[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

Recent developments in the quantitative analysis of complex networks, based largely on graph theory, have been rapidly translated to studies of brain network organization. The brain's structural and functional systems have features of complex networks--such as small-world topology, highly connected hubs and modularity--both at the whole-brain scale of human neuroimaging and at a cellular scale in non-human animals. In this article, we review studies investigating complex brain networks in diverse experimental modalities (including structural and functional MRI, diffusion tensor imaging, magnetoencephalography and electroencephalography in humans) and provide an accessible introduction to the basic principles of graph theory. We also highlight some of the technical challenges and key questions to be addressed by future developments in this rapidly moving field.

Complex brain networks: graph theoretical analysis of structural and functional systems

http://brainimaging.waisman.wisc.edu/~chung/neuro.processing/literature/rubinov.2010.NI.network.pdf

Complex network measures of brain connectivity: uses and interpretations.

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

The majority of functional neuroscience studies have focused on the brain's response to a task or stimulus. However, the brain is very active even in the absence of explicit input or output. In this Article we review recent studies examining spontaneous fluctuations in the blood oxygen level dependent (BOLD) signal of functional magnetic resonance imaging as a potentially important and revealing manifestation of spontaneous neuronal activity. Although several challenges remain, these studies have provided insight into the intrinsic functional architecture of the brain, variability in behaviour and potential physiological correlates of neurological and psychiatric disease.

/pdf/spontaneous-fluctuations-in-brain-activity-observed-with-32z1nyfc7n.pdf

Spontaneous fluctuations in brain activity observed with functional magnetic resonance imaging.

Small-world properties have been demonstrated for many complex networks. Here, we applied the discrete wavelet transform to functional magnetic resonance imaging (fMRI) time series, acquired from healthy volunteers in the resting state, to estimate frequency-dependent correlation matrices characterizing functional connectivity between 90 cortical and subcortical regions. After thresholding the wavelet correlation matrices to create undirected graphs of brain functional networks, we found a small-world topology of sparse connections most salient in the low-frequency interval 0.03–0.06 Hz. Global mean path length (2.49) was approximately equivalent to a comparable random network, whereas clustering (0.53) was two times greater; similar parameters have been reported for the network of anatomical connections in the macaque cortex. The human functional network was dominated by a neocortical core of highly connected hubs and had an exponentially truncated power law degree distribution. Hubs included recently evolved regions of the heteromodal association cortex, with long-distance connections to other regions, and more cliquishly connected regions of the unimodal association and primary cortices; paralimbic and limbic regions were topologically more peripheral. The network was more resilient to targeted attack on its hubs than a comparable scale-free network, but about equally resilient to random error. We conclude that correlated, low-frequency oscillations in human fMRI data have a small-world architecture that probably reflects underlying anatomical connectivity of the cortex. Because the major hubs of this network are critical for cognition, its slow dynamics could provide a physiological substrate for segregated and distributed information processing.

/pdf/a-resilient-low-frequency-small-world-human-brain-functional-1zjdpdkq9s.pdf

A Resilient, Low-Frequency, Small-World Human Brain Functional Network with Highly Connected Association Cortical Hubs

Brain anatomical networks are sparse, complex, and have economical small-world properties. We investigated the efficiency and cost of human brain functional networks measured using functional magnetic resonance imaging (fMRI) in a factorial design: two groups of healthy old (N = 11; mean age = 66.5 years) and healthy young (N = 15; mean age = 24.7 years) volunteers were each scanned twice in a no-task or “resting” state following placebo or a single dose of a dopamine receptor antagonist (sulpiride 400 mg). Functional connectivity between 90 cortical and subcortical regions was estimated by wavelet correlation analysis, in the frequency interval 0.06–0.11 Hz, and thresholded to construct undirected graphs. These brain functional networks were small-world and economical in the sense of providing high global and local efficiency of parallel information processing for low connection cost. Efficiency was reduced disproportionately to cost in older people, and the detrimental effects of age on efficiency were localised to frontal and temporal cortical and subcortical regions. Dopamine antagonism also impaired global and local efficiency of the network, but this effect was differentially localised and did not interact with the effect of age. Brain functional networks have economical small-world properties—supporting efficient parallel information transfer at relatively low cost—which are differently impaired by normal aging and pharmacological blockade of dopamine transmission.

/pdf/efficiency-and-cost-of-economical-brain-functional-networks-11pk03qiol.pdf

Efficiency and cost of economical brain functional networks.

Brain function depends on adaptive self-organization of large-scale neural assemblies, but little is known about quantitative network parameters governing these processes in humans. Here, we describe the topology and synchronizability of frequency-specific 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 finger-tapping task, whereas the other half were studied at rest. We found that brain functional networks were characterized by small-world properties at all six wavelet scales considered, corresponding approximately to classical δ (low and high), θ, α, β, and γ 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 γ 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 β and γ 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.

/pdf/adaptive-reconfiguration-of-fractal-small-world-human-brain-2mke1s0v7g.pdf

Adaptive reconfiguration of fractal small-world human brain functional networks

http://www.gipsa-lab.grenoble-inp.fr/~sophie.achard/mes_images/Neuroimage.2008.pdf

Age-related changes in modular organization of human brain functional networks

Endophenotypes (intermediate phenotypes) are objective, heritable, quantitative traits hypothesized to represent genetic risk for polygenic disorders at more biologically tractable levels than distal behavioural and clinical phenotypes. It is theorized that endophenotype models of disease will help to clarify both diagnostic classification and aetiological understanding of complex brain disorders such as obsessive-compulsive disorder (OCD). To investigate endophenotypes in OCD, we measured brain structure using magnetic resonance imaging (MRI), and behavioural performance on a response inhibition task (Stop-Signal) in 31 OCD patients, 31 of their unaffected first-degree relatives, and 31 unrelated matched controls. Both patients and relatives had delayed response inhibition on the Stop-Signal task compared with healthy controls. We used a multivoxel analysis method (partial least squares) to identify large-scale brain systems in which anatomical variation was associated with variation in performance on the response inhibition task. Behavioural impairment on the Stop-Signal task, occurring predominantly in patients and relatives, was significantly associated with reduced grey matter in orbitofrontal and right inferior frontal regions and increased grey matter in cingulate, parietal and striatal regions. A novel permutation test indicated significant familial effects on variation of the MRI markers of inhibitory processing, supporting the candidacy of these brain structural systems as endophenotypes of OCD. In summary, structural variation in large-scale brain systems related to motor inhibitory control may mediate genetic risk for OCD, representing the first evidence for a neurocognitive endophenotype of OCD.

/pdf/neurocognitive-endophenotypes-of-obsessive-compulsive-2tm6b0cn52.pdf

Sophie Achard

Papers

A Resilient, Low-Frequency, Small-World Human Brain Functional Network with Highly Connected Association Cortical Hubs

Efficiency and cost of economical brain functional networks.

Adaptive reconfiguration of fractal small-world human brain functional networks

Age-related changes in modular organization of human brain functional networks

Neurocognitive endophenotypes of obsessive-compulsive disorder