title: Partial covariance based functional connectivity computation using Ledoit-Wolf covariance regularization.
abstract: 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.
authors.affiliation: Department of Neurology, Washington University in St. Louis, St. Louis, MO 63110, USA. Electronic address: brierm@wusm.wustl.edu.
authors.forename: Matthew R
authors.initials: MR
authors.lastname: Brier
authors.affiliation: Department of Radiology, Washington University in St. Louis, St. Louis, MO 63110, USA.
authors.forename: Anish
authors.initials: A
authors.lastname: Mitra
authors.affiliation: Department of Mathematics, Washington University in St. Louis, St. Louis, MO 63110, USA.
authors.forename: John E
authors.initials: JE
authors.lastname: McCarthy
authors.affiliation: Department of Neurology, Washington University in St. Louis, St. Louis, MO 63110, USA; Department of Radiology, Washington University in St. Louis, St. Louis, MO 63110, USA; Department of Biomedical Engineering, Washington University in St. Louis, St. Louis, MO 63110, USA.
authors.forename: Beau M
authors.initials: BM
authors.lastname: Ances
authors.affiliation: Department of Radiology, Washington University in St. Louis, St. Louis, MO 63110, USA; Department of Neurology, Washington University in St. Louis, St. Louis, MO 63110, USA.
authors.forename: Abraham Z
authors.initials: AZ
authors.lastname: Snyder
mesh_terms: D000293:Adolescent; D000328:Adult; D001921:Brain / Q000502:physiology*; D063132:Connectome / Q000379:methods*; D003627:Data Interpretation, Statistical; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging; D008875:Middle Aged; D055815:Young Adult