van den Heuvel M P, Stam C J, Boersma M, Hulshoff Pol H E
Rudolf Magnus Institute of Neuroscience, University Medical Center Utrecht, Department of Psychiatry, Utrecht, The Netherlands.
Neuroimage. 2008 Nov 15;43(3):528-39. doi: 10.1016/j.neuroimage.2008.08.010. Epub 2008 Aug 22.
The brain is a complex dynamic system of functionally connected regions. Graph theory has been successfully used to describe the organization of such dynamic systems. Recent resting-state fMRI studies have suggested that inter-regional functional connectivity shows a small-world topology, indicating an organization of the brain in highly clustered sub-networks, combined with a high level of global connectivity. In addition, a few studies have investigated a possible scale-free topology of the human brain, but the results of these studies have been inconclusive. These studies have mainly focused on inter-regional connectivity, representing the brain as a network of brain regions, requiring an arbitrary definition of such regions. However, using a voxel-wise approach allows for the model-free examination of both inter-regional as well as intra-regional connectivity and might reveal new information on network organization. Especially, a voxel-based study could give information about a possible scale-free organization of functional connectivity in the human brain. Resting-state 3 Tesla fMRI recordings of 28 healthy subjects were acquired and individual connectivity graphs were formed out of all cortical and sub-cortical voxels with connections reflecting inter-voxel functional connectivity. Graph characteristics from these connectivity networks were computed. The clustering-coefficient of these networks turned out to be much higher than the clustering-coefficient of comparable random graphs, together with a short average path length, indicating a small-world organization. Furthermore, the connectivity distribution of the number of inter-voxel connections followed a power-law scaling with an exponent close to 2, suggesting a scale-free network topology. Our findings suggest a combined small-world and scale-free organization of the functionally connected human brain. The results are interpreted as evidence for a highly efficient organization of the functionally connected brain, in which voxels are mostly connected with their direct neighbors forming clustered sub-networks, which are held together by a small number of highly connected hub-voxels that ensure a high level of overall connectivity.
大脑是一个由功能连接区域组成的复杂动态系统。图论已成功用于描述此类动态系统的组织。最近的静息态功能磁共振成像研究表明，区域间功能连接呈现小世界拓扑结构，这表明大脑是由高度聚集的子网组成，并伴有高水平的全局连接。此外，一些研究探讨了人类大脑可能存在的无标度拓扑结构，但这些研究结果尚无定论。这些研究主要集中在区域间连接，将大脑视为脑区网络，需要对此类区域进行任意定义。然而，使用基于体素的方法可以对区域间以及区域内连接进行无模型检查，并可能揭示有关网络组织的新信息。特别是，基于体素的研究可以提供有关人类大脑功能连接可能存在的无标度组织的信息。获取了28名健康受试者的静息态3特斯拉功能磁共振成像记录，并从所有皮质和皮质下体素中形成个体连接图，连接反映了体素间功能连接。计算了这些连接网络的图特征。结果表明，这些网络的聚类系数远高于可比随机图的聚类系数，同时平均路径长度较短，表明存在小世界组织。此外，体素间连接数量的连接分布遵循幂律缩放，指数接近2，表明存在无标度网络拓扑结构。我们的研究结果表明，功能连接的人类大脑具有小世界和无标度相结合的组织。这些结果被解释为功能连接大脑高效组织的证据，其中体素大多与其直接邻居相连，形成聚集子网，这些子网由少量高度连接的枢纽体素连接在一起，确保了高水平的整体连接。
