# On the Operational Utility of Measures of Multichannel EEGs

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Participants

## 3. Data

## 4. Measures

## 5. Results

## 6. Discussion

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Tononi, G. Consciousness as integrated information: A provisional manifesto. Biol. Bull.
**2008**, 215, 216–242. [Google Scholar] [CrossRef] [PubMed] - Tegmark, M. Improved measures of integrated information. PLoS Comput. Biol.
**2016**, 12, e10051. [Google Scholar] [CrossRef] - Mediano, P.A.M.; Seth, A.K.; Barrett, A.B. Measuring integrated information: Comparison of candidate measures in theory and simulation. Entropy
**2019**, 21, 17. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Berger, H. Über das Elektroenkephalogramm des Menchen. Archive für Psychiatrie und Nervenkrankheiten
**1929**, 87, 527–570. [Google Scholar] [CrossRef] - Adrian, E.D.; Matthews, B.H.C. The Berger rhythm: Potential changes from the occipital lobes of man. Brain
**1934**, 57, 355–385. [Google Scholar] [CrossRef] - Hartoyo, A.; Cadusch, P.J.; Liley, D.T.J.; Hicks, D.G. Inferring a simple mechanism for alpha-blocking by fitting a neural population model to EEG spectra. PLoS Comput. Biol.
**2020**, 16, e1007662. [Google Scholar] [CrossRef] [PubMed] - Liley, D.T.J.; Muthukumaraswamy, D.S. Evidence that alpha blocking is due to increases in system-level oscillatory damping and not neuronal population desynchronization. NeuroImage
**2020**, 208, 116408. [Google Scholar] [CrossRef] - Rapp, P.E.; Cellucci, C.J.; Watanabe, T.A.A.; Albano, A.M. Quantitative characterization of the complexity of multichannel human EEGs. Int. J. Bifurc. Chaos
**2005**, 15, 1737–1744. [Google Scholar] [CrossRef] - Lempel, A.; Ziv, J. On the complexity of finite sequences. IEEE Trans. Inf. Theory
**1976**, IT-22, 75–81. [Google Scholar] [CrossRef] - Golub, G.H.; Reinsch, C. Singular value decomposition and least squares solutions. Numer. Math.
**1970**, 14, 403–420. [Google Scholar] [CrossRef] - Golub, G.H.; Reinsch, C. Handbook for Automatic Computation. Vol. II. Linear Algebra; Springer: Heidelberg, Germany, 1971; pp. 134–151. [Google Scholar]
- Watanabe, T.A.A.; Cellucci, C.J.; Kohegyi, E.; Bashore, T.R.; Josiassen, R.C.; Greenbaun, N.N.; Rapp, P.E. The algorithmic complexity of multichannel EEGs is sensitive to changes in behavior. Psychophysiology
**2003**, 40, 77–97. [Google Scholar] [CrossRef] [PubMed] - Tononi, G.; Sporns, O.; Edelman, G. A measure for brain complexity: Relating functional segregation and integration in the nervous system. Proc. Natl. Acad. Sci. USA
**1994**, 91, 5033–5037. [Google Scholar] [CrossRef] [PubMed] [Green Version] - van Putten, M.J.A.M.; Stam, C.J. Application of a neural complexity measure to multichannel EEG. Phys. Lett.
**2001**, 281A, 131–141. [Google Scholar] [CrossRef] - Morgera, S.D. Information theoretic covariance complexity and its relation to pattern recognition. IEEE Trans. Syst. Man Cybern.
**1985**, 15, 608–619. [Google Scholar] [CrossRef] - Tononi, G. Information measures for conscious experience. Arch. Ital. Biol.
**2001**, 139, 367–371. [Google Scholar] [PubMed] - Tononi, G.; Sporns, O. Measuring information integration. BMC Neurosci.
**2003**, 4, 31. [Google Scholar] - Tononi, G. An information integration theory of consciousness. BMC Neurosci.
**2004**, 5, 42–63. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Oizumi, M.; Albantakis, L.; Tononi, G. From phenomenology to the mechanisms of consciousness: Integrated information theory 3.0. PLoS Comput. Biol.
**2014**, 10, e1003588. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Griffith, V. A principled infotheoretic φ-like measure. arXiv
**2014**, arXiv:1401.0978v3[cs.IT]2014-10-09. [Google Scholar] - van Walsum, A.M.; Pijnenburg, Y.A.; Berendse, H.W.; Van Dijk, B.W.; Knol, D.L.; Scheltens, P.; Stam, C.J. A neural complexity measures applied to MEG data in Alzheimer’s disease. Clin. Neurophysiol.
**2003**, 114, 1034–1040. [Google Scholar] [CrossRef] - Trujillo, L.; Stanfield-Wiswell, C.T.; Vela, R.D. The effect of electroencephalogram (EEG) reference on information theoretic measures of the complexity and integration of EEG signals. Front. Neurosci.
**2017**, 11, 425. [Google Scholar] [CrossRef] [PubMed] - Rousseeuw, P.J.; Croux, C. Alternatives to the median absolute deviation. J. Am. Stat. Assoc.
**1993**, 88, 1273–1283. [Google Scholar] [CrossRef] - Efron, B. Better bootstrap confidence intervals. J. Am. Stat. Assoc.
**1987**, 82, 171–185. [Google Scholar] [CrossRef] - McKhann, G.; Drachman, D.; Folstein, M.; Katzman, R.; Price, D.; Stadlan, E.M. Clinical diagnosis of Alzheimer’s disease: Report of the NINCDS-ADRDA Work Group under the auspices of the Department of Health and Human Services Task Force on Alzheimer’s disease. Neurology
**1984**, 34, 939–944. [Google Scholar] [CrossRef] [PubMed] [Green Version] - van Albada, S.J.; Robinson, P.A. Transformation of arbitrary distributions to the normal distribution with application to EEG test-retest reliability. J. Neurosci. Methods
**2007**, 161, 205–211. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**Eyes-open versus eyes-closed effect size as quantified by the standard estimator $({\widehat{\mu}}_{\mathrm{open}}-{\widehat{\mu}}_{\mathrm{closed}})/{\widehat{\sigma}}_{\mathrm{open}-\mathrm{closed}}$ for five measures. Note that the effect size estimates are unitless. Confidence intervals were determined with a bias-corrected and adjusted bootstrap. (

**Top**) Effect sizes calculated with signals that contain the alpha component. (

**Bottom**) Effect sizes calculated after the alpha component had been removed with an 8–13 Hz stopband filter.

**Table 1.**The sample averages and standard deviations of the difference scores for measures between eyes-open and eyes-closed, estimates of $({\mu}_{\mathrm{open}}-{\mu}_{\mathrm{closed}})/{\sigma}_{\mathrm{open}-\mathrm{closed}}$, and 95% confidence intervals for the effect size without (top CI) and with (bottom CI) Bonferroni correction for 5 comparisons. (Top) Measures calculated with signals that contain the alpha component. (Bottom) Measures calculated after the alpha component had been removed with an 8–13 Hz stopband filter.

Measures | Eyes-Open—Eyes-Closed | Estimated | 95% CI |
---|---|---|---|

(Alpha Band Present) | Mean ± StDev | Effect Size | |

Binary Lempel–Ziv | 63.4167 | 1.63 | (1.17, 2.26) |

Signals mean normalized | ± 36.9360 | (1.07, 2.53) | |

Binary Lempel–Ziv | 51.2500 | 1.56 | (1.13, 2.27) |

Signals normalized by mean | ±31.5873 | (1.03, 2.61) | |

and by standard deviation | |||

${C}_{N}$ | −0.6469 | −1.60 | (−2.53, −1.12) |

Tononi et al., 1994 | ±0.3973 | (−3.01, −0.99) | |

Equation (4) | |||

$\psi $$p=1$ | −0.8556 | −1.40 | (−2.13, −0.90) |

Mediano et al., 2019 | ±0.5906 | (−2.42, −0.76) | |

Equation (23) | |||

$\psi $p via BIC | 0.2013 | 0.99 | (0.13, 1.93) |

Mediano et al., 2019 | ±0.1944 | (−0.25, 2.15) | |

Equation (23) | |||

Measures | Eyes-Open—Eyes-Closed | Estimated | 95% CI |

(Alpha Band Removed) | Mean ± StDev | Effect Size | |

Binary Lempel–Ziv | 42.7500 | 1.33 | (0.72, 2.05) |

Signals mean normalized | ±30.8460 | (0.53, 2.3) | |

Binary Lempel–Ziv | 39.6667 | 1.35 | (0.65, 2.52) |

Signals normalized by mean | ±28.2081 | (0.43, 3.25) | |

and by standard deviation | |||

${C}_{N}$ | −0.2102 | −0.57 | (−1.33, −0.52) |

Tononi et al., 1994 | ±0.3658 | (−1.34, 0.22) | |

Equation (4) | |||

$\psi $$p=1$ | −0.6755 | −1.34 | (−2.35, −0.75) |

Mediano et al., 2019 | ±0.4900 | (−2.90, −0.60) | |

Equation (23) | |||

$\psi $p via BIC | 0.0679 | 0.31 | (−0.32, 0.90) |

Mediano et al., 2019 | ±0.2093 | (−0.65, 1.14) | |

Equation (23) |

**Table 2.**Estimates and 95% bootstrap confidence intervals for Kendall’s tau within-subject, between measures in the eyes-open and eyes-closed conditions. (Top) Measures calculated with signals that contain the alpha component. (Bottom) Measures calculated after the alpha component had been removed with an 8–13 Hz stopband filter.

Alpha Band | LZ1 | LZ2 | ${\mathit{C}}_{\mathit{N}}$ | $\mathit{\psi}$$\mathit{p}=1$ | $\mathit{\psi}$p via BIC |
---|---|---|---|---|---|

Present | |||||

LZ1 | – | 0.8436 | −0.4218 | −0.3636 | 0.4000 |

(0.718, 0.945) | (−0.612, −0.202) | (−0.613, −0.076) | (0.102, 0.654) | ||

LZ2 | – | −0.4058 | −0.4130 | 0.3406 | |

(−0.638, −0.152) | (−0.645, −0.116) | (0.065, 0.58) | |||

${C}_{N}$ | – | 0.2246 | −0.3351 | ||

(−0.09, 0.523) | (−0.670, −0.015) | ||||

$\psi $$p=1$ | – | −0.4203 | |||

(−0.668, −0.129) | |||||

Alpha Band | LZ1 | LZ2 | ${\mathit{C}}_{\mathit{N}}$ | $\mathbf{\psi}$$\mathit{p}=\mathbf{1}$ | $\mathbf{\psi}$$\mathit{p}$via BIC |

Removed | |||||

LZ1 | – | 0.6374 | −0.0873 | −0.1673 | 0.1164 |

(0.349, 0.831) | (−0.387, 0.25) | (−0.468, 0.157) | (−0.130, 0.356) | ||

LZ2 | – | −0.2190 | −0.1971 | 0.1679 | |

(−0.543, 0.142) | (−0.455, 0.085) | (−0.099, 0.425) | |||

${C}_{N}$ | – | 0.1522 | −0.0435 | ||

(−0.5, 0.184) | (−0.346, 0.269) | ||||

$\psi $$p=1$ | – | −0.2971 | |||

(−0.549, −0.019) |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Darmon, D.; Watanabe, T.; Cellucci, C.; Rapp, P.E.
On the Operational Utility of Measures of Multichannel EEGs. *Entropy* **2021**, *23*, 1434.
https://doi.org/10.3390/e23111434

**AMA Style**

Darmon D, Watanabe T, Cellucci C, Rapp PE.
On the Operational Utility of Measures of Multichannel EEGs. *Entropy*. 2021; 23(11):1434.
https://doi.org/10.3390/e23111434

**Chicago/Turabian Style**

Darmon, David, Tomas Watanabe, Christopher Cellucci, and Paul E. Rapp.
2021. "On the Operational Utility of Measures of Multichannel EEGs" *Entropy* 23, no. 11: 1434.
https://doi.org/10.3390/e23111434