Adaptive reconfiguration of fractal small-world human brain functional networks

Abstract

Brain function depends on adaptive self-organization of largescale neural assemblies, but little is known about quantitative network parameters governing these processes in humans. Here, we describe the topology and synchronizability of frequencyspecific brain functional networks using wavelet decomposition of magnetoencephalographic time series, followed by construction and analysis of undirected graphs. Magnetoencephalographic data were acquired from 22 subjects, half of whom performed a fingertapping task, whereas the other half were studied at rest. We found that brain functional networks were characterized by smallworld properties at all six wavelet scales considered, corresponding approximately to classical ␦ (low and high), , ␣, ␤, and ␥ frequency bands. Global topological parameters (path length, clustering) were conserved across scales, most consistently in the frequency range 2-37 Hz, implying a scale-invariant or fractal small-world organization. Dynamical analysis showed that networks were located close to the threshold of order/disorder transition in all frequency bands. The highest-frequency ␥ network had greater synchronizability, greater clustering of connections, and shorter path length than networks in the scaling regime of (lower) frequencies. Behavioral state did not strongly influence global topology or synchronizability; however, motor task performance was associated with emergence of long-range connections in both ␤ and ␥ networks. Long-range connectivity, e.g., between frontal and parietal cortex, at high frequencies during a motor task may facilitate sensorimotor binding. Human brain functional networks demonstrate a fractal small-world architecture that supports critical dynamics and task-related spatial reconfiguration while preserving global topological parameters. magnetoencephalography ͉ wavelet ͉ graph theory ͉ connectivity ͉ binding C oherent or correlated oscillation of large-scale, distributed neural networks is widely regarded as an important physiological substrate for motor, perceptual and cognitive representations in the brain (1, 2). The topological description of brain networks promises quantitative insight into functionally relevant parameters because their topology strongly influences their dynamic properties such as speed and specialization of information processing, learning, and robustness against pathological attack by disease (3).The topology of networks can range from entirely random to fully ordered (a lattice). In this spectrum, small-world topology is characteristic of complex networks that demonstrate both clustered or cliquish interconnectivity within groups of nodes sharing many nearest neighbors in common (like regular lattices), and a short path length between any two nodes in the network (like random graphs) (3). This is an attractive configuration, in principle, for the anatomical and functional architecture of the brain, because small-world networks are known to optimize information transfer, increase the rate of learning, and support both segregated and...

Small worlds inside big brains

“…The symmetric binary matrix is interpreted as an undirected graph and is analyzed by using network-analytic tools that measure clustering, path length, centrality, and synchronizability. Bassett et al (1) find that the global topology of the functional networks at different frequency bands is both highly clustered and highly integrated, forming a small world, in accordance with several earlier reports of small-world brain functional networks obtained from neurophysiological and neuroimaging data sets (13-15).…”

“…Bassett et al (1) provide strong new evidence for the existence in the human brain of functional networks exhibiting small-world attributes. Their approach is based on a novel application of wavelet analysis to MEG recordings obtained from human subjects who were either at rest or engaged in a finger-tapping task.…”

“…This integration happens without the need for a central controller or executive: It is the functional outcome of dynamic interactions within and between the complex structural networks of the brain. In this issue of PNAS, the study by Bassett et al (1) reveals the existence of largescale functional networks in magnetoencephalographic (MEG) recordings with attributes that are preserved across multiple frequency bands and that flexibly adapt to task demands. These networks exhibit ''small-world'' structure, i.e., high levels of clustering and short path lengths.…”

Firing Patterns in Coupled Systems of Inhibitory Neurons

“…V3, 4,6 (c) V3, V4, and V6 the results for a larger system. We made a regular onedimensional ring of n neurons (here, n=24) with connections up to the second-nearest neighbors.…”

“…Recently, complex network structures, such as smallworld [1] and scale-free [2,3] structures, have been found in various real neuronal networks [4,5]. Synchronization in neuronal networks has also been found and synchronous activities play an important role in information processing in the brain [6].…”