# 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

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**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