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Bayesian Estimation of Conditional Independence Graphs Improves Functional Connectivity Estimates.

ABSTRACT: Functional connectivity concerns the correlated activity between neuronal populations in spatially segregated regions of the brain, which may be studied using functional magnetic resonance imaging (fMRI). This coupled activity is conveniently expressed using covariance, but this measure fails to distinguish between direct and indirect effects. A popular alternative that addresses this issue is partial correlation, which regresses out the signal of potentially confounding variables, resulting in a measure that reveals only direct connections. Importantly, provided the data are normally distributed, if two variables are conditionally independent given all other variables, their respective partial correlation is zero. In this paper, we propose a probabilistic generative model that allows us to estimate functional connectivity in terms of both partial correlations and a graph representing conditional independencies. Simulation results show that this methodology is able to outperform the graphical LASSO, which is the de facto standard for estimating partial correlations. Furthermore, we apply the model to estimate functional connectivity for twenty subjects using resting-state fMRI data. Results show that our model provides a richer representation of functional connectivity as compared to considering partial correlations alone. Finally, we demonstrate how our approach can be extended in several ways, for instance to achieve data fusion by informing the conditional independence graph with data from probabilistic tractography. As our Bayesian formulation of functional connectivity provides access to the posterior distribution instead of only to point estimates, we are able to quantify the uncertainty associated with our results. This reveals that while we are able to infer a clear backbone of connectivity in our empirical results, the data are not accurately described by simply looking at the mode of the distribution over connectivity. The implication of this is that deterministic alternatives may misjudge connectivity results by drawing conclusions from noisy and limited data.

SUBMITTER: Hinne M

PROVIDER: S-EPMC4634993 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:Highlights: Hamming Distance is applied to distinguish the difference of functional connectivity networkThe orientations of sources are testified to influence the scalp Functional Connectivity Graph (FCG) from different references significantlyREST, the reference electrode standardization technique, is proved to have an overall stable and excellent performance in variable situations. The choice of an electroencephalograph (EEG) reference is a practical issue for the study of brain functional connectivity. To study how EEG reference influence functional connectivity estimation (FCE), this study compares the differences of FCE resulting from the different references such as REST (the reference electrode standardization technique), average reference (AR), linked mastoids (LM), and left mastoid references (LR). Simulations involve two parts. One is based on 300 dipolar pairs, which are located on the superficial cortex with a radial source direction. The other part is based on 20 dipolar pairs. In each pair, the dipoles have various orientation combinations. The relative error (RE) and Hamming distance (HD) between functional connectivity matrices of ideal recordings and that of recordings obtained with different references, are metrics to compare the differences of the scalp functional connectivity graph (FCG) derived from those two kinds of recordings. Lower RE and HD values imply more similarity between the two FCGs. Using the ideal recording (IR) as a standard, the results show that AR, LM and LR perform well only in specific conditions, i.e., AR performs stable when there is no upward component in sources' orientation. LR achieves desirable results when the sources' locations are away from left ear. LM achieves an indistinct difference with IR, i.e., when the distribution of source locations is symmetric along the line linking the two ears. However, REST not only achieves excellent performance for superficial and radial dipolar sources, but also achieves a stable and robust performance with variable source locations and orientations. Benefitting from the stable and robust performance of REST vs. other reference methods, REST might best recover the real FCG of EEG. Thus, REST based FCG may be a good candidate to compare the FCG of EEG based on different references from different labs.

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Bayesian Estimation of Conditional Independence Graphs Improves Functional Connectivity Estimates.

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