Abstract
Whole brain weighted connectivity networks were extracted from high resolution diffusion MRI data of 14 healthy volunteers. A statistically robust technique was proposed for the removal of questionable connections. Unlike most previous studies our methods are completely adapted for networks with arbitrary weights. Conventional statistics of these weighted networks were computed and found to be comparable to existing reports. After a robust fitting procedure using multiple parametric distributions it was found that the weighted node degree of our networks is best described by the normal distribution, in contrast to previous reports which have proposed heavy tailed distributions. We show that post-processing of the connectivity weights, such as thresholding, can influence the weighted degree asymptotics. The clustering coefficients were found to be distributed either as gamma or power-law distribution, depending on the formula used. We proposed a new hierarchical graph clustering approach, which revealed that the brain network is divided into a regular base-2 hierarchical tree. Connections within and across this hierarchy were found to be uncommonly ordered. The combined weight of our results supports a hierarchically ordered view of the brain, whose connections have heavy tails, but whose weighted node degrees are comparable.
Highlights
Diffusion MRI, the measurement of the extent and direction of water diffusion, makes possible a minute interrogation of extant white matter fiber architecture of the brain
The structural volumes were parcellated into cortical structures, using Individual Brain Atlases using Statistical Parametric Mapping (IBASPM)/SPM5 software and the brain atlas created in standardized Montreal Neurological Institute (MNI) space [11] provided in the Automatic Anatomical Labeling (AAL) software package [12]
In this study we considered connectivity between 90 Regions of Interest (ROIs) in the cerebrum
Summary
Diffusion MRI, the measurement of the extent and direction of water diffusion, makes possible a minute interrogation of extant white matter fiber architecture of the brain. These techniques make it possible to extract the whole brain connectivity information of the structural brain network It was shown by various authors [1,2,3,4,5,6] that brain networks appear to satisfy so-called small-world and/or scale-free properties, for a good review see [7]. Network measures based on topology, including small world indices, might become unreliable Another major problem is that most reported studies rely, at some stage or another of their analysis, on unweighted networks obtained by converting real-valued connectivity weights into binary zero-one connections. Further analysis reveals that the brain on the medium spatial scale, far from having an unpredictable or random network structure, is hierarchically organized as a regular tree of base two. In the Discussion section we elaborate on the extent to which these observations are supported by prior brain research
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