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Artifacts in Simultaneous hdEEG/fMRI Imaging: A Nonlinear Dimensionality Reduction Approach^{ †}

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

- Data were preprocessed by state-of-the-art methods to first eliminate most of the variance in the artifacts.
- Through ICA, 5-min sections of the signal were selected. A time-domain ICA algorithm was employed to obtain independent components and spatial weights. In addition, spatial weights and Fourier spectra were normalized with respect to their Root Mean Square (RMS) value.
- We reduced the topomap space to two dimensions for better visual inspection. Multidimensional space is demanding for automatic clustering and it is not possible to have optical control of separated clusters. The nonlinear method t-SNE (t-distributed stochastic neighbor embedding) should respect the original layout of the EEG space.
- The DBSCAN algorithm (density-based spatial clustering of applications with noise) was used to cluster the 2D space (the reduced space of topographic maps). This algorithm does not require input for the number of clusters that are not primarily visible in hidden structures. The DBSCAN algorithm determines this parameter itself and is able to separate the nested clusters.
- We applied several criteria (autocorrelation, focal topography and focal trial activity) to the original dataset and detected whether certain criteria matched some clusters. In this way, it was possible to identify a criterion that would be suitable for describing a particular artifact.
- The median and mean of topomaps, Fourier spectra and time series were investigated to generalize cluster patterns. These characteristics allowed for the assignment of the activity to individual artifacts.

#### 2.1. Data Preprocessing

#### 2.2. ICA and Normalization

#### 2.3. t-SNE Component Embedding

#### 2.4. DBSCAN Clustering

#### 2.5. Applied Criteria

## 3. Results

#### 3.1. Space after t-SNE

#### 3.2. DBSCAN Clustering

#### 3.3. Meaning of the Clusters

#### 3.3.1. EOG Artifact

#### 3.3.2. EMG Artifact

#### 3.3.3. Gradient Artifact

#### 3.3.4. ECG Artifact

#### 3.3.5. Line Noise Artifact

#### 3.3.6. Undefined Clusters

#### 3.4. EEG Criteria

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

EEG | Electroencephalography |

fMRI | Functional magnetic resonance imaging |

DBSCAN | Density-based spatial clustering of applications with noise |

ICA | Independent component analysis |

PCA | Principal component analysis |

tSNE | t-distributed stochastic neighbor embedding |

GA | Gradient artifact |

PA | Pulsion (cardioballistic) artifact |

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**Figure 1.**Schema of semiautomatic extraction of artifacts from simultaneously recorded electroencephalogram (EEG) in functional magentic resonance imagin (fMRI).

**Figure 2.**Reduced space of spectra to 2D from independent components (ICs) after using the t-distributed stochastic neighbor embedding (t-SNE) method with a perplexity of 30 (

**left**). Reduced space of spectra to 3D from ICs after using the t-SNE method with a perplexity of 30 (

**right**).

**Figure 3.**Reduced space of topomaps after using the t-SNE method to 2D space (

**left**). Reduced space of topomaps after the using t-SNE method to 3D space (

**right**). In both examples, a perplexity of 30 was used.

**Figure 4.**Reduced space of topomaps after using t-SNE with a perplexity of 40 (

**top left**). Reduced space of topomaps after using t-SNE with a perplexity of 30 (

**top right**). Reduced space of topomaps after using t-SNE with a perplexity of 20 (

**bottom**). For all settings, the perplexity was used to reduce IC space.

**Figure 5.**Result after applying the clustering algorithm Density-based spatial clustering of applications with noise (DBSCAN) to the IC space resulting from the t-SNE method with a perplexity of 30. The result shows 20 clusters (each cluster is labeled by a number and is a different color).

**Figure 6.**An example of all map types—mean topomaps from cluster 11 (

**left**), median topomaps from cluster 11 (

**middle**) and variance topomaps from cluster 11 (

**right**).

**Figure 7.**Mean topomaps representing 20 clusters after using the t-SNE method with a perplexity of 30. A perplexity of 40 had the same topomaps that differed in sequence. The mean and median topomaps have similar characters but the variance has no meaningful value. Topomaps were clustered from IC space.

**Figure 8.**Mean topomaps representing 11 clusters after using the t-SNE method with a perplexity of 20. The mean and median topomaps have similar characters but the variance has no meaningful value, similar to the case with perplexities of 30 and 40. Topomaps were clustered from IC space.

**Figure 9.**Topomaps of the clusters representing electrooculographic (EOG) artifacts from different eye activity (

**top**). Time-series graphs of a 10-s section of the signal that were clustered into the same cluster by IC topomaps (

**below**). Arrows point to an example of the EOG artifacts, which are manifested as “rectangular steps” in the time-series graphs.

**Figure 10.**Topomaps of clusters that represent electromyographic (EMG) artifacts (

**top**). The mean power spectrum after median filtration of the CL9 cluster, which represents EMG artifacts (

**bottom**).

**Figure 11.**Topomaps of the clusters representing gradient artifact (GA) residues from magnet coil switching (

**top**). The mean power spectrum of the GA found for cluster CL10 (

**bottom**). Arrows show the amplitudes at 36, 54, $72,$ and 90 Hz (spacing of 18 Hz). The mean power spectra for clusters CL2 and CL4 are similar in appearance.

**Figure 12.**Topomap of cluster CL18 representing an electrocardiographic (ECG) artifact (

**top**). Time-series graphs of a 10-second section of the signal clustered into the same cluster by IC topomaps. The arrows indicate an example of the ECG peak residuum, which manifested in the time-series graphs.

**Figure 13.**Topomaps of clusters CL6 and CL12, which have a distinctive peak at a frequency of 50 Hz, as line noise artifacts (

**top**). The mean power spectrum of cluster CL6 with a distinctive peak at a frequency of 50 Hz (arrow).

**Figure 14.**Commonly used EEG criteria displayed in IC space. The autocorrelation criterion on a logarithmic scale (

**top left**); the focal criterion on a logarithmic scale (

**top right**); the focal trial criterion on a non-logarithmic scale (

**below**). The dimensions are formed by topomaps and are dimensionless.

**Table 1.**The number of noise points and number of clusters resulting from DBSCAN for different values of perplexity in the t-SNE method used on IC space.

Perplexity [-] | No. of Clusters [-] | No. of Noise Points [-] |
---|---|---|

20 | 11 | 1678 |

30 | 20 | 525 |

40 | 20 | 858 |

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**MDPI and ACS Style**

Piorecky, M.; Koudelka, V.; Strobl, J.; Brunovsky, M.; Krajca, V.
Artifacts in Simultaneous hdEEG/fMRI Imaging: A Nonlinear Dimensionality Reduction Approach. *Sensors* **2019**, *19*, 4454.
https://doi.org/10.3390/s19204454

**AMA Style**

Piorecky M, Koudelka V, Strobl J, Brunovsky M, Krajca V.
Artifacts in Simultaneous hdEEG/fMRI Imaging: A Nonlinear Dimensionality Reduction Approach. *Sensors*. 2019; 19(20):4454.
https://doi.org/10.3390/s19204454

**Chicago/Turabian Style**

Piorecky, Marek, Vlastimil Koudelka, Jan Strobl, Martin Brunovsky, and Vladimir Krajca.
2019. "Artifacts in Simultaneous hdEEG/fMRI Imaging: A Nonlinear Dimensionality Reduction Approach" *Sensors* 19, no. 20: 4454.
https://doi.org/10.3390/s19204454