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.
Highlights
In the early days of neuroscience much attention was devoted to identifying the functional specialization of different brain areas [1]
Significant neuroscientific effort is devoted to elucidating functional connectivity between spatially segregated brain regions
One frequently advocated metric for functional connectivity is partial correlation, which is related to conditional independence: if two regions are independent, conditioned on all other regions, their partial correlation is zero, assuming Gaussian data
Summary
In the early days of neuroscience much attention was devoted to identifying the functional specialization of different brain areas [1]. This focus has shifted towards revealing how these areas are organized into networks and how these networks, rather than their individual constituents, are related to cognition [2,3,4] and neurological or psychological pathology [5,6,7]. Structural connectivity is concerned with the anatomical whitematter fiber bundles that connect remote regions of the brain. It may be estimated in vivo by diffusion weighted MRI (dMRI), which measures the fractional anisotropy of the diffusion of water molecules [11]. Functional connectivity in turn expresses the (degree of) dependency between the neuronal activity of separate brain regions [6, 12] and is typically measured noninvasively via either functional MRI, electro- or magnetoencephalography (fMRI, EEG and MEG, respectively) [13]
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