# Information Dynamics of the Brain, Cardiovascular and Respiratory Network during Different Levels of Mental Stress

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## Abstract

**:**

## 1. Introduction

## 2. Information Decomposition

## 3. Materials and Methods

#### 3.1. Hardware Configuration

#### 3.2. Data Acquisition

- rest (12 $\mathrm{min}$);
- mental arithmetic/serious game (7 $\mathrm{min}$);
- recovery (12 $\mathrm{min}$).

#### 3.3. Data Pre-Processing and Analysis

#### 3.4. Statistical Analysis

## 4. Results

## 5. Discussion

#### 5.1. Information Produced and Stored in the Nodes of the Human Physiological Network

#### 5.2. Information Transfer across the Nodes of the Human Physiological Network

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**ECG, respiratory signal and BVP acquired from the wearable sensors. The red dots indicates what concerns the ECG, the detection of the R picks; for the respiratory signal, the corresponding value; and for the BVP the point of maximum derivative.

**Figure 3.**RR interval, respiratory and PAT time series measured for a representative subject during the resting phase (REST), the serious game test (SG) and the mental arithmetic test (MA).

**Figure 4.**Brain wave amplitude (PSD of a sliding window of 2 $\mathrm{s}$ of duration with 50% overlap) time series measured for a representative subject as the time course of the $\delta $, $\theta $, $\alpha $, $\beta $ EEG power during the resting phase (REST), the serious game test (SG) and the mental arithmetic test (MA).

**Figure 5.**Boxplots of the information storage ${S}_{j}$ (p < 0.05) for the seven time series under consideration during rest (REST), mental arithmetic (MA), and serious game (SG). The lines under the boxplots indicate significant differences between the linked mental states as determined by the ANOVA test; moreover, the names of the time series that are significantly different from the one under consideration for any assigned mental state, listed above each boxplot.

**Figure 6.**Boxplots of the new information ${N}_{j}$ (p < 0.05) for the seven time series under consideration during rest (REST), mental arithmetic (MA), and serious game (SG). The lines under the boxplots indicate significant differences between the linked mental states as determined by the ANOVA test; moreover, the names of the time series that are significantly different from the one under consideration for any assigned mental state, listed above each boxplot.

**Figure 7.**Boxplots of the total information transfer ${T}_{j}$ (p < 0.05) for the seven time series under consideration during rest (REST), mental arithmetic (MA), and serious game (SG). The lines under the boxplots indicate significant differences between the linked mental states as determined by the ANOVA test; moreover, the names of the time series that are significantly different from the one under consideration for any assigned mental state, listed above each boxplot.

**Figure 8.**Information transfer for the cardiorespiratory-brain network using the conditional information transfer ${T}_{i\to j|k}$. The arrows thickness is proportional to the number of subjects for which that link is statistically significant (p < 0.05) using an F-test. The magnitude of ${T}_{j}$ for each node is coded accordingly to the colorbar on the left.

Time Series | Information Dynamic Indices |
---|---|

cardiac period (RR interval) | Information Storage (${S}_{j}$) |

respiration (RESP) | New Information (${N}_{j}$) |

pulse arrival time (PAT) | Information Transfer (${T}_{j}$) |

EEG ${\delta}_{F3}$ power | Conditional Information Transfer (${T}_{i\to j|\mathbf{k}}$) |

EEG ${\theta}_{F3}$ power | |

EEG ${\alpha}_{F3}$ power | |

EEG ${\beta}_{F3}$ power |

**Table 2.**Median values of ${S}_{j}$ for the seven time series under consideration during rest (REST), mental arithmetic (MA), and serious game (SG).

RR | RESP | PAT | δ | θ | α | β | |
---|---|---|---|---|---|---|---|

REST | 0.560 | 0.401 | 0.117 | 0.039 | 0.013 | 0.015 | 0.031 |

MA | 0.490 | 0.200 | 0.088 | 0.032 | 0.014 | 0.016 | 0.022 |

SG | 0.434 | 0.300 | 0.099 | 0.024 | 0.022 | 0.013 | 0.017 |

**Table 3.**Median values of ${N}_{j}$ for the seven time series under consideration during rest (REST), mental arithmetic (MA), and serious game (SG).

RR | RESP | PAT | δ | θ | α | β | |
---|---|---|---|---|---|---|---|

REST | 0.674 | 0.951 | 1.155 | 1.347 | 1.357 | 1.365 | 1.362 |

MA | 0.772 | 1.117 | 1.222 | 1.333 | 1.369 | 1.364 | 1.342 |

SG | 0.777 | 0.965 | 1.178 | 1.349 | 1.351 | 1.357 | 1.343 |

**Table 4.**Median values of ${T}_{j}$ for the seven time series under consideration during rest (REST), mental arithmetic (MA), and serious game (SG).

RR | RESP | PAT | δ | θ | α | β | |
---|---|---|---|---|---|---|---|

REST | 0.163 | 0.123 | 0.104 | 0.036 | 0.045 | 0.043 | 0.040 |

MA | 0.159 | 0.104 | 0.088 | 0.047 | 0.037 | 0.039 | 0.041 |

SG | 0.177 | 0.120 | 0.081 | 0.040 | 0.050 | 0.040 | 0.045 |

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**MDPI and ACS Style**

Zanetti, M.; Faes, L.; Nollo, G.; De Cecco, M.; Pernice, R.; Maule, L.; Pertile, M.; Fornaser, A.
Information Dynamics of the Brain, Cardiovascular and Respiratory Network during Different Levels of Mental Stress. *Entropy* **2019**, *21*, 275.
https://doi.org/10.3390/e21030275

**AMA Style**

Zanetti M, Faes L, Nollo G, De Cecco M, Pernice R, Maule L, Pertile M, Fornaser A.
Information Dynamics of the Brain, Cardiovascular and Respiratory Network during Different Levels of Mental Stress. *Entropy*. 2019; 21(3):275.
https://doi.org/10.3390/e21030275

**Chicago/Turabian Style**

Zanetti, Matteo, Luca Faes, Giandomenico Nollo, Mariolino De Cecco, Riccardo Pernice, Luca Maule, Marco Pertile, and Alberto Fornaser.
2019. "Information Dynamics of the Brain, Cardiovascular and Respiratory Network during Different Levels of Mental Stress" *Entropy* 21, no. 3: 275.
https://doi.org/10.3390/e21030275