# A Framework to Assess the Information Dynamics of Source EEG Activity and Its Application to Epileptic Brain Networks

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## Abstract

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## 1. Introduction

## 2. Framework for the Quantification of EEG Source Information Dynamics

#### 2.1. Theoretical Formulation

#### 2.2. Practical Estimation

#### 2.2.1. Common Spatial Patterns (CSP)

#### 2.2.2. VAR Modeling of Reduced EEG Components

#### 2.2.3. Independent Component Analysis (ICA)

#### 2.2.4. Unmixing

#### 2.2.5. VAR Modeling of Source Signals

#### 2.2.6. Yule-Walker Inverse Solution

#### 2.2.7. Computation of Information Measures from VAR Sub-Models

## 3. Simulation Study

## 4. Application to EEG Signals in Epileptic Children

#### 4.1. Experimental Protocol, Data Preprocessing and Statistical Analysis

#### 4.2. Results

#### 4.2.1. EEG Model Identification and Validation

#### 4.2.2. Information Dynamics from EEG Scalp Signals

#### 4.2.3. Information Dynamics from EEG Sources

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Friston, K.J. Functional and effective connectivity: A review. Brain Connect.
**2011**, 1, 13–36. [Google Scholar] [CrossRef] - Gershon, A.; Devulapalli, P.; Zonjy, B.; Ghosh, K.; Tatsuoka, C.; Sahoo, S.S. Computing Functional Brain Connectivity in Neurological Disorders: Efficient Processing and Retrieval of Electrophysiological Signal Data. AMIA Summits Transl. Sci. Proc.
**2019**, 2019, 107. [Google Scholar] [PubMed] - Van Mierlo, P.; Papadopoulou, M.; Carrette, E.; Boon, P.; Vandenberghe, S.; Vonck, K.; Marinazzo, D. Functional brain connectivity from EEG in epilepsy: Seizure prediction and epileptogenic focus localization. Prog. Neurobiol.
**2014**, 121, 19–35. [Google Scholar] [CrossRef] [PubMed] - O’Reilly, C.; Lewis, J.D.; Elsabbagh, M. Is functional brain connectivity atypical in autism? A systematic review of EEG and MEG studies. PLoS ONE
**2017**, 12, e0175870. [Google Scholar] [CrossRef] [PubMed] - Milton, J.G.; Chkhenkeli, S.A.; Towle, V.L. Brain connectivity and the spread of epileptic seizures. In Handbook of Brain Connectivity; Springer: Berlin/Heidelberg, Germany, 2007; pp. 477–503. [Google Scholar]
- Coito, A.; Michel, C.M.; van Mierlo, P.; Vulliémoz, S.; Plomp, G. Directed functional brain connectivity based on EEG source imaging: Methodology and application to temporal lobe epilepsy. IEEE Trans. Biomed. Eng.
**2016**, 63, 2619–2628. [Google Scholar] [CrossRef] - Wendling, F.; Chauvel, P.; Biraben, A.; Bartolomei, F. From intracerebral EEG signals to brain connectivity: Identification of epileptogenic networks in partial epilepsy. Front. Syst. Neurosci.
**2010**, 4, 154. [Google Scholar] [CrossRef][Green Version] - Lehnertz, K.; Ansmann, G.; Bialonski, S.; Dickten, H.; Geier, C.; Porz, S. Evolving networks in the human epileptic brain. Phys. D Nonlinear Phenom.
**2014**, 267, 7–15. [Google Scholar] [CrossRef][Green Version] - Pereda, E.; Quiroga, R.Q.; Bhattacharya, J. Nonlinear multivariate analysis of neurophysiological signals. Prog. Neurobiol.
**2005**, 77, 1–37. [Google Scholar] [CrossRef][Green Version] - Sakkalis, V. Review of advanced techniques for the estimation of brain connectivity measured with EEG/MEG. Comput. Biol. Med.
**2011**, 41, 1110–1117. [Google Scholar] [CrossRef] - Wendling, F.; Ansari-Asl, K.; Bartolomei, F.; Senhadji, L. From EEG signals to brain connectivity: A model-based evaluation of interdependence measures. J. Neurosci. Methods
**2009**, 183, 9–18. [Google Scholar] [CrossRef][Green Version] - Astolfi, L.; Cincotti, F.; Mattia, D.; Marciani, M.G.; Baccala, L.A.; de Vico Fallani, F.; Salinari, S.; Ursino, M.; Zavaglia, M.; Ding, L.; et al. Comparison of different cortical connectivity estimators for high-resolution EEG recordings. Hum. Brain Mapp.
**2007**, 28, 143–157. [Google Scholar] [CrossRef] [PubMed][Green Version] - Faes, L.; Erla, S.; Nollo, G. Measuring Connectivity in Linear Multivariate Processes: Definitions, Interpretation, and Practical Analysis. Comput. Math. Methods Med.
**2012**, 2012, 140513. [Google Scholar] [CrossRef] [PubMed] - Barnett, L.; Seth, A. The MVGC Multivariate Granger Causality Toolbox: A New Approach to Granger-causal Inference. J. Neurosci. Methods
**2013**, 223. [Google Scholar] [CrossRef] [PubMed][Green Version] - Porta, A.; Faes, L. Wiener–Granger causality in network physiology with applications to cardiovascular control and neuroscience. Proc. IEEE
**2015**, 104, 282–309. [Google Scholar] [CrossRef] - Barrett, A.B.; Barnett, L. Granger causality is designed to measure effect, not mechanism. Front. Neuroinform.
**2013**, 7, 6. [Google Scholar] [CrossRef][Green Version] - Lai, M.; Demuru, M.; Hillebrand, A.; Fraschini, M. A comparison between scalp-and source-reconstructed EEG networks. Sci. Rep.
**2018**, 8, 1–8. [Google Scholar] [CrossRef][Green Version] - Nunez, P.; Srinivasan, R.; Westdorp, A.; Wijesinghe, R.; Tucker, D.; Silberstein, R.; Cadusch, P. EEG coherency I: Statistics, reference electrode, volume conduction, Laplacians, cortical imaging, and interpretation at multiple scales. Electroencephalogr. Clin. Neurophysiol.
**1997**, 103, 499–515. [Google Scholar] [CrossRef] - Louis, E.K.S.; Frey, L.C.; Britton, J.W.; Hopp, J.L.; Korb, P.J.; Koubeissi, M.Z.; Lievens, W.E.; Pestana-Knight, E.M. Electroencephalography (EEG): An Introductory Text and Atlas of Normal and Abnormal Findings in Adults, Children, and Infants; American Epilepsy Society: Chicago, IL, USA, 2016. [Google Scholar] [CrossRef]
- van den Broek, S.P.; Reinders, F.; Donderwinkel, M.; Peters, M. Volume conduction effects in EEG and MEG. Electroencephalogr. Clin. Neurophysiol.
**1998**, 106, 522–534. [Google Scholar] [CrossRef] - Brunner, C.; Billinger, M.; Seeber, M.; Mullen, T.; Makeig, S. Volume Conduction Influences Scalp-Based Connectivity Estimates. Front. Comput. Neurosci.
**2016**, 10. [Google Scholar] [CrossRef][Green Version] - Van de Steen, F.; Faes, L.; Karahan, E.; Songsiri, J.; Valdes-Sosa, P.A.; Marinazzo, D. Critical comments on EEG sensor space dynamical connectivity analysis. Brain Topogr.
**2019**, 32, 643–654. [Google Scholar] [CrossRef][Green Version] - Schoffelen, J.M.; Gross, J. Source connectivity analysis with MEG and EEG. Hum. Brain Mapp.
**2009**, 30, 1857–1865. [Google Scholar] [CrossRef] [PubMed] - Horwitz, B. The elusive concept of brain connectivity. Neuroimage
**2003**, 19, 466–470. [Google Scholar] [CrossRef] - Baillet, S.; Riera, J.; Marin, G.; Mangin, J.; Aubert, J.; Garnero, L. Evaluation of inverse methods and head models for EEG source localization using a human skull phantom. Phys. Med. Biol.
**2001**, 46, 77. [Google Scholar] [CrossRef] [PubMed] - Makeig, S.; Bell, A.J.; Jung, T.P.; Sejnowski, T.J. Independent component analysis of electroencephalographic data. In Proceedings of the Advances in Neural Information Processing Systems, Denver, CO, USA, 2–5 December 1996; pp. 145–151. [Google Scholar]
- Gomez-Herrero, G.; Atienza, M.; Egiazarian, K.; Cantero, J. Measuring directional coupling between EEG sources. NeuroImage
**2008**, 43, 497–508. [Google Scholar] [CrossRef] [PubMed] - Billinger, M.; Brunner, C.; Müller-Putz, G. SCoT: A Python toolbox for EEG source connectivity. Front. Neuroinform.
**2014**, 8, 22. [Google Scholar] [CrossRef] [PubMed] - Lotte, F.; Guan, C. Regularizing common spatial patterns to improve BCI designs: Unified theory and new algorithms. IEEE Trans. Biomed. Eng.
**2010**, 58, 355–362. [Google Scholar] [CrossRef][Green Version] - Faes, L.; Porta, A.; Nollo, G. Information Decomposition in Bivariate Systems: Theory and Application to Cardiorespiratory Dynamics. Entropy
**2015**, 17, 277–303. [Google Scholar] [CrossRef] - Barachant, A.; Bonnet, S.; Congedo, M.; Jutten, C. Common Spatial Pattern revisited by Riemannian Geometry. In Proceedings of the 2010 IEEE International Workshop on Multimedia Signal Processing, Saint Malo, France, 4–6 October 2010; pp. 472–476. [Google Scholar] [CrossRef][Green Version]
- Faes, L.; Porta, A.; Nollo, G.; Javorka, M. Information decomposition in multivariate systems: Definitions, implementation and application to cardiovascular networks. Entropy
**2017**, 19, 5. [Google Scholar] [CrossRef] - Faes, L.; Nollo, G.; Porta, A. Information decomposition: A tool to dissect cardiovascular and cardiorespiratory complexity. In Complexity and Nonlinearity in Cardiovascular Signals; Springer: Berlin/Heidelberg, Germany, 2017; pp. 87–113. [Google Scholar]
- Luetkepohl, H. The New Introduction to Multiple Time Series Analysis; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2005. [Google Scholar] [CrossRef]
- Mahdi, E.; Mcleod, I. Improved multivariate portmanteau test. J. Time Ser. Anal.
**2012**, 33. [Google Scholar] [CrossRef] - Lee, T.; Girolami, M.; Sejnowski, T. Independent component analysis using an extended Infomax algorithm for mixed subGaussian and superGaussian sources. Neural Comput.
**1999**, 11, 417–441. [Google Scholar] [CrossRef] - Delorme, A.; Makeig, S. EEGLAB: An open source toolbox for analysis of single-trial EEG dynamics including independent component analysis. J. Neurosci. Methods
**2004**, 134, 9–21. [Google Scholar] [CrossRef] [PubMed][Green Version] - Naik, G.R.; Kumar, D.K. An overview of independent component analysis and its applications. Informatica
**2011**, 35, 63–81. [Google Scholar] - Faes, L.; Erla, S.; Porta, A.; Nollo, G. A framework for assessing frequency domain causality in physiological time series with instantaneous effects. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci.
**2013**, 371, 20110618. [Google Scholar] [CrossRef] [PubMed][Green Version] - Pernice, R.; Faes, L.; Kotiuchyi, I.; Stivala, S.; Busacca, A.; Popov, A.; Kharytonov, V. Time, frequency and information domain analysis of short-term heart rate variability before and after focal and generalized seizures in epileptic children. Physiol. Meas.
**2019**, 40, 074003. [Google Scholar] [CrossRef] - Kotiuchyi, I.; Seleznov, I.; Faes, L.; Pernice, R.; Kharytonov, V.; Popov, A. Pre-and post-ictal brain activity characterization using combined source decomposition and connectivity estimation in epileptic children. In Proceedings of the 2019 IEEE Signal Processing Symposium (SPSympo), Krakow, Poland, 17–19 September 2019; pp. 126–129. [Google Scholar] [CrossRef]
- Mitze, T. Empirical Modelling in Regional Science: Towards a Global Time–Space–Structural Analysis; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2012; Volume 657. [Google Scholar]
- Cohen, J. Statistical Power Analysis for the Behavioral Sciences; Academic Press: Cambridge, MA, USA, 2013. [Google Scholar]
- Sawilowsky, S.S. New effect size rules of thumb. J. Mod. Appl. Stat. Methods
**2009**, 8, 26. [Google Scholar] [CrossRef] - Vicente, R.; Wibral, M.; Lindner, M.; Pipa, G. Transfer entropy—A model-free measure of effective connectivity for the neurosciences. J. Comput. Neurosci.
**2011**, 30, 45–67. [Google Scholar] [CrossRef][Green Version] - Wibral, M.; Lizier, J.; Vögler, S.; Priesemann, V.; Galuske, R. Local active information storage as a tool to understand distributed neural information processing. Front. Neuroinform.
**2014**, 8, 1. [Google Scholar] [CrossRef][Green Version] - Faes, L.; Marinazzo, D.; Nollo, G.; Porta, A. An information-theoretic framework to map the spatiotemporal dynamics of the scalp electroencephalogram. IEEE Trans. Biomed. Eng.
**2016**, 63, 2488–2496. [Google Scholar] [CrossRef] - Faes, L.; Nollo, G.; Porta, A. Compensated transfer entropy as a tool for reliably estimating information transfer in physiological time series. Entropy
**2013**, 15, 198–219. [Google Scholar] [CrossRef][Green Version] - Camfield, P.; Camfield, C. Incidence, prevalence and aetiology of seizures and epilepsy in children. Epileptic Disord.
**2015**, 17, 117–123. [Google Scholar] [CrossRef] - Barnett, L.; Lizier, J.T.; Harré, M.; Seth, A.K.; Bossomaier, T. Information flow in a kinetic Ising model peaks in the disordered phase. Phys. Rev. Lett.
**2013**, 111, 177203. [Google Scholar] [CrossRef] [PubMed][Green Version] - Bossomaier, T.; Barnett, L.; Steen, A.; Harré, M.; d’Alessandro, S.; Duncan, R. Information flow around stock market collapse. Account. Financ.
**2018**, 58, 45–58. [Google Scholar] [CrossRef] - Marinazzo, D.; Pellicoro, M.; Wu, G.; Angelini, L.; Cortés, J.M.; Stramaglia, S. Information transfer and criticality in the Ising model on the human connectome. PLoS ONE
**2014**, 9, e93616. [Google Scholar] [CrossRef] [PubMed] - Nuzzi, D.; Pellicoro, M.; Angelini, L.; Marinazzo, D.; Stramaglia, S. Synergistic information in a dynamical model implemented on the human structural connectome reveals spatially distinct associations with age. Netw. Neurosci.
**2020**, 4, 910–924. [Google Scholar] [CrossRef] - Wibral, M.; Vicente, R.; Lizier, J.T. Directed Information Measures in Neuroscience; Springer: Berlin/Heidelberg, Germany, 2014. [Google Scholar]
- Proix, T.; Jirsa, V.K.; Bartolomei, F.; Guye, M.; Truccolo, W. Predicting the spatiotemporal diversity of seizure propagation and termination in human focal epilepsy. Nat. Commun.
**2018**, 9, 1–15. [Google Scholar] [CrossRef][Green Version] - Park, J.; Vaca, G. Epileptic seizure semiology in infants and children. Seizure
**2019**, 77. [Google Scholar] [CrossRef] - Aanestad, E.; Gilhus, N.; Brogger, J. Interictal epileptiform discharges vary across age groups. Clin. Neurophysiol.
**2019**, 131. [Google Scholar] [CrossRef] - Gruszczyńska, I.; Mosdorf, R.; Sobaniec, P.; Żochowska Sobaniec, M.; Borowska, M. Epilepsy identification based on EEG signal using RQA method. Adv. Med Sci.
**2019**, 64, 58–64. [Google Scholar] [CrossRef] - Okanari, K.; Maruyama, S.; Suzuki, H.; Shibata, T.; Kouzmitcheva Pulcine, E.; Donner, E.; Otsubo, H. Autonomic dysregulation in children with epilepsy with postictal generalized EEG suppression following generalized convulsive seizures. Epilepsy Behav.
**2019**, 102, 106688. [Google Scholar] [CrossRef] - Van Mierlo, P.; Höller, Y.; Focke, N.; Vulliemoz, S. Network Perspectives on Epilepsy Using EEG/MEG Source Connectivity. Front. Neurol.
**2019**, 10. [Google Scholar] [CrossRef][Green Version]

**Figure 1.**Description of the methodology adopted in this work to assess information dynamics of EEG cortical sources. The EEG signals (in the number of D signals, each with length of N samples, collected over K trials during H conditions) are reduced in dimension by CSP (from D signals to Q components), and their time-lagged and instantaneous interactions are described respectively by a VAR model and by ICA; then, source dynamics are reconstructed via unmixing of the scalp signals, their interactions are retrieved through VAR modeling and solution of Yule-Walker equations, and information measures are computed from sub-models relevant to specific sources. In the figure, blue and red arrows refer to analysis steps performed on the whole dataset and on single trials, respectively. More details on the analysis are provided in the text.

**Figure 2.**Estimation of information dynamics for the simulated scenarios. Plots depict the distributions across 10 trials of the information storage (${S}_{j}$, circles) and the total information transfer (${T}_{j}$, squares), as well as the color-coded median values of the conditional information transfer (${T}_{i,j\to k}$, connectivity matrices) computed for the simulated scalp signals (

**a**,

**b**) and for the cortical sources reconstructed using the proposed approach (

**c**,

**d**) in the first condition of absence of connectivity (

**a**,

**c**) and in the second condition with unidirectional source propagation (

**b**,

**d**). The filled symbols in (

**c**,

**d**) indicate the exact values of the information stored in each cortical source and the total information transferred to it.

**Figure 3.**Examples of EEG signals recorded with monopolar montage with the reference electrode placed on the ipsilateral ear at the onset of focal (

**a**) and generalized (

**b**) seizures. In the two cases, seizure onsets are marked with dashed lines. It can be noticed that the epileptiform discharges begin in the left frontotemporal region with later bilateral synchronization in the right frontal region in (

**a**), and in all brain areas at the same time in (

**b**).

**Figure 4.**Contribution to the total squared Riemannian distance provided by the eigenvalues ${\lambda}_{j}$ corresponding to each spatial filter ${c}_{j}$ ($j=1,\dots ,19$) of the CSP matrix obtained for the generalized seizures trials classified as $base$ and $pre$. Black and red dots identify the selected spatial filters and the discarded filters, respectively.

**Figure 5.**Information dynamics of scalp EEG signals measured during generalized seizures. Panels report the boxplot distribution and individual subject values (average over network nodes and trials) of the information storage ${S}_{j}$, total information transfer ${T}_{j}$, conditional information transfer ${T}_{i\to j|k}$, and number of significant links ${N}_{i\to j|k}$ in the three analyzed conditions $base$, $pre$, $post$. Statistically significant differences between pairs of distributions: *, p < 0.05 $base$ vs. $post$; #, p < 0.05 $pre$ vs. $post$.

**Figure 6.**Information dynamics of scalp EEG signals measured during focal seizures. Plots and symbols are as in Figure 5.

**Figure 7.**Information dynamics of source EEG signals measured during generalized seizures. Panels report the boxplot distribution and individual subject values (average over network nodes and trials) of the information storage ${S}_{j}$, total information transfer ${T}_{j}$, conditional information transfer ${T}_{i\to j|k}$, and number of significant links ${N}_{i\to j|k}$ in the three analyzed conditions $base$, $pre$, $post$. Statistically significant difference between pairs of distributions (p < 0.05) are marked with *; p-values < 0.1 are written in bold.

**Figure 8.**Information dynamics of source EEG signals measured during focal seizures. Plots and symbols are as in Figure 7.

N. Subjects | Group | Seizure Type |
---|---|---|

1 | Focal | Left temporal and frontal-temporal |

1 | Focal | Right frontal-temporal |

1 | Focal | Central |

1 | Focal | Right frontal-temporal and frontal-central |

1 | Focal | Right central |

1 | Focal | Left frontal-temporal with secondary bilateral synchronization |

2 | Focal | Right frontal |

1 | Focal | Bifocal asynchronous epileptiform activity in the right frontal-temporal, left central-parietal and parietal |

1 | Focal | Central-parietal |

1 | Focal | Left central-temporal |

4 | Focal | Unknown |

1 | Generalized | Idiopathic generalized seizures with typical absences |

1 | Generalized | Vesta Lennox–Gastaut syndrome, asymmetric infantile spasms |

1 | Generalized | Absence seizures |

1 | Generalized | Generalized tonic, myoclonic seizures |

1 | Generalized | Jeavons syndrome, myoclonic seizures |

$\mathit{Base}-\mathit{Pre}$ | $\mathit{Pre}-\mathit{Post}$ | $\mathit{Base}-\mathit{Post}$ | |
---|---|---|---|

${S}_{j}$ | 0.022 | 2.330 | 2.314 |

${T}_{j}$ | −0.016 | 2.097 | 1.954 |

${T}_{i\to j|k}$ | −0.183 | 2.739 | 2.538 |

${N}_{i\to j|k}$ | −0.383 | 2.827 | 2.314 |

$\mathit{Base}-\mathit{Pre}$ | $\mathit{Pre}-\mathit{Post}$ | $\mathit{Base}-\mathit{Post}$ | |
---|---|---|---|

${S}_{j}$ | 0.354 | 0.550 | 0.809 |

${T}_{j}$ | 0.246 | 0.551 | 0.797 |

${T}_{i\to j|k}$ | 0.293 | 0.426 | 0.838 |

${N}_{i\to j|k}$ | −0.497 | 0.361 | −0.049 |

$\mathit{Base}-\mathit{Pre}$ | $\mathit{Pre}-\mathit{Post}$ | $\mathit{Base}-\mathit{Post}$ | |
---|---|---|---|

${S}_{j}$ | 0.155 | 2.233 | 2.315 |

${T}_{j}$ | −0.763 | 2.023 | 1.652 |

${T}_{i\to j|k}$ | 0.106 | 1.960 | 1.990 |

${N}_{i\to j|k}$ | −1.002 | 1.155 | 0.438 |

$\mathit{Base}-\mathit{Pre}$ | $\mathit{Pre}-\mathit{Post}$ | $\mathit{Base}-\mathit{Post}$ | |
---|---|---|---|

${S}_{j}$ | 0.123 | 0.684 | 0.741 |

${T}_{j}$ | −0.487 | 0.853 | 0.440 |

${T}_{i\to j|k}$ | −0.548 | 0.817 | 0.389 |

${N}_{i\to j|k}$ | −0.709 | 0.588 | −0.203 |

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**MDPI and ACS Style**

Kotiuchyi, I.; Pernice, R.; Popov, A.; Faes, L.; Kharytonov, V.
A Framework to Assess the Information Dynamics of Source EEG Activity and Its Application to Epileptic Brain Networks. *Brain Sci.* **2020**, *10*, 657.
https://doi.org/10.3390/brainsci10090657

**AMA Style**

Kotiuchyi I, Pernice R, Popov A, Faes L, Kharytonov V.
A Framework to Assess the Information Dynamics of Source EEG Activity and Its Application to Epileptic Brain Networks. *Brain Sciences*. 2020; 10(9):657.
https://doi.org/10.3390/brainsci10090657

**Chicago/Turabian Style**

Kotiuchyi, Ivan, Riccardo Pernice, Anton Popov, Luca Faes, and Volodymyr Kharytonov.
2020. "A Framework to Assess the Information Dynamics of Source EEG Activity and Its Application to Epileptic Brain Networks" *Brain Sciences* 10, no. 9: 657.
https://doi.org/10.3390/brainsci10090657