# fNIRS Complexity Analysis for the Assessment of Motor Imagery and Mental Arithmetic Tasks

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Block Design

#### 2.2. Hemoglobin Extraction from fNIRS Signals

#### 2.3. fNIRS Data Preprocessing

#### 2.4. Entropy Analysis

#### 2.5. Statistical Analysis

## 3. Results

#### 3.1. Nonlinearity Test

#### 3.2. Analysis of Repetitions within Tasks

#### 3.3. Between-Task Statistical Analysis

#### 3.4. Multiple Comparison Analysis

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Position of the Optodes. Positions labeled with “D” refer to detectors while positions labeled with “S” are sources. The lines demonstrate coupling between sources and detectors.

**Figure 3.**Topographic maps from channel-wise third moment tests displaying the fraction of time series from each channel having statistical significance, where the colorbar indicates the value of the fraction.

**Figure 4.**p-value topographic maps from channel-wise Friedman tests displaying significant statistical differences between all tasks in the experimental protocol (baseline, mental arithmetic, right hand, and left hand motor imagery). Y (green) areas indicate where we could reject the null hypothesis that activity was the same in all the tasks, whereas N (white) areas indicate where we could not reject the null hypothesis.

**Figure 5.**p-value topographic maps from channel-wise Wilcoxon non-parametric tests displaying significant statistical differences between mental arithmetic activity and baseline activity. Y (green) areas indicate statistically significant changes between tasks, whereas N indicates non-significant changes. The colormap topoplots display estimate differences between baseline (B) and mental arithmetic (M) tasks, with red indicating higher values for mental arithmetic than baseline and blue indicating lower values for mental arithmetic as compared to baseline.

**Figure 6.**p-value topographic maps from channel-wise Wilcoxon non-parametric tests displaying significant statistical differences between left hand imagery activity and baseline activity. Y (green) areas indicate statistically significant changes between tasks, whereas N indicates non-significant changes. The colormap topoplots display estimate differences between baseline (B) and left hand imagery (L) tasks, with red indicating higher values for left hand imagery vs baseline and blue indicating lower values for left hand imagery vs baseline.

**Figure 7.**p-value topographic maps from channel-wise Wilcoxon non-parametric tests displaying significant statistical differences between right hand imagery activity and baseline activity. Y (green) areas indicate statistically significant changes between tasks, whereas N indicates non-significant changes. The colormap topoplots display estimate differences between baseline (B) and right hand imagery (R) tasks, with red indicating higher values for right hand imagery vs baseline and blue indicating lower values for right hand imagery vs baseline.

**Figure 8.**p-value topographic maps from channel-wise Wilcoxon non-parametric tests displaying significant statistical differences between left hand imagery and right hand imagery activities. Y (green) areas indicate statistically significant changes between tasks, whereas N indicates non-significant changes. The colormap topoplots display estimate differences between left hand imagery (L) and right hand imagery (R) tasks, with red indicating higher values for right hand imagery than left hand imagery and blule indicating lower values for right hand imagery than left hand imagery.

**Table 1.**Table of statistical power p-values from the Friedman analysis. p-values are bonferroni corrected. * denotes that using an alpha of 0.01 we must reject the null hypothesis that there were no significant variations between repetitions. This particularly occurs for FuzzyEn in the total and the concatenated case for deoxyhemoglobin.

Metric | Mental Arithmetic | Left Hand Imagery | Right Hand Imagery | Baseline |
---|---|---|---|---|

HbO | 0.1735 | 0.1147 | 0.0331 | 0.7383 |

Hb | 0.0870 | 0.0841 | 0.1735 | 0.0039 |

Total Hb | 0.0331 | 0.2449 | 0.0965 | 0.0501 |

$SampE{n}_{HbO}$ | 0.0610 | 0.1414 | 0.0976 | 0.1375 |

$SampE{n}_{Hb}$ | 0.0891 | 0.2844 | 0.0101 | 0.0262 |

$SampE{n}_{Total}$ | 0.2013 | 0.2528 | 0.0501 | 0.0554 |

$SampE{n}_{concat}$ | 0.0408 | 0.1147 | 0.0106 | 0.1735 |

$FuzzyE{n}_{HbO}$ | 0.0934 | 0.0023 | 0.0501 | 0.0219 |

$FuzzyE{n}_{Hb}$ | 0.0145 | 0.0106 | 0.0556 | 0.0408 |

${}^{*}FuzzyE{n}_{Total}$ | 0.0708 | 0.0051 | 0.0243 | 0.0243 |

${}^{*}FuzzyE{n}_{concat}$ | 0.0219 | 0.0078 | 0.1735 | 0.0078 |

$DistE{n}_{HbO}$ | 0.6658 | 0.1735 | 0.1147 | 0.1619 |

$DistE{n}_{Hb}$ | 0.1272 | 0.0115 | 0.0709 | 0.2209 |

$DistE{n}_{Total}$ | 0.0871 | 0.0501 | 0.1411 | 0.0874 |

$DistE{n}_{concat}$ | 0.0408 | 0.1619 | 0.0118 | 0.0408 |

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**MDPI and ACS Style**

Ghouse, A.; Nardelli, M.; Valenza, G. fNIRS Complexity Analysis for the Assessment of Motor Imagery and Mental Arithmetic Tasks. *Entropy* **2020**, *22*, 761.
https://doi.org/10.3390/e22070761

**AMA Style**

Ghouse A, Nardelli M, Valenza G. fNIRS Complexity Analysis for the Assessment of Motor Imagery and Mental Arithmetic Tasks. *Entropy*. 2020; 22(7):761.
https://doi.org/10.3390/e22070761

**Chicago/Turabian Style**

Ghouse, Ameer, Mimma Nardelli, and Gaetano Valenza. 2020. "fNIRS Complexity Analysis for the Assessment of Motor Imagery and Mental Arithmetic Tasks" *Entropy* 22, no. 7: 761.
https://doi.org/10.3390/e22070761