Summary articles
Annual Research Review: Growth connectomics – the organization and reorganization
of brain networks during normal and abnormal development - Petra E. Vertes, and
Edward T. Bullmore
Background: We first give a brief introduction to graph theoretical analysis and its
application to the study of brain network topology or connectomics. Within this framework,
we review the existing empirical data on developmental changes in brain network
organization across a range of experimental modalities (including structural and functional
MRI, diffusion tensor imaging, magnetoencephalography and electroencephalography in
humans). Synthesis: We discuss preliminary evidence and current hypotheses for how the
emergence of network properties correlates with concomitant cognitive and behavioural
changes associated with development. We highlight some of the technical and conceptual
challenges to be addressed by future developments in this rapidly moving field. Given the
parallels previously discovered between neural systems across species and over a range of
spatial scales, we also review some recent advances in developmental network studies at the
cellular scale. We highlight the opportunities presented by such studies and how they may
complement neuroimaging in advancing our understanding of brain development. Finally, we
note that many brain and mind disorders are thought to be neurodevelopmental in origin and
that charting the trajectory of brain network changes associated with healthy development
also sets the stage for understanding abnormal network development. Conclusions: We
therefore briefly review the clinical relevance of network metrics as potential diagnostic
markers and some recent efforts in computational modelling of brain networks which might
contribute to a more mechanistic understanding of neurodevelopmental disorders in future.
Introduction
One strategy that may help us to address these key questions in future is to focus especially on
the organization (and reorganization over developmental time) of brain networks. The
network perspective is likely to be informative for two convergent reasons. First, we already
know that changes in synaptic connectivity and axonal myelination are among the key
microscopic processes in postnatal development; and that changes in cortical thickness and
white matter volume are among the most well-replicated magnetic resonance imaging (MRI)
markers of macroscopic development. Second, we also know that ‘higher-order’ cognitive
processes that will be fundamental to successful adult independence – such as planning,
problem solving, working memory – are not phrenologically localized to a specific brain
region.
Background and scope
Brain graphs and growth connectomics
Graph theory is sufficiently general to encompass network analysis over a wide range of
neuroscientific modalities – from multielectrode array recordings of neuronal cultures in vitro
to functional MRI recordings of whole-brain resting state dynamics in vivo. Thus, graphs
create an opportunity to use the same mathematical language to quantify aspects of brain
network development at micro- and macrolevels of measurement.
Both macro- and microscale brain networks as well as many other complex systems –
from social networks to the internet – share certain key organizational principles (Figure 1).
One well-known example of widely shared organizational structure is the small-world
phenomenon, whereby networks are simultaneously highly clustered (nodes that are
,connected to each other are also likely to have many nearest (first degree) neighbours in
common) and highly efficient (the average path length between a pair of nodes is short).
Hubs are also found in
almost all complex networks.
Hubs can be defined in many
ways, but the simplest definition
is as high-degree nodes, where the
degree of a node is the number of
edges that connect it to other
nodes in the network.
Another ubiquitous feature
of network organization is
modularity. Much like companies,
brain systems tend to be
organized in modules with a high
level of interaction within
modules and sparser connectivity
between them. Modules also tend
to be hierarchically organized and
are spanned by a number of
highly connected nodes, or hubs
(Figure 1A).
The economics of brain network
organization
One way of thinking about this
question is to ask: what kind of
selection pressures would favour emergence of brain network topology? And is it likely that
the same selection pressures would also favour emergence of network topology in a nearly
universal class of spatially embedded systems for information exchange?
High-cost network features have been associated with benefits to integrated
information processing both theoretically and to some extent empirically. Rich clubs of high-
degree cortical hubs in the human fMRI coactivation network are analogously important for
‘higher-order’ executive functions such as planning and working memory.
It is important also to note that the optimal outcome of such trade-offs between
competitive natural selection criteria will not be fixed over developmental time. Most
obviously the configuration of functional networks must be dynamically variable as
environmental contingencies and demands for cognitive processing vary from moment to
moment. The connectomics literature to date has mainly focused on the timeaveraged
organization of functional networks measured during nominally constant experimental
conditions.
Some stylized facts about brain development
To contextualize the more recent, and still incomplete, results of growth connectomics, we
will first rehearse some ‘stylized facts’ about human brain development that are more
certainly known at this time (see Figure 2).
The bulk of neurogenesis and neuronal migration is thought to be complete by about
week 20 after conception at which point axons begin to form and the density of synapses
increases steadily (by about 4% per week) until week 27 after conception. The period leading
up to birth is characterized by an exuberant increase in axonal growth.
, These key
microscopic
processes of
the
consolidation
phase (cell
loss, synaptic
pruning,
myelination)
are broadly
convergent
with
developmental
changes in
macroscopic
measurements
made by
neuroimaging.
MRI studies have consistently shown decreasing grey matter volume and cortical thickness,
and
increasing white matter volume, both over the age range 7–24 years, approximately.
Recent reviews of brain network development
In this review, we extend these previous accounts of brain network development, integrate
results from all macroscopic neuroimaging modalities, include insights gained from the
growth of microscopic neuronal networks, and emphasize in particular the potential driving
forces shaping brain networks into their observed organization. Given this broad scope, the
current review is necessarily selective. It aims to provide a balanced and contextualized
synthesis of the literature on graph theoretical analysis of brain networks during development
to stimulate further research in growth connectomics.
Normative development of brain networks
Macroanatomical networks
Large-scale brain anatomical networks describe the ‘wiring diagram’ of the whole brain, or a
large part of it, showing how different cortical and subcortical regions (in the order of mm
volume) are interconnected by white matter tracts or fascicles consisting of large numbers of
parallel axonal projections.
White matter tractography networks (DTI). In DTI, each voxel of the brain is associated with
a tensor representing the rate of water diffusion along different directions at that point in
space. This information can also be summarized by the metric of fractional anisotropy (FA),
which is a scalar value between zero and one describing the degree of anisotropy of the
diffusion process at every voxel.
Fractional anisotropy is therefore thought to reflect fibre density, axonal diameter, and
myelination in white matter, but this complex measure inevitably combines several poorly
understood biophysical properties of white matter.
In addition to computing FA, the principal direction of the diffusion tensor can be used
to track white matter fibres along their length. Such tractography algorithms are therefore able
, to infer the patterns of white matter connectivity between predefined grey matter regions of
interest (ROIs) across the whole brain.
Despite such differences in methodology, diffusion imaging studies have yielded
convergent results on the broad topological features of both adult and developing brain
networks.
A range of paediatric studies have shown that many of the broad topological features
of the human DTI connectome – such as small-worldness or hubs – are already established at
birth.
Over the course of normal development, human DTI networks gradually mature from
local, proximity-based connectivity patterns designed to support primary functions to a more
distributed, integrative topology thought to be favourable for supporting higher cognitive
functioning. The remodelling of anatomical networks over the course of postnatal
development is thought to predominantly reflect the fact that myelination and myelin
maturation occur asynchronously across various axonal tracts.
Unfortunately, not all known neurodevelopmental processes are appropriately captured
in tractography data.
Grey matter covariance networks (MRI). In addition to diffusion imaging, brain structural
networks have also been mapped using cross-correlations in morphological metrics, such as
cortical thickness or volume, measured in conventional MRI data on large groups of
individuals. . A limitation of this approach – so-called structural covariance network analysis
– is that it results in a single network for the entire group of subjects under study.
Network analysis of structural covariance networks revealed many of the same
topological properties as found in DTI networks including smallworldness and modularity.
Subsequent longitudinal studies have tightened the explanatory link between structural
covariance and coordinated development of pairs of brain regions.
Macrofunctional networks
Resting state fMRI functional connectivity networks. Functional MRI (fMRI) was originally
used to determine the function of individual brain regions by measuring the blood oxygen
level-dependent (BOLD) signal as a proxy of neuronal activity during various tasks. As in
anatomical networks, the ROIs chosen as the nodes of a functional network vary between
studies in their location, size and number.
Numerous paediatric resting state fMRI studies have shown the existence of correlated
spontaneous activity in infants and young children at various stages of development including
premature infants scanned before and at term equivalence as well as scans during foetal life.
In older children (between the ages of 4 and 14), most studies have focussed on
describing the state of functional connectivity within the default mode network. Studies
examining the presence and maturity of the DMN in this age range, as well as the level of
connectivity in anterior–posterior directions more generally, have thus far revealed
imperfectly consistent results.
The first explicit use of graph theory in developmental studies of functional data
focussed on 210 subjects between 7 and 35 years old and studied how the modular structure
of a network comprising 39 task-defined ROIs changed over this age range. The study found
that the cinguloopercular and fronto-parietal components of the task control network, that are
normally distinct in adults, were initially merged in children.
These changes in modular organization were also echoed by studies of degree and
betweenness centrality during infancy, in infants versus adults, and children versus adults.
