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Assessing brain structural and functional connectivity with graph theoretical analysis
Neuroimaging methods provide a powerful tool to investigate brain connectivity, and have been widely applied to study the mutual relationship between structural and functional connections between brain regions in healthy subjects and in patients. Several studies have demonstrated that structurally connected cortical regions in the adult, healthy brain exhibit stronger and more consistent functional connectivity than structurally unconnected regions. However, the picture that emerges from studies in patients affected by brain disease and neurological conditions is more complex. A striking example is that of subjects with Agenesis of the Corpus Callosum (ACC), a congenital condition whereby the main bundle of white matter fibers connecting the two cerebral hemispheres does not form during brain development. Recent studies in ACC subjects, whose structural connectivity is dramatically impaired, have shown intact bilateral functional connectivity patterns, thus challenging the view that structural and functional connectivity are straightforwardly related. The underpinnings of the abnormal relationship between structural and functional connectivity in this and other brain disorders are unknown, and their investigation may provide insight into the underlying pathophysiological mechanisms, and possibly into compensatory mechanisms that may promote recovery of functional connectivity in case of congenital or acquired white matter loss.
The ability to quantitatively compare structural and functional connectivity would be important to assess the relationship between these two measures of interregional connections in the healthy brain and in diseased states. While selected connectivity paths can be assessed with seed-region-based methods, there is no generally established hypothesis-free approach to measuring global differences in different connectivity measures. Graph-theoretical analysis is attracting increasing attention as a general and powerful framework to analyze brain connectivity networks, and may provide a rigorous theoretical basis to study connectivity and disconnectivity in the brain. Here, I shall describe recent developments in complex network theory and its application to the study of topological aspects of brain connectivity, including the relation between structural and functional connectivity in models of brain disease. I will also discuss open problems in brain connectivity analysis that may be amenable to solution via graph-theoretical methods.