Abstract
Functional connectomes are commonly analysed as sparse graphs, constructed by thresholding cross-correlations between regional neurophysiological signals. Thresholding generally retains the strongest edges (correlations), either by retaining edges surpassing a given absolute weight, or by constraining the edge density. The latter (more widely used) method risks inclusion of false positive edges at high edge densities and exclusion of true positive edges at low edge densities. Here we apply new wavelet-based methods, which enable construction of probabilistically-thresholded graphs controlled for type I error, to a dataset of resting-state fMRI scans of 56 patients with schizophrenia and 71 healthy controls. By thresholding connectomes to fixed edge-specific P value, we found that functional connectomes of patients with schizophrenia were more dysconnected than those of healthy controls, exhibiting a lower edge density and a higher number of (dis)connected components. Furthermore, many participants' connectomes could not be built up to the fixed edge densities commonly studied in the literature (∼5–30%), while controlling for type I error. Additionally, we showed that the topological randomisation previously reported in the schizophrenia literature is likely attributable to “non-significant” edges added when thresholding connectomes to fixed density based on correlation. Finally, by explicitly comparing connectomes thresholded by increasing P value and decreasing correlation, we showed that probabilistically thresholded connectomes show decreased randomness and increased consistency across participants. Our results have implications for future analysis of functional connectivity using graph theory, especially within datasets exhibiting heterogenous distributions of edge weights (correlations), between groups or across participants.
Highlights
Relationships between neurophysiological signals are thought to underlie communication in the brain (Fries, 2005); a complete description of such “functional connectivity” is called a functional connectome (Biswal et al, 2010)
There were no significant differences in nodal connectivity strength attributable to greater connectivity strength in participants with schizophrenia compared to healthy controls
We found that global efficiency was significantly increased in the group that contained non-significant edges compared to the group where all edges showed PFDR < 0.01, across connection densities, for both healthy controls and patients with schizophrenia (PMWU < 0.05 at 1-35% density, Pperm < 0.05 at 1% and 3-35% density; Fig. 5D)
Summary
Relationships between neurophysiological signals are thought to underlie communication in the brain (Fries, 2005); a complete description of such “functional connectivity” is called a functional connectome (Biswal et al, 2010). Functional connectomes are commonly analysed as sparse graphs, constructed by thresholding statistical associations (usually, correlations) between pairs of regional neurophysiological signals. The resulting sparse graphs can subsequently be characterised using summary measures of topological organization, indicative of features such as network integration or segregation (Rubinov and Sporns, 2010). As such measures are non-trivially dependent on the density of the underlying graph (van Wijk et al, 2010), weighted functional connectomes are traditionally thresholded to fixed edge density to enable comparisons of graphtheoretical measures across participants. While there have been recent efforts to determine a-priori thresholds (e.g. De Vico Fallani et al (2017), based on the cost-efficiency trade-off (Bullmore and Sporns, 2012)), a statistically principled framework for thresholding individual graphs and analysing brain network connectivity has been lacking
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