Abstract
Functional brain connectivity is the co-occurrence of brain activity in different areas during resting and while doing tasks. The data of interest are multivariate timeseries measured simultaneously across brain parcels using resting-state fMRI (rfMRI). We analyze functional connectivity using two heteroscedasticity models. Our first model is low-dimensional and scales linearly in the number of brain parcels. Our second model scales quadratically. We apply both models to data from the Human Connectome Project (HCP) comparing connectivity between short and conventional sleepers. We find stronger functional connectivity in short than conventional sleepers in brain areas consistent with previous findings. This might be due to subjects falling asleep in the scanner. Consequently, we recommend the inclusion of average sleep duration as a covariate to remove unwanted variation in rfMRI studies. A power analysis using the HCP data shows that a sample size of 40 detects 50% of the connectivity at a false discovery rate of 20%. We provide implementations using R and the probabilistic programming language Stan.
Highlights
Functional connectivity focuses on the exploration of neurophysiological measures of brain activity between brain regions (Friston, 2011; Smith, 2012; Varoquaux and Craddock, 2013)
The Human Connectome Project (HCP) released a dataset with 820 timeseries of normal healthy subjects measured during resting-state fMRI
We introduced two new models for functional connectivity
Summary
Functional connectivity focuses on the exploration of neurophysiological measures of brain activity between brain regions (Friston, 2011; Smith, 2012; Varoquaux and Craddock, 2013). Functional connectivity is the problem of estimating covariance matrices, precision matrices, or correlation matrices from timeseries data. These matrices encode the level of connectivity between any two brain regions. More elaborate estimators need to be employed, such as Models for Functional Connectivity the Graphical Lasso (Friedman et al, 2008) estimator for inversecovariance matrices or the Ledoit-Wolf shrinkage estimator (Ledoit and Wolf, 2004) for correlation matrices Application of these methods to rfMRI are available (Varoquaux et al, 2010a,b; Smith et al, 2011; Ryali et al, 2012; Varoquaux et al, 2012; Liang et al, 2016)
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