Conceived and designed the experiments: DAF ALC BLS SEP. Performed the experiments: DAF ALC JDP. Analyzed the data: DAF ALC JDP. Contributed reagents/materials/analysis tools: DAF ALC JDP NUFD JAC FMM BLS SEP. Wrote the paper: DAF ALC JDP BLS SEP.
The authors have declared that no competing interests exist.
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.
The first two decades of life represent a period of extraordinary developmental change in sensory, motor, and cognitive abilities. One of the ultimate goals of developmental cognitive neuroscience is to link the complex behavioral milestones that occur throughout this time period with the equally intricate functional and structural changes of the underlying neural substrate. Achieving this goal would not only give us a deeper understanding of normal development but also a richer insight into the nature of developmental disorders. In this report, we use computational analyses, in combination with a recently developed MRI technique that measures spontaneous brain activity, to help us to understand the principles that guide the maturation of the human brain. We find that brain regions in children communicate with other regions more locally but that over age communication becomes more distributed. Interestingly, the efficiency of communication in children (measured as a ‘small world’ network) is comparable to that of the adult. We argue that these findings have important implications for understanding both the maturation and the function of neural systems in typical and atypical development.
The mature human brain is both structurally and functionally specialized, such that discrete areas of the cerebral cortex perform distinct types of information processing. These areas are organized into 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.
A major portion of the work investigating the nature of functional human brain development is based on results from functional magnetic resonance imaging (fMRI) studies. By examining the differences in the fMRI activation profile of a particular brain region between children, adolescents, and adults, the developmental trajectory of that region's involvement in a cognitive task can be outlined
In addition to fMRI activation studies, the relatively new and increasingly utilized method of resting state functional connectivity MRI (rs-fcMRI) allows for a complementary examination of the functional relationships between regions across development. Resting state fcMRI is based on the discovery that spontaneous low-frequency (<∼0.1 Hz) blood oxygen level dependent (BOLD) signal fluctuations in sometimes distant, but functionally-related grey matter regions, show strong correlations at rest
In addition, because rs-fcMRI does not require active engagement in a behavioral task, it unburdens experimental design, subject compliance, and training demands. Thus, rs-fcMRI is becoming a frequently used tool for examining changes in network structure in disease
In previous work regarding task-level control in adults, we applied rs-fcMRI to a set of regions derived from an fMRI meta-analysis that included studies of control-demanding tasks. This analysis revealed that brain regions exhibiting different combinations of control signals across many tasks are grouped into distinct “fronto-parietal” and “cingulo-opercular” functional networks
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.
Regions of Interest (ROI) | ROI Abbreviations | Coordinates | Functional Network | Network Color | ||
dorsolateral prefrontal cortex | dlPFC | −43 | 22 | 34 | Fronto_Parietal | Yellow |
dorsolateral prefrontal cortex | dlPFC | 43 | 22 | 34 | Fronto_Parietal | Yellow |
Frontal | frontal | −41 | 3 | 36 | Fronto_Parietal | Yellow |
Frontal | frontal | 41 | 3 | 36 | Fronto_Parietal | Yellow |
mid cingulate cortex | mCC | 0 | −29 | 30 | Fronto_Parietal | Yellow |
inferior parietal lobule | IPL | −51 | −51 | 36 | Fronto_Parietal | Yellow |
inferior parietal lobule | IPL | 51 | −47 | 42 | Fronto_Parietal | Yellow |
intraparietal sulcus | IPS | −31 | −59 | 42 | Fronto_Parietal | Yellow |
intraparietal sulcus | IPS | 30 | −61 | 39 | Fronto_Parietal | Yellow |
Precuneus | Precun | −9 | −72 | 37 | Fronto_Parietal | Yellow |
Precuneus | Precun | 10 | −69 | 39 | Fronto_Parietal | Yellow |
anterior Prefrontal Cortex | aPFC | −28 | 51 | 15 | Cingulo_Opercular | Black |
anterior Prefrontal Cortex | aPFC | 27 | 50 | 23 | Cingulo_Opercular | Black |
anterior insula/frontal operculum | aI/fO | −35 | 14 | 5 | Cingulo_Opercular | Black |
anterior insula/frontal operculum | aI/fO | 36 | 16 | 4 | Cingulo_Opercular | Black |
dorsal anterior cingulate/medial superior frontal cortex | dACC/msFC | −1 | 10 | 46 | Cingulo_Opercular | Black |
superior frontal cortex | ant thal | −12 | −15 | 7 | Cingulo_Opercular | Black |
anterior thalamus | ant thal | 10 | −15 | 8 | Cingulo_Opercular | Black |
anterior thalamus | amPFC | 1 | 54 | 21 | Default | Red |
ventromedial prefrontal cortex | vmPFC | −3 | 39 | −2 | Default | Red |
superior frontal cortex | sup frontal | −14 | 38 | 52 | Default | Red |
superior frontal cortex | sup frontal | 17 | 37 | 52 | Default | Red |
inferior temporal | inf templ | −61 | −33 | −15 | Default | Red |
inferior temporal | inf templ | 65 | −17 | −15 | Default | Red |
parahippocampal | parahippo | −22 | −26 | −16 | Default | Red |
parahippocampal | parahippo | 25 | −26 | −14 | Default | Red |
posterior cingulate cortex | pCC | −2 | −36 | 37 | Default | Red |
lateral parietal | latP | −47 | −67 | 36 | Default | Red |
lateral parietal | latP | 53 | −67 | 36 | Default | Red |
retro splenial | retro splen | 3 | −51 | 8 | Default | Red |
lateral cerebellum | lat cereb | −32 | −66 | −29 | Cerebellar | Blue |
lateral cerebellum | lat cereb | 31 | −61 | −29 | Cerebellar | Blue |
inferior cerebellum | inf cereb | −19 | −78 | −33 | Cerebellar | Blue |
inferior cerebellum | inf cereb | 18 | −80 | −33 | Cerebellar | Blue |
Along with these two task control networks
Another functional network, and one of the most prominent sets of regions to be examined with rs-fcMRI, is the “default mode network”. The default mode network (frequently described as being composed of the bilateral posterior cingulate/precuneus, inferior parietal cortex, and ventromedial prefrontal cortex) was first characterized by a consistent decrease in activity during goal-directed tasks compared to baseline
In two prior developmental studies, we used rs-fcMRI to examine the development of the task control and cerebellar functional networks
The development of the default mode network was independently examined in a separate analysis
The observation that different analyses suggested different developmental features suggests a need for a more nuanced and integrated characterization of the development of functional networks. The goal of this manuscript is to employ several different network analysis tools to provide such a characterization. Visualization techniques such as spring embedding, and quantitative measures, including ‘small world’ metrics and community detection algorithms, will be applied to these networks in an attempt to identify principles for the changes observed across development.
Because of the overlapping and sometimes inconsistent use of terminology between neuroscience and the computational sciences, we will briefly define two terms for the purposes of this paper. The term “networks” will be used in the typical cognitive neuroscience formulation: a group of functionally related brain regions (as described above). The overall collection of regions (encompassing all four “networks”) will be referred to as the “graph.”
Graph theory analyses were applied to 210 subjects, aged 7–31, to investigate the emergence of temporal correlations in spontaneous BOLD activity between regions of the default mode, cerebellar, and two task-control networks. For this initial analysis, average age-group matrices were created using a sliding boxcar grouping of subjects in age-order (i.e., group1: subjects 1–60, group2: subjects 2–61, group3: subjects 3–62, etc.). This generated a series of groups with average ages ranging from 8.48 years to 25.58 years. Each of the groups' average correlation matrices was converted into a graph, with correlations between regions greater than or equal to 0.1 considered as functionally connected.
In a first analysis, we used a visualization algorithm commonly used in graph theoretic analyses known as spring embedding that aids in the qualitative interpretation of graphs (
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 (
By creating spring embedded graphs for each of the sliding boxcar groups in age-order, a movie representation can be made that shows the development of the network relationships (from average age 8.48 to 25.48 years) (
One of the primary observations from the movie relates to this anatomical-functional distinction. In children, regions appear to be largely arranged by anatomical proximity. This arrangement can be seen in
A group of regions in the frontal cortex provides a particularly salient example of segregation. Frontal cortex contains regions that, in adults, are members of each of the task-control networks (e.g., dlPFC, frontal, dACC/msFC) and the default network (e.g., vmPFC, amPFC). As can be seen in
Accompanying this segregation is strong integration within the functional networks. The default mode network provides the clearest example. As illustrated in
The qualitative observations noted above can be quantified using community structure detection tools. Using such an approach is particularly important because of the bias inherent in relying on qualitative methods for deciding whether groups of regions that appear to be clustered are indeed clustered, and because of the
“A good division of a graph into communities is not merely one in which there are few edges between communities; it is one in which there are fewer than expected edges between communities. If the number of edges between two groups is only what one would expect on the basis of random chance, then few thoughtful observers would claim this constitutes evidence of meaningful community structure. On the other hand, if the number of edges between groups is significantly less than we expect by chance, or equivalently if the number within groups is significantly more, then it is reasonable to conclude that something interesting is going on
Among the many methods used to detect communities in graphs, the modularity optimization algorithm of Newman is one of the most efficient and accurate to date
Measures of modularity (Q) were high, and did not show large changes across the age range (
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
As in
As previously reported
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
However, there are some interesting nuances to this trend that deserve mention. For instance, not all short-range functional connections decrease in strength over age (
In a seminal 1998 paper, Watts and Strogatz noted that the topology of many complex systems can be described as “small world”, a type of graph architecture that efficiently permits both local and distributed processing. Graphs with a regular, lattice-like structure have abundant short-range connections, but no long-range connections. Local interactions are thus efficient, but distributed processes involving distant nodes require the traversal of many intermediate connections. Conversely, completely randomly connected graphs are fairly efficient at transferring distant or long-range signals across a network, but they are poor at local, short-range information transfer.
Watts and Strogatz, and others, often describe “small world” properties with two metrics: the average clustering coefficient and average path length of a graph. The clustering coefficient measures how well connected the neighbors of a node are to one another. The average path length measures the average minimum number of steps needed to go between any two nodes. Lattices, optimized for local processes, have high average clustering coefficients but long average path lengths. Conversely, random graphs, which have no preference for short-range connections, have low average clustering coefficients
As previously reported
The combination of graph theoretic analyses and rs-fcMRI allowed for the examination of the dynamic relationships between multiple networks over development. In the current manuscript, we examined four networks - the cingulo-opercular, fronto-parietal, cerebellar, and default mode networks. As illustrated by qualitative observations in
In the following section, these results are discussed considering two postulates: (1) the temporal pattern of spontaneous activity measured by rs-fcMRI represents a history of repeated co-activation between regions, and (2) the brain attempts to use the most efficient processing pathways available when faced with specific processing demands.
As early as 1875 spontaneous synchronized neural activity has been used to study various aspects of adult brain organization
If we consider the previously mentioned postulates, our results suggest that, typically, the most efficient way for children to respond to processing demands is to utilize more “local” level interactions as compared to adulthood. That is, in childhood there is, relatively greater co-activation of anatomically proximal regions than for adults with similar processing demands. A clear example of this is seen in Brown et al.
If the correlations we find in children already represent 7 years of experience-driven tuning, why should additional experience lead to a distributed solution? Under the current proposal, it is not clear then why resting state functional connectivity would change so dramatically over the reported age range. One could argue that the general experiential environment and processing demands systematically change to encourage increasing use of long-range, distributed processing relationships. We believe, however, that at least part of the explanation lies in the interaction of these “environmental demands” with maturational changes of the neural substrate.
By approximately 9 months of age the elaboration of most, if not all, short and long-range axonal connections between brain regions is thought to be complete
Another commonly referenced postnatal event is myelination. As with synaptic pruning, myelination continues to occur through young adulthood. Increased myelination is thought to proceed from primary sensory and motor regions to association areas
Considering the continually changing nature of the neural substrate over development, a context for changes in rs-fcMRI can be created. For instance, as previously mentioned, increased signal propagation through the addition of a myelin sheath likely allows for more efficient communication between distant regions
In other words, as myelination continues through development and allows for more effective long-distance neural pathways, repeated co-activation becomes more prevalent between many distant regions, and less so between many locally aligned regions, thus changing synaptic efficiencies. The statistical histories of such interactions, stored as relative synaptic weights, are then revealed via rs-fcMRI, and would lead to the “local to distributed” organization principle seen here.
It is important to note, however, that improved communication between distant regions (via myelination) would not necessarily cause a wholesale decrease in connections that were originally organized locally. Many of these local connections likely continue to contribute to the most efficient “solution” for any particular task and remain in use. In fact, the change in dynamics may actually contribute to distinct local connections increasing with time. This possibility may underlie the increases in strength of specific short-range connections seen in
Along the same lines, as Fuster
We note that recent results in the aging literature suggest that many of the trajectories observed in the current manuscript continue inversely with advancing age
The “local to distributed” organizing principle resonates with recent suggestions that perceptual and cognitive development involve the simultaneous segregation and integration of information processing streams
Interactive specialization predicts that shortly after birth, large sets of regions and pathways will be partially active during specific task conditions, However, as these pathways interact and compete with each other throughout development, selected regions will come online, be maintained, or become selectively activated or “tuned” as particular pathways dominate for specific task demands. Thus, regional specialization relies on the evolving and continuous interactions with other brain regions over development. If one extends this framework to the network level, the increases, decreases, and maintenance of correlation strengths seen between regions may reflect “specialization” of specific neural pathways to form the functional networks seen in adults.
The “local to distributed” developmental trajectory, discussed above, seems to be driven by an abundance of local, short range connections that generally decrease in strength over age as well as distant, long range connections that generally increase in strength over age. Given the more prevalent short-range connections in children, we expected a more lattice-like structure, with high clustering coefficients and relatively high path lengths. The results, however, clearly indicated that path lengths were near those of equivalent random graphs, and that the child functional networks are already organized as small world networks.
This result can be explained in the context of the re-wiring procedure discussed by Watts and Strogatz
While we identified small world properties in both child and adult graphs, the size of the graph is relatively small with only 34 nodes. Therefore, it is possible that with an increased number of nodes the specific results identified here will change, a possibility that will be addressed in further studies.
The regions used in the present analyses were all derived from adult imaging studies. It seems likely that additional regions may be included in one or more of these networks in childhood. In addition, individual differences with regards to the regions and networks chosen likely exist. Future work that includes regions derived from studies using a child population and obtaining the functional connections within subjects from individually defined functional areas may refine the networks and developmental timecourses presented here
Of note, resting-state functional connectivity has been reported to be constrained by anatomical distance (i.e., correlations between regions decrease as a function of distance following an inverse square law)
A limitation of rs-fcMRI in general is the restricted frequency distribution that can be examined. rs-fcMRI is used to measure correlations in a very low frequency range, typically below 0.1 Hz. Dynamic changes in correlations in other frequency distributions could exist (for example see
Nonetheless, the general results presented here represent a strong set of hypotheses to be tested in broader domains and larger-scale brain graphs. First, that by age 8 years, regional relationships, as defined by rs-fcMRI, are organized as small-world-like networks, which, relative to adults, emphasize local connections. Second, that for the same regions, adult networks show similar network metrics but with regional relationships that have a longer-range, more distributed structure reflecting adult functional histories. In other words, the modular structure of large-scale brain networks will change with age, but even school age children will show relatively efficient processing architecture.
Subjects were recruited from Washington University and the local community. Participants were screened with a questionnaire to ensure that they had no history of neurological/psychiatric diagnoses or drug abuse. Informed consent was obtained from all subjects in accordance with the guidelines and approval of the Washington University Human Studies Committee.
fMRI data were acquired on a Siemens 1.5 Tesla MAGNETOM Vision system (Erlangen, Germany). Structural images were obtained using a sagittal magnetization-prepared rapid gradient echo (MP-RAGE) three-dimensional T1-weighted sequence (TE = 4 ms, TR = 9.7 ms, TI = 300 ms, flip angle = 12 deg, 128 slices with 1.25×1×1 mm voxels). Functional images were obtained using an asymmetric spin echo echo-planar sequence sensitive to blood oxygen level-dependent (BOLD) contrast (volume TR = 2.5 sec, T2* evolution time = 50 ms, α = 90°, in-plane resolution 3.75×3.75 mm). Whole brain coverage was obtained with 16 contiguous interleaved 8 mm axial slices acquired parallel to the plane transecting the anterior and posterior commissure (AC-PC plane). Steady state magnetization was assumed after 4 frames (∼10 s).
Functional images were first processed to reduce artifacts
For rs-fcMRI analyses as previously described
Resting state (fixation) data from 210 subjects (66 aged 7–9; 53 aged 10–15; 91 aged 19–31) were included in the analyses. For each subject at least 555 seconds (9.25 minutes) of resting state BOLD data were collected. 34 previously published regions comprising 4 functional networks (i.e., cingulo-opercular, fronto-parietal, cerebellar, and default networks; see
To examine the functional connections within and between the large set of regions used in this manuscript we chose to use graph theory. Graph theory is particularly well suited to study large-scale systems organization across development, but requires the data be organized into specific correlation matrices. To do this, for each of the 210 subjects, the resting state BOLD timeseries from each region was correlated with the timeseries from every other region, creating 210 square correlation matrices (34×34). Average group matrices were then created using a sliding boxcar grouping of subjects in age-order (i.e., group1: subjects 1–60, group2: subjects 2–61, group3: subjects 3–62, … group151: subjects 151–210), thus generating a series of groups with average ages ranging from 8.48 years old to 25.48 years old with each group composed of 60 subjects. Average correlation coefficients (r) for each group were generated from the subjects' individual matrices using the Schmidt-Hunter method for meta-analyses of r-values
To generate a dynamic representation of the functional connections between regions across development, each of the groups' correlation matrices was converted into a thresholded graph, such that correlations higher than r≥0.1 were considered connections, while correlations lower than the threshold were not connections.
For our initial analyses
Communities for our graph were detected with the modularity optimization method of Newman
To characterize the relationship between connection length and the change in correlation strength over development, we split all 561 possible connections into 4 groups based on vector distance. Since using vector distance as an approximate for connectional distance is much more inconsistent when comparing ROIs across the midline, only intrahemispheric connections or connections to midline structures (i.e., within 5 mm of the midline) were examined. These connections were then sorted by connection length and plotted on a graph where the x-axis corresponds to the child correlation strengths and the y-axis corresponds to the adult correlation strengths (
The small-world metrics were calculated according to descriptions by Watts and Strogatz
Modularity remains relatively high across age and does not differ between children and adults across differing thresholds. Blue dots represent modularity and red dots represent graph connectedness. A graph in which there is a path between all nodes represents 100% graph connectedness, whereas a fragmented network in which some nodes cannot reach the rest has a lower graph connectedness (see
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Scatterplot of modularity as a function of age. Each point in the graph represents the modularity calculated for each individual subject. A threshold of r≥0.1 was applied to each subject's matrices before calculations were performed and denotes connected versus non-connected region pairs (see
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Reducing the boxcar size does not substantially alter community assignments over age. The same procedure as presented in
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An extended version of
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Clustering coefficients and path lengths do not differ between children and adults across differing thresholds with respect to comparable lattice and random graphs. For children all parameters across thresholds were calculated from the first 60 subjects in age order (i.e., subjects 1–60, average age 8.48). For adults, all parameters across thresholds were calculated from the last 60 subjects in age order (i.e., subjects 151–210, average age 25.48. (A) Clustering Coefficients across thresholds for children compared to equivalent lattice and random networks. (B) Path lengths across thresholds for children compared to equivalent lattice and random graphs. (C) Clustering Coefficients across thresholds for adults compared to equivalent lattice and random graphs. (D) Path lengths across thresholds for adults compared to equivalent lattice and random graphs. At all thresholds examined, both children and adults show relatively high clustering coefficients and low path lengths, consistent with ‘small world’ topology.
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Connection strength as a function of distance for all possible connections is similar between children and adults. The relationship of correlation as a function of distance is described by the inverse square law, r∼1/D2, as reported in
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Variation of information (VOI) in observed and equivalent random networks subjected to perturbation alpha. VOI is a measure of how much information is not shared between two sets of community assignments and allows for the quantification of network robustness (see
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Over age, the graph architecture matures from a “local” organization to a “distributed” organization. This movie shows 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. This is the full movie that
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Reducing the boxcar size to 40 subjects does not change qualitative patterns observed with the 60 subject boxcar. The same procedure as presented in
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We thank Marcus Raichle, Steven M. Nelson, Alecia C. Vogel, and Adriana Hernandez for technical assistance and helpful discussions, and Mark McAvoy and Abraham Z. Snyder for help with data analysis.