Whole-brain anatomical networks: Does the choice of nodes matter?
Introduction
Modeling the whole human brain as a network, the so-called human connectome (Sporns et al., 2005), has gained significant interest in the last few years. Two distinct types of whole brain networks have now been empirically mapped using different magnetic resonance imaging (MRI) modalities: anatomical networks and functional networks.
An anatomical brain network is derived from diffusion-MRI (d-MRI) and models the axonal fiber bundles that support information transfer between spatially isolated grey-matter regions. Structural connectivity is therefore often referred to as anatomical or physical connectivity and can be mapped in vivo with tractographic methods. On the other hand, a functional brain network is typically derived from measures of functional connectivity; in particular, correlated activity between regions over time, assessed using either resting-state functional-MRI (rs-fMRI), magnetoencephalography (MEG) or electroencephalography (EEG).
Efforts have been devoted to elucidating the topological properties of human brain networks in both health and disease. A summary of some studies is shown in Table 1.
Topological properties can be mathematically analyzed by characterizing the brain as an undirected graph, where each region-of-interest composing a grey-matter parcellation serves as a node and each link represents some statistical measure of association, such as correlations in physiological time series; interconnecting axonal fiber pathways; or inter-regional covariance in anatomical parameters such as cortical thickness (Bullmore et al., 2009).
The two most ubiquitous topological properties that brain networks have been tested for are scale-freeness in nodal distribution (Amaral et al., 2000) and small-worldness (Watts and Strogatz, 1998). It has been shown that the topology of both anatomical and functional brain networks exhibit small-world properties (Bullmore et al., 2009). Such networks are characterized by a high degree of locally clustered, cliquish, connectivity and low mean path length (i.e. nodes can connect with each other through only a few hops). Some studies have also claimed that the brain is scale-free (e.g. (Eguiluz et al., 2005, Van den Heuvel et al., 2008), though this view is disputed (e.g. Achard et al., 2006, Gong et al., 2009). Scale-freeness implies the existence of a few highly connected hub nodes, which endow a scale-free network with superior tolerance to random node failures (Albert et al., 2000, Kaiser et al., 2007). Recent studies have demonstrated these networks measures are altered in the diseased brain (e.g. He et al., 2008He et al., 2009, Liu et al., 2008, Wang et al., 2009b).
At the microscopic scale, nodes composing a neural network naturally correspond to individual neurons. However, at the macroscopic scale, it is unclear how grey-matter should be parcellated in order to define a set of nodes, and at what scale this parcellation should be performed. The lack of a natural correspondence between network nodes and grey-matter regions-of-interest has resulted in the analysis of brain networks across a range of nodal scales spanning three orders of magnitude, from less than 102 nodes, up to more than 105. The scale of a parcellation can affect regional connectivity estimates, particularly in anatomical networks, as exemplified in Fig. 1. This figure shows an example of a forking U-fiber that is poorly characterized due to the use of a too coarse parcellation.
Most studies have utilized a subset of the 90 non-cerebellar regions-of-interest composing the automated anatomical labeling (AAL) parcellation atlas (Tzourio-Mazoyer et al., 2002) to serve as nodes (see Table 1). In the case of functional connectivity, (Wang et al., 2009a) statistically tested differences in the topological properties of an AAL-based network with a network based on an 70-node parcellation. While both networks exhibited robust small-world attributes and an exponentially truncated power law degree distribution, several topological parameters were found to exhibit significant variations across the two networks.
The substantial disparity in parcellation scales across different studies raises a question: Does scale matter? Since an underlying neuronal/axonal network is not necessarily endowed with the same properties as its macroscopic approximation, do claims of the form “human brain network shown to exhibit topological property X” need to be interpreted with respect to scale? For example, the discrepancy between Eguiluz et al., 2005, Van den Heuvel et al., 2008 versus Achard et al., 2006, Gong et al., 2009 (i.e. power law nodal distribution versus exponentially truncated power law) may be attributable to the orders of magnitude difference in scales considered.
This paper seeks to systematically evaluate the dependence of whole-brain anatomical networks over a range of nodal scales, a variety of grey-matter parcellations as well as different diffusion-MRI acquisition protocols. To this end, networks were analyzed across scales ranging from 100 to 4000 nodes. For each scale, 100 random parcellations of grey-matter were generated. Two distinct tractographic methods were then used to determine which pairs of nodes were anatomically connected.
A variety of local and global topological properties were computed for each of the 100 networks, including small-worldness, path length, clustering coefficient, nodal degree distribution, efficiency and betweenness centrality. The variation of each topological parameter across the 100 networks was then assessed to evaluate the discrepancy in parameter estimates that can be solely attributable to the choice of parcellation. Quantifying parcellation-driven discrepancies is important because the choice of parcellation is usually arbitrary or random.
It was found that topological properties vary markedly with scale. For example, if one experimenter uses the AAL template, while another uses a random 4000-node template, the value of small-worldness measured by the two experimenters will be discrepant by approximately 95% (σALL = 1.9 vs. σ4000 = 53.6 ± 2.2). Although small-world attributes were found at all scales, the extent of small-worldness was found to increase as scale is made finer, resulting from a large increase in clustering. Exponential nodal degree distributions were also found at all scales. These findings suggest scale does not matter if the experimenter simply seeks a yes/no determination about whether or not a network is small-world or scale-free, but scale does matter if the experimenter seeks to quantify the extent to which the network exhibits these topological properties. The variation in topological properties for networks of the same scale, but with different nodal parcellations was found to be more subtle (< 3%).
Section snippets
Methods
An overview of the processing pipeline is shown in Fig. 2. Each of the ensuing subsections is dedicated to a particular stage of the pipeline.
Results
The first topological property considered was small-worldness, σ = γ/λ. Fig. 4 shows small-worldness plotted as a function of the number of network nodes. A distinct trace is shown for HARDI (blue) and DTI (red). The dashed lines correspond to 95% confidence intervals. Fig. 4 also shows a sagittal representation of some arbitrarily chosen parcellations of varying scale.
The variability in the σ-ratio is rather small across parcellations of the same scale which can be assessed by the tightness of
Discussion and conclusions
In most natural and engineered networks, what constitutes a node and what constitutes a link is clear and well-defined. For example, in social networks, nodes represent individuals (or organizations), while links represent relationships, friendships, etc. When the Internet is modeled as a network, nodes represent computers (or routers), while links represent the wiring and optical fibers that interconnect them. In food webs, nodes represent particular species of animal, while links represent
Acknowledgments
The computing resources utilized to undertake this project were provided by the Florey Neuroscience Institutes and the Department of Electrical & Electronic Engineering at the University of Melbourne. We thank Professors G.F. Egan and I. Mareels for facilitating access to these computing resources. Software development was supported by a Human Brain Project grant from the National Institute of Biomedical Imaging & Bioengineering and the National Institute of Mental Health. Many of the graph
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