# Analysis of Meditation vs. Sensory Engaged Brain States Using Shannon Entropy and Pearson’s First Skewness Coefficient Extracted from EEG Data

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## Abstract

**:**

## 1. Introduction

## 2. Materials

_{1,3}and A

_{1,10}are empty as reference points for the position of the pre-frontal cortex; see Figure 1.

**Meditation (MED):**Participants were asked to engage in the meditation of their choice for 7 min with their eyes closed. Alternatively, if people were unfamiliar with meditating, they were asked to relax with their eyes closed. After the proper preparation, each participant pressed the space bar key on the keyboard to signal the beginning of the meditation period, which continued until the preprogramed end signal informed them of the end of the session.**Video (VDO):**In this final modality, the participants were presented with a video containing a sequence of ambiguous images with the song ‘Imagine’ by John Lennon, playing throughout the video. The ambiguous images aimed to evoke mental responses similar to the well-known Necker cube. The ambiguous images used in this task were designed by Oleg Shupliak, and they can be found in [39]. The duration of this experiment was 1 min and 50 s for each participant. There was no task the participants were asked to perform besides watching the video and listening to the song. After reading the instructions, the participants pressed the space bar key on the keyboard to signal the beginning of the video-watching period, until the video finished playing.

## 3. Methods

#### 3.1. Preprocessing

_{t}) over a time window of 500 ms for each electrode in the 12 × 12 matrix, where the index ‘t’ in PSD

_{t}refers to time. After that, we evaluated two (2) information measures, namely, the Shannon entropy or diversity index (H) and Pearson’s first skewness coefficient (PSk), both based on power and frequency band, taken as a histogram and empirical probability function. Both H and PSk have shown to be good indices to classify the different brain dynamics [5].

- 8 ms for anti-alias filter, which essentially accounts for the required time of the amplifier to do the conversion;
- 14 ms for the screen refresh rate, adding to a total of a 22 ms shift to match the recorded event markers with the actual event time.

#### 3.2. Entropy and Information Theoretical Indices

- 3.
- Entropy measure (H), as introduced by Shannon [46], providing us with the degree of randomness in an EEG signal.
- 4.
- PSk as a measure of information derived from the frequency distribution structure represented by the degree of asymmetry, which was derived by [47] and discussed by [48]. The version of the PSk (1st order skewness coefficient) described and formulated in [49] in terms of the mean, standard deviation and mode (dominant frequency or frequency band) is used for this study.

#### 3.3. Computation of the H and PSk Indices

_{i}corresponds to the power of frequency band ‘i’, and TP is the total power computed as:

_{t}, as mentioned above, is computed as:

_{PSDt}represents the standard deviation of the PSD

_{t}, and where power is taken as a function of frequency and, therefore, frequency band, described here as PW

_{i}(FB

_{i}).

_{i}derived from the PSD

_{t}, where the number of a particular band is described by a fixed number ‘i’ for all PSD

_{t}for any participants and modalities, as follows:

_{c}, as described by [50], something left outside of the scope of our study. However, H

_{c}may be useful when comparing brain dynamics for different brain areas in different bands, participants and modalities that depend on unique and specific probability distributions. This analysis included every electrode, as well as brain areas represented by their corresponding set of electrodes, from where we derived H and PSk indices for our analysis, as shown in Figure 3.

#### 3.4. Analysis of Multi-Variate EEG Data

_{t}, is derived from the equation $NW=\frac{L}{500}$, where L is the time length (in ms) of a particular experiment for participant p in modality m, and where the length for each window t equals 500 ms.

## 4. Results

#### 4.1. Qualitative Analysis of the EEG Data

_{t}, such as the Dominant Frequency band, for example, need further investigation and analysis, which is left for future studies.

#### 4.2. Detailed Quantitative Analysis of Brain Dynamics

## 5. Discussion

#### 5.1. Discrimination across Modalities and Brain Regions for a Representative Participant (P10)

#### 5.2. Discrimination Results in Populations of Meditators and Non-Meditator Participants

## 6. Conclusions

- We conjecture that more relaxed states showing alpha dominance, accompanied with lower values of H and PSk, are achieved by: (1) masterful meditators, (2) people who practice relaxation techniques and (3) people who are naturally more relaxed (less stressed), who might be able to mitigate environmental signals and demands when existing in such relaxed emotional and coherent mental states. This we can derive from the data associated with the modality VDO when contrasted with the one of MED for both groups: Meditator and Non-Meditator. It is relevant to note that the Meditator group showed lower values for H than the Non-Meditator group, which indicates that meditative states are more likely different than relaxed states when participants have their eyes closed.
- We conjecture that meditators may carry these relaxed states into other activities, possibly due to the lasting psychophysiological effects derived from meditative practices [28,57,58,59] translating and continuing into other areas of life. This will require further investigation and studies with a larger sample size.
- When comparing the overall mean values for each modality, MED displays the smallest values of H and PSk, and VDO displays the largest for both groups. The overall distribution and values, however, are significantly different. These findings indicate that there is a distinct difference between meditators and non-meditators in brain dynamics, and that H and PSk taken together are a useful element to analyze and differentiate various cognitive states. Statistical hypothesis tests indicate that the H index is useful to discriminate between Meditator and Non-Meditator participants during MED over both the PF and OCC areas (p = 0.03), while the PSk index is useful to discriminate Meditators from Non-Meditators based on the PF areas for both MED and VDO (p = 0.05).

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Illustration of electrode arrangements; (

**a**) displays the EEG electrodes positions and numbers, and (

**b**) shows a representation matrix (A) of 12 × 12 for the EEG 128-channel sensor net over the whole scalp, with some electrode positions repeated to fill the matrix array. This matrix presents the areas of the brain according to the corresponding color, as shown in the legend to the right of the matrix. The left and right hemispheres divide the matrix into 2 equal and symmetrical parts of 2 sub matrices of 12 × 6 each. Positions A

_{1,3}and A

_{1,10}, starting from the bottom left, are empty.

**Figure 2.**Illustration of the proposed approach to derive the H and PSk values from the power spectrum, and specifically PSk from the dominant frequency band; the frequency resolution in the computation of the power spectrum is 1 Hz. The numerical values are given as illustrations for typical experiments; details are described in the next section.

**Figure 3.**(

**a**) Matrix representation of the EEG array; (

**b**) a spatial 2D landscape associated with different brain areas, derived from the mean values of PSk, and (

**c**) a 2D landscape plot derived from the mean values of H.

**Figure 4.**Illustration of the results for eleven (11) Meditators; (

**a**) values for H (2nd and 4th row) and PSk (1st and 3rd row) in MED modality; (

**b**)values for H (2nd and 4th row) and PSk (1st and 3rd row) in VDO modality.

**Figure 5.**Illustration of the results for nine (9) Non-Meditators; (

**a**) values for H (2nd and 4th row) and PSk (1st and 3rd row) in MED modality; (

**b**) values for H (2nd and 4th row) and PSk (1st and 3rd row) in VDO modality.

**Figure 6.**Normalized overall mean values for the statistical indices with confidence intervals for both groups (Meditators, Non-Meditators), in both modalities (MED, VDO); (

**a**) index PSk; (

**b**) index H.

**Figure 7.**Overall normalized mean values for H (X-axis) vs. PSk (Y-axis) for both modalities (MED, VDO); (

**a**) Meditators; (

**b**) Non-Meditators.

**Figure 8.**Shows scatter plots of H (x-axis) vs. PSk (y-axis) and their corresponding histograms for the mean values, ${\overline{H}}_{e}^{p,m}and{\overline{PSk}}_{e}^{p,m},$computed for each of the 128 electrodes (e =1128), for participants P3 (p = 3) and P4 (p = 4) in MED (m = 1) and VDO (m = 2). Each electrode is represented by a small circle, and its color identifies a brain area, where red corresponds to the frontal area, blue to the central and black to the posterior area. The larger circles represent the overall mean value per brain area.

**Figure 9.**Mean values for the H and PSk time series in time steps of 0.5 s for P10, both for the PF and OCC areas of the brain. (

**a**) H for the PF and OCC areas in MED, (

**b**) PSk for the PF and OCC areas in MED, (

**c**) H for the PF and OCC areas in VDO and (

**d**) PSK for the PF and OCC areas in VDO. The vertical arrows with stars on subplots (

**a**,

**b**) indicate possible anticorrelation events between the occipital and prefrontal areas.

**Figure 10.**Histograms of H and PSk in various modalities and brain areas of P10; (

**a**) (top) histograms for H and PSk for the PF region for P10 in MED, and (bottom) histograms for H and PSk for the OCC region in MED. (

**b**) (top) histograms for H and PSk for the PF region for P10 in VDO, and (bottom) histograms for H and PSk for the OCC region in VDO.

**Figure 11.**Shows coefficients of correlation between H and PSk for: (

**a**) PF area in MED for P10, (

**b**) OCC area in MED for P10, (

**c**) PF area in VDO for P10 and (

**d**), (

**b**) OCC area in VDO for P10.

**Figure 12.**Correlation matrix for: (

**a**) H in MED, (

**b**) H in VDO, (

**c**) PSk in MED, (

**d**) PSk in VDO. Please note that, based on Figure 1b, the PF region is described by electrodes with relatively low serial numbers starting with 1 and extending to lower/mid 30′s, and some with very high numbers, while OCC electrodes have numbers starting from around 63 and up to about 99.

**Table 1.**H mean values (${\overline{\mathit{H}}}_{\mathbf{1}}{}^{\mathbf{1}},{\overline{\mathit{H}}}_{\mathbf{1}}{}^{\mathbf{2}}$, ${\overline{\mathit{H}}}_{\mathbf{2}}{}^{\mathbf{1}}\mathit{a}\mathit{n}\mathit{d}{\overline{\mathit{H}}}_{\mathbf{2}}{}^{\mathbf{2}}$) and their confidence intervals, for both groups in both modalities.

Group/Modality | MED | VDO |
---|---|---|

Meditator | 0.87 ± 0.033 | 0.99 ± 0.007 |

Non-Meditator | 0.92 ± 0.043 | 0.98 ± 0.016 |

**Table 2.**PSk mean values (${\overline{\mathit{P}\mathit{S}\mathit{k}}}_{\mathbf{1}}{}^{\mathbf{1}},{\overline{\mathit{P}\mathit{S}\mathit{k}}}_{\mathbf{1}}{}^{\mathbf{2}}$, ${\overline{\mathit{P}\mathit{S}\mathit{k}}}_{\mathbf{2}}{}^{\mathbf{1}}\mathit{a}\mathit{n}\mathit{d}{\overline{\mathit{P}\mathit{S}\mathit{k}}}_{\mathbf{2}}{}^{\mathbf{2}}$) and their confidence intervals, for both groups in both modalities.

Group/Modality | MED | VDO |
---|---|---|

Meditator | 0.72 ± 0.049 | 0.98 ± 0.016 |

Non-Meditator | 0.76 ± 0.124 | 0.99 ± 0.021 |

**Table 3.**p-values of the t-tests with unequal variances, regarding the hypothesis H0: μ1 = μ2; results are given for the MED vs. VDO modalities, respectively, for all brain regions.

Test | p-Value | H0: μ1 = μ2 |
---|---|---|

Meditators vs. Non-Meditators for MED (H) | 0.033 | Reject |

Meditators vs. Non-Meditators for MED (PSk) | 0.255 | Accept |

Meditators vs. Non-Meditators for VDO (H) | 0.5 | Accept |

Meditators vs. Non-Meditators for VDO (PSk) | 0.955 | Accept |

**Table 4.**Shows the coefficient of correlation (r) between H and PSk in the different modalities of MED and VDO, for both the PF and OCC areas of the brain, for P10.

Modality and Brain Region | Mean Value Correlation Coefficient (r) | Lower Bound | Upper Bound |
---|---|---|---|

MED-PF | 0.8649 | 0.832 | 0.908 |

MED-OCC | 0.7355 | 0.669 | 0.811 |

VDO-PF | 0.6011 | 0.5 | 0.7 |

VDO-OCC | 0.5792 | 0.475 | 0.685 |

**Table 5.**Displays

**p**-values and results for various unequal variance t-tests of hypothesis, where H0: μ1 = μ2, allowing for a comparison between the MED vs. VDO modalities for the PF and OCC areas based on the H index.

Test | p-Value | H0: μ1 = μ2 |
---|---|---|

Meditators vs. Non-Meditators for MED (PF) | 0.0218 | Reject |

Meditators vs. Non-Meditators for MED (OCC) | 0.0290 | Reject |

Meditators vs. Non-Meditators for VDO (PF) | 0.0841 | Accept |

Meditators vs. Non-Meditators for VDO (OCC) | 0.1718 | Accept |

**Table 6.**Displays p-values and results for various unequal variance t-tests of hypothesis, where H0: μ1 = μ2, allowing for a comparison between the MED vs. VDO modalities for the PF and OCC areas based on the PSk index.

Test | p-Value | H0: μ1 = μ2 |
---|---|---|

Meditators vs. Non-Meditators for MED (PF) | 0.0437 | Reject |

Meditators vs. Non-Meditators for MED (OCC) | 0.0936 | Accept |

Meditators vs. Non-Meditators for VDO (PF) | 0.0112 | Reject |

Meditators vs. Non-Meditators for VDO (OCC) | 0.8738 | Accept |

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**MDPI and ACS Style**

Davis, J.J.J.; Kozma, R.; Schübeler, F.
Analysis of Meditation vs. Sensory Engaged Brain States Using Shannon Entropy and Pearson’s First Skewness Coefficient Extracted from EEG Data. *Sensors* **2023**, *23*, 1293.
https://doi.org/10.3390/s23031293

**AMA Style**

Davis JJJ, Kozma R, Schübeler F.
Analysis of Meditation vs. Sensory Engaged Brain States Using Shannon Entropy and Pearson’s First Skewness Coefficient Extracted from EEG Data. *Sensors*. 2023; 23(3):1293.
https://doi.org/10.3390/s23031293

**Chicago/Turabian Style**

Davis, Joshua J. J., Robert Kozma, and Florian Schübeler.
2023. "Analysis of Meditation vs. Sensory Engaged Brain States Using Shannon Entropy and Pearson’s First Skewness Coefficient Extracted from EEG Data" *Sensors* 23, no. 3: 1293.
https://doi.org/10.3390/s23031293