# Linear and Nonlinear Quantitative EEG Analysis during Neutral Hypnosis following an Opened/Closed Eye Paradigm

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Participants

#### 2.2. Experimental Protocol

#### 2.3. Data Acquisition and Preprocessing

#### 2.4. Power Analysis

#### 2.5. Lempel-Ziv Complexity Analysis

#### 2.6. Tsallis Entropy

#### 2.7. Statistical Analysis

## 3. Results

#### 3.1. Power Analysis

#### 3.2. Lempel-Ziv Complexity Analysis

#### 3.3. Tsallis Entropy Analysis

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schematic illustration of the LZC estimation procedure for one exemplary EEG channel, within a single experimental condition. (a) The EEG data is first undersampled to the sampling frequency of 256 Hz. (b) Then, a band-pass filter in the range (1–35) Hz is applied. (c) Bad channels are identified and rejected, and (d) the Artifact Subspace Reconstruction (ASR) algorithm is applied in order to remove short-time high-amplitude artifacts from the data. Afterwards, (e) bad channels are recovered through interpolation, and the data is referenced to its average. Finally, (f) Independent Component Analysis (ICA) is applied to the data, and components reflecting artifacts activity are removed. (g) Each preprocessed EEG channel is segmented into non-overlapping windows of 39 s length. (h) For each window, the data is transformed into a binary sequence by comparing the time series with its median value. (i) The scanning process is applied to the binary sequence, and (j) the complexity value for the particular window is obtained. Finally, (k) the complexity of each window is averaged, to obtain the complexity of the EEG channel, in a particular experimental condition.

**Figure 2.**Within-group analysis of Total Power Spectral Density (TPSD) (blue boxes) and Power Spectral Density (PSD) (green boxes) in the $\delta $, $\theta $, $\alpha $, and $\beta $ frequency bands for High-Susceptible (HS) (

**left**), Medium-Susceptible (MS) (

**center**), and Low-Susceptible (LS) (

**right**) subjects, respectively (p < 0.05, False-Discovery-Rate corrected). The red color in the maps corresponds to higher levels of power in the second condition compared to the first, whereas the blue color in the maps corresponds to lower levels of power in the second condition compared to the first.

**Figure 3.**Within-group analysis of Lempel-Ziv Complexity (LZC) (blue boxes) and frequency-banded LZC (fLZC) (green boxes) in the $\delta $, $\theta $, $\alpha $, and $\beta $ frequency bands for High-Susceptible (HS) (

**left**), Medium-Susceptible (MS) (

**center**), and Low-Susceptible (LS) (

**right**) subjects, respectively ($p<0.05$, False-Discovery-Rate corrected). The red color in the maps corresponds to higher levels of complexity in the second condition compared to the first, whereas the blue color in the maps corresponds to lower levels of complexity in the second condition compared to the first.

**Figure 4.**Between-group analysis of Lempel-Ziv Complexity (LZC) within each experimental condition was conducted with a Kruskal–Wallis test ($p<0.05$, corrected with Tukey–Kramer critical value). From left to right: experimental conditions. Red color indicates a significant difference between the groups (i.e., $p<0.05$), whereas blue color indicates no between-group difference (i.e., $p>0.05$).

**Figure 5.**Between-group analysis of frequency-banded Lempel-Ziv Complexity (fLZC) within each experimental condition was conducted with a Kruskal–Wallis test ($p<0.05$, corrected with Tukey–Kramer critical value). Columns: experimental conditions; rows: frequency bands of interest, i.e., $\delta $, $\theta $, $\alpha $, and $\beta $ bands. Red color indicates a significant difference between the groups (i.e., $p<0.05$), whereas blue color indicates no between-group difference (i.e., $p>0.05$).

**Figure 6.**Post hoc analysis results of the Kruskal–Wallis between-group analysis of Tsallis Entropy ($p<0.05$, corrected with the Tukey–Kramer critical value). From left to right: experimental conditions. Red color indicates a higher level of entropy in HS, compared to MS, whereas blue color indicates no significant difference between the two groups.

**Figure 7.**Post hoc analysis results of the Kruskal–Wallis between-group analysis of frequency-banded Tsallis Entropy ($p<0.05$, corrected with the Tukey–Kramer critical value), in the $\delta $, $\theta $, $\alpha $, and $\beta $ bands. From left to right: experimental conditions. Red color indicates a higher level of entropy in HS, compared to MS, whereas blue color indicates no significant difference between the two groups.

**Table 1.**Post hoc analysis of between-group Lempel-Ziv Complexity (LZC) during Closed-Eye Rest ($C{E}_{R}$) (median ± median absolute deviation (mad)). Groups consisted of 9 High-Susceptible (HS), 16 Medium-Susceptible (MS), and 9 Low-Susceptible subjects. Rows: electrodes; results are grouped by pairwise comparisons between groups. Significant differences are highlighted in bold. p-values corrected with the Tukey–Kramer critical value.

HS vs. MS | |||

median ± mad | median ± mad | p-value | |

Fp1 | 0.4146 ± 0.0424 | 0.4861 ± 0.0491 | 0.0317 |

F7 | 0.4225 ± 0.0374 | 0.4943 ± 0.0381 | 0.0232 |

F3 | 0.4126 ± 0.0262 | 0.4784 ± 0.0391 | 0.0324 |

Pz | 0.4106 ± 0.0278 | 0.4458 ± 0.0359 | 0.1233 |

HS vs. LS | |||

median ± mad | median ± mad | p-value | |

Fp1 | 0.4146 ± 0.0424 | 0.4650 ± 0.0285 | 0.2317 |

F7 | 0.4225 ± 0.0374 | 0.4837 ± 0.0310 | 0.0615 |

F3 | 0.4126 ± 0.0262 | 0.4664 ± 0.0248 | 0.0597 |

Pz | 0.4106 ± 0.0278 | 0.4465 ± 0.0258 | 0.0404 |

MS vs. LS | |||

median ± mad | median ± mad | p-value | |

Fp1 | 0.4146 ± 0.0424 | 0.4650 ± 0.0285 | 0.7812 |

F7 | 0.4225 ± 0.0374 | 0.4837 ± 0.0310 | 0.9971 |

F3 | 0.4126 ± 0.0262 | 0.4664 ± 0.0248 | 0.9979 |

Pz | 0.4106 ± 0.0278 | 0.4465 ± 0.0258 | 0.7097 |

**Table 2.**Post hoc analysis of between-group frequency-banded Lempel-Ziv Complexity (fLZC) during Closed-Eye Rest ($C{E}_{R}$) in the $\delta $, $\theta $, $\alpha $, and $\beta $ frequency bands (median ± median absolute deviation (mad)). Groups consisted of 9 High-Susceptible (HS), 16 Medium-Susceptible (MS), and 9 Low-Susceptible subjects. Rows: electrodes; results are grouped by pairwise comparisons between groups. Significant differences are highlighted in bold. p-values corrected with the Tukey–Kramer critical value.

HS vs. MS | ||||

median ± mad | median ± mad | p-value | ||

$\beta $ | F7 | 0.4531 ± 0.0079 | 0.4601 ± 0.0108 | 0.4469 |

HS vs. LS | ||||

median ± mad | median ± mad | p-value | ||

$\beta $ | F7 | 0.4531 ± 0.0079 | 0.4704 ± 0.0088 | 0.0144 |

MS vs. LS | ||||

median ± mad | median ± mad | p-value | ||

$\beta $ | F7 | 0.4601 ± 0.0108 | 0.4704 ± 0.0088 | 0.1247 |

**Table 3.**Post hoc analysis of between-group frequency-banded Lempel-Ziv Complexity (fLZC) during Closed-Eye Hypnosis ($C{E}_{H}$) in the $\delta $, $\theta $, $\alpha $, and $\beta $ frequency bands (median ± median absolute deviation (mad)). Groups consisted of 9 High-Susceptible (HS), 16 Medium-Susceptible (MS), and 9 Low-Susceptible subjects. Rows: electrodes; results are grouped by pairwise comparisons between groups. Significant differences are highlighted in bold. p-values corrected with the Tukey–Kramer critical value.

HS vs. MS | ||||

median ± mad | median ± mad | p-value | ||

$\alpha $ | C3 | 0.2352 ± 0.0206 | 0.2478 ± 0.0159 | 0.6142 |

C4 | 0.2299 ± 0.0162 | 0.2508 ± 0.0161 | 0.1663 | |

T5 | 0.2339 ± 0.0094 | 0.2472 ± 0.0122 | 0.1472 | |

Pz | 0.2299 ± 0.0136 | 0.2455 ± 0.0139 | 0.1423 | |

HS vs. LS | ||||

median ± mad | median ± mad | p-value | ||

$\alpha $ | C3 | 0.2352 ± 0.0206 | 0.2599 ± 0.0098 | 0.0154 |

C4 | 0.2299 ± 0.0162 | 0.2579 ± 0.0109 | 0.0166 | |

T5 | 0.2339 ± 0.0094 | 0.2579 ± 0.0120 | 0.0404 | |

Pz | 0.2299 ± 0.0136 | 0.2532 ± 0.0158 | 0.0485 | |

MS vs. LS | ||||

median ± mad | median ± mad | p-value | ||

$\alpha $ | C3 | 0.2478 ± 0.0159 | 0.2599 ± 0.0098 | 0.0722 |

C4 | 0.2508 ± 0.0161 | 0.2579 ± 0.0109 | 0.3966 | |

T5 | 0.2472 ± 0.0122 | 0.2579 ± 0.0120 | 0.6563 | |

Pz | 0.2455 ± 0.0139 | 0.2532 ± 0.0158 | 0.7168 |

**Table 4.**Post hoc analysis of between-group frequency-banded Lempel-Ziv Complexity (fLZC) during Opened-Eye Hypnosis ($O{E}_{H}$) in the $\delta $, $\theta $, $\alpha $, and $\beta $ frequency bands (median ± median absolute deviation (mad)). Groups consisted of 9 High-Susceptible (HS), 16 Medium-Susceptible (MS), and 9 Low-Susceptible subjects. Rows: electrodes; results are grouped by pairwise comparisons between groups. Significant differences are highlighted in bold. p-values corrected with the Tukey–Kramer critical value.

HS vs. MS | ||||

median ± mad | median ± mad | p-value | ||

$\alpha $ | C3 | 0.2425 ± 0.0271 | 0.2372 ± 0.0152 | 0.8871 |

HS vs. LS | ||||

median ± mad | median ± mad | p-value | ||

$\alpha $ | C3 | 0.2425 ± 0.0271 | 0.2578 ± 0.0135 | 0.0547 |

MS vs. LS | ||||

median ± mad | median ± mad | p-value | ||

$\alpha $ | C3 | 0.2372 ± 0.0152 | 0.2578 ± 0.0135 | 0.0809 |

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**MDPI and ACS Style**

Rho, G.; Callara, A.L.; Petri, G.; Nardelli, M.; Scilingo, E.P.; Greco, A.; Pascalis, V.D.
Linear and Nonlinear Quantitative EEG Analysis during Neutral Hypnosis following an Opened/Closed Eye Paradigm. *Symmetry* **2021**, *13*, 1423.
https://doi.org/10.3390/sym13081423

**AMA Style**

Rho G, Callara AL, Petri G, Nardelli M, Scilingo EP, Greco A, Pascalis VD.
Linear and Nonlinear Quantitative EEG Analysis during Neutral Hypnosis following an Opened/Closed Eye Paradigm. *Symmetry*. 2021; 13(8):1423.
https://doi.org/10.3390/sym13081423

**Chicago/Turabian Style**

Rho, Gianluca, Alejandro Luis Callara, Giovanni Petri, Mimma Nardelli, Enzo Pasquale Scilingo, Alberto Greco, and Vilfredo De Pascalis.
2021. "Linear and Nonlinear Quantitative EEG Analysis during Neutral Hypnosis following an Opened/Closed Eye Paradigm" *Symmetry* 13, no. 8: 1423.
https://doi.org/10.3390/sym13081423