Functional brain networks develop from a "local to distributed" organization

Abstract

The mature human brain is organized into a collection of specialized functional networks that flexibly interact to support various cognitive functions. Studies of development often attempt to identify the organizing principles that guide the maturation of these functional networks. In this report, we combine resting state functional connectivity MRI (rs-fcMRI), graph analysis, community detection, and spring-embedding visualization techniques to analyze four separate networks defined in earlier studies. As we have previously reported, we find, across development, a trend toward 'segregation' (a general decrease in correlation strength) between regions close in anatomical space and 'integration' (an increased correlation strength) between selected regions distant in space. The generalization of these earlier trends across multiple networks suggests that this is a general developmental principle for changes in functional connectivity that would extend to large-scale graph theoretic analyses of large-scale brain networks. Communities in children are predominantly arranged by anatomical proximity, while communities in adults predominantly reflect functional relationships, as defined from adult fMRI studies. In sum, over development, the organization of multiple functional networks shifts from a local anatomical emphasis in children to a more "distributed" architecture in young adults. We argue that this "local to distributed" developmental characterization has important implications for understanding the development of neural systems underlying cognition. Further, graph metrics (e.g., clustering coefficients and average path lengths) are similar in child and adult graphs, with both showing "small-world"-like properties, while community detection by modularity optimization reveals stable communities within the graphs that are clearly different between young children and young adults. These observations suggest that early school age children and adults both have relatively efficient systems that may solve similar information processing problems in divergent ways.

Figure 1. Anatomical location of regions shown in Table 1.

Regions are colored by network membership (red – default mode network; black – cingulo-opercular network; yellow – fronto-parietal network; blue – cerebellar network) and shown on an inflated cortical surface represention.

Figure 2. Over age the graph architecture matures from a “local” organization to a “distributed” organization.

In this figure we show the dynamic development and interaction of positive correlations between the two task control networks, the default network, and cerebellar network using spring embedding. The figure highlights the segregation of local, anatomically clustered regions and the integration of functional networks over development. A and B represent individual screen shots (at average ages 8.48, 13.21, and 25.48 years) of dynamic movies (Video S1) of the transition in the network architecture from child to adult ages. Nodes are color coded by their adult network profile (core of the nodes) and also by their anatomical location (node outlines). Black – cingulo-opercular network; Yellow – fronto-parietal network; Red – default network; Blue – cerebellar network; Light blue – frontal cortex; Grey – parietal cortex; Green - temporal cortex, Pink – cerebellum, Light pink – thalamus. Connections with r≥0.1 were considered connected. (A) In children regions are largely organized by their anatomical location, but over age anatomically clustered regions segregate. The cluster of frontal regions (highlighted in light blue) best demonstrates this segregation. (B) In children the more distributed adult functional networks are in many ways disconnected. Over development the functional networks integrate. The isolated regions of the default mode network in childhood (highlighted in light red) that coalesce into a highly correlated network best illustrate this integration. Over age node organization shifts from the “local” arrangement in children to the “distributed” organization commonly observed in adults.

Figure 3. Modularity and ‘small world’ topology remain constant over age.

In this figure a modularity optimization algorithm is applied, and average clustering coefficients and average path lengths are calculated for each average matrix of the ‘sliding boxcar’ across age (see Materials and Methods). A threshold of r≥0.1 was applied to the matrices before calculations were performed and denotes connected versus non-connected region pairs (see Materials and Methods). (A) From childhood through adulthood modularity (Q) remains high and constant. This result is not dependent on a specific threshold as shown in Figure S1. (Note: All age graphs to the right the asterisk show 100% graph connectedness, meaning there is a path between every node in the network. Graphs to the left of the asterisk are 78% graph connected, on average. For details see Materials and Methods and Figure S1). (B) Relative to equivalent lattice and random networks, average clustering coefficients remain high across age and do not appear to be different between children and adults. (C) Relative to equivalent lattice and random networks, average path lengths remain low across age and do not appear to be different between children and adults. High clustering coefficients and short path lengths suggest a ‘small world’ organization that does not change across the age range studied here. 95% confidence intervals are also plotted for clustering coefficients and path lengths for the generated random graphs.

Figure 4. Despite high modularity in both children and adults, community assignments change over age.

As in Figure 3, a modularity algorithm was applied to each matrix of the sliding boxcar across age (A) and with varying thresholds (B, C). Region legends are color coded by anatomy on the left and by adult functional network on the right (colors match Figure 2). (A) The left side of the box represents the community assignments for the youngest subjects (i.e., subjects 1–60), and the right side of the box represents the community assignments for the oldest subjects (i.e., subjects 151–210) - an age scale is presented at the top. As can be seen in the left of panel A, the modularity algorithm divided regions into communities arranged by anatomical proximity. Over age this organization transitions into modules arranged by adult functional properties. For this central panel a threshold of r≥0.1 was used to denote connected versus non-connected region pairs. (B) Community assignments of the youngest boxcar (subjects 1–60), at thresholds ranging from 0 to 0.20. Regardless of threshold regions are largely organized by anatomical proximity in this youngest age group. (C) Community assignments of the oldest boxcar (subjects 151–210), at thresholds ranging from 0 to 0.20. Regardless of threshold regions are largely organized by adult function in this oldest group.

Figure 5. The “local to distributed” maturation is supported by a general decrease in functional connections between regions close in space, an increase in functional connection between regions distant in space, and the maintenance of several short and long-range connections that do not change with age.

In this figure, functional connections are divided based on distance. Short-range functional connections are in (A,B), long-range functional connections (C,D) (y-axis, adult r-values; x-axis child r-values). Warm colors represent functional connections that are significantly greater in adults than children. Cool colors represent functional connections that are significantly greater in children than adults. Functional connections that do not significantly change with age are plotted in grey. As can be seen in (A,B), the majority of short-range functional connections that significantly change with age tend to decrease. The majority of long-range functional connections (C,D) that significantly change with age increase over time. However, many long and short-range functional connections do not significantly change over age (grey). In addition, while few, some long and short-range functional connections go against the general trend of short-range connections “growing down” and long-range functional connections “growing up.” See Figure S2 for an extended version of this figure, which includes a visualization of these functional connections on a semi-transparent brain.