# Multiscale Entropy of Cardiac and Postural Control Reflects a Flexible Adaptation to a Cognitive Task

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Population

^{2}, respectively. Among the women, four were using oral contraceptives, five reported being in the follicular phase of their menstrual cycle and three were in the luteal phase. All volunteers had a university education.

#### 2.2. Protocol

#### 2.3. Recordings of RR Interval Time Series

#### 2.4. Recordings of Center of Pressure Time Series

#### 2.5. Cognitive Tasks

#### 2.6. Analysis of RR Interval Time Series: Classic Indices

#### 2.7. Analysis of Center of Pressure Time Series: Classic Indices

#### 2.8. Analysis of Complexity: Entropy Indices

- At each scale factor of $\tau $, the number of matched vector pairs ${n}_{k,\tau}^{m+1}$ and ${n}_{k,\tau}^{m}$ is calculated for all $\left(k\right)\tau $ coarse-grained series, with $m$ corresponding to the sequence length considered. In the present study, $m=2$.
- The RCMSE at a scale factor of $\tau $ is provided as follows, with $r$ corresponding to the tolerance for matches. In the present study, $r=0.15$ of the standard deviation of the initial time series $x$ [30].$$RCMSE\left(x,\tau ,m,r\right)=-ln\left(\frac{{{\displaystyle \sum}}_{k=1}^{\tau}{n}_{k,\tau}^{m+1}}{{{\displaystyle \sum}}_{k=1}^{\tau}{n}_{k,\tau}^{m}}\right)$$

_{C}) and postural entropy index (E

_{P}) are the area under the corresponding RCMSE curves (areas calculated using the trapezoidal rule) (Figure 1) [1,27]. As recommended by Gow et al. [31], entropy indices were computed after pre-processing time series using empirical mode decomposition (EMD) [32]. EMD decomposes a signal into a sum of intrinsic mode functions (IMFs) and a residual trend. This residual trend was subtracted to remove the drift, which has been identified as a source of error in entropy assessments [31].

#### 2.9. Statistical Analyses

## 3. Results

#### 3.1. Classic Indices in Temporal and Frequency Domains

#### 3.2. Entropy Indices

_{C}and E

_{P}) are presented in Table 1. As a main finding here, the E

_{C}index obtained during Cog was higher than the index obtained during Ref (p = 0.016, two-tail Wilcoxon test).

#### 3.3. ROC Curves Analysis

## 4. Discussion

## 5. Conclusions

## 6. Limitations

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Cardiac entropy index (E

_{C},

**left**) and postural entropy index (E

_{P},

**right**), calculated from the areas under the refined composite multiscale entropy (RCMSE) curves.

**Figure 2.**Top: RR interval time series from a representative participant in reference (Ref,

**left**) and cognitive (Cog,

**right**) conditions. Middle and bottom: anteroposterior (AP,

**middle**) and mediolateral (ML,

**bottom**) center of pressure (COP) time series, the horizontal axes are the same for these plots.

**Figure 3.**Refined composite multiscale entropy (RCMSE) analysis of RR interval time series (

**left**) and center of pressure time series on anteroposterior axis (

**right**) during reference (Ref) and cognitive (Cog) conditions. The RCMSE curves were obtained by connecting the group mean values of sample entropy for each scale. The error bars represent standard errors. The RCMSE curves for the surrogate shuffled time series are also presented.

**Figure 4.**Receiver operating characteristic (ROC) curves (sensitivity vs 1-specificity) for cardiac (

**left**) and postural (

**right**) indices. RMSSD: root mean square of successive differences; LF: low frequency; HF: high frequency; E

_{C}: cardiac entropy index; AP: anteroposterior; E

_{P}: postural entropy index; ML: mediolateral.

**Table 1.**Classic and entropy indices calculated from RR interval time series and from anteroposterior and mediolateral center of pressure time series, during reference and cognitive conditions.

Heart Rate Dynamics | Ref | Cog |
---|---|---|

RR intervals (ms) | 952 ± 120 | 915 ± 131 ^{**} |

RMSSD (ms) | 58 ± 36 | 52 ± 30 |

LFs (ms^{2}) | 2243 ± 2058 | 1894 ± 1602 |

HFs (ms^{2}) | 1459 ± 1448 | 1150 ± 1196 |

LFs/HFs | 2.96 ± 3.09 | 2.82 ± 2.62 |

E_{C} | 5.45 ± 0.60 | 5.75 ± 0.69 ^{*} |

Postural Dynamics | Ref | Cog |

95% confidence ellipse (mm^{2}) | 217.5 ± 148.5 | 184.7 ± 103.5 |

AP velocity (mm·s^{−1}) | 4.4 ± 1.1 | 5.1 ± 1.2 ^{***} |

AP energy (mm^{2}) | 10.29 ± 19.1 | 9.04 ± 5.5 |

AP E_{P} | 11.81 ± 3.07 | 14.45 ± 3.27 ^{***} |

ML velocity (mm·s^{−1}) | 4.9 ± 1.6 | 5.3 ± 1.5 ^{*} |

ML energy (mm^{2}) | 6.42 ± 3.59 | 8.00 ± 5.54 |

ML E_{P} | 13.99 ± 2.76 | 14.72 ± 3.03 |

_{C}: cardiac entropy index; AP: anteroposterior; E

_{P}: postural entropy index; ML: mediolateral. Differences between Ref and Cog are expressed as

^{***}p < 0.001,

^{**}p < 0.01,

^{*}p < 0.05.

Heart Rate Dynamics | J | AUC |
---|---|---|

RR intervals | 0.22 | 0.59 |

RMSSD | 0.13 | 0.54 |

LFs | 0.19 | 0.54 |

HFs | 0.13 | 0.54 |

LFs/HFs | 0.16 | 0.52 |

E_{C} | 0.31 | 0.67 |

Postural Dynamics | J | AUC |

95% confidence ellipse (mm^{2}) | 0.15 | 0.55 |

AP velocity | 0.44 | 0.71 |

AP energy | 0.15 | 0.51 |

AP E_{P} | 0.41 | 0.72 |

ML velocity | 0.27 | 0.60 |

ML energy | 0.21 | 0.67 |

ML E_{P} | 0.18 | 0.56 |

_{C}: cardiac entropy index; AP: anteroposterior; E

_{P}: postural entropy index; ML: mediolateral.

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**MDPI and ACS Style**

Blons, E.; Arsac, L.M.; Gilfriche, P.; Deschodt-Arsac, V. Multiscale Entropy of Cardiac and Postural Control Reflects a Flexible Adaptation to a Cognitive Task. *Entropy* **2019**, *21*, 1024.
https://doi.org/10.3390/e21101024

**AMA Style**

Blons E, Arsac LM, Gilfriche P, Deschodt-Arsac V. Multiscale Entropy of Cardiac and Postural Control Reflects a Flexible Adaptation to a Cognitive Task. *Entropy*. 2019; 21(10):1024.
https://doi.org/10.3390/e21101024

**Chicago/Turabian Style**

Blons, Estelle, Laurent M. Arsac, Pierre Gilfriche, and Veronique Deschodt-Arsac. 2019. "Multiscale Entropy of Cardiac and Postural Control Reflects a Flexible Adaptation to a Cognitive Task" *Entropy* 21, no. 10: 1024.
https://doi.org/10.3390/e21101024