# On the Spatial Distribution of Temporal Complexity in Resting State and Task Functional MRI

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data and Preprocessing

#### 2.2. Temporal Complexity Analysis of fMRI

#### 2.3. Task Specificity of fMRI Complexity

#### 2.4. Spatial Distribution of fMRI Complexity across Grey Matter

## 3. Results

#### 3.1. FMRI Represents Complex Behaviour during Rest and Task

#### 3.2. Task Engagement Lowers Complexity of BOLD Activity

#### 3.3. Complex Dynamics Exist in the Brain Structural-Functional Coupling

#### 3.4. Spatial Patterns of Complex Dynamics in fMRI

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Multiscale Entropy Analysis

## Appendix B. The Graph Surrogate Method for fMRI Complexity Analysis

#### Appendix B.1. Combining Brain Structure and Function

#### Appendix B.2. Spatial Harmonics of Brain Structure

#### Appendix B.3. Graph Surrogate Generation

#### Appendix B.4. Regarding Linearity

#### Appendix B.5. Regarding Functional Connectivity

#### Appendix B.6. Regarding the fMRI Temporal Correlation Matrix

#### Appendix B.7. Regarding Temporal Complexity

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**Figure 1.**(

**A**) The temporal complexity analysis procedure of fMRI in this study. (

**B**) The process of generating graph surrogates from functional and structural MRI.

**Figure 2.**(

**A**) Normalized power spectra of RSNs averaged over all subjects. (

**B**) Corresponding $\beta $ exponents as the slope of RSN-wise normalized logarithmic power spectra, estimated within the frequency band of 0.01–0.2 Hz. (

**C**) Task fMRI protocol overview for Language, Motor, Social, and Working Memory tasks in HCP. Each yellow block represents an event trial and the trial blocks of each column in the event designs are identical. Each column represents a stimulus type referred to as a condition and has been denoted as ${C}_{i}$ in the figure. See [45] for the description of each condition in four HCP tasks. (

**D**) RSN-wise normalized logarithmic power spectra averaged over all subjects, after regressing out the block designs from task fMRI through GLM. Abbreviations: GLM = general linear modelling; VIS = visual, SM = somatomotor; DA = dorsal attention; VA = ventral attention; L = limbic; FP = frontoparietal; DMN = default mode network; numbered C = Condition.

**Figure 3.**(

**A**) Spatial distributions of the Hurst exponent across brain regions (averaged over subjects). The brain maps of 2 rest runs have been averaged. (

**B**) Histograms of the group mean Hurst exponent over 360 brain regions for 4 task runs and 2 rest runs (averaged). Classification loss of pair-wise comparison of mental tasks using binary SVM classifiers with linear kernel: (

**C**) Hurst exponent; and (

**D**) multiscale entropy-based complexity index. The classification loss values have been color coded from dark blue (near zero) to bright red (near 1), and also mentioned on each pair. Abbreviations: WMemory = working memory; Rest1LR = first rest run with left-to-right slicing; Rest2LR = second rest run with left-to-right slicing.

**Figure 4.**(

**A**) Spatial distributions of the entropy-based complexity index across brain regions (averaged over subjects); (

**B**) Joint distribution of the Hurst exponent and complexity index extracted from the rest and task fMRI datasets, averaged across all subjects. The brain maps of 2 rest runs are averaged. Abbreviation: WMemory = working memory.

**Figure 5.**(

**A**) Logarithmic plots of the power spectral density functions of brain graph signals (i.e., the projection of the fMRI data at rest and task onto brain structure) versus brain spatial harmonics. The plots of two rest runs are averaged. Each grey curve belongs to a single subject and the red curves represent group mean. All curves are normalized to 1. (

**B**) Multiscale entropy patterns of the graph signals, colour coded by their associated brain spatial harmonyic (

**C**) The complexity indices associated with the multiscale entropy curves of (

**B**).

**Figure 6.**(

**A**) Spatial distribution of group-mean fMRI temporal complexity across brain areas for 4 task runs and the average rest run. All maps are thresholded using the graph surrogate data generation [43] at the subject level p-value of 0.01 and family-wise error corrected at the p-value of 0.01. (

**B**) Pie charts are the percentage of suprathreshold ROIs in 7 RSNs after graph surrogate testing, normalized by the number of ROIs. See Table 2 for the values of pie slices. Abbreviations: VIS = visual; SM = somatomotor; DA = dorsal attention; VA = ventral attention; L = limbic, FP = frontoparietal; DMN = default mode network; WMemory = working memory.

**Figure 7.**Group-level mean and standard deviation of the Hurst exponent and area under the curve of multiscale entropy at 7 resting state networks. Abbreviations: VIS = visual; SM = somatomotor; DA = dorsal attention; VA = ventral attention; L = limbic; FP = frontoparietal; DMN = default mode network; WMemory = working memory.

Run | Session | ${\mathit{N}}_{\mathit{T}\mathit{R}}$ | Length in Minutes | No. of Conditions | No. of Trials |
---|---|---|---|---|---|

1 | Rest1LR | 399 | 4.8 | - | - |

2 | Rest2LR | 399 | 4.8 | - | - |

5 | Language | 305 | 3.67 | 2 | 11 |

6 | Motor | 273 | 3.29 | 5 | 10 |

7 | Social | 263 | 3.17 | 2 | 5 |

8 | Working Memory | 395 | 4.74 | 8 | 8 |

**Table 2.**Percentage of suprathreshold ROIs in 7 RSNs after the graph surrogate testing of brain complexity maps in Figure 6 (normalized by the number of ROIs). Abbreviations: VIS = visual; SM = somatomotor; DA = dorsal attention; VA = ventral attention; L = limbic; FP = frontoparietal; DMN = default mode network.

Task Name | VIS | SM | DA | VA | L | FP | DMN |
---|---|---|---|---|---|---|---|

Rest1LR | 5.3% | 0.6% | 3.6% | 1.7% | 0% | 3.3% | 2.5% |

Rest2LR | 7.5% | 1.4% | 4.7% | 1.7% | 0% | 3.6% | 3.1% |

Language | 7.8% | 1.4% | 5.3% | 1.7% | 0% | 3.6% | 2.5% |

Motor | 6.7% | 0.6% | 5.3% | 1.4% | 0% | 3.6% | 3.3% |

Social | 4.2% | 0.3% | 1.9% | 1.1% | 0% | 3.1% | 2.2% |

Working Memory | 7.8% | 5% | 7.5% | 3.6% | 0% | 8.9% | 7.8% |

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Omidvarnia, A.; Liégeois, R.; Amico, E.; Preti, M.G.; Zalesky, A.; Van De Ville, D.
On the Spatial Distribution of Temporal Complexity in Resting State and Task Functional MRI. *Entropy* **2022**, *24*, 1148.
https://doi.org/10.3390/e24081148

**AMA Style**

Omidvarnia A, Liégeois R, Amico E, Preti MG, Zalesky A, Van De Ville D.
On the Spatial Distribution of Temporal Complexity in Resting State and Task Functional MRI. *Entropy*. 2022; 24(8):1148.
https://doi.org/10.3390/e24081148

**Chicago/Turabian Style**

Omidvarnia, Amir, Raphaël Liégeois, Enrico Amico, Maria Giulia Preti, Andrew Zalesky, and Dimitri Van De Ville.
2022. "On the Spatial Distribution of Temporal Complexity in Resting State and Task Functional MRI" *Entropy* 24, no. 8: 1148.
https://doi.org/10.3390/e24081148