Complex modular structure of large-scale brain networks

The role of the thalamus in modular functional networks in temporal lobe epilepsy with cognitive impairment

OBJECTIVE

Cognitive deficit is common in patients with temporal lobe epilepsy (TLE). Here, we aimed to investigate the modular architecture of functional networks associated with distinct cognitive states in TLE patients together with the role of the thalamus in modular networks.

METHODS

Resting-state functional magnetic resonance imaging scans were acquired from 53 TLE patients and 37 matched healthy controls. All patients received the Montreal Cognitive Assessment test and accordingly were divided into TLE patients with normal cognition (TLE-CN, n = 35) and TLE patients with cognitive impairment (TLE-CI, n = 18) groups. The modular properties of functional networks were calculated and compared including global modularity Q, modular segregation index, intramodular connections, and intermodular connections. Thalamic subdivisions corresponding to the modular networks were generated by applying a 'winner-take-all' strategy before analyzing the modular properties (participation coefficient and within-module degree z-score) of each thalamic subdivision to assess the contribution of the thalamus to modular functional networks. Relationships between network properties and cognitive performance were then further explored.

RESULTS

Both TLE-CN and TLE-CI patients showed lower global modularity, as well as lower modular segregation index values for the ventral attention network and the default mode network. However, different patterns of intramodular and intermodular connections existed for different cognitive states. In addition, both TLE-CN and TLE-CI patients exhibited anomalous modular properties of functional thalamic subdivisions, with TLE-CI patients presenting a broader range of abnormalities. Cognitive performance in TLE-CI patients was not related to the modular properties of functional network but rather to the modular properties of functional thalamic subdivisions.

CONCLUSIONS

The thalamus plays a prominent role in modular networks and potentially represents a key neural mechanism underlying cognitive impairment in TLE.

Cortico-spinal modularity in the parieto-frontal system: A new perspective on action control

Classical neurophysiology suggests that the motor cortex (MI) has a unique role in action control. In contrast, this review presents evidence for multiple parieto-frontal spinal command modules that can bypass MI. Five observations support this modular perspective: (i) the statistics of cortical connectivity demonstrate functionally-related clusters of cortical areas, defining functional modules in the premotor, cingulate, and parietal cortices; (ii) different corticospinal pathways originate from the above areas, each with a distinct range of conduction velocities; (iii) the activation time of each module varies depending on task, and different modules can be activated simultaneously; (iv) a modular architecture with direct motor output is faster and less metabolically expensive than an architecture that relies on MI, given the slow connections between MI and other cortical areas; (v) lesions of the areas composing parieto-frontal modules have different effects from lesions of MI. Here we provide examples of six cortico-spinal modules and functions they subserve: module 1) arm reaching, tool use and object construction; module 2) spatial navigation and locomotion; module 3) grasping and observation of hand and mouth actions; module 4) action initiation, motor sequences, time encoding; module 5) conditional motor association and learning, action plan switching and action inhibition; module 6) planning defensive actions. These modules can serve as a library of tools to be recombined when faced with novel tasks, and MI might serve as a recombinatory hub. In conclusion, the availability of locally-stored information and multiple outflow paths supports the physiological plausibility of the proposed modular perspective.

Hierarchical overlapping modular structure in the human cerebral cortex improves individual identification

The idea that brain networks have a hierarchical modular organization is pervasive. Increasing evidence suggests that brain modules overlap. However, little is known about the hierarchical overlapping modular structure in the brain. In this study, we developed a framework to uncover brain hierarchical overlapping modular structures based on a nested-spectral partition algorithm and an edge-centric network model. Overlap degree between brain modules is symmetrical across hemispheres, with highest overlap observed in the control and salience/ventral attention networks. Furthermore, brain edges are clustered into two groups: intrasystem and intersystem edges, to form hierarchical overlapping modules. At different levels, modules are self-similar in the degree of overlap. Additionally, the brain's hierarchical structure contains more individual identifiable information than a single-level structure, particularly in the control and salience/ventral attention networks. Our results offer pathways for future studies aimed at relating the organization of hierarchical overlapping modules to brain cognitive behavior and disorders.

Modules in connectomes of phase-synchronization comprise anatomically contiguous, functionally related regions

Modules in brain functional connectomes are essential to balancing segregation and integration of neuronal activity. Connectomes are the complete set of pairwise connections between brain regions. Non-invasive Electroencephalography (EEG) and Magnetoencephalography (MEG) have been used to identify modules in connectomes of phase-synchronization. However, their resolution is suboptimal because of spurious phase-synchronization due to EEG volume conduction or MEG field spread. Here, we used invasive, intracerebral recordings from stereo-electroencephalography (SEEG, N = 67), to identify modules in connectomes of phase-synchronization. To generate SEEG-based group-level connectomes affected only minimally by volume conduction, we used submillimeter accurate localization of SEEG contacts and referenced electrode contacts in cortical gray matter to their closest contacts in white matter. Combining community detection methods with consensus clustering, we found that the connectomes of phase-synchronization were characterized by distinct and stable modules at multiple spatial scales, across frequencies from 3 to 320 Hz. These modules were highly similar within canonical frequency bands. Unlike the distributed brain systems identified with functional Magnetic Resonance Imaging (fMRI), modules up to the high-gamma frequency band comprised only anatomically contiguous regions. Notably, the identified modules comprised cortical regions involved in shared repertoires of sensorimotor and cognitive functions including memory, language and attention. These results suggest that the identified modules represent functionally specialised brain systems, which only partially overlap with the brain systems reported with fMRI. Hence, these modules might regulate the balance between functional segregation and functional integration through phase-synchronization.

The pyramid representation of the functional network using resting-state fMRI

Background

Resting-state functional magnetic resonance imaging (RS-fMRI) has been proved to be a useful tool to study the brain mechanism in the quest to probe the distinct pattern of inter-region interactions in the brain. As an important application of RS-fMRI, the graph-based approach characterizes the brain as a complex network. However, the network is susceptible to its scale that determines the trade-off between sensitivity and anatomical variability.

Objective

To balance sensitivity and anatomical variability, a pyramid representation of the functional network is proposed, which is composed of five individual networks reconstructed at multiple scales.

Methods

The pyramid representation of the functional network was applied to two groups of participants, including patients with Alzheimer's disease (AD) and normal elderly (NC) individuals, as a demonstration. Features were extracted from the multi-scale networks and were evaluated with their inter-group differences between AD and NC, as well as the discriminative power in recognizing AD. Moreover, the proposed method was also validated by another dataset from people with autism.

Results

The different features reflect the highest sensitivity to distinguish AD at different scales. In addition, the combined features have higher accuracy than any single scale-based feature. These findings highlight the potential use of multi-scale features as markers of the disrupted topological organization in AD networks.

Conclusion

We believe that multi-scale metrics could provide a more comprehensive characterization of the functional network and thus provide a promising solution for representing the underlying functional mechanism in the human brain on a multi-scale basis.

A mixed-modeling framework for whole-brain dynamic network analysis

The emerging area of dynamic brain network analysis has gained considerable attention in recent years. However, development of multivariate statistical frameworks that allow for examining the associations between phenotypic traits and dynamic patterns of system-level properties of the brain, and drawing statistical inference about such associations, has largely lagged behind. To address this need we developed a mixed-modeling framework that allows for assessing the relationship between any desired phenotype and dynamic patterns of whole-brain connectivity and topology. This novel framework also allows for simulating dynamic brain networks with respect to desired covariates. Unlike current tools, which largely use data-driven methods, our model-based method enables aligning neuroscientific hypotheses with the analytic approach. We demonstrate the utility of this model in identifying the relationship between fluid intelligence and dynamic brain networks by using resting-state fMRI (rfMRI) data from 200 participants in the Human Connectome Project (HCP) study. We also demonstrate the utility of this model to simulate dynamic brain networks at both group and individual levels. To our knowledge, this approach provides the first model-based statistical method for examining dynamic patterns of system-level properties of the brain and their relationships to phenotypic traits as well as simulating dynamic brain networks.

In recent years, a growing body of studies have aimed at analyzing the brain as a complex dynamic system by using various neuroimaging data. This has opened new avenues to answer compelling questions about the brain function in health and disease. However, methods that allow for providing statistical inference about how the complex interactions of the brain are associated with desired phenotypes are to be developed for a more profound insight. This study introduces a promising regression-based model to relate dynamic brain networks to desired phenotypes and provide statistical inference. Moreover, it can be used for simulating dynamic brain networks with respect to desired phenotypes at the group and individual levels.

Inner Hemispheric and Interhemispheric Connectivity Balance in the Human Brain

The connectome of the brain has a great impact on the function of the brain as the structure of the connectome affects the speed and efficiency of information transfer. As a highly energy-consuming organ, an efficient network structure is essential. A previous study has shown consistent overall brain connectivity across a large variety of species. This connectivity conservation was explained by a balance between interhemispheric and intrahemispheric connections; that is, spices with highly connected hemispheres appear to have weaker interhemisphere connections. This study examines this connectivity trade-off in the human brain using diffusion-based tractography and network analysis in the Human Connectome Project (970 subjects, 527 female). We explore the biological origins of this phenomenon, heritability, and the effect on cognitive measures.The proportion of commissural fibers in the brain had a negative correlation to hemispheric efficiency, pointing to a trade-off between inner hemispheric and interhemispheric connectivity. Network hubs including anterior and middle cingulate cortex, superior frontal areas, medial occipital areas, the parahippocampal gyrus, post- and precentral gyri, and the precuneus had the strongest contribution to this phenomenon. Other results show a high heritability as well as a strong connection to crystalized intelligence. This work presents cohort-based network analysis research, spanning a large variety of samples and exploring the overall architecture of the human connectome. Our results show a connectivity conservation phenomenon at the base of the overall brain network architecture. This network structure may explain much of the functional, behavioral, and cognitive variability among different brains.SIGNIFICANCE STATEMENT The network structure of the brain is at the basis of every brain function as it dictates the characteristics of information transfer. Understanding the patterns and mechanisms that guide the connectome structure is crucial to understanding the brain itself. Here we unravel the mechanism at the base of the connectivity conservation phenomenon by exploring the interaction between hemispheric and commissural connectivity in a large-scale cohort-based connectivity study. We describe the trade-off between the two components and examine the origins of the trade-off and observe the effect on cognitive abilities and behavior.

Modularity-Guided Functional Brain Network Analysis for Early-Stage Dementia Identification

Function brain network (FBN) analysis has shown great potential in identifying brain diseases, such as Alzheimer's disease (AD) and its prodromal stage, namely mild cognitive impairment (MCI). It is essential to identify discriminative and interpretable features from function brain networks, so as to improve classification performance and help us understand the pathological mechanism of AD-related brain disorders. Previous studies usually extract node statistics or edge weights from FBNs to represent each subject. However, these methods generally ignore the topological structure (such as modularity) of FBNs. To address this issue, we propose a modular-LASSO feature selection (MLFS) framework that can explicitly model the modularity information to identify discriminative and interpretable features from FBNs for automated AD/MCI classification. Specifically, the proposed MLFS method first searches the modular structure of FBNs through a signed spectral clustering algorithm, and then selects discriminative features via a modularity-induced group LASSO method, followed by a support vector machine (SVM) for classification. To evaluate the effectiveness of the proposed method, extensive experiments are performed on 563 resting-state functional MRI scans from the public ADNI database to identify subjects with AD/MCI from normal controls and predict the future progress of MCI subjects. Experimental results demonstrate that our method is superior to previous methods in both tasks of AD/MCI identification and MCI conversion prediction, and also helps discover discriminative brain regions and functional connectivities associated with AD.

Spike signal transmission between modules and the predictability of spike activity in modular neuronal networks

Modularity is a common feature of the nervous system across species and scales. Although it has been qualitatively investigated in network science, very little is known about how it affects spike signal transmission in neuronal networks at the mesoscopic level. Here, a neuronal network model is built to simulate dynamic interactions among different modules of neuronal networks. This neuronal network model follows the organizational principle of modular structure. The neurons can generate spikes like biological neurons, and changes in the strength of synaptic connections conform to the STDP learning rule. Based on this neuronal network model, we first quantitatively studied whether and to what extent the connectivity within and between modules can affect spike signal transmission, and found that spike signal transmission heavily depends on the connectivity between modules, but has little to do with the connectivity within modules. More importantly, we further found that the spike activity of a module can be predicted according to the spike activities of its adjacent modules through building a resting-state functional connectivity matrix.

Network-based brain computer interfaces: principles and applications

Brain-computer interfaces (BCIs) make possible to interact with the external environment by decoding the mental intention of individuals. BCIs can therefore be used to address basic neuroscience questions but also to unlock a variety of applications from exoskeleton control to neurofeedback (NFB) rehabilitation. In general, BCI usability critically depends on the ability to comprehensively characterize brain functioning and correctly identify the user's mental state. To this end, much of the efforts have focused on improving the classification algorithms taking into account localized brain activities as input features. Despite considerable improvement BCI performance is still unstable and, as a matter of fact, current features represent oversimplified descriptors of brain functioning. In the last decade, growing evidence has shown that the brain works as a networked system composed of multiple specialized and spatially distributed areas that dynamically integrate information. While more complex, looking at how remote brain regions functionally interact represents a grounded alternative to better describe brain functioning. Thanks to recent advances in network science, i.e. a modern field that draws on graph theory, statistical mechanics, data mining and inferential modelling, scientists have now powerful means to characterize complex brain networks derived from neuroimaging data. Notably, summary features can be extracted from these networks to quantitatively measure specific organizational properties across a variety of topological scales. In this topical review, we aim to provide the state-of-the-art supporting the development of a network theoretic approach as a promising tool for understanding BCIs and improve usability.

Tau pathology in early Alzheimer's disease is linked to selective disruptions in neurophysiological network dynamics

Understanding the role of Tau protein aggregation in the pathogenesis of Alzheimer's disease is critical for the development of new Tau-based therapeutic strategies to slow or prevent dementia. We tested the hypothesis that Tau pathology is associated with functional organization of widespread neurophysiological networks. We used electro-magnetoencephalography with [¹⁸F]AV-1451 PET scanning to quantify Tau-dependent network changes. Using a graph theoretical approach to brain connectivity, we quantified nodal measures of functional segregation, centrality, and the efficiency of information transfer and tested them against levels of [¹⁸F]AV-1451. Higher Tau burden in early Alzheimer's disease was associated with a shift away from the optimal small-world organization and a more fragmented network in the beta and gamma bands, whereby parieto-occipital areas were disconnected from the anterior parts of the network. Similarly, higher Tau burden was associated with decreases in both local and global efficiency, especially in the gamma band. The results support the translational development of neurophysiological "signatures" of Alzheimer's disease, to understand disease mechanisms in humans and facilitate experimental medicine studies.

Modeling the temporal network dynamics of neuronal cultures

Neurons form complex networks that evolve over multiple time scales. In order to thoroughly characterize these networks, time dependencies must be explicitly modeled. Here, we present a statistical model that captures both the underlying structural and temporal dynamics of neuronal networks. Our model combines the class of Stochastic Block Models for community formation with Gaussian processes to model changes in the community structure as a smooth function of time. We validate our model on synthetic data and demonstrate its utility on three different studies using in vitro cultures of dissociated neurons.

Sample Entropy Combined with the K-Means Clustering Algorithm Reveals Six Functional Networks of the Brain

Identifying brain regions contained in brain functional networks and functions of brain functional networks is of great significance in understanding the complexity of the human brain. The 160 regions of interest (ROIs) in the human brain determined by the Dosenbach’s template have been divided into six functional networks with different functions. In the present paper, the complexity of the human brain is characterized by the sample entropy (SampEn) of dynamic functional connectivity (FC) which is obtained by analyzing the resting-state functional magnetic resonance imaging (fMRI) data acquired from healthy participants. The 160 ROIs are clustered into six clusters by applying the K-means clustering algorithm to the SampEn of dynamic FC as well as the static FC which is also obtained by analyzing the resting-state fMRI data. The six clusters obtained from the SampEn of dynamic FC and the static FC show very high overlap and consistency ratios with the six functional networks. Furthermore, for four of six clusters, the overlap ratios corresponding to the SampEn of dynamic FC are larger than that corresponding to the static FC, and for five of six clusters, the consistency ratios corresponding to the SampEn of dynamic FC are larger than that corresponding to the static FC. The results show that the combination of machine learning methods and the FC obtained using the blood oxygenation level-dependent (BOLD) signals can identify the functional networks of the human brain, and nonlinear dynamic characteristics of the FC are more effective than the static characteristics of the FC in identifying brain functional networks and the complexity of the human brain.

Effective degrees of freedom of the Pearson's correlation coefficient under autocorrelation

The dependence between pairs of time series is commonly quantified by Pearson's correlation. However, if the time series are themselves dependent (i.e. exhibit temporal autocorrelation), the effective degrees of freedom (EDF) are reduced, the standard error of the sample correlation coefficient is biased, and Fisher's transformation fails to stabilise the variance. Since fMRI time series are notoriously autocorrelated, the issue of biased standard errors - before or after Fisher's transformation - becomes vital in individual-level analysis of resting-state functional connectivity (rsFC) and must be addressed anytime a standardised Z-score is computed. We find that the severity of autocorrelation is highly dependent on spatial characteristics of brain regions, such as the size of regions of interest and the spatial location of those regions. We further show that the available EDF estimators make restrictive assumptions that are not supported by the data, resulting in biased rsFC inferences that lead to distorted topological descriptions of the connectome on the individual level. We propose a practical "xDF" method that accounts not only for distinct autocorrelation in each time series, but instantaneous and lagged cross-correlation. We find the xDF correction varies substantially over node pairs, indicating the limitations of global EDF corrections used previously. In addition to extensive synthetic and real data validations, we investigate the impact of this correction on rsFC measures in data from the Young Adult Human Connectome Project, showing that accounting for autocorrelation dramatically changes fundamental graph theoretical measures relative to no correction.

Volume entropy for modeling information flow in a brain graph

Brain regions send and receive information through neuronal connections in an efficient way. In this paper, we modelled the information propagation in brain networks by a generalized Markov system associated with a new edge-transition matrix, based on the assumption that information flows through brain networks forever. From this model, we derived new global and local network measures, called a volume entropy and the capacity of nodes and edges on FDG PET and resting-state functional MRI. Volume entropy of a metric graph, a global measure of information, measures the exponential growth rate of the number of network paths. Capacity of nodes and edges, a local measure of information, represents the stationary distribution of information propagation in brain networks. On the resting-state functional MRI of healthy normal subjects, these measures revealed that volume entropy was significantly negatively correlated to the aging and capacities of specific brain nodes and edges underpinned which brain nodes or edges contributed these aging-related changes.

Topological structures are consistently overestimated in functional complex networks

Functional complex networks have meant a pivotal change in the way we understand complex systems, being the most outstanding one the human brain. These networks have classically been reconstructed using a frequentist approach that, while simple, completely disregards the uncertainty that derives from data finiteness. We provide here an alternative solution based on Bayesian inference, with link weights treated as random variables described by probability distributions, from which ensembles of networks are sampled. By using both statistical and topological considerations, we prove that the role played by links’ uncertainty is equivalent to the introduction of a random rewiring, whose omission leads to a consistent overestimation of topological structures. We further show that this bias is enhanced in short time series, suggesting the existence of a theoretical time resolution limit for obtaining reliable structures. We also propose a simple sampling process for correcting topological values obtained in frequentist networks. We finally validate these concepts through synthetic and real network examples, the latter representing the brain electrical activity of a group of people during a cognitive task.

Connectivity in fMRI: Blind Spots and Breakthroughs

In recent years, driven by scientific and clinical concerns, there has been an increased interest in the analysis of functional brain networks. The goal of these analyses is to better understand how brain regions interact, how this depends upon experimental conditions and behavioral measures and how anomalies (disease) can be recognized. In this paper, we provide, first, a brief review of some of the main existing methods of functional brain network analysis. But rather than compare them, as a traditional review would do, instead, we draw attention to their significant limitations and blind spots. Then, second, relevant experts, sketch a number of emerging methods, which can break through these limitations. In particular we discuss five such methods. The first two, stochastic block models and exponential random graph models, provide an inferential basis for network analysis lacking in the exploratory graph analysis methods. The other three addresses: network comparison via persistent homology, time-varying connectivity that distinguishes sample fluctuations from neural fluctuations, and network system identification that draws inferential strength from temporal autocorrelation.

Small-world human brain networks: Perspectives and challenges

Modelling the human brain as a complex network has provided a powerful mathematical framework to characterize the structural and functional architectures of the brain. In the past decade, the combination of non-invasive neuroimaging techniques and graph theoretical approaches enable us to map human structural and functional connectivity patterns (i.e., connectome) at the macroscopic level. One of the most influential findings is that human brain networks exhibit prominent small-world organization. Such a network architecture in the human brain facilitates efficient information segregation and integration at low wiring and energy costs, which presumably results from natural selection under the pressure of a cost-efficiency balance. Moreover, the small-world organization undergoes continuous changes during normal development and ageing and exhibits dramatic alterations in neurological and psychiatric disorders. In this review, we survey recent advances regarding the small-world architecture in human brain networks and highlight the potential implications and applications in multidisciplinary fields, including cognitive neuroscience, medicine and engineering. Finally, we highlight several challenging issues and areas for future research in this rapidly growing field.

Memory-Efficient Analysis of Dense Functional Connectomes

The functioning of the human brain relies on the interplay and integration of numerous individual units within a complex network. To identify network configurations characteristic of specific cognitive tasks or mental illnesses, functional connectomes can be constructed based on the assessment of synchronous fMRI activity at separate brain sites, and then analyzed using graph-theoretical concepts. In most previous studies, relatively coarse parcellations of the brain were used to define regions as graphical nodes. Such parcellated connectomes are highly dependent on parcellation quality because regional and functional boundaries need to be relatively consistent for the results to be interpretable. In contrast, dense connectomes are not subject to this limitation, since the parcellation inherent to the data is used to define graphical nodes, also allowing for a more detailed spatial mapping of connectivity patterns. However, dense connectomes are associated with considerable computational demands in terms of both time and memory requirements. The memory required to explicitly store dense connectomes in main memory can render their analysis infeasible, especially when considering high-resolution data or analyses across multiple subjects or conditions. Here, we present an object-based matrix representation that achieves a very low memory footprint by computing matrix elements on demand instead of explicitly storing them. In doing so, memory required for a dense connectome is reduced to the amount needed to store the underlying time series data. Based on theoretical considerations and benchmarks, different matrix object implementations and additional programs (based on available Matlab functions and Matlab-based third-party software) are compared with regard to their computational efficiency. The matrix implementation based on on-demand computations has very low memory requirements, thus enabling analyses that would be otherwise infeasible to conduct due to insufficient memory. An open source software package containing the created programs is available for download.

Modularity in network neuroscience and neural reuse

Neural reuse allegedly stands in stark contrast against a modular view of the brain. However, the development of unique modularity algorithms in network science has provided the means to identify functionally cooperating, specialized subsystems in a way that remains consistent with the neural reuse view and offers a set of rigorous tools to fully engage in Anderson's (2014) research program.

Estimating functional brain networks by incorporating a modularity prior

Functional brain network analysis has become one principled way of revealing informative organization architectures in healthy brains, and providing sensitive biomarkers for diagnosis of neurological disorders. Prior to any post hoc analysis, however, a natural issue is how to construct "ideal" brain networks given, for example, a set of functional magnetic resonance imaging (fMRI) time series associated with different brain regions. Although many methods have been developed, it is currently still an open field to estimate biologically meaningful and statistically robust brain networks due to our limited understanding of the human brain as well as complex noises in the observed data. Motivated by the fact that the brain is organized with modular structures, in this paper, we propose a novel functional brain network modeling scheme by encoding a modularity prior under a matrix-regularized network learning framework, and further formulate it as a sparse low-rank graph learning problem, which can be solved by an efficient optimization algorithm. Then, we apply the learned brain networks to identify patients with mild cognitive impairment (MCI) from normal controls. We achieved 89.01% classification accuracy even with a simple feature selection and classification pipeline, which significantly outperforms the conventional brain network construction methods. Moreover, we further explore brain network features that contributed to MCI identification, and discovered potential biomarkers for personalized diagnosis.

Graph theoretic network analysis reveals protein pathways underlying cell death following neurotropic viral infection

Complex protein networks underlie any cellular function. Certain proteins play a pivotal role in many network configurations, disruption of whose expression proves fatal to the cell. An efficient method to tease out such key proteins in a network is still unavailable. Here, we used graph-theoretic measures on protein-protein interaction data (interactome) to extract biophysically relevant information about individual protein regulation and network properties such as formation of function specific modules (sub-networks) of proteins. We took 5 major proteins that are involved in neuronal apoptosis post Chandipura Virus (CHPV) infection as seed proteins in a database to create a meta-network of immediately interacting proteins (1^st order network). Graph theoretic measures were employed to rank the proteins in terms of their connectivity and the degree upto which they can be organized into smaller modules (hubs). We repeated the analysis on 2^nd order interactome that includes proteins connected directly with proteins of 1^st order. FADD and Casp-3 were connected maximally to other proteins in both analyses, thus indicating their importance in neuronal apoptosis. Thus, our analysis provides a blueprint for the detection and validation of protein networks disrupted by viral infections.

An algebraic topological method for multimodal brain networks comparisons

Understanding brain connectivity is one of the most important issues in neuroscience. Nonetheless, connectivity data can reflect either functional relationships of brain activities or anatomical connections between brain areas. Although both representations should be related, this relationship is not straightforward. We have devised a powerful method that allows different operations between networks that share the same set of nodes, by embedding them in a common metric space, enforcing transitivity to the graph topology. Here, we apply this method to construct an aggregated network from a set of functional graphs, each one from a different subject. Once this aggregated functional network is constructed, we use again our method to compare it with the structural connectivity to identify particular brain regions that differ in both modalities (anatomical and functional). Remarkably, these brain regions include functional areas that form part of the classical resting state networks. We conclude that our method -based on the comparison of the aggregated functional network- reveals some emerging features that could not be observed when the comparison is performed with the classical averaged functional network.

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.

Between-network connectivity occurs in brain regions lacking layer IV input

To better understand the cortical circuitry underlying connectivity between large-scale neural networks, we develop a novel, data-driven approach to identify potential integration subregions. Between-network connectivity (BNC) associated with any anatomical region is the amount of connectivity between that point and all large-scale networks, as measured using simple and multiple correlations. It is straightforward to calculate and applicable to functional networks identified using independent components analysis. We calculated BNC for all fMRI voxels within the brain and compared the results to known regional cytoarchitectural patterns. Based on previous observations of the relationship between macroscopic connectivity and microscopic cytoarchitecture, we predicted that areas with high BNC will be located in paralimbic subregions with an undifferentiated laminar structure. Results suggest that the anterior insula and dorsal posterior cingulate cortices play prominent roles in information integration. Cytoarchitecturely, these areas show agranular or dysgranular cytologies with absent or disrupted cortical layer IV. Since layer IV is the primary recipient of feed-forward thalamocortical connections, and due to the exclusive nature of driving connections to this layer, we suggest that the absence of cortical layer IV might allow for information to be exchanged across networks, and is an organizational characteristic of brain-subregions serving as inter-network communication hubs.

Experimental synchronization of chaos in a large ring of mutually coupled single-transistor oscillators: phase, amplitude, and clustering effects

In this paper, experimental evidence of multiple synchronization phenomena in a large (n = 30) ring of chaotic oscillators is presented. Each node consists of an elementary circuit, generating spikes of irregular amplitude and comprising one bipolar junction transistor, one capacitor, two inductors, and one biasing resistor. The nodes are mutually coupled to their neighbours via additional variable resistors. As coupling resistance is decreased, phase synchronization followed by complete synchronization is observed, and onset of synchronization is associated with partial synchronization, i.e., emergence of communities (clusters). While component tolerances affect community structure, the general synchronization properties are maintained across three prototypes and in numerical simulations. The clusters are destroyed by adding long distance connections with distant notes, but are otherwise relatively stable with respect to structural connectivity changes. The study provides evidence that several fundamental synchronization phenomena can be reliably observed in a network of elementary single-transistor oscillators, demonstrating their generative potential and opening way to potential applications of this undemanding setup in experimental modelling of the relationship between network structure, synchronization, and dynamical properties.

Changes in global and regional modularity associated with increasing working memory load

Using graph theory measures common to complex network analyses of neuroimaging data, the objective of this study was to explore the effects of increasing working memory processing load on functional brain network topology in a cohort of young adults. Measures of modularity in complex brain networks quantify how well a network is organized into densely interconnected communities. We investigated changes in both the large-scale modular organization of the functional brain network as a whole and regional changes in modular organization as demands on working memory increased from n = 1 to n = 2 on the standard n-back task. We further investigated the relationship between modular properties across working memory load conditions and behavioral performance. Our results showed that regional modular organization within the default mode and working memory circuits significantly changed from 1-back to 2-back task conditions. However, the regional modular organization was not associated with behavioral performance. Global measures of modular organization did not change with working memory load but were associated with individual variability in behavioral performance. These findings indicate that regional and global network properties are modulated by different aspects of working memory under increasing load conditions. These findings highlight the importance of assessing multiple features of functional brain network topology at both global and regional scales rather than focusing on a single network property.

Functional cortical network in alpha band correlates with social bargaining

Solving demanding tasks requires fast and flexible coordination among different brain areas. Everyday examples of this are the social dilemmas in which goals tend to clash, requiring one to weigh alternative courses of action in limited time. In spite of this fact, there are few studies that directly address the dynamics of flexible brain network integration during social interaction. To study the preceding, we carried out EEG recordings while subjects played a repeated version of the Ultimatum Game in both human (social) and computer (non-social) conditions. We found phase synchrony (inter-site-phase-clustering) modulation in alpha band that was specific to the human condition and independent of power modulation. The strength and patterns of the inter-site-phase-clustering of the cortical networks were also modulated, and these modulations were mainly in frontal and parietal regions. Moreover, changes in the individuals’ alpha network structure correlated with the risk of the offers made only in social conditions. This correlation was independent of changes in power and inter-site-phase-clustering strength. Our results indicate that, when subjects believe they are participating in a social interaction, a specific modulation of functional cortical networks in alpha band takes place, suggesting that phase synchrony of alpha oscillations could serve as a mechanism by which different brain areas flexibly interact in order to adapt ongoing behavior in socially demanding contexts.

Stochastic geometric network models for groups of functional and structural connectomes

Structural and functional connectomes are emerging as important instruments in the study of normal brain function and in the development of new biomarkers for a variety of brain disorders. In contrast to single-network studies that presently dominate the (non-connectome) network literature, connectome analyses typically examine groups of empirical networks and then compare these against standard (stochastic) network models. The current practice in connectome studies is to employ stochastic network models derived from social science and engineering contexts as the basis for the comparison. However, these are not necessarily best suited for the analysis of connectomes, which often contain groups of very closely related networks, such as occurs with a set of controls or a set of patients with a specific disorder. This paper studies important extensions of standard stochastic models that make them better adapted for analysis of connectomes, and develops new statistical fitting methodologies that account for inter-subject variations. The extensions explicitly incorporate geometric information about a network based on distances and inter/intra hemispherical asymmetries (to supplement ordinary degree-distribution information), and utilize a stochastic choice of network density levels (for fixed threshold networks) to better capture the variance in average connectivity among subjects. The new statistical tools introduced here allow one to compare groups of networks by matching both their average characteristics and the variations among them. A notable finding is that connectomes have high "smallworldness" beyond that arising from geometric and degree considerations alone.

Fast construction of voxel-level functional connectivity graphs

Background

Graph-based analysis of fMRI data has recently emerged as a promising approach to study brain networks. Based on the assessment of synchronous fMRI activity at separate brain sites, functional connectivity graphs are constructed and analyzed using graph-theoretical concepts. Most previous studies investigated region-level graphs, which are computationally inexpensive, but bring along the problem of choosing sensible regions and involve blurring of more detailed information. In contrast, voxel-level graphs provide the finest granularity attainable from the data, enabling analyses at superior spatial resolution. They are, however, associated with considerable computational demands, which can render high-resolution analyses infeasible. In response, many existing studies investigating functional connectivity at the voxel-level reduced the computational burden by sacrificing spatial resolution.

Methods

Here, a novel, time-efficient method for graph construction is presented that retains the original spatial resolution. Performance gains are instead achieved through data reduction in the temporal domain based on dichotomization of voxel time series combined with tetrachoric correlation estimation and efficient implementation.

Results

By comparison with graph construction based on Pearson’s r, the technique used by the majority of previous studies, we find that the novel approach produces highly similar results an order of magnitude faster.

Conclusions

Its demonstrated performance makes the proposed approach a sensible and efficient alternative to customary practice. An open source software package containing the created programs is freely available for download.

Influence of wiring cost on the large-scale architecture of human cortical connectivity

In the past two decades some fundamental properties of cortical connectivity have been discovered: small-world structure, pronounced hierarchical and modular organisation, and strong core and rich-club structures. A common assumption when interpreting results of this kind is that the observed structural properties are present to enable the brain's function. However, the brain is also embedded into the limited space of the skull and its wiring has associated developmental and metabolic costs. These basic physical and economic aspects place separate, often conflicting, constraints on the brain's connectivity, which must be characterized in order to understand the true relationship between brain structure and function. To address this challenge, here we ask which, and to what extent, aspects of the structural organisation of the brain are conserved if we preserve specific spatial and topological properties of the brain but otherwise randomise its connectivity. We perform a comparative analysis of a connectivity map of the cortical connectome both on high- and low-resolutions utilising three different types of surrogate networks: spatially unconstrained ('random'), connection length preserving ('spatial'), and connection length optimised ('reduced') surrogates. We find that unconstrained randomisation markedly diminishes all investigated architectural properties of cortical connectivity. By contrast, spatial and reduced surrogates largely preserve most properties and, interestingly, often more so in the reduced surrogates. Specifically, our results suggest that the cortical network is less tightly integrated than its spatial constraints would allow, but more strongly segregated than its spatial constraints would necessitate. We additionally find that hierarchical organisation and rich-club structure of the cortical connectivity are largely preserved in spatial and reduced surrogates and hence may be partially attributable to cortical wiring constraints. In contrast, the high modularity and strong s-core of the high-resolution cortical network are significantly stronger than in the surrogates, underlining their potential functional relevance in the brain.

Node accessibility in cortical networks during motor tasks

Recent findings suggest that the preparation and execution of voluntary self-paced movements are accompanied by the coordination of the oscillatory activities of distributed brain regions. Here, we use electroencephalographic source imaging methods to estimate the cortical movement-related oscillatory activity during finger extension movements. Then, we apply network theory to investigate changes (expressed as differences from the baseline) in the connectivity structure of cortical networks related to the preparation and execution of the movement. We compute the topological accessibility of different cortical areas, measuring how well an area can be reached by the rest of the network. Analysis of cortical networks reveals specific agglomerates of cortical sources that become less accessible during the preparation and the execution of the finger movements. The observed changes neither could be explained by other measures based on geodesics or on multiple paths, nor by power changes in the cortical oscillations.

Graph theoretical analysis of developmental patterns of the white matter network

Understanding the development of human brain organization is critical for gaining insight into how the enhancement of cognitive processes is related to the fine-tuning of the brain network. However, the developmental trajectory of the large-scale white matter (WM) network is not fully understood. Here, using graph theory, we examine developmental changes in the organization of WM networks in 180 typically-developing participants. WM networks were constructed using whole brain tractography and 78 cortical regions of interest were extracted from each participant. The subjects were first divided into 5 equal sample size (n = 36) groups (early childhood: 6.0–9.7 years; late childhood: 9.8–12.7 years; adolescence: 12.9–17.5 years; young adult: 17.6–21.8 years; adult: 21.9–29.6 years). Most prominent changes in the topological properties of developing brain networks occur at late childhood and adolescence. During late childhood period, the structural brain network showed significant increase in the global efficiency but decrease in modularity, suggesting a shift of topological organization toward a more randomized configuration. However, while preserving most topological features, there was a significant increase in the local efficiency at adolescence, suggesting the dynamic process of rewiring and rebalancing brain connections at different growth stages. In addition, several pivotal hubs were identified that are vital for the global coordination of information flow over the whole brain network across all age groups. Significant increases of nodal efficiency were present in several regions such as precuneus at late childhood. Finally, a stable and functionally/anatomically related modular organization was identified throughout the development of the WM network. This study used network analysis to elucidate the topological changes in brain maturation, paving the way for developing novel methods for analyzing disrupted brain connectivity in neurodevelopmental disorders.

Evaluation of node-inhomogeneity effects on the functional brain network properties using an anatomy-constrained hierarchical brain parcellation

To investigate functional brain networks, many graph-theoretical studies have defined nodes in a graph using an anatomical atlas with about a hundred partitions. Although use of anatomical node definition is popular due to its convenience, functional inhomogeneity within each node may lead to bias or systematic errors in the graph analysis. The current study was aimed to show functional inhomogeneity of a node defined by an anatomical atlas and to show its effects on the graph topology. For this purpose, we compared functional connectivity defined using 138 resting state fMRI data among 90 cerebral nodes from the automated anatomical labeling (AAL), which is an anatomical atlas, and among 372 cerebral nodes defined using a functional connectivity-based atlas as a ground truth, which was obtained using anatomy-constrained hierarchical modularity optimization algorithm (AHMO) that we proposed to evaluate the graph properties for anatomically defined nodes. We found that functional inhomogeneity in the anatomical parcellation induced significant biases in estimating both functional connectivity and graph-theoretical network properties. We also found very high linearity in major global network properties and nodal strength at all brain regions between anatomical atlas and functional atlas with reasonable network-forming thresholds for graph construction. However, some nodal properties such as betweenness centrality did not show significant linearity in some regions. The current study suggests that the use of anatomical atlas may be biased due to its inhomogeneity, but may generally be used in most neuroimaging studies when a single atlas is used for analysis.

Disrupted modular organization of resting-state cortical functional connectivity in U.S. military personnel following concussive 'mild' blast-related traumatic brain injury

Blast-related traumatic brain injury (TBI) has been one of the "signature injuries" of the wars in Iraq and Afghanistan. However, neuroimaging studies in concussive 'mild' blast-related TBI have been challenging due to the absence of abnormalities in computed tomography or conventional magnetic resonance imaging (MRI) and the heterogeneity of the blast-related injury mechanisms. The goal of this study was to address these challenges utilizing single-subject, module-based graph theoretic analysis of resting-state functional MRI (fMRI) data. We acquired 20min of resting-state fMRI in 63 U.S. military personnel clinically diagnosed with concussive blast-related TBI and 21 U.S. military controls who had blast exposures but no diagnosis of TBI. All subjects underwent an initial scan within 90days post-injury and 65 subjects underwent a follow-up scan 6 to 12months later. A second independent cohort of 40 U.S. military personnel with concussive blast-related TBI served as a validation dataset. The second independent cohort underwent an initial scan within 30days post-injury. 75% of the scans were of good quality, with exclusions primarily due to excessive subject motion. Network analysis of the subset of these subjects in the first cohort with good quality scans revealed spatially localized reductions in the participation coefficient, a measure of between-module connectivity, in the TBI patients relative to the controls at the time of the initial scan. These group differences were less prominent on the follow-up scans. The 15 brain areas with the most prominent reductions in the participation coefficient were next used as regions of interest (ROIs) for single-subject analyses. In the first TBI cohort, more subjects than would be expected by chance (27/47 versus 2/47 expected, p<0.0001) had 3 or more brain regions with abnormally low between-module connectivity relative to the controls on the initial scans. On the follow-up scans, more subjects than expected by chance (5/37, p=0.044) but fewer subjects than on the initial scans had 3 or more brain regions with abnormally low between-module connectivity. Analysis of the second TBI cohort validation dataset with no free parameters provided a partial replication; again more subjects than expected by chance (8/31, p=0.006) had 3 or more brain regions with abnormally low between-module connectivity on the initial scans, but the numbers were not significant (2/27, p=0.276) on the follow-up scans. A single-subject, multivariate analysis by probabilistic principal component analysis of the between-module connectivity in the 15 identified ROIs, showed that 31/47 subjects in the first TBI cohort were found to be abnormal relative to the controls on the initial scans. In the second TBI cohort, 9/31 patients were found to be abnormal in identical multivariate analysis with no free parameters. Again, there were not substantial differences on the follow-up scans. Taken together, these results indicate that single-subject, module-based graph theoretic analysis of resting-state fMRI provides potentially useful information for concussive blast-related TBI if high quality scans can be obtained. The underlying biological mechanisms and consequences of disrupted between-module connectivity are unknown, thus further studies are required.

A hybrid CPU-GPU accelerated framework for fast mapping of high-resolution human brain connectome

Recently, a combination of non-invasive neuroimaging techniques and graph theoretical approaches has provided a unique opportunity for understanding the patterns of the structural and functional connectivity of the human brain (referred to as the human brain connectome). Currently, there is a very large amount of brain imaging data that have been collected, and there are very high requirements for the computational capabilities that are used in high-resolution connectome research. In this paper, we propose a hybrid CPU-GPU framework to accelerate the computation of the human brain connectome. We applied this framework to a publicly available resting-state functional MRI dataset from 197 participants. For each subject, we first computed Pearson's Correlation coefficient between any pairs of the time series of gray-matter voxels, and then we constructed unweighted undirected brain networks with 58 k nodes and a sparsity range from 0.02% to 0.17%. Next, graphic properties of the functional brain networks were quantified, analyzed and compared with those of 15 corresponding random networks. With our proposed accelerating framework, the above process for each network cost 80∼150 minutes, depending on the network sparsity. Further analyses revealed that high-resolution functional brain networks have efficient small-world properties, significant modular structure, a power law degree distribution and highly connected nodes in the medial frontal and parietal cortical regions. These results are largely compatible with previous human brain network studies. Taken together, our proposed framework can substantially enhance the applicability and efficacy of high-resolution (voxel-based) brain network analysis, and have the potential to accelerate the mapping of the human brain connectome in normal and disease states.

Human brain functional network changes associated with enhanced and impaired attentional task performance

How is the cognitive performance of the human brain related to its topological and spatial organization as a complex network embedded in anatomical space? To address this question, we used nicotine replacement and duration of attentionally demanding task performance (time-on-task), as experimental factors expected, respectively, to enhance and impair cognitive function. We measured resting-state fMRI data, performance and brain activation on a go/no-go task demanding sustained attention, and subjective fatigue in n = 18 healthy, briefly abstinent, cigarette smokers scanned repeatedly in a placebo-controlled, crossover design. We tested the main effects of drug (placebo vs Nicorette gum) and time-on-task on behavioral performance and brain functional network metrics measured in binary graphs of 477 regional nodes (efficiency, measure of integrative topology; clustering, a measure of segregated topology; and the Euclidean physical distance between connected nodes, a proxy marker of wiring cost). Nicotine enhanced attentional task performance behaviorally and increased efficiency, decreased clustering, and increased connection distance of brain networks. Greater behavioral benefits of nicotine were correlated with stronger drug effects on integrative and distributed network configuration and with greater frequency of cigarette smoking. Greater time-on-task had opposite effects: it impaired attentional accuracy, decreased efficiency, increased clustering, and decreased connection distance of networks. These results are consistent with hypothetical predictions that superior cognitive performance should be supported by more efficient, integrated (high capacity) brain network topology at greater connection distance (high cost). They also demonstrate that brain network analysis can provide novel and theoretically principled pharmacodynamic biomarkers of pro-cognitive drug effects in humans.

Analyzing complex functional brain networks: Fusing statistics and network science to understand the brain*†

Complex functional brain network analyses have exploded over the last decade, gaining traction due to their profound clinical implications. The application of network science (an interdisciplinary offshoot of graph theory) has facilitated these analyses and enabled examining the brain as an integrated system that produces complex behaviors. While the field of statistics has been integral in advancing activation analyses and some connectivity analyses in functional neuroimaging research, it has yet to play a commensurate role in complex network analyses. Fusing novel statistical methods with network-based functional neuroimage analysis will engender powerful analytical tools that will aid in our understanding of normal brain function as well as alterations due to various brain disorders. Here we survey widely used statistical and network science tools for analyzing fMRI network data and discuss the challenges faced in filling some of the remaining methodological gaps. When applied and interpreted correctly, the fusion of network scientific and statistical methods has a chance to revolutionize the understanding of brain function.

Metastability and chimera states in modular delay and pulse-coupled oscillator networks

Modular networks of delay-coupled and pulse-coupled oscillators are presented, which display both transient (metastable) synchronization dynamics and the formation of a large number of "chimera" states characterized by coexistent synchronized and desynchronized subsystems. We consider networks based on both community and small-world topologies. It is shown through simulation that the metastable behaviour of the system is dependent in all cases on connection delay, and a critical region is found that maximizes indices of both metastability and the prevalence of chimera states. We show dependence of phase coherence in synchronous oscillation on the level and strength of external connectivity between communities, and demonstrate that synchronization dynamics are dependent on the modular structure of the network. The long-term behaviour of the system is considered and the relevance of the model briefly discussed with emphasis on biological and neurobiological systems.

An exponential random graph modeling approach to creating group-based representative whole-brain connectivity networks

Group-based brain connectivity networks have great appeal for researchers interested in gaining further insight into complex brain function and how it changes across different mental states and disease conditions. Accurately constructing these networks presents a daunting challenge given the difficulties associated with accounting for inter-subject topological variability. Viable approaches to this task must engender networks that capture the constitutive topological properties of the group of subjects' networks that it is aiming to represent. The conventional approach has been to use a mean or median correlation network (Achard et al., 2006; Song et al., 2009; Zuo et al., 2011) to embody a group of networks. However, the degree to which their topological properties conform with those of the groups that they are purported to represent has yet to be explored. Here we investigate the performance of these mean and median correlation networks. We also propose an alternative approach based on an exponential random graph modeling framework and compare its performance to that of the aforementioned conventional approach. Simpson et al. (2011) illustrated the utility of exponential random graph models (ERGMs) for creating brain networks that capture the topological characteristics of a single subject's brain network. However, their advantageousness in the context of producing a brain network that "represents" a group of brain networks has yet to be examined. Here we show that our proposed ERGM approach outperforms the conventional mean and median correlation based approaches and provides an accurate and flexible method for constructing group-based representative brain networks.

Emergence of structural patterns out of synchronization in networks with competitive interactions

Synchronization is a collective phenomenon occurring in systems of interacting units, and is ubiquitous in nature, society and technology. Recent studies have enlightened the important role played by the interaction topology on the emergence of synchronized states. However, most of these studies neglect that real world systems change their interaction patterns in time. Here, we analyze synchronization features in networks in which structural and dynamical features co-evolve. The feedback of the node dynamics on the interaction pattern is ruled by the competition of two mechanisms: homophily (reinforcing those interactions with other correlated units in the graph) and homeostasis (preserving the value of the input strength received by each unit). The competition between these two adaptive principles leads to the emergence of key structural properties observed in real world networks, such as modular and scale-free structures, together with a striking enhancement of local synchronization in systems with no global order.

Modules and brain mapping

This review highlights the key role of modularity and the additive factors method in functional neuroimaging. Our focus is on structure–function mappings in the human brain and how these are disclosed by brain mapping. We describe how modularity of processing (and possibly processes) was a key point of reference for establishing functional segregation as a principle of brain organization. Furthermore, modularity plays a crucial role when trying to characterize distributed brain responses in terms of functional integration or coupling among brain areas. We consider additive factors logic and how it helped to shape the design and interpretation of studies at the inception of brain mapping, with a special focus on factorial designs. We look at factorial designs in activation experiments and in the context of lesion–deficit mapping. In both cases, the presence or absence of interactions among various experimental factors has proven essential in understanding the context-sensitive nature of distributed but modular processing and discerning the nature of (potentially degenerate) structure–function relationships in cognitive neuroscience.

Group-ICA Model Order Highlights Patterns of Functional Brain Connectivity

Resting-state networks (RSNs) can be reliably and reproducibly detected using independent component analysis (ICA) at both individual subject and group levels. Altering ICA dimensionality (model order) estimation can have a significant impact on the spatial characteristics of the RSNs as well as their parcellation into sub-networks. Recent evidence from several neuroimaging studies suggests that the human brain has a modular hierarchical organization which resembles the hierarchy depicted by different ICA model orders. We hypothesized that functional connectivity between-group differences measured with ICA might be affected by model order selection. We investigated differences in functional connectivity using so-called dual regression as a function of ICA model order in a group of unmedicated seasonal affective disorder (SAD) patients compared to normal healthy controls. The results showed that the detected disease-related differences in functional connectivity alter as a function of ICA model order. The volume of between-group differences altered significantly as a function of ICA model order reaching maximum at model order 70 (which seems to be an optimal point that conveys the largest between-group difference) then stabilized afterwards. Our results show that fine-grained RSNs enable better detection of detailed disease-related functional connectivity changes. However, high model orders show an increased risk of false positives that needs to be overcome. Our findings suggest that multilevel ICA exploration of functional connectivity enables optimization of sensitivity to brain disorders.

Sparse brain network recovery under compressed sensing

Partial correlation is a useful connectivity measure for brain networks, especially, when it is needed to remove the confounding effects in highly correlated networks. Since it is difficult to estimate the exact partial correlation under the small- n large- p situation, a sparseness constraint is generally introduced. In this paper, we consider the sparse linear regression model with a l(1)-norm penalty, also known as the least absolute shrinkage and selection operator (LASSO), for estimating sparse brain connectivity. LASSO is a well-known decoding algorithm in the compressed sensing (CS). The CS theory states that LASSO can reconstruct the exact sparse signal even from a small set of noisy measurements. We briefly show that the penalized linear regression for partial correlation estimation is related to CS. It opens a new possibility that the proposed framework can be used for a sparse brain network recovery. As an illustration, we construct sparse brain networks of 97 regions of interest (ROIs) obtained from FDG-PET imaging data for the autism spectrum disorder (ASD) children and the pediatric control (PedCon) subjects. As validation, we check the network reproducibilities by leave-one-out cross validation and compare the clustered structures derived from the brain networks of ASD and PedCon.