TY - JOUR
T1 - Partial covariance based functional connectivity computation using Ledoit-Wolf covariance regularization
AU - Brier, Matthew R.
AU - Mitra, Anish
AU - McCarthy, John E.
AU - Ances, Beau M.
AU - Snyder, Abraham Z.
N1 - Funding Information:
This work was supported by grants from the National Institutes of Health (BMA: R01NR12657 , R01NR012907 , and R01NR014449 ; AZS: P30NS048056 ) the Alzheimer’s Association (BMA), and the Paula and Rodger O. Riney Fund. JEM was supported by NSF DMS 1300280 . Research reported in this publication was also supported by the Washington University Institute of Clinical and Translational Sciences grant UL1 TR000448 from the National Center for Advancing Translational Sciences (NCATS) of the National Institutes of Health (NIH). The content is solely the responsibility of the authors and does not necessarily represent the official view of the NIH. The authors also wish to acknowledge the support of the Biostatistics Core and NCI Cancer Center Support Grant P30 CA091842 , Siteman Comprehensive Cancer Center, for supporting the REDCap clinical data capture service as a research resource at WUSM.
Publisher Copyright:
© 2015 Elsevier Inc.
PY - 2015/11/1
Y1 - 2015/11/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84938684031&partnerID=8YFLogxK
U2 - 10.1016/j.neuroimage.2015.07.039
DO - 10.1016/j.neuroimage.2015.07.039
M3 - Article
C2 - 26208872
AN - SCOPUS:84938684031
VL - 121
SP - 29
EP - 38
JO - NeuroImage
JF - NeuroImage
SN - 1053-8119
ER -