Dataset Information

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.

SUBMITTER: Brier MR

PROVIDER: S-EPMC4604032 | biostudies-literature | 2015 Nov

REPOSITORIES: biostudies-literature

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Partial covariance based functional connectivity computation using Ledoit-Wolf covariance regularization.

Brier Matthew R MR Mitra Anish A McCarthy John E JE Ances Beau M BM Snyder Abraham Z AZ

NeuroImage 20150721

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. ...[more]

PMID: 26208872

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Project description:Resting-state functional magnetic resonance imaging allows one to study brain functional connectivity, partly motivated by evidence that patients with complex disorders, such as Alzheimer's disease, may have altered functional brain connectivity patterns as compared with healthy subjects. A functional connectivity network describes statistical associations of the neural activities among distinct and distant brain regions. Recently, there is a major interest in group-level functional network analysis; however, there is a relative lack of studies on statistical inference, such as significance testing for group comparisons. In particular, it is still debatable which statistic should be used to measure pairwise associations as the connectivity weights. Many functional connectivity studies have used either (full or marginal) correlations or partial correlations for pairwise associations. This article investigates the performance of using either correlations or partial correlations for testing group differences in brain connectivity, and how sparsity levels and topological structures of the connectivity would influence statistical power to detect group differences. Our results suggest that, in general, testing group differences in networks deviates from estimating networks. For example, high regularization in both covariance matrices and precision matrices may lead to higher statistical power; in particular, optimally selected regularization (e.g., by cross-validation or even at the true sparsity level) on the precision matrices with small estimation errors may have low power. Most importantly, and perhaps surprisingly, using either correlations or partial correlations may give very different testing results, depending on which of the covariance matrices and the precision matrices are sparse. Specifically, if the precision matrices are sparse, presumably and arguably a reasonable assumption, then using correlations often yields much higher powered and more stable testing results than using partial correlations; the conclusion is reversed if the covariance matrices, not the precision matrices, are sparse. These results may have useful implications to future studies on testing functional connectivity differences.

Project description:Characterizing interactions between multiple brain regions is important for understanding brain function. Functional connectivity measures based on partial correlation provide an estimate of the linear conditional dependence between brain regions after removing the linear influence of other regions. Estimation of partial correlations is, however, difficult when the number of regions is large, as is now increasingly the case with a growing number of large-scale brain connectivity studies. To address this problem, we develop novel methods for estimating sparse partial correlations between multiple regions in fMRI data using elastic net penalty (SPC-EN), which combines L1- and L2-norm regularization We show that L1-norm regularization in SPC-EN provides sparse interpretable solutions while L2-norm regularization improves the sensitivity of the method when the number of possible connections between regions is larger than the number of time points, and when pair-wise correlations between brain regions are high. An issue with regularization-based methods is choosing the regularization parameters which in turn determine the selection of connections between brain regions. To address this problem, we deploy novel stability selection methods to infer significant connections between brain regions. We also compare the performance of SPC-EN with existing methods which use only L1-norm regularization (SPC-L1) on simulated and experimental datasets. Detailed simulations show that the performance of SPC-EN, measured in terms of sensitivity and accuracy is superior to SPC-L1, especially at higher rates of feature prevalence. Application of our methods to resting-state fMRI data obtained from 22 healthy adults shows that SPC-EN reveals a modular architecture characterized by strong inter-hemispheric links, distinct ventral and dorsal stream pathways, and a major hub in the posterior medial cortex - features that were missed by conventional methods. Taken together, our findings suggest that SPC-EN provides a powerful tool for characterizing connectivity involving a large number of correlated regions that span the entire brain.

Project description:BackgroundPremenstrual syndrome (PMS) is a menstrual-related disorder, characterized by physical, emotional, behavioral and cognitive symptoms. However, the neuropathological mechanisms of PMS remain unclear. This study aimed to investigate the frequency-specific functional connectivity density (FCD) and structural covariance in PMS.MethodsFunctional and T1-weighted structural data were obtained from 35 PMS patients and 36 healthy controls (HCs). This study was a cross-sectional and prospective design. The local/long-range FCD (LFCD/LRFCD) across slow-4 (0.027-0.073 Hz) and slow-5 (0.01-0.027 Hz) bands were computed, and two-way analysis of variance (ANOVA) was performed to ascertain the main effects of group and interaction effects between group and frequency band. Receiver operating characteristic (ROC) curve was performed to investigate reliable biomarkers for identifying PMS from HCs. Based on the ROC results, characterized the changes of whole-brain structural covariance patterns of striatum subregions in two groups. Correlation analysis was applied to examine relationships between the clinical symptoms and abnormal brain regions.ResultsCompared with HCs, PMS patients exhibited: (I) aberrant functional communication in the middle cingulate cortex and precentral gyrus; (II) significant frequency band-by-group interaction effects of the striatum, thalamus and orbitofrontal cortex; (III) the better classification ability of the LFCD in the striatum in ROC analysis (slow-5); (IV) decreased gray matter volumes in the caudate subregions and decreased structural associations of between the caudate subregions and frontal cortex; (V) the LFCD value in thalamus were significantly negatively correlated with the sleep problems (slow-5).ConclusionsBased on multi-modal magnetic resonance imaging (MRI) analysis, this study might imply the aberrant emotional regulation and cognitive function related to menstrual cycle in PMS and improve our understanding of the pathophysiologic mechanism in PMS from novel perspective.

Dataset Information

Partial covariance based functional connectivity computation using Ledoit-Wolf covariance regularization.

Publications

Partial covariance based functional connectivity computation using Ledoit-Wolf covariance regularization.

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