# SEED-G: Simulated EEG Data Generator for Testing Connectivity Algorithms

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## Abstract

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## 1. Introduction

## 2. Toolbox Description

- The generation of a predefined ground-truth connectivity model with:
- a selected size (number of signals to be generated);
- a selected density;
- parameters randomly assigned within a given range;
- stationary or time-resolved connectivity values.

- The generation of pseudo-EEG time series with:
- spectral similarity to reference EEG scalp- or source-level data;
- given length in terms of number of samples;
- number of trials;
- predefined SNR;
- inter-trial variability;
- presence of ocular artifacts.

#### 2.1. Simulated Data Generation

#### 2.2. Realistic Features Modeling

## 3. Evaluation of SEED-G Toolbox Performances

#### 3.1. Methods

#### 3.1.1. Pseudo-EEG Time Series Generation

- “Model size” is the number of time series composing the dataset. Levels: (5, 10, 19, 32, 60) nodes, simulating a range between few electrodes and the most commonly used extended 10–20 scalp EEG montage.
- “Network density” is the percentage of non-null coefficients. Levels: (5%, 10%, 20%, 30%) of the possible connections.
- “Real sources” are the percentage of real sources included as sources in the model with respect to all generated signals. Levels: (20%, 30%, 50%) of the number of the generated time series.

#### 3.1.2. Performance Parameters

#### 3.2. Results

## 4. SEED-G Toolbox Application: Evaluation of the Inter-Trial Variability Effect on PDC Estimates

- by increasing/decreasing the value of some existing connections in the ground-truth network (Study I);
- by modifying the ground-truth network density by adding some spurious connections to the existing ones (Study II).

#### 4.1. Methods

#### 4.1.1. Study I: The Effect of Unstable Connectivity Values

- Model size: 5, 10, 20 nodes;
- Network density: 20% of the possible connections;
- Connections’ intensity: randomly selected in the range [−0.5:0.5];
- Percentage of modified trials: 1, 10, 30, 50% of the total number of the generated trials;
- Percentage of modified links across-trials: 10, 20, 50% of existing connections;
- Amplitude of the variation: 20, 50, 70% of the original value of the connection;
- Type of variation: positive (increase), negative (decrease).

#### 4.1.2. Study II: The Effect of Spurious Connections

- Model size: 5, 10, 20 nodes;
- Network density: 20% of the possible connections;
- Connections’ intensity: randomly selected in the range [−0.5:0.5];
- Percentage of modified trials: 1, 10, 30, 50% of the total number of trials generated;
- Percentage of added spurious links: 10, 20, 30% of all existing connections.

#### 4.2. Results

#### 4.2.1. Study I: The Effect of Unstable Connectivity Values

#### 4.2.2. Study II: The Effect of Spurious Connections

## 5. Discussion

## 6. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**main**: it is the core of the toolbox and contains all the functions for the generation of EEG data according to a predefined ground-truth network.**dependencies**: containing parts of other toolboxes required to successfully run SEED-G functions. The links to the full packages can be found in the documentation on the GitHub page. The additional packages are Brain Connectivity Toolbox (BCT) [40], FieldTrip [41], Multivariate Granger Causality Toolbox (MVGC) [24], and AsympPDC Package (PDC_AsympSt) [42,43]. Additionally, the implemented forward model is solved according to the New York Head (NYH) model, whose parameters are contained in the structure available on the ICBM-NY platform [28].**real data**: containing real EEG data acquired from one healthy subject during resting state at scalp level (‘EEG_real_sources.mat’) and its reconstructed version in source domain (‘sLOR_cortical_sources.mat’). These signals can be employed to extract the AR components to be included in the model to generate data with the same spectral properties of the real ones.**demo**: containing examples of MATLAB scripts to be used to learn the different functionalities of the toolbox. For example, the code ‘run_generation.m’ allows to specify the directory containing the real sources and each specific input of the function ‘simulatedData_generation.m’.**auxiliary functions**: containing either original MATLAB functions or modified version of free available functions.

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**Figure 1.**SEED-G generator framework. Block diagram describing the main steps at the basis of the data generator.

**Figure 2.**Pseudo-EEG data with ocular artifacts. Time series simulated using SEED-G toolbox (pseudo-EEG signals) and real ocular blinks (eye-blink) were summed up to obtain a realistic dataset (pseudo-EEG data with blink). The eye-blink component was weighted by a correlation coefficient whose value depends on the position of the simulated sensor (Pearson’s correlation between real EEG dataset acquired with a standard 60-channel montage, and an EOG channel). Frontal electrodes are maximally affected by the presence of the blinks; indeed, the correlation coefficient is equal to 1 for the electrode FPz (red portion of the mask). The same coefficient is equal to 0.5 for the sensor FCz, reflecting the fact that more central sensors show attenuated ocular components.

**Figure 3.**SEED-G performances in terms of computational time and percentage of realistic data generated: (

**a**) Mean and standard deviation of the computational time computed over 300 iterations were shown as functions of the number of time series (Model size) and the number of existing connections (Network density). The number of real sources included is equal to 30%. Except for some 60-node models, all the simulated datasets composed by 100 trials were generated in less than 10 s. (*) encodes the fact that no dataset with that specific combination of features could be generated with 1000 attempts; (

**b**) Mean and standard deviation of the percentage of EEG-like signals (EEGl-s) computed over 300 iterations were reported as functions of Model size and of the number of real sources included in the connectivity model (Real sources). The density of the network is equal to 10%. On average, more than 80% of the generated data reported EEG-like spectral properties.

**Figure 4.**Simulation study for the PDC robustness assessment. Block diagram describing the simulation framework built for quantifying the effect of the inter-trial variability on connectivity estimates’ performances.

**Figure 5.**PDC percentage estimate error with respect to the imposed connectivity model. Results of the four-way ANOVA performed using Relative Error as dependent variable. The investigated factors are: the number of connections with variable weight (MOD_CON), the amplitude of the weight variation quantified as percentage of the initial value (VAR), the percentage of modified trials (TRIALS), and the type of variation (number of connections on which to apply a value variation (VAR_DIR) which can be either a reduction (panel

**a**) or an increase (panel

**b**). The bars represent the 95% confidence interval.

**Figure 6.**False positive and false negative in PDC estimates. Results of the three-way ANOVA performed to compare FPR (panel

**a**) and FNR (panel

**b**) in different experimental conditions defined by the number of existing spurious connections (SPURIOUS), the percentage of modified trials (TRIALS), and the dimension of the model (MOD_SIZE). The bars represent the 95% confidence interval.

**Table 1.**Results of the four-way ANOVA (F-value) performed on the Relative Error evaluated after estimating PDC values on 5-, 10- and 20-node models.

5 Nodes | 10 Nodes | 20 Nodes | |
---|---|---|---|

VAR_DIR | 98 | 162 | 15 |

VAR | 995 | 2992 | 7275 |

MOD_CON | 1237 | 4290 | 10176 |

TRIALS | 1415 | 2860 | 6190 |

VAR × VAR_DIR | 5 | 33 | 904 |

MOD_CON × VAR_DIR | 2.91^{(NS)} | 22 | 558 |

MOD_CON × VAR | 340 | 1806 | 5205 |

TRIALS × VAR_DIR | 37 | 87 | 45 |

TRIALS × VAR | 756 | 1676 | 4061 |

TRIALS × MOD_CON | 690 | 1994 | 6458 |

MOD_CON × VAR × VAR_DIR | 13 | 167 | 1361 |

TRIALS × VAR × VAR_DIR | 8 | 28 | 539 |

TRIALS × MOD_CON × VAR_DIR | 4 | 24 | 376 |

MOD_CON × VAR × TRIALS | 132 | 405 | 1345 |

MOD_CON × VAR × TRIALS × VAR_DIR | 4 | 39 | 322 |

^{NS}Factor of the ANOVA non-significant. When nothing is specified, p < 0.001.

**Table 2.**Results of the three-way ANOVA (F-value) performed on the performance parameters FPR and FNR, evaluated after estimating and validating PDC matrices.

FPR * | FNR * | |
---|---|---|

MOD_SIZE | 740.7 | 251.1 |

SPURIOUS | 237.3 | 118.7 |

TRIALS | 77.3 | 189.4 |

SPURIOUS × MOD_SIZE | 186.8 | 88.0 |

TRIALS × MOD_SIZE | 39.6 | 149.3 |

SPURIOUS × TRIALS | 4.2 | 50.7 |

SPURIOUS × TRIALS × MOD_SIZE | 6.8 | 33.6 |

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**MDPI and ACS Style**

Anzolin, A.; Toppi, J.; Petti, M.; Cincotti, F.; Astolfi, L.
SEED-G: Simulated EEG Data Generator for Testing Connectivity Algorithms. *Sensors* **2021**, *21*, 3632.
https://doi.org/10.3390/s21113632

**AMA Style**

Anzolin A, Toppi J, Petti M, Cincotti F, Astolfi L.
SEED-G: Simulated EEG Data Generator for Testing Connectivity Algorithms. *Sensors*. 2021; 21(11):3632.
https://doi.org/10.3390/s21113632

**Chicago/Turabian Style**

Anzolin, Alessandra, Jlenia Toppi, Manuela Petti, Febo Cincotti, and Laura Astolfi.
2021. "SEED-G: Simulated EEG Data Generator for Testing Connectivity Algorithms" *Sensors* 21, no. 11: 3632.
https://doi.org/10.3390/s21113632