Network analysis: applications for the developing brain

Abstract

Development of the human brain follows a complex trajectory of age-specific anatomical and physiological changes. The application of network analysis provides an illuminating perspective on the dynamic interregional and global properties of this intricate and complex system. Here, we provide a critical synopsis of methods of network analysis with a focus on developing brain networks. After discussing basic concepts and approaches to network analysis, we explore the primary events of anatomical cortical development from gestation through adolescence. Upon this framework, we describe early work revealing the evolution of age-specific functional brain networks in normal neurodevelopment. Finally, we review how these relationships can be altered in disease and perhaps even rectified with treatment. While this method of description and inquiry remains in early form, there is already substantial evidence that the application of network models and analysis to understanding normal and abnormal human neural development holds tremendous promise for future discovery.

Figure 1

Example illustration of constructing functional networks from voltage signals. (A) In this simulated example, electroencephalogram (EEG) data are recorded from 2 electrodes on the scalp surface. The EEG data (black and upper gray curve) are simple sinusoids with added noise, and the lower gray trace is the middle trace shifted to the right by ~25 ms—this time advance of the EEG signal causes it to align with the top (black) trace, indicated by the vertical dashed lines. Because the 2 signals align, the cross correlation is strong enough, and we connect the 2 electrodes with an edge (black line) to form a simple 2-node network. (B) In this contrasting example, the EEG data never match, no matter the choice of time shift, and the 2-node network lacks an edge. (C) Simulated multivariate data recorded from many EEG electrodes, results in (D) a much more complicated network.

Figure 2

Two larger networks consisting of 200 nodes. (A,B) We arrange the nodes (gray) in the network as a ring, although this does not suggest a literal spatial sensor location in the “real” recording space. Each node represents an individual electrode or sensor, and each edge (black line) indicates sufficiently strong coupling between activity recorded simultaneously at 2 nodes. For such large networks, the network structure becomes much more difficult to characterize through visual inspection. (C,D) The degree distributions for each network. For the network in (A) most of the nodes have a degree near 5. For the network in (B), most of the nodes have a degree less than 5, but some nodes have a high degree (up to 35 edges).

Figure 3

An example 5-node network to illustrate 3 simple measures of network structure. (A) We label the 5-nodes (circles) with roman numerals and connect the nodes with edges (lines). The number in parentheses next to each node indicates its degree (d). (B) To determine the clustering coefficient of node ii, we first determine its nearest neighbors (the other 2 nodes in the network are grayed out). We then determine if an edge exists between these neighbors (the dotted line). Because this edge exists in (A), the 3 nodes form a triangle or cluster.

Figure 4

Dynamic sequence of gray matter maturation over the cortical surface from age 5 to 20 years, demonstrating maturation of primary motor and sensory regions before association cortices and prefrontal cortices. (Reprinted with permission from Gogtay N, Giedd JN, Lusk L, et al. Dynamic mapping of human cortical development during childhood through early adulthood. Proc Natl Acad Sci U S A. 2004;101:8174–8179. Copyright 2004 National Academy of Sciences.)

Figure 5

Observed timeline of some of the progressive and regressive structural changes present over the course of prenatal through adolescent brain development. This figure can be taken to represent the general hierarchical elaboration of forebrain neural systems where the events in primary representations anticipate those in successively more integrative regions. (Reprinted with permission from Casey BJ, Tottenham N, Liston C, Durston S. Imaging the developing brain: what have we learned about cognitive development? Trends Cogn Sci. 2005;9:104–110. Copyright 2005 Elsevier Ltd.)

Figure 6

Representative axial fractional anisotropy maps at 0, 3, 6, 9, 12, 24, 36, and 48 months. (Reprinted with permission from Hermoye L, Saint-Martin C, Cosnard G, et al. Pediatric diffusion tensor imaging: normal database and observation of the white matter maturation in early childhood. Neuroimage. 2006;29:493–504. Copyright 2006 Elsevier, Ltd.)

Figure 7

Graph visualization of the correlation between default network regions in children (aged 7–9 years) and in adults (aged 21–31 years) represented in pseudoanatomical organization. Statistically significant differences in functional connectivity between children and adults are highlighted on the right. Connections between interhemispheric homotopic regions are relatively prominent in both children and adults, however the default network is fragmented with sparse connections in children compared with adults. (Adapted with permission from Fair DA, Cohen AL, Dosenbach NU, et al. The maturing architecture of the brain’s default network. Proc Natl Acad Sci U S A. 2008;105: 4028–4032. Copyright 2008 National Academy of Sciences.)