Statistical Brain Network Analysis

Abstract

The recent fusion of network science and neuroscience has catalyzed a paradigm shift in how we study the brain and led to the field of brain network analysis. Brain network analyses hold great potential in helping us understand normal and abnormal brain function by providing profound clinical insight into links between system-level properties and health and behavioral outcomes. Nonetheless, methods for statistically analyzing networks at the group and individual levels have lagged behind. We have attempted to address this need by developing three complementary statistical frameworks-a mixed modeling framework, a distance regression framework, and a hidden semi-Markov modeling framework. These tools serve as synergistic fusions of statistical approaches with network science methods, providing needed analytic foundations for whole-brain network data. Here we delineate these approaches, briefly survey related tools, and discuss potential future avenues of research. We hope this review catalyzes further statistical interest and methodological development in the field.

Keywords: connectivity; connectomics; graphs; network neuroscience; neuroimaging; statistical models.

Figure 1

Schematic for generating static and dynamic brain networks from fMRI time-series data, adapted with permission from Tomlinson et al. (2022b) and Bahrami et al. (2022a). (a) Functional connectivity between brain areas is estimated based on average association of time-series pairs during the entire scanning time to produce a single connection matrix. (b) Time series are first filtered and prewhitened to remove artifacts and address autocorrelation (Honari et al. 2019). Then, using a sliding-window correlation approach, functional connectivity between brain areas is estimated between all time-series pairs at each shift to produce a connection matrix at that shift. By moving the window across the entire length of the time series, a series of dynamic connection matrices is produced for each participant. For both static and dynamic networks, a threshold is often applied to the matrix to remove negative connections. Abbreviations: fMRI, functional magnetic resonance imaging; ROI, region of interest.

Figure 2

Modeling a set of time-varying brain networks as a function of endogenous (network measures) and exogenous variables of interest (age, gender, disease status, etc.).

Figure 3

Visualization of differences in DMN organization between FW and NFW (a) and associations between childhood pesticide exposure and DMN organization in FW (b). Brain networks of FW with high exposure in panel $b$ are similar to the brain networks of FW in panel $a$, and the brain networks of FW with low exposure are similar to the brain networks of NFW in panel $a$. This shows the contribution of childhood exposure to pesticides to the differences observed between FW and NFW. Adapted with permission from Bahrami et al. (2022b). Abbreviations: DMN, default mode network; FW, farmworkers; NFW, nonfarmworkers.

Figure 4

Diagram of important differences found between the brain networks in young and older adults when comparing their visual-state to resting-state networks. The nodes represent brain regions, the edge thickness represents the strength of functional connections between them, and the node color indicates the module membership. Young adults’ brains shift to a functional architecture comprising a resilient core of interconnected high-degree/high-strength/globally efficient hubs without increasing wiring cost, by minimizing intermodule connectivity, when comparing their visual-state to resting-state networks. This shift does not occur for older adults, and furthermore, their wiring cost increases (i.e., their networks become more densely connected with random connections). Adapted with permission from Simpson et al. (2019).

Figure 5

Diagram of the effect of fluid intelligence on the relationship between modularity and dynamic connectivity. The nodes represent brain regions, and edges represent dynamic functional connections. Three communities are marked with separate colors: dark red, light blue, and purple. The within- and between-community connections are shown in yellow and black, respectively. Fluctuations in modularity are predominantly determined by between-community connections in individuals with lower intelligence scores. In participants with higher intelligence scores, fluctuations in modularity are less determined by between-community connections (thicker dark edges in top right network) and more determined by within-community connections (thicker yellow edges in top right network). Intelligence score was modeled as a continuous variable, but for illustrative purposes we show higher and lower intelligence score levels. Adapted with permission from Bahrami et al. (2022a).

Figure 6

WFU_MMNET main starting (left) and statistical modeling (right) GUIs. Modeling is done in two main steps. In the first step, using imaging data files (and atlas files), initial modeling files are constructed through the Network_Model GUI (not shown). In the second step, using generated files from the first step, final modeling files are generated, and the statistical models are fitted. The second step is done through the Statistical_Model GUI that interfaces with SAS, R, and Python. Abbreviation: GUI, graphical user interface.

Figure 7

Power results for Simulation 1. Abbreviations: GLS, feasible generalized least squares; ILE, individual-level fixed effects; MDMR, multivariate distance matrix regression. Adapted with permission from Tomlinson et al. (2022b).

Figure 8

Maps showing the location of network hubs (top 20% degree) in each group. The top of each panel shows the sagittal view and the bottom shows the axial view. Adapted with permission from Tomlinson et al. (2022b).

Figure 9

Results for the Task 1 simulation. Black horizontal lines are shown at 5% and 80% for aid in referencing type I error (age and sex) and power (IQ and treatment), respectively. Abbreviations: 3M_BANTOR, Mixed Model for Multitask (and multisession) BrAin NeTwOrk Regression; EUC, Euclidean distance; JD, Jaccard distance; KS, Kolmogorov–Smirnov; LERM, log-Euclidean Riemannian metric; MDMR, multivariate distance matrix regression; PCD, Pearson correlation distance; SLE, scan-level fixed effects. Adapted with permission from Tomlinson et al. (2022a).

Figure 10

A subset of results from a simulation study. The HSMM (top right) more accurately estimates true sojourn time distributions (top left) than the standard HMM (bottom left) and sliding-window analysis (bottom right). Abbreviations: HMM, hidden Markov model; HSMM, hidden semi-Markov model. Adapted with permission from Shappell et al. (2019).

Figure 11

(Left column) Estimated sojourn distributions of the ADHD and TD groups for two states that revealed statistically significant group differences (p-values < 0.05). (Right column) Pearson correlation matrices for both network states. Abbreviations: ADHD, attention-deficit/hyperactivity disorder; DAN, dorsal attention network; DMN, default mode network; FP, frontoparietal; SAL/VAN, salience/ventral attention network; SM, somatomotor; TD, typically developing. Adapted with permission from Shappell et al. (2021).