Accurately Modeling the Resting Brain Functional Correlations Using Wave Equation With Spatiotemporal Varying Hypergraph Laplacian

How spontaneous brain neural activities emerge from the underlying anatomical architecture, characterized by structural connectivity (SC), has puzzled researchers for a long time. Over the past decades, much effort has been directed toward the graph modeling of SC, in which the brain SC is generally...

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Bibliographic Details
Published in:IEEE transactions on medical imaging Vol. 41; no. 12; pp. 3787 - 3798
Main Authors: Wang, Yanjiang, Ma, Jichao, Chen, Xue, Liu, Baodi
Format: Journal Article
Language:English
Published: New York IEEE 01.12.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Brain
Brain connectivity
Brain modeling
Correlation
Couplings
Formulas (mathematics)
Graph representations
Graph theory
Graphical representations
Laplace equations
Mathematical models
Modelling
Neural activity
Neural networks
Predictive models
Propagation
resonance
Resonant frequencies
spatiotemporal varying hypergraph Laplacian
structure-function relation
wave equation
Wave equations
Wave propagation
ISSN:0278-0062, 1558-254X, 1558-254X
Online Access:Get full text
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Summary:How spontaneous brain neural activities emerge from the underlying anatomical architecture, characterized by structural connectivity (SC), has puzzled researchers for a long time. Over the past decades, much effort has been directed toward the graph modeling of SC, in which the brain SC is generally considered as relatively invariant. However, the graph representation of SC is unable to directly describe the connections between anatomically unconnected brain regions and fail to model the negative functional correlations. Here, we extend the static graph model to a spatiotemporal varying hypergraph Laplacian diffusion (STV-HGLD) model to describe the propagation of the spontaneous neural activity in human brain by incorporating the Laplacian of the hypergraph representation of the structural connectome (<inline-formula> <tex-math notation="LaTeX">{h} </tex-math></inline-formula>SC) into the regular wave equation. Theoretical solution shows that the dynamic functional couplings between brain regions fluctuate in the form of an exponential wave regulated by the spatiotemporal varying Laplacian of <inline-formula> <tex-math notation="LaTeX">{h} </tex-math></inline-formula>SC. Empirical study suggests that the cortical wave might give rise to resonance with SC during the self-organizing interplay between excitation and inhibition among brain regions, which orchestrates the cortical waves propagating with harmonics emanating from the <inline-formula> <tex-math notation="LaTeX">{h} </tex-math></inline-formula>SC while being bound by the natural frequencies of SC. Besides, the average statistical dependencies between brain regions, normally defined as the functional connectivity (FC), arises just at the moment before the cortical wave reaches the steady state after the wave spreads across all the brain regions. Comprehensive tests on four extensively studied empirical brain connectome datasets with different resolutions confirm our theory and findings.
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ISSN:0278-0062
1558-254X
1558-254X
DOI:10.1109/TMI.2022.3196007