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Front. Neurosci. | doi: 10.3389/fnins.2018.00287

Sparse Estimation of Resting-State Effective Connectivity from fMRI Cross-Spectra

  • 1Dept. Radiology, Medical Physics, Medical Center - University of Freiburg, Faculty of Medicine, University of Freiburg, Germany
  • 2BrainLinks-BrainTools Cluster of Excellence, University of Freiburg, Germany
  • 3Bernstein Center Freiburg and Faculty of Biology, University of Freiburg, Germany

In fMRI, functional connectivity is conventionally characterized by correlations between fMRI time series, which are intrinsically undirected measures of connectivity. Yet, some information about the directionality of network connections can nevertheless be extracted from the matrix of pairwise temporal correlations between all considered time series, when expressed in the frequency-domain as a cross-spectral density matrix. Using a sparsity prior, it then becomes possible to determine a unique directed network topology that best explains the observed undirected correlations, without having to rely on temporal precedence relationships that may not be valid in fMRI.

Applying this method on simulated data with 100 nodes yielded excellent retrieval of the underlying directed networks under a wide variety of conditions. Importantly, the method did not depend on temporal precedence to establish directionality, thus reducing susceptibility to hemodynamic variability. The computational efficiency of the algorithm was sufficient to enable whole-brain estimations, thus circumventing the problem of missing nodes that otherwise occurs in partial-brain analyses. Applying the method to real resting-state fMRI data acquired with a high temporal resolution, the inferred networks showed good consistency with structural connectivity obtained from diffusion tractography in the same subjects. Interestingly, this agreement could also be seen when considering high-frequency rather than low-frequency connectivity (average correlation: r = 0.26 for f < 0.3 Hz, r = 0.43 for 0.3 < f < 5 Hz). Moreover, this concordance was significantly better (p<0.05) than for networks obtained with conventional functional connectivity based on correlations (average correlation r = 0.18).

The presented methodology thus appears to be well-suited for fMRI, particularly given its lack of explicit dependence on temporal lag structure, and is readily applicable to whole-brain effective connectivity estimation.

Keywords: effective connectivity, functional connectivity, structural connectivity, fMRI, resting state, Correlation

Received: 31 Aug 2017; Accepted: 11 Apr 2018.

Edited by:

Jorge Bosch-Bayard, Instituto de Neurobiología, Universidad Nacional Autonoma de Mexico, Mexico

Reviewed by:

Felix Carbonell, Biospective Inc., Canada
Jan C. De Munck, Medical Center, VU University Amsterdam, Netherlands  

Copyright: © 2018 Lennartz, Schiefer, Rotter, Hennig and LeVan. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: Ms. Carolin Lennartz, University of Freiburg, Dept. Radiology, Medical Physics, Medical Center - University of Freiburg, Faculty of Medicine, Freiburg, Germany,