Abstract
Connectome mapping using techniques such as functional magnetic resonance imaging (fMRI) has become a focus of systems neuroscience. There remain many statistical challenges in analysis of functional connectivity and network architecture from BOLD fMRI multivariate time series. One key statistic for any time series is its (effective) degrees of freedom, df, which will generally be less than the number of time points (or nominal degrees of freedom, N). If we know the df, then probabilistic inference on other fMRI statistics, such as the correlation between two voxel or regional time series, is feasible. However, we currently lack good estimators of df in fMRI time series, especially after the degrees of freedom of the “raw” data have been modified substantially by denoising algorithms for head movement. Here, we used a wavelet-based method both to denoise fMRI data and to estimate the (effective) df of the denoised process. We show that seed voxel correlations corrected for locally variable df could be tested for false positive connectivity with better control over Type I error and greater specificity of anatomical mapping than probabilistic connectivity maps using the nominal degrees of freedom. We also show that wavelet despiked statistics can be used to estimate all pairwise correlations between a set of regional nodes, assign a P value to each edge, and then iteratively add edges to the graph in order of increasing P. These probabilistically thresholded graphs are likely more robust to regional variation in head movement effects than comparable graphs constructed by thresholding correlations. Finally, we show that time-windowed estimates of df can be used for probabilistic connectivity testing or dynamic network analysis so that apparent changes in the functional connectome are appropriately corrected for the effects of transient noise bursts. Wavelet despiking is both an algorithm for fMRI time series denoising and an estimator of the (effective) df of denoised fMRI time series. Accurate estimation of df offers many potential advantages for probabilistically thresholding functional connectivity and network statistics tested in the context of spatially variant and non-stationary noise. Code for wavelet despiking, seed correlational testing and probabilistic graph construction is freely available to download as part of the BrainWavelet Toolbox at www.brainwavelet.org.
Highlights
Connectome mapping has become a major focus of neuroscience research in the last few years
In a previous paper (Patel et al, 2014), we described a new wavelet-based method for denoising motion artifacts from resting-state functional MRI (fMRI) time series, which we called “wavelet despiking”
In order to threshold these maps by an FDR-adjusted P value, we first needed an estimate of the degrees of freedom
Summary
Connectome mapping has become a major focus of neuroscience research in the last few years. Functional mapping techniques, such as functional MRI (fMRI), are among the most commonly used tools for investigating the network architecture of the brain. We are currently somewhat limited in our ability to use probabilistic reasoning to test estimates of functional connectivity – such as the correlation between two fMRI times series – against an appropriate null hypothesis with good control over Type I error rates. ⁎ Corresponding author at: Brain Mapping Unit, Behavioral and Clinical Neuroscience. Sir William Hardy Building, Downing Site, University of Cambridge, CB2 3EB, UK. To illustrate our new methods for statistical inference, we used 3 cohorts.
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