Watanabe E, Kiyono K.
Association between Multiscale Entropy Characteristics of Heart Rate Variability and Ischemic Stroke Risk in Patients with Permanent Atrial Fibrillation. *Entropy*. 2017; 19(12):672.
https://doi.org/10.3390/e19120672

**Chicago/Turabian Style**

Matsuoka, Ryo, Kohzoh Yoshino, Eiichi Watanabe, and Ken Kiyono.
2017. "Association between Multiscale Entropy Characteristics of Heart Rate Variability and Ischemic Stroke Risk in Patients with Permanent Atrial Fibrillation" *Entropy* 19, no. 12: 672.
https://doi.org/10.3390/e19120672