Brain Network Analysis: Separating Cost from Topology Using Cost-Integration

Abstract

A statistically principled way of conducting brain network analysis is still lacking. Comparison of different populations of brain networks is hard because topology is inherently dependent on wiring cost, where cost is defined as the number of edges in an unweighted graph. In this paper, we evaluate the benefits and limitations associated with using cost-integrated topological metrics. Our focus is on comparing populations of weighted undirected graphs that differ in mean association weight, using global efficiency. Our key result shows that integrating over cost is equivalent to controlling for any monotonic transformation of the weight set of a weighted graph. That is, when integrating over cost, we eliminate the differences in topology that may be due to a monotonic transformation of the weight set. Our result holds for any unweighted topological measure, and for any choice of distribution over cost levels. Cost-integration is therefore helpful in disentangling differences in cost from differences in topology. By contrast, we show that the use of the weighted version of a topological metric is generally not a valid approach to this problem. Indeed, we prove that, under weak conditions, the use of the weighted version of global efficiency is equivalent to simply comparing weighted costs. Thus, we recommend the reporting of (i) differences in weighted costs and (ii) differences in cost-integrated topological measures with respect to different distributions over the cost domain. We demonstrate the application of these techniques in a re-analysis of an fMRI working memory task. We also provide a Monte Carlo method for approximating cost-integrated topological measures. Finally, we discuss the limitations of integrating topology over cost, which may pose problems when some weights are zero, when multiplicities exist in the ranks of the weights, and when one expects subtle cost-dependent topological differences, which could be masked by cost-integration.

Breakdown of the brain’s functional network modularity with awareness

“…Awareness may be associated with a widespread increase in functional connectivity across modules rather than within modules. These results are also in line with reports that manipulations of working memory load can increase intermodular communication and decrease modularity in the absence of global efficiency changes (25), lending credence to our conclusion that decreased functional modularity with awareness results from widespread increased intermodular connectivity.…”

“…When examining a large set of ROIs that encompass the different networks of the human cerebral cortex (21, 22), we can apply graph theory analyses to estimate the extent to which key measures of global information processing are altered by the state of awareness. This approach has been previously applied to study differences in cognitive states (23)(24)(25)(26)(27)(28)(29)(30)(31). Although recent studies have taken advantage of graph theory analysis to examine the connectivity patterns that precede a conscious event (32) or following pharmacologically induced loss of consciousness (33), this approach had yet to be used for characterizing the topology associated with conscious target perception per se, a necessary test for global theories of awareness.…”

Valproate treatment normalizes EEG functional connectivity in successfully treated idiopathic generalized epilepsy patients

“…Statistical parametric network (SPN) terminology has been introduced (Ginestet et al, 2011). In our study we generated population and treatment-related differential SPNs which provide a statistical method to investigate differences of connections.…”

Quantifying Individual Brain Connectivity with Functional Principal Component Analysis for Networks

“…When network connectivity measures are used to compare the networks of different subjects, the prevailing approach is to use subject-specific thresholds so that the resulting networks have the same density, that is, an equal number of edges (Bassett et al, 2012;Hosseini et al, 2012a;Van Wijk et al, 2010). While some studies have conducted network analyses by choosing a single density (Bassett et al, 2009), it is more common to construct and compare networks over a range of density values Ginestet et al, 2011;Hosseini and Kesler, 2013;Hosseini et al, 2012a;Klimm et al, 2014;Lynall et al, 2010;Siebenhühner et al, 2013;Singhet al, 2013;Yu et al, 2011). In this case, the connectivity measure used to summarize the network is a function of the density, so that methods of functional data analysis (FDA) are applicable [for an introduction to FDA, see, e.g., Ramsay and Silverman (2005)].…”

“…Specifically, the ubiquitous approach for comparing two groups (e.g., healthy/diseased or young/elderly) is to compare their mean connectivity curves through a permutation test (Bassett et al, 2012;Hosseini and Kesler, 2013;Hosseini et al, 2012a;Klimm et al, 2014;Siebenhühner et al, 2013;Singh et al, 2013). An alternative is the socalled ''area under the curve'' or cost integration approach (Ginestet et al, 2011), although there is a consensus that the resulting inference is less powerful as it is less sensitive to curve shape. While such tests of group mean differences have yielded interesting scientific findings, they are insufficient for identifying differences in variance, for example, or, more importantly, for inferring relationships with a continuous covariate such as age.…”