Cognitive function is driven by dynamic interactions between large-scale neural circuits or networks, enabling behaviour. However, fundamental principles constraining these dynamic network processes have remained elusive. Here we use tools from control and network theories to offer a mechanistic explanation for how the brain moves between cognitive states drawn from the network organization of white matter microstructure. Our results suggest that densely connected areas, particularly in the default mode system, facilitate the movement of the brain to many easily reachable states. Weakly connected areas, particularly in cognitive control systems, facilitate the movement of the brain to difficult-to-reach states. Areas located on the boundary between network communities, particularly in attentional control systems, facilitate the integration or segregation of diverse cognitive systems. Our results suggest that structural network differences between cognitive circuits dictate their distinct roles in controlling trajectories of brain network function.

Small-world networks, according to Watts and Strogatz, are a class of networks that are ''highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs.'' These characteristics result in networks with unique properties of regional specialization with efficient information transfer. Social networks are intuitive examples of this organization, in which cliques or clusters of friends being interconnected but each person is really only five or six people away from anyone else. Although this qualitative definition has prevailed in network science theory, in application, the standard quantitative application is to compare path length (a surrogate measure of distributed processing) and clustering (a surrogate measure of regional specialization) to an equivalent random network. It is demonstrated here that comparing network clustering to that of a random network can result in aberrant findings and that networks once thought to exhibit small-world properties may not. We propose a new small-world metric, x (omega), which compares network clustering to an equivalent lattice network and path length to a random network, as Watts and Strogatz originally described. Example networks are presented that would be interpreted as small-world when clustering is compared to a random network but are not small-world according to x. These findings have important implications in network science because small-world networks have unique topological properties, and it is critical to accurately distinguish them from networks without simultaneous high clustering and short path length.

Literature has shown that exercise is beneficial for cognitive function in older adults and that aerobic fitness is associated with increased hippocampal tissue and blood volumes. The current study used novel network science methods to shed light on the neurophysiological implications of exercise-induced changes in the hippocampus of older adults. Participants represented a volunteer subgroup of older adults that were part of either the exercise training (ET) or healthy aging educational control (HAC) treatment arms from the Seniors Health and Activity Research Program Pilot (SHARP-P) trial. Following the 4-month interventions, MRI measures of resting brain blood flow and connectivity were performed. The ET group's hippocampal cerebral blood flow (CBF) exhibited statistically significant increases compared to the HAC group. Novel whole-brain network connectivity analyses showed greater connectivity in the hippocampi of the ET participants compared to HAC. Furthermore, the hippocampus was consistently shown to be within the same network neighborhood (module) as the anterior cingulate cortex only within the ET group. Thus, within the ET group, the hippocampus and anterior cingulate were highly interconnected and localized to the same network neighborhood. This project shows the power of network science to investigate potential mechanisms for exercise-induced benefits to the brain in older adults. We show a link between neurological network features and CBF, and it is possible that this alteration of functional brain networks may lead to the known improvement in cognitive function among older adults following exercise.

Although graph theory has been around since the 18th century, the field of network science is more recent and continues to gain popularity, particularly in the field of neuroimaging. The field was propelled forward when Watts and Strogatz introduced their small-world network model, which described a network that provided regional specialization with efficient global information transfer. This model is appealing to the study of brain connectivity, as the brain can be viewed as a system with various interacting regions that produce complex behaviors. In practice, graph metrics such as clustering coefficient, path length, and efficiency measures are often used to characterize system properties. Centrality metrics such as degree, betweenness, closeness, and eigenvector centrality determine critical areas within the network. Community structure is also essential for understanding network organization and topology. Network science has led to a paradigm shift in the neuroscientific community, but it should be viewed as more than a simple ''tool du jour.'' To fully appreciate the utility of network science, a greater understanding of how network models apply to the brain is needed. An integrated appraisal of multiple network analyses should be performed to better understand network structure rather than focusing on univariate comparisons to find significant group differences; indeed, such comparisons, popular with traditional functional magnetic resonance imaging analyses, are arguably no longer relevant with graph-theory based approaches. These methods necessitate a philosophical shift toward complexity science. In this context, when correctly applied and interpreted, network scientific methods have a chance to revolutionize the understanding of brain function.

Network science offers computational tools to elucidate the complex patterns of interactions evident in neuroimaging data. Recently, these tools have been used to detect dynamic changes in network connectivity that may occur at short time scales. The dynamics of fMRI connectivity, and how they differ across timescales, are far from understood. A simple way to interrogate dynamics at different timescales is to alter the size of the time window used to extract sequential (or rolling) measures of functional connectivity. Here, in n = 82 participants performing three distinct cognitive visual tasks in recognition memory and strategic attention, we subdivided regional BOLD time series into variable sized time windows and determined the impact of time window size on observed dynamics. Specifically, we applied a multilayer community detection algorithm to identify temporal communities and we calculated network flexibility to quantify changes in these communities over time. Within our frequency band of interest, large and small windows were associated with a narrow range of network flexibility values across the brain, while medium time windows were associated with a broad range of network flexibility values. Using medium time windows of size 75–100 s, we uncovered brain regions with low flexibility (considered core regions, and observed in visual and attention areas) and brain regions with high flexibility (considered periphery regions, and observed in subcortical and temporal lobe regions) via comparison to appropriate dynamic network null models. Generally, this work demonstrates the impact of time window length on observed network dynamics during task performance, offering pragmatic considerations in the choice of time window in dynamic network analysis. More broadly, this work reveals organizational principles of brain functional connectivity that are not accessible with static network approaches.

Wavelet methods are widely used to decompose fMRI, EEG, or MEG signals into time series representing neurophysiological activity in fixed frequency bands. Using these time series, one can estimate frequency-band specific functional connectivity between sensors or regions of interest, and thereby construct functional brain networks that can be examined from a graph theoretic perspective. Despite their common use, however, practical guidelines for the choice of wavelet method, filter, and length have remained largely undelineated. Here, we explicitly explore the effects of wavelet method (MODWT vs. DWT), wavelet filter (Daubechies Extremal Phase, Daubechies Least Asymmetric, and Coiflet families), and wavelet length (2 to 24)—each essential parameters in wavelet-based methods—on the estimated values of graph metrics and in their sensitivity to alterations in psychiatric disease. We observe that the MODWT method produces less variable estimates than the DWT method. We also observe that the length of the wavelet filter chosen has a greater impact on the estimated values of graph metrics than the type of wavelet chosen. Furthermore, wavelet length impacts the sensitivity of the method to detect differences between health and disease and tunes classification accuracy. Collectively, our results suggest that the choice of wavelet method and length significantly alters the reliability and sensitivity of these methods in estimating values of metrics drawn from graph theory. They furthermore demonstrate the importance of reporting the choices utilized in neuroimaging studies and support the utility of exploring wavelet parameters to maximize classification accuracy in the development of biomarkers of psychiatric disease and neurological disorders.

The reliability of graph metrics calculated in network analysis is essential to the interpretation of complex network organization. These graph metrics are used to deduce the small-world properties in networks. In this study, we investigated the test-retest reliability of graph metrics from functional magnetic resonance imaging data collected for two runs in 45 healthy older adults. Graph metrics were calculated on data for both runs and compared using intraclass correlation coefficient (ICC) statistics and Bland–Altman (BA) plots. ICC scores describe the level of absolute agreement between two measurements and provide a measure of reproducibility. For mean graph metrics, ICC scores were high for clustering coefficient (ICC = 0.86), global efficiency (ICC = 0.83), path length (ICC = 0.79), and local efficiency (ICC = 0.75); the ICC score for degree was found to be low (ICC = 0.29). ICC scores were also used to generate reproducibility maps in brain space to test voxel-wise reproducibility for unsmoothed and smoothed data. Reproducibility was uniform across the brain for global efficiency and path length, but was only high in network hubs for clustering coefficient, local efficiency, and degree. BA plots were used to test the measurement repeatability of all graph metrics. All graph metrics fell within the limits for repeatability. Together, these results suggest that with exception of degree, mean graph metrics are reproducible and suitable for clinical studies. Further exploration is warranted to better understand reproducibility across the brain on a voxel-wise basis.

Human behavior is supported by flexible neurophysiological processes that enable the fine‐scale manipulation of information across distributed neural circuits. Yet, approaches for understanding the dynamics of these circuit interactions have been limited. One promising avenue for quantifying and describing these dynamics lies in multilayer network models. Here, networks are composed of nodes (which represent brain regions) and time‐dependent edges (which represent statistical similarities in activity time series). We use this approach to examine functional connectivity measured by non‐invasive neuroimaging techniques. These multilayer network models facilitate the examination of changes in the pattern of statistical interactions between large‐scale brain regions that might facilitate behavior. In this study, we define and exercise two novel measures of network reconfiguration, and demonstrate their utility in neuroimaging data acquired as healthy adult human subjects learn a new motor skill. In particular, we identify putative functional modules in multilayer networks and characterize the degree to which nodes switch between modules. Next, we define cohesive switches, in which a set of nodes moves between modules together as a group, and we define disjoint switches, in which a single node moves between modules independently from other nodes. Together, these two concepts offer complementary yet distinct insights into the changes in functional connectivity that accompany motor learning. More generally, our work offers statistical tools that other researchers can use to better understand the reconfiguration patterns of functional connectivity over time. Hum Brain Mapp 38:4744–4759, 2017. © 2017 The Authors Human Brain Mapping Published by Wiley Periodicals, Inc.