Sample Entropy Combined with the K-Means Clustering Algorithm Reveals Six Functional Networks of the Brain

Abstract

Identifying brain regions contained in brain functional networks and functions of brain functional networks is of great significance in understanding the complexity of the human brain. The 160 regions of interest (ROIs) in the human brain determined by the Dosenbach’s template have been divided into six functional networks with different functions. In the present paper, the complexity of the human brain is characterized by the sample entropy (SampEn) of dynamic functional connectivity (FC) which is obtained by analyzing the resting-state functional magnetic resonance imaging (fMRI) data acquired from healthy participants. The 160 ROIs are clustered into six clusters by applying the K-means clustering algorithm to the SampEn of dynamic FC as well as the static FC which is also obtained by analyzing the resting-state fMRI data. The six clusters obtained from the SampEn of dynamic FC and the static FC show very high overlap and consistency ratios with the six functional networks. Furthermore, for four of six clusters, the overlap ratios corresponding to the SampEn of dynamic FC are larger than that corresponding to the static FC, and for five of six clusters, the consistency ratios corresponding to the SampEn of dynamic FC are larger than that corresponding to the static FC. The results show that the combination of machine learning methods and the FC obtained using the blood oxygenation level-dependent (BOLD) signals can identify the functional networks of the human brain, and nonlinear dynamic characteristics of the FC are more effective than the static characteristics of the FC in identifying brain functional networks and the complexity of the human brain.

Diverging functional connectivity timescales: Capturing distinct aspects of cognitive performance in early psychosis

“…Nevertheless, the observed relationships between ESE at different levels and behavior, oscillatory dynamics and neurotransmitter densities suggest relevant information can be extracted from the timescales of TVFC. Finally, in the past we and others have equated high (single-scale) SampEn with high complexity (Hirsch & Wohlschlaeger, 2022; Jia & Gu, 2019a, 2019b; Jia et al, 2017), but others have argued that such an interpretation requires a multi-scale entropy analysis (Costa, Goldberger, & Peng, 2002; A. C. Yang et al, 2015). While we have avoided the notion of complexity in the present study, it should be noted that contrary to BOLD SampEn, ESE at our scale of interest captured most of the behaviorally relevant information in healthy subjects (S. S. Menon & Krishnamurthy, 2019).…”

“…SampEn is defined as resulting in a nonnegative number, with higher values indicative of less regularity in the signal (Richman & Moorman, 2000). To ensure comparability of our results with past investigations, we used the standard parameter values of m = 2 and ε = 0.20 (Hirsch & Wohlschlaeger, 2022; Jia & Gu, 2019b). For BOLD signals of at least 97 timepoints evidence suggests that results from SampEn analyses are robust to parameter changes (Albert C. Yang, Tsai, Lin, & Peng, 2018), and similar results were obtained for ESE (Jia et al, 2017).…”

Anomaly Detection for Time Series with Difference Rate Sample Entropy and Generative Adversarial Networks

“…, x n 􏼈 􏼉, it is defined as shown in ( 3). e length of subseries B m+1 (r) is the length of m + 1 mean subseries similarity probability and r is the similarity threshold [19,20].…”

Flexible Brain Transitions Between Hierarchical Network Segregation and Integration Predict Human Behavior

“…This hierarchical organization provides several promising advantages regarding brain dynamics, including greater robustness, adaptivity and functional diversity 21,23,26 . The classic modular partition based on the modularity maximization method or previously defined modular partitions (e.g., functional subsystems) is performed at a single level and is incapable of revealing the hierarchical modular organization 2,27,28 , which limits further inference about how the hierarchical segregated and integrated processes shape an individual's cognitive abilities. Recently, a nested-spectral partition (NSP) method based on eigenmodes was found to effectively detect hierarchical modules in brain networks 21 , and a concept of hierarchically nested segregation and integration was proposed based on these hierarchical modules.…”