A mixed-modeling framework for whole-brain dynamic network analysis

Abstract

The emerging area of dynamic brain network analysis has gained considerable attention in recent years. However, development of multivariate statistical frameworks that allow for examining the associations between phenotypic traits and dynamic patterns of system-level properties of the brain, and drawing statistical inference about such associations, has largely lagged behind. To address this need we developed a mixed-modeling framework that allows for assessing the relationship between any desired phenotype and dynamic patterns of whole-brain connectivity and topology. This novel framework also allows for simulating dynamic brain networks with respect to desired covariates. Unlike current tools, which largely use data-driven methods, our model-based method enables aligning neuroscientific hypotheses with the analytic approach. We demonstrate the utility of this model in identifying the relationship between fluid intelligence and dynamic brain networks by using resting-state fMRI (rfMRI) data from 200 participants in the Human Connectome Project (HCP) study. We also demonstrate the utility of this model to simulate dynamic brain networks at both group and individual levels. To our knowledge, this approach provides the first model-based statistical method for examining dynamic patterns of system-level properties of the brain and their relationships to phenotypic traits as well as simulating dynamic brain networks.

Keywords: Dynamic brain networks; Mixed models; Multivariate; Simulation; fMRI.

Figure 1.

Dynamic brain networks as a function of endogenous and exogenous variables of interest. Dynamic patterns of brain connectivity (presence/absence and strength) is modeled as a function of (dynamic) nodal and global network metrics (e.g., clustering coefficient, global efficiency, etc.) and exogenous covariates, including phenotypes (e.g., blood measurements and brain damage) and possible confounding effects (e.g., hypertension and smoking).

Figure 2.

Schematic for generating dynamic brain networks from fMRI time series. Time series are first filtered and prewhitened to remove the undesired undershoots/overshoots in the middle as well as undesired effects of autocorrelation. 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 time series, a series of dynamic connection matrices will be produced for each participant. A threshold is applied to the matrix to remove negative connections. These networks are subsequently used for analyses.

Figure 3.

Cartoon depiction of fluid intelligence effects on dynamic brain networks. The nodes represent brain regions, and edges represent dynamic functional connections. To illustrate the effects of fluid intelligence on dynamic changes of modularity as interpreted from Table 3, three artificial communities marked with separate colors (dark red, light blue, and purple) are shown in this figure. The within- and between-community connections are shown with the yellow and black colors, respectively. As this figure illustrates, dynamic changes of modularity are predominantly determined by between-community connections for any level of intelligence (here two levels are shown: low and high). However, when comparing the more and less intelligent participants (networks on the right), in more intelligent participants, dynamic changes of modularity are less determined by between-community connections (thicker dark edges in top right), and dynamic changes of within-community connections also play more important roles in changing the modularity (thicker yellow edges in top right network). We should note that fluid intelligence was modeled as a continuous variable, but for illustrative purposes we show higher and lower intelligence levels. We have made a movie that better illustrates how dynamic patterns of whole-brain modularity are affected across a range of fluid intelligence values (Supporting Information Movie S1).

Figure 4.

Observed and simulated dynamic networks for two randomly selected participants. For each participant, two randomly selected dynamic networks (DNet #) are shown on the left, and for each dynamic network, two randomly selected simulated networks (from the 10 simulation realizations) are shown on the right. We have shown the HCP individual IDs on the left. All networks are thresholded to maintain the top 5% of strongest connections. The size and color of each node represent the degree of that node.