Alexander Schäfer

Resting developments: a review of fMRI post-processing methodologies for spontaneous brain activity.

Analytic tools for addressing spontaneous brain activity, as acquired with fMRI during the “resting-state,” have grown dramatically over the past decade. Along with each new technique, novel hypotheses about the functional organization of the brain are also available to researchers. We review six prominent categories of resting-state fMRI data analysis: seed-based functional connectivity, independent component analysis, clustering, pattern classification, graph theory, and two “local” methods. In surveying these methods, we address their underlying assumptions, methodologies, and novel applications.

A Comparison between Uni- and Bilateral tDCS Effects on Functional Connectivity of the Human Motor Cortex.

Transcranial direct current stimulation (tDCS) over the primary motor cortex (M1) has been shown to induce changes in motor performance and learning. Recent studies indicate that tDCS is capable of modulating widespread neural network properties within the brain. However the temporal evolution of online- and after-effects of tDCS on functional connectivity (FC) within and across the stimulated motor cortices (M1) still remain elusive. In the present study, two different tDCS setups were investigated: (i) unilateral M1 tDCS (anode over right M1, cathode over the contralateral supraorbital region) and (ii) bilateral M1 tDCS (anode over right M1, cathode over left M1). In a randomized single-blinded cross-over design, 12 healthy subjects underwent functional magnetic resonance imaging at rest before, during and after 20 min of either bi-, unilateral, or sham M1 tDCS. Seed-based FC analysis was used to investigate tDCS-induced changes across and within M1. We found that bilateral M1 tDCS induced (a) a decrease in interhemispheric FC during stimulation and (b) an increase in intracortical FC within right M1 after termination of the intervention. While unilateral M1 tDCS also resulted in similar effects during stimulation, no such changes could be observed after termination of tDCS. Our results provide evidence that depending on the electrode montage, tDCS acts upon a modulation of either intracortical and/or interhemispheric processing of M1.

Dynamic modulation of intrinsic functional connectivity by transcranial direct current stimulation.

Transcranial direct current stimulation (tDCS) is a noninvasive brain stimulation technique capable of modulating cortical excitability and thereby influencing behavior and learning. Recent evidence suggests that bilateral tDCS over both primary sensorimotor cortices (SM1) yields more prominent effects on motor performance in both healthy subjects and chronic stroke patients than unilateral tDCS over SM1. To better characterize the underlying neural mechanisms of this effect, we aimed to explore changes in resting-state functional connectivity during both stimulation types. In a randomized single-blind crossover design, 12 healthy subjects underwent functional magnetic resonance imaging at rest before, during, and after 20 min of unilateral, bilateral, and sham tDCS stimulation over SM1. Eigenvector centrality mapping (ECM) was used to investigate tDCS-induced changes in functional connectivity patterns across the whole brain. Uni- and bilateral tDCS over SM1 resulted in functional connectivity changes in widespread brain areas compared with sham stimulation both during and after stimulation. Whereas bilateral tDCS predominantly modulated changes in primary and secondary motor as well as prefrontal regions, unilateral tDCS affected prefrontal, parietal, and cerebellar areas. No direct effect was seen under the stimulating electrode in the unilateral condition. The time course of changes in functional connectivity in the respective brain areas was nonlinear and temporally dispersed. These findings provide evidence toward a network-based understanding regarding the underpinnings of specific tDCS interventions.

Parameterized computational complexity of finding small-diameter subgraphs

Finding subgraphs of small diameter in undirected graphs has been seemingly unexplored from a parameterized complexity perspective. We perform the first parameterized complexity study on the corresponding NP-hard s-Club problem. We consider two parameters: the solution size and its dual.

Three-Dimensional Mean-Shift Edge Bundling for the Visualization of Functional Connectivity in the Brain

Functional connectivity, a flourishing new area of research in human neuroscience, carries a substantial challenge for visualization: while the end points of connectivity are known, the precise path between them is not. Although a large body of work already exists on the visualization of anatomical connectivity, the functional counterpart lacks similar development. To optimize the clarity of whole-brain and complex connectivity patterns in three-dimensional brain space, we develop mean-shift edge bundling, which reveals the multitude of connections as derived from correlations in the brain activity of cortical regions.

Connexel visualization: A software implementation of glyphs and edge-bundling for dense connectivity data using brainGL

The visualization of brain connectivity becomes progressively more challenging as analytic and computational advances begin to facilitate connexel-wise analyses, which include all connections between pairs of voxels. Drawing full connectivity graphs can result in depictions that, rather than illustrating connectivity patterns in more detail, obfuscate patterns owing to the data density. In an effort to expand the possibilities for visualization, we describe two approaches for presenting connexels: edge-bundling, which clarifies structure by grouping geometrically similar connections; and, connectivity glyphs, which depict a condensed connectivity map at each point on the cortical surface. These approaches can be applied in the native brain space, facilitating interpretation of the relation of connexels to brain anatomy. The tools have been implemented as part of brainGL, an extensive open-source software for the interactive exploration of structural and functional brain data.