Abstract
This article proposes a Bayesian hierarchical mixture model to analyze functional brain connectivity where mixture components represent “positively connected” and “non-connected” brain regions. Such an approach provides a data-informed separation of reliable and spurious connections in contrast to arbitrary thresholding of a connectivity matrix. The hierarchical structure of the model allows simultaneous inferences for the entire population as well as for each individual subject. A new connectivity measure, the posterior probability of a given pair of brain regions of a specific subject to be connected given the observed correlation of regions' activity, can be computed from the model fit. The posterior probability reflects the connectivity of a pair of regions relative to the overall connectivity pattern of an individual, which is overlooked in traditional correlation analyses. This article demonstrates that using the posterior probability might diminish the effect of spurious connections on inferences, which is present when a correlation is used as a connectivity measure. In addition, simulation analyses reveal that the sparsification of the connectivity matrix using the posterior probabilities might outperform the absolute thresholding based on correlations. Therefore, we suggest that posterior probability might be a beneficial measure of connectivity compared with the correlation. The applicability of the introduced method is exemplified by a study of functional resting-state brain connectivity in older adults.
Highlights
Measures of functional connectivity characterize functional architecture of the human brain by quantifying statistical dependencies between neuronal activity in distinct brain regions (Friston, 2011; Biswal et al, 1995; Sporns, 2012; Smith et al, 2011)
In the case of functional magnetic resonance imaging, neuronal activity is indirectly measured by the blood oxygenation-level-dependent (BOLD) signal
There is still an ongoing debate about the nature of negative correlations of the BOLD signal, with some studies suggesting that negative correlations have a biological basis, and others reporting those correlations as pure artifacts of preprocessing (Fox et al, 2009; Murphy et al, 2009; Murphy and Fox, 2017)
Summary
Measures of functional connectivity characterize functional architecture of the human brain by quantifying statistical dependencies between neuronal activity in distinct brain regions (Friston, 2011; Biswal et al, 1995; Sporns, 2012; Smith et al, 2011). In the case of functional magnetic resonance imaging (fMRI), neuronal activity is indirectly measured by the blood oxygenation-level-dependent (BOLD) signal. The connectivity matrix, constructed from the correlations between all pairs of considered brain regions, includes strong positive correlations representing reliable connections, weak correlations likely representing spurious connections (e.g., noise), as well as negative correlations. A challenging step in the connectivity analyses is a sparsification of the connectivity matrix to analyze only reliable connections and to diminish the impact of the spurious connections on further inferences
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