Evolution of brain network dynamics in neurodevelopment

Abstract

Cognitive function evolves significantly over development, enabling flexible control of human behavior. Yet, how these functions are instantiated in spatially distributed and dynamically interacting networks, or graphs, that change in structure from childhood to adolescence is far from understood. Here we applied a novel machine-learning method to track continuously overlapping and time-varying subgraphs in the brain at rest within a sample of 200 healthy youth (ages 8-11 and 19-22) drawn from the Philadelphia Neurodevelopmental Cohort. We uncovered a set of subgraphs that capture surprisingly integrated and dynamically changing interactions among known cognitive systems. We observed that subgraphs that were highly expressed were especially transient, flexibly switching between high and low expression over time. This transience was particularly salient in a subgraph predominantly linking frontoparietal regions of the executive system, which increases in both expression and flexibility from childhood to young adulthood. Collectively, these results suggest that healthy development is accompanied by an increasing precedence of executive networks and a greater switching of the regions and interactions subserving these networks.

Keywords: Energy; Entropy; Executive function; Flexibility; Matrix factorization; Neurodevelopment; Subgraph.

Figure 1.. Schematic overview of the approach. (A) Resting-state fMRI BOLD signals were obtained from 264 functional regions of interest in cortical and subcortical areas, spanning 13 cognitive systems (Power et al., 2011). (B) Each regional BOLD signal was divided into 51 time windows, each 20 repetition times (TRs) in duration, with 90% overlap. (C) We computed the wavelet coherence between each pair of regional BOLD signals for every time window to obtain a multilayer network in which brain regions were treated as network nodes, and window-specific estimates of coherence were treated as layer-specific network edges. (D) We next unfolded the unique connections of the multilayer network and concatenated the data for all subjects (left). We then used a nonnegative matrix factorization approach, which decomposes the concatenated matrix into a matrix W of subgraphs and a matrix H of time-dependent coefficients that quantify the level of expression in each time window for each subgraph (right).

Figure 2.

Mapping of subgraphs to cognitive systems. (A) From non-negative matrix factorization, we obtained a set of ten subgraphs, each capturing a unique pattern of connections among the 264 cortical and subcortical areas that was significantly expressed during the resting-state scan. Here we show an example of computing the within-system connectivity and between-system connectivity for the visual system in the ninth subgraph. From the raw subgraph (left), the within-system connectivity is computed as the average of the edge weights between nodes within a system (e.g., visual–visual edges), and the between-system connectivity is computed as the average of the edge weights between nodes from two different systems (e.g., visual–sensory edges). This approach allows us to summarize the relationship between the subgraph structure and the cognitive systems expressed in each subgraph in a 13 × 13 matrix (right). (B). We computed the average within-system and between-system connectivities for the 13 cognitive systems in each subgraph, normalizing the color bar between 0 and 1. We then compared the connectivity in each subgraph to permuted null graphs to identify which cognitive systems were significantly expressed in each subgraph (see Methods). The significantly expressed systems are depicted in brain volume renderings (the matrices themselves are not thresholded by significance). We observed that many subgraphs are distributed in nature, capturing interactions among multiple cognitive systems (e.g., Subgraphs 1 and 2), while others are localized in nature (e.g., Subgraph 9).

Figure 3.

Energy and entropy of subgraph expression. (A) For each subgraph, we averaged the energy and entropy of the corresponding time-dependent coefficients across all subjects. We observed a high correlation between the log of subgraph energy and entropy (Pearson correlation coefficient r = 0.99, p < 0.001). The default mode subgraph (shown in green) is an interesting deviation from the trend (left). We observed an interesting trend between the localities of the subgraphs (as measured by the skewness of the subgraph strength; see Methods) and subgraph energy, suggesting that more distributed subgraphs have higher energy, and more localized subgraphs have lower energy (right). (B) Examples of a high-energy, high-entropy signal (executive); a low-energy, low-entropy signal (visual); and a high-energy, low-entropy signal (default mode) for a representative subject (left), and the cognitive systems associated with these signals (right). In general, we observed that subgraphs with high-energy, high-entropy expression patterns tended to involve multiple distributed interacting cognitive systems, while subgraphs with low-energy, low-entropy expression patterns tended to involve fewer localized cognitive systems.

Figure 4.

Age-related differences in subgraph expression. We observed significant differences between the two age groups in the standardized energy and entropy of the first subgraph, composed predominantly of regions in the frontal and parietal cortices subserving executive function (left). Standardized energy (middle) and standardized entropy (right) were both higher in the young adult group, suggesting higher levels of expression as well as a greater tendency to change expression level.