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Higher-order interactions in macroscopic functional networks of the brain and its relation to BOLD global signal

Xuhui Huang1, 2, Congying Chu1, 2, Kaibin Xu1, 2, Tianzi Jiang1, 2, 3 and Shan Yu1, 2*
  • 1 Institute of Automation, Chinese Academy of Sciences, Brainnetome Center, China
  • 2 Institute of Automation, Chinese Academy of Sciences, National Laboratory of Pattern Recognition, China
  • 3 Institute of Automation, Chinese Academy of Sciences, CAS Center for Excellence in Brain Science, China

Introduction: Functional networks of the brain are usually studied at the macroscopic level by extracting pair-wise interactions based on BOLD signals. However, higher-order interactions (HOIs), i.e., the ones that manifest only in triplets, quadruplets, etc., could have important effects on network activities but have not been fully examined at the macroscopic level. Specifically, the relation between HOIs and the global signal (GS), which reflects the common fluctuations among all brain areas, remains unclear. To address these issues, here we first characterized HOIs in macroscopic functional networks based on resting state (rs) fMRI data with and without global signal regression (GSR), and then studied the relation between HOIs and GS, as well as other possible mechanism that can give rise to HOIs, by simulating BOLD signals in distributed brain networks. Methods: The data set is the first and second scanning of 100 subjects in HCP Q3 (TR=720ms, 1200 frames in each scanning). In total, 226,000 frames (about 48 hours) of imaging data were used. Standard preprocessing was applied, including head motion correction, 0.01-0.1Hz filtering and regressing movement. Simulated BOLD signals were generated by combining a mean-field network model with the Balloon-Windkessel hemodynamic model (Deco et al. 2013). To quantify network activities and the strength of HOIs, we used a threshold for individual ROIs and then converted the original signals into binary time series, based on if the amplitude is above the threshold or not. Results: We analyzed activities of the Fronto-Parietal Network (FPN, 11 ROIs) and the Default Mode Network (DMN, 12 ROIs). To measure the effect of HOIs on network activities, we separately applied a pair-wise model (Ising model, Schneidman et al. 2006) and a model with thresholding-induced HOIs (DG model, Macke et al. 2009; Yu et al. 2011) to the data. We use the Jensen–Shannon (JS) divergence to estimate the accuracy of the two models. For GSR data, we found that, consistent with a recent study under GSR condition (Watanabe et al., 2013), the Ising model gave reasonably accurate description of probability distributions of network states, and its JS divergence was slightly larger than that of the DG model (less than 1.5 times for both networks), implying weak HOIs in the data; However, for data without GSR, the Ising model became much worse (with 2.5~4 times larger JS divergence) than the DG model, suggesting a stronger effect of HOIs in such condition. Importantly, the DG model’s performance was the same for data with and without GSR, indicating that the increased HOIs with GS can be explained as a thresholding-induced effect, rather than an intrinsic feature of brain activities. Next we tried to understand these empirical results by simulating both neuronal activities and BOLD signals in a network model with excitatory coupling between brain areas, in which the strengths of common input and pair-wise coupling were changed systemically. We found that, in both neuronal and BOLD signals, strong common input, which serves as a source for the global signal, led to significant HOIs. Consistent with our empirical results, such HOIs could also be explained by the DG model. In addition, we found that the coupling strength has very little effect on the strength of HOIs in the network. These results shed new light on understanding both weak HOIs in data with GSR and apparently strong HOIs in data without GSR. Conclusion: We found that, although there are sizable HOIs in brain’s functional networks in data without GSR, they are mainly due to the thresholding operation introduced in the data analysis. The true, intrinsic HOIs in BOLD signals are therefore weak regardless of GSR. This warrants the use of methods based on pair-wise interactions in studying functional networks. We also found that such lack of intrinsic HOIs may be resulted from the fact that brain areas usually interact with each other via pair-wise, excitatory connections, suggesting that the lack of intrinsic HOIs may be a generic property of such networks.

Acknowledgements

This work was supported by Hundred-Talent Program of Chinese Academy of Sciences (for SY), the National Key Basic Research and Development Program (973) (Grant No. 2011CB707800), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB02030300), and the Natural Science Foundation of China (Grant Nos. 91132301, 91432302).

References

Schneidman, E., Berry, M. J., Segev, R., & Bialek, W. (2006). Weak pairwise correlations imply strongly correlated network states in a neural population. Nature, 440(7087), 1007–12

Macke, J. H., Berens, P., Ecker, A. S., Tolias, A. S., & Bethge, M. (2009). Generating spike trains with specified correlation coefficients. Neural Computation, 21(2), 397-423.

Yu, S., Yang, H., Nakahara, H., Santos, G. S., Nikolić, D., & Plenz, D. (2011). Higher-order interactions characterized in cortical activity. The Journal of Neuroscience, 31(48), 17514-17526.

Watanabe, T, et al. (2013). A pairwise maximum entropy model accurately describes resting-state human brain networks. Nature communications, 4, 1370.

Deco G et al. (2013). Resting-state functional connectivity emerges from structurally and dynamically shaped slow linear fluctuations. The Journal of Neuroscience, 33(27), 11239–52

Keywords: HCP data, global signal regression, pair-wise interactions, fronto-parietal network, Default Mode Network, Ising Model, Dg model, mean-field network model

Conference: Neuroinformatics 2015, Cairns, Australia, 20 Aug - 22 Aug, 2015.

Presentation Type: Poster, to be considered for oral presentation

Topic: Neuroimaging

Citation: Huang X, Chu C, Xu K, Jiang T and Yu S (2015). Higher-order interactions in macroscopic functional networks of the brain and its relation to BOLD global signal. Front. Neurosci. Conference Abstract: Neuroinformatics 2015. doi: 10.3389/conf.fnins.2015.91.00028

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Received: 30 May 2015; Published Online: 05 Aug 2015.

* Correspondence: Prof. Shan Yu, Institute of Automation, Chinese Academy of Sciences, Brainnetome Center, Beijing, 100190, China, shan.yu@nlpr.ia.ac.cn