Additional Affiliations
Medicine
Document Type
Article
Publication Date
11-1-2015
Originally Published In
Neuroimage. 2015 Nov 1;121:29-38. doi: 10.1016/j.neuroimage.2015.07.039.
Abstract
Highlights •We use the well characterized matrix regularization technique described by Ledoit and Wolf to calculate high dimensional partial correlations in fMRI data. •Using this approach we demonstrate that partial correlations reveal RSN structure suggesting that RSNs are defined by widely and uniquely shared variance. •Partial correlation functional connectivity is sensitive to changes in brain state indicating that they contain functional information. Functional connectivity refers to shared signals among brain regions and is typically assessed in a task free state. Functional connectivity commonly is quantified between signal pairs using Pearson correlation. However, resting-state fMRI is a multivariate process exhibiting a complicated covariance structure. Partial covariance assesses the unique variance shared between two brain regions excluding any widely shared variance, hence is appropriate for the analysis of multivariate fMRI datasets. However, calculation of partial covariance requires inversion of the covariance matrix, which, in most functional connectivity studies, is not invertible owing to rank deficiency. Here we apply Ledoit–Wolf shrinkage (L2 regularization) to invert the high dimensional BOLD covariance matrix. We investigate the network organization and brain-state dependence of partial covariance-based functional connectivity. Although RSNs are conventionally defined in terms of shared variance, removal of widely shared variance, surprisingly, improved the separation of RSNs in a spring embedded graphical model. This result suggests that pair-wise unique shared variance plays a heretofore unrecognized role in RSN covariance organization. In addition, application of partial correlation to fMRI data acquired in the eyes open vs. eyes closed states revealed focal changes in uniquely shared variance between the thalamus and visual cortices. This result suggests that partial correlation of resting state BOLD time series reflect functional processes in addition to structural connectivity.
ORCID
http://orcid.org/0000-0003-0036-7606 [McCarthy]
Recommended Citation
Brier, Matthew R.; Mitra, Anish; McCarthy, John E.; Ances, Beau M.; and Snyder, Abraham Z., "Partial covariance based functional connectivity computation using Ledoit-Wolf covariance regularization" (2015). Mathematics Faculty Publications. 35.
https://openscholarship.wustl.edu/math_facpubs/35
Embargo Period
11-1-2016
Included in
Applied Mathematics Commons, Neuroscience and Neurobiology Commons, Other Analytical, Diagnostic and Therapeutic Techniques and Equipment Commons
Comments
Accepted manuscript version of Neuroimage. 2015 Nov 1;121:29-38. doi: 10.1016/j.neuroimage.2015.07.039. Copyright © 2015 Elsevier Inc.