Identifying structure-function relationships in task-related networks.

<p>(a) In both representative and subject-specific brain networks, we identify brain regions that belong to the task-positive and task-negative network described in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003591#pcbi.1003591-Fox2" target="_blank">[7]</a>, and we label all remaining regions as “other” regions. There are six possible types of couplings between these three types of regions. We focus on three of these couplings: those between two task-negative regions (), between two task-positive regions (), and between a task-positive and a task-negative region (). These couplings are highlighted in the axial view of the representative brain network. (b) We compute measures of structural (SC) and functional (FC) connectivity between each pair of regions by measuring the number of white matter streamlines linking two regions (SC) and the task-dependent strength of functional correlation between BOLD time series measured within regions (FC). The pie chart shows the decomposition of all structural connections into those that link two task-positive (), two task-negative (), one task-positive and one task-negative (), and all other regions (). (c) We assess variations in these number densities as we bias toward increasingly strong functional correlations. This relationship is illustrated here for the representative brain network, where variations , , and are shown as a function of the resting-state threshold . This can be understood as computing the change in composition of the pie chart shown in (b) while incrementally biasing toward strongly-correlated region pairs with functional correlations above the threshold value . Inset: complementary cumulative distribution function (cCDF) of FC<i>_R</i> computed for , , and couplings, where the ) measures the probability of finding for every value of . The variable threshold selects the subset of connections with . (d) The changes in , , and densities can be compactly represented by comparing the degree of within-network coupling, quantified by the relative change in versus densities (), with the degree of between-network coupling, quantified by the change in density (). This representation reveals that strong resting-state FC is supported by strong local coupling within the task-negative network, represented by the increase in relative to density, and weak coupling between task-positive and task-negative networks, represented by the decrease in density.