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Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network representation involves often covert theoretical assumptions and methodological choices which affect the way networks are reconstructed from experimental data, and ultimately the resulting network properties and their interpretation. Here, we review some fundamental conceptual underpinnings and technical issues associated with brain network reconstruction, and discuss how their mutual influence concurs in clarifying the organization of brain function.

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Brain connectivity with functional magnetic resonance imaging (fMRI) is a popular approach for detecting differences between healthy and clinical populations. Before creating a functional brain network, the fMRI time series must undergo several preprocessing steps to control for artifacts and to improve data quality. However, preprocessing may affect the results in an undesirable way. Spatial smoothing, for example, is known to alter functional network structure. Yet, its effects on group-level network differences remain unknown. Here, we investigate the effects of spatial smoothing on the difference between patients and controls for two clinical conditions: autism spectrum disorder and bipolar disorder, considering fMRI data smoothed with Gaussian kernels (0-32 mm). We find that smoothing affects network differences between groups. For weighted networks, incrementing the smoothing kernel makes networks more different. For thresholded networks, larger smoothing kernels lead to more similar networks, although this depends on the network density. Smoothing also alters the effect sizes of the individual link differences. This is independent of the region of interest (ROI) size, but varies with link length. The effects of spatial smoothing are diverse, nontrivial, and difficult to predict. This has important consequences: The choice of smoothing kernel affects the observed network differences.

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The properties of functional brain networks strongly depend on how their nodes are chosen. Commonly, nodes are defined by Regions of Interest (ROIs), predetermined groupings of fMRI measurement voxels. Earlier, we demonstrated that the functional homogeneity of ROIs, captured by their spatial consistency, varies widely across ROIs in commonly used brain atlases. Here, we ask how ROIs behave as nodes of dynamic brain networks. To this end, we use two measures: spatiotemporal consistency measures changes in spatial consistency across time and network turnover quantifies the changes in the local network structure around an ROI. We find that spatial consistency varies non-uniformly in space and time, which is reflected in the variation of spatiotemporal consistency across ROIs. Furthermore, we see time-dependent changes in the network neighborhoods of the ROIs, reflected in high network turnover. Network turnover is nonuniformly distributed across ROIs: ROIs with high spatiotemporal consistency have low network turnover. Finally, we reveal that there is rich voxel-level correlation structure inside ROIs. Because the internal structure and the connectivity of ROIs vary in time, the common approach of using static node definitions may be surprisingly inaccurate. Therefore, network neuroscience would greatly benefit from node definition strategies tailored for dynamical networks.

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Graph-theoretical methods have rapidly become a standard tool in studies of the structure and function of the human brain. Whereas the structural connectome can be fairly straightforwardly mapped onto a complex network, there are more degrees of freedom in constructing networks that represent functional connections between brain areas. For functional magnetic resonance imaging (fMRI) data, such networks are typically built by aggregating the blood-oxygen-level dependent signal time series of voxels into larger entities (such as Regions of Interest in some brain atlas) and determining their connection strengths from some measure of time-series correlations. Although it is evident that the outcome must be affected by how the voxel-level time series are treated at the preprocessing stage, there is a lack of systematic studies of the effects of preprocessing on network structure. Here, we focus on the effects of spatial smoothing, a standard preprocessing method for fMRI. We apply various levels of spatial smoothing to resting-state fMRI data and measure the changes induced in functional networks. We show that the level of spatial smoothing clearly affects the degrees and other centrality measures of functional network nodes; these changes are non-uniform, systematic, and depend on the geometry of the brain. The composition of the largest connected network component is also affected in a way that artificially increases the similarity of the networks of different subjects. Our conclusion is that wherever possible, spatial smoothing should be avoided when preprocessing fMRI data for network analysis.

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The functional network approach, where fMRI BOLD time series are mapped to networks depicting functional relationships between brain areas, has opened new insights into the function of the human brain. In this approach, the choice of network nodes is of crucial importance. One option is to consider fMRI voxels as nodes. This results in a large number of nodes, making network analysis and interpretation of results challenging. A common alternative is to use predefined clusters of anatomically close voxels, Regions of Interest (ROIs). This approach assumes that voxels within ROIs are functionally similar. Because these two approaches result in different network structures, it is crucial to understand what happens to network connectivity when moving from the voxel level to the ROI level. We show that the consistency of ROIs, defined as the mean Pearson correlation coefficient between the time series of their voxels, varies widely in resting-state experimental data. Therefore the assumption of similar voxel dynamics within each ROI does not generally hold. Further, the time series of low-consistency ROIs may be highly correlated, resulting in spurious links in ROI-level networks. Based on these results, we recommend that averaging BOLD signals over anatomically defined ROIs should be carefully considered.

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BACKGROUND: Source-reconstructed magneto- and electroencephalography (M/EEG) are promising tools for investigating the human functional connectome. To reduce data, decrease noise, and obtain results directly comparable to magnetic resonance imaging (MRI), M/EEG source data can be collapsed into a cortical parcellation. For most collapsing approaches, however, it remains unclear if collapsed parcel time series accurately represent the coherent source dynamics within each parcel. NEW METHOD: We introduce a collapse-weighting-operator optimization approach that maximizes parcel fidelity, i.e., the phase correlation between original source dynamics and collapsed parcel time series, and thereby the accuracy with which the source dynamics are retained in forward and inverse modeling. RESULTS: The sparse, optimized weighting operator increased parcel fidelity 57-73% and true positive rate of interaction mapping from 0.33 to 0.84 in comparison to a non-sparse weighting approach. These improvements were robust for variable source topographies and parcellation resolutions. Critically, in real inverse-modeled MEG data, the optimized operator yielded close-to-perfect intra-parcel coherence. COMPARISON WITH EXISTING METHODS: Previous suggestions for obtaining parcel time series include averaging all source time series within each anatomical parcel or using exclusively the time series of the voxel with maximum power. These methods are sensitive to signal heterogeneity and outlier sources. The approach advanced here avoids these problems. CONCLUSIONS: The optimized operator is suitable for collapsing real source-reconstructed M/EEG data into any cortical parcellation. The enhanced time series reconstruction fidelity yields improved accuracy of subsequent analyses of both local dynamics and large-scale interaction mapping.

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Scale-free fluctuations are ubiquitous in behavioral performance and neuronal activity. In time scales from seconds to hundreds of seconds, psychophysical dynamics and the amplitude fluctuations of neuronal oscillations are governed by power-law-form long-range temporal correlations (LRTCs). In millisecond time scales, neuronal activity comprises cascade-like neuronal avalanches that exhibit power-law size and lifetime distributions. However, it remains unknown whether these neuronal scaling laws are correlated with those characterizing behavioral performance or whether neuronal LRTCs and avalanches are related. Here, we show that the neuronal scaling laws are strongly correlated both with each other and with behavioral scaling laws. We used source reconstructed magneto- and electroencephalographic recordings to characterize the dynamics of ongoing cortical activity. We found robust power-law scaling in neuronal LRTCs and avalanches in resting-state data and during the performance of audiovisual threshold stimulus detection tasks. The LRTC scaling exponents of the behavioral performance fluctuations were correlated with those of concurrent neuronal avalanches and LRTCs in anatomically identified brain systems. The behavioral exponents also were correlated with neuronal scaling laws derived from a resting-state condition and with a similar anatomical topography. Finally, despite the difference in time scales, the scaling exponents of neuronal LRTCs and avalanches were strongly correlated during both rest and task performance. Thus, long and short time-scale neuronal dynamics are related and functionally significant at the behavioral level. These data suggest that the temporal structures of human cognitive fluctuations and behavioral variability stem from the scaling laws of individual and intrinsic brain dynamics.

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