Connectivity differences in brain networks

Abstract

The scenario considered here is one where brain connectivity is represented as a network and an experimenter wishes to assess the evidence for an experimental effect at each of the typically thousands of connections comprising the network. To do this, a univariate model is independently fitted to each connection. It would be unwise to declare significance based on an uncorrected threshold of α = 0.05, since the expected number of false positives for a network comprising N = 90 nodes and N(N − 1)/2 = 4005 connections would be 200. Control of Type I errors over all connections is therefore necessary. The network-based statistic (NBS) and spatial pairwise clustering (SPC) are two distinct methods that have been used to control family-wise errors when assessing the evidence for an experimental effect with mass univariate testing. The basic principle of the NBS and SPC is the same as supra-threshold voxel clustering. Unlike voxel clustering, where the definition of a voxel cluster is unambiguous, ‘clusters’ formed among supra-threshold connections can be defined in different ways. The NBS defines clusters using the graph theoretical concept of connected components. SPC on the other hand uses a more stringent pairwise clustering concept. The purpose of this article is to compare the pros and cons of the NBS and SPC, provide some guidelines on their practical use and demonstrate their utility using a case study involving neuroimaging data.

Introduction

There has been a shift in imaging neuroscience from brain activation to brain connectivity (Friston, 2009, Sporns, in press). Central to this shift in focus has been an emphasis on studying large-scale brain networks composed of nodes and connections (Bullmore and Sporns, 2009, Habeck and Moeller, 2011, He and Evans, 2010, Kaiser, 2011, Sporns, 2011, Wig et al., 2011). Nodes represent brain regions and the connections formed between pairs of nodes represent some measure of interaction between them, as inferred from neuroimaging data (Rubinov and Sporns, 2011).

Brain networks have been found to exhibit various nontrivial topological features, such as small-world organization, modular structure and highly connected hubs (Achard et al., 2006, Bassett and Bullmore, 2006, Hagmann et al., 2008, van den Heuvel et al., 2008). The goal of numerous studies has been to elucidate differences in these topological properties over developmental stages (Fair et al., 2009), in clinical conditions (e.g. Lynall et al., 2011, He et al., 2008, van den Heuvel et al., 2010) and in relation to different experimental conditions and cognitive states (e.g. Bassett et al., 2011, Fornito et al., 2011a, Kitzbichler et al., 2011) as well as genetic influences (Fornito et al., 2011b).

The interpretation of topological differences found in brain networks is not always straightforward, however. Topological properties derived from the characteristic path length in functional brain networks (Wang et al., 2010) are particularly difficult to interpret because functional networks are intrinsically fully connected. Therefore, the “path length” between a pair of regions is already explicitly captured by the strength of the direct connection (Rubinov and Sporns, 2010). Negative functional connections complicate the interpretation of path length as well (Chen et al., 2011).

Furthermore, topological differences can in some circumstances be a complex manifestation of simple differences in connectivity strength. Steps taken to disambiguate topological differences from simple differences in connectivity strength are equivocal and typically require the selection of arbitrary thresholds to transform connectivity strength from a continuous to a binary scale (Ginestet et al., 2011, van Wijk et al., 2010) (see Fig. 1).

Elucidating differences in the strength of connectivity is therefore an important undertaking in and of itself. Differences in connectivity strength are more basic than topological differences and as such are more straightforward to interpret.

This article considers exploratory methods for assessing the evidence of an experimental effect at each of the typically thousands of connections comprising a brain network. The experimental effect may be, for example, an association between connectivity strength and diagnostic status in a case-control study or contextual changes during performance of a cognitive task (Bressler and Menon, 2010).

The scenario considered is one in which connectivity is measured between every pair of many distinct brain regions. Connectivity includes anatomical connectivity inferred from fiber tracking methods (Bassett et al., 2010, Li et al., in press) and cortical thickness/volume estimates (Bassett et al., 2008, He et al., 2007) as well as functional connectivity inferred from functional imaging (van den Heuvel and Hulshoff Pol, 2010) or electromagnetic tomography (Schoffelen and Gross, 2011). To enable inferential statistics, the same connectivity measurements are repeated for each subject comprising a case-control study or in the same subject during different experimental conditions. A univariate model is then independently fitted to each connection to assess the evidence of an experimental effect. This involves computing a test statistic and corresponding p-value for the contrast of interest.

The total number of connections is typically in the thousands. Control of Type I errors among all connections is therefore essential. The network-based statistic (NBS) (Zalesky et al., 2010a) and spatial pairwise clustering (SPC) (Hipp et al., 2011, Zalesky et al., in press) are two distinct methods that have been used to control family-wise errors when assessing the evidence for an experimental effect with mass univariate testing. The family-wise error rate refers to the likelihood of committing one or more Type I errors among all connections (Nichols and Hayasaka, 2003).

The basic principle of the NBS and SPC is the same as supra-threshold voxel clustering in traditional task-based functional-MRI activation studies (Bullmore et al., 1999, Nichols and Holmes, 2001). Whereas voxel clustering pertains to mass univariate testing of brain activation, the NBS and SPC pertain to mass univariate testing of brain connectivity. Unlike voxel clustering, where the definition of a voxel cluster is unambiguous, ‘clusters’ formed among supra-threshold connections can be defined in different ways. The only obvious way to form voxel clusters is to cluster supra-threshold voxels that share at least one common face, edge or corner. Supra-threshold voxels refers to voxels having a test statistic that exceeds a chosen cluster-forming threshold.

In contrast, there is not one obvious way to form ‘clusters’ among supra-threshold connections. The NBS defines clusters using the graph theoretical concept of connected components. SPC on the other hand uses a more stringent pairwise clustering concept. With the development of these two complimentary methods, experimenters face a choice: NBS or SPC?

This choice is addressed by comparing the pros and cons of the NBS and SPC, providing some guidelines on their practical use and demonstrating their utility using a case study involving connectivity measurements inferred from electroencephalography data. Note that the NBS is freely available as part of the Brain Connectivity Toolbox (http://www.brain-connectivity-toolbox.net/) and Connectome Mapping Toolkit (http://www.connectomics.org).