Journal
NEUROIMAGE
Volume 172, Issue -, Pages 728-739Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.neuroimage.2018.02.016
Keywords
Graph theory; Networks; Functional network; Structural network; Eigen decomposition; Laplacian
Funding
- NIH [R01 NS075425, R01 EB022717]
- NATIONAL INSTITUTE OF BIOMEDICAL IMAGING AND BIOENGINEERING [R01EB022717] Funding Source: NIH RePORTER
- NATIONAL INSTITUTE OF NEUROLOGICAL DISORDERS AND STROKE [R01NS075425, R01NS092802] Funding Source: NIH RePORTER
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How structural connectivity (SC) gives rise to functional connectivity (FC) is not fully understood. Here we mathematically derive a simple relationship between SC measured from diffusion tensor imaging, and FC from resting state fMRI. We establish that SC and FC are related via (structural) Laplacian spectra, whereby FC and SC share eigenvectors and their eigenvalues are exponentially related. This gives, for the first time, a simple and analytical relationship between the graph spectra of structural and functional networks. Laplacian eigenvectors are shown to be good predictors of functional eigenvectors and networks based on independent component analysis of functional time series. A small number of Laplacian eigenmodes are shown to be sufficient to reconstruct FC matrices, serving as basis functions. This approach is fast, and requires no time-consuming simulations. It was tested on two empirical SC/FC datasets, and was found to significantly outperform generative model simulations of coupled neural masses.
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