Sophie Achard

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

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.

Efficiency and Cost of Economical Brain Functional Networks

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.

Adaptive reconfiguration of fractal small-world human 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.

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

Graph theory allows us to quantify any complex system, e.g., in social sciences, biology or technology, that can be abstractly described as a set of nodes and links. Here we derived human brain functional networks from fMRI measurements of endogenous, low frequency, correlated oscillations in 90 cortical and subcortical regions for two groups of healthy (young and older) participants. We investigated the modular structure of these networks and tested the hypothesis that normal brain aging might be associated with changes in modularity of sparse networks. Newmans modularity metric was maximised and topological roles were assigned to brain regions depending on their specific contributions to intra- and inter-modular connectivity. Both young and older brain networks demonstrated significantly non-random modularity. The young brain network was decomposed into 3 major modules: central and posterior modules, which comprised mainly nodes with few inter-modular connections, and a dorsal fronto-cingulo-parietal module, which comprised mainly nodes with extensive inter-modular connections. The mean network in the older group also included posterior, superior central and dorsal fronto-striato-thalamic modules but the number of intermodular connections to frontal modular regions was significantly reduced, whereas the number of connector nodes in posterior and central modules was increased.

Graph analysis of functional brain networks: practical issues in translational neuroscience

The brain can be regarded as a network: a connected system where nodes, or units, represent different specialized regions and links, or connections, represent communication pathways. From a functional perspective, communication is coded by temporal dependence between the activities of different brain areas. In the last decade, the abstract representation of the brain as a graph has allowed to visualize functional brain networks and describe their non-trivial topological properties in a compact and objective way. Nowadays, the use of graph analysis in translational neuroscience has become essential to quantify brain dysfunctions in terms of aberrant reconfiguration of functional brain networks. Despite its evident impact, graph analysis of functional brain networks is not a simple toolbox that can be blindly applied to brain signals. On the one hand, it requires the know-how of all the methodological steps of the pipeline that manipulate the input brain signals and extract the functional network properties. On the other hand, knowledge of the neural phenomenon under study is required to perform physiologically relevant analysis. The aim of this review is to provide practical indications to make sense of brain network analysis and contrast counterproductive attitudes.

Hubs of brain functional networks are radically reorganized in comatose patients.

Human brain networks have topological properties in common with many other complex systems, prompting the following question: what aspects of brain network organization are critical for distinctive functional properties of the brain, such as consciousness? To address this question, we used graph theoretical methods to explore brain network topology in resting state functional MRI data acquired from 17 patients with severely impaired consciousness and 20 healthy volunteers. We found that many global network properties were conserved in comatose patients. Specifically, there was no significant abnormality of global efficiency, clustering, small-worldness, modularity, or degree distribution in the patient group. However, in every patient, we found evidence for a radical reorganization of high degree or highly efficient “hub” nodes. Cortical regions that were hubs of healthy brain networks had typically become nonhubs of comatose brain networks and vice versa. These results indicate that global topological properties of complex brain networks may be homeostatically conserved under extremely different clinical conditions and that consciousness likely depends on the anatomical location of hub nodes in human brain networks.

Machine Learning with Brain Graphs: Predictive Modeling Approaches for Functional Imaging in Systems Neuroscience

The observation and description of the living brain has attracted a lot of research over the past centuries. Many noninvasive imaging modalities have been developed, such as topographical techniques based on the electromagnetic field potential [i.e., electroencephalography (EEG) and magnetoencephalography (MEG)], and tomography approaches including positron emission tomography and magnetic resonance imaging (MRI). Here we will focus on functional MRI (fMRI) since it is widely deployed for clinical and cognitive neurosciences today, and it can reveal brain function due to neurovascular coupling (see ?From Brain Images to fMRI Time Series?). It has led to a much better understanding of brain function, including the description of brain areas with very specialized functions such as face recognition. These neuroscientific insights have been made possible by important methodological advances in MR physics, signal processing, and mathematical modeling.

Use of Advanced Magnetic Resonance Imaging Techniques in Neuromyelitis Optica Spectrum Disorder.

Brain parenchymal lesions are frequently observed on conventional magnetic resonance imaging (MRI) scans of patients with neuromyelitis optica (NMO) spectrum disorder, but the specific morphological and temporal patterns distinguishing them unequivocally from lesions caused by other disorders have not been identified. This literature review summarizes the literature on advanced quantitative imaging measures reported for patients with NMO spectrum disorder, including proton MR spectroscopy, diffusion tensor imaging, magnetization transfer imaging, quantitative MR volumetry, and ultrahigh-field strength MRI. It was undertaken to consider the advanced MRI techniques used for patients with NMO by different specialists in the field. Although quantitative measures such as proton MR spectroscopy or magnetization transfer imaging have not reproducibly revealed diffuse brain injury, preliminary data from diffusion-weighted imaging and brain tissue volumetry indicate greater white matter than gray matter degradation. These findings could be confirmed by ultrahigh-field MRI. The use of nonconventional MRI techniques may further our understanding of the pathogenic processes in NMO spectrum disorders and may help us identify the distinct radiographic features corresponding to specific phenotypic manifestations of this disease.

Identifiability of post-nonlinear mixtures

This letter deals with the resolution of the blind source separation problem using the independent component analysis method in post-nonlinear mixtures. Using the sole hypothesis of the source independence is not obvious to reconstruct the sources in nonlinear mixtures. Here, we prove the identifiability under weak assumptions on the mixture matrix and density sources.

Reliability of graph analysis of resting state fMRI using test-retest dataset from the Human Connectome Project

The exploration of brain networks with resting-state fMRI (rs-fMRI) combined with graph theoretical approaches has become popular, with the perspective of finding network graph metrics as biomarkers in the context of clinical studies. A preliminary requirement for such findings is to assess the reliability of the graph based connectivity metrics. In previous test-retest (TRT) studies, this reliability has been explored using intraclass correlation coefficient (ICC) with heterogeneous results. But the issue of sample size has not been addressed. Using the large TRT rs-fMRI dataset from the Human Connectome Project (HCP), we computed ICCs and their corresponding p-values (applying permutation and bootstrap techniques) and varied the number of subjects (from 20 to 100), the scan duration (from 400 to 1200 time points), the cost and the graph metrics, using the Anatomic-Automatic Labelling (AAL) parcellation scheme. We quantified the reliability of the graph metrics computed both at global and regional level depending, at optimal cost, on two key parameters, the sample size and the number of time points or scan duration. In the cost range between 20% to 35%, most of the global graph metrics are reliable with 40 subjects or more with long scan duration (14min 24s). In large samples (for instance, 100 subjects), most global and regional graph metrics are reliable for a minimum scan duration of 7min 14s. Finally, for 40 subjects and long scan duration (14min 24s), the reliable regions are located in the main areas of the default mode network (DMN), the motor and the visual networks.