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Complex modular structure of large-scale brain networks

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Abstract

Modular structure is ubiquitous among real-world networks from related proteins to social groups. Here we analyze the modular organization of brain networks at a large scale (voxel level) extracted from functional magnetic resonance imaging signals. By using a random-walk-based method, we unveil the modularity of brain webs and show modules with a spatial distribution that matches anatomical structures with functional significance. The functional role of each node in the network is studied by analyzing its patterns of inter- and intramodular connections. Results suggest that the modular architecture constitutes the structural basis for the coexistence of functional integration of distant and specialized brain areas during normal brain activities at rest.

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... Integration may also refer to areas that are both highly connected throughout the brain and whose connections are bridges between segregated processing networks. In this sense, integration areas refer to connector hubs (Guimera and Amaral, 2005;Valencia et al., 2009;Zamora-López et al., 2010) or the rich club hubs of the brain's structural core (Hagmann et al., 2008;van den Heuvel and Sporns, 2011). ...
... Areas previously identified as connector hubs also showed BNC (He et al., 2009;Valencia et al., 2009). However, the reverse is not always true. ...
... However, the reverse is not always true. The thalamus and temporoparietal junction have been identified as connector hubs in some (Valencia et al., 2009) but not all studies (He et al., 2009), possibly due to differing anatomical resolution. Lastly, most richclub hubs such as the PCC, paracentral lobule, and parietal lobes, were associated with high BNC (Hagmann et al., 2008;van den Heuvel and Sporns, 2011). ...
... Because of the large number of nodes, the construction and analysis of voxel-level graphs can involve considerable computational efforts. In response, the computational burden has often been reduced by sacrificing spatial resolution (using relatively large voxels to begin with or reslicing the data to a lower resolution) thus reducing the number of nodes in the graph [15,[25][26][27]. While reduction of spatial resolution is undesirable in general (given that the main advantage of fMRI as compared to other methods such as EEG/MEG is its superior spatial resolution), it can even render a study infeasible, e.g., when investigating very small brain structures or different regions that lie in close proximity to each other. ...
... In most previous studies investigating voxel-level functional connectivity graphs, internodal functional connectivity is measured using Pearson's sample correlation coefficient r [2,8,13,15,[21][22][23][24][25][26][27][29][30][31]. When using Pearson correlation as a measure of functional connectivity, it seems sensible to assume bivariate normality with respect to the distribution of pairwise observations arising from each pair of voxel time series. ...
... However, with high-resolution data sets, such analyses can become infeasible due to the computational demands involved. Most previous studies investigating voxel-level functional connectivity graphs relied on Pearson's r for estimating internodal functional connectivity [2,8,13,15,[21][22][23][24][25][26][27][29][30][31]. As demonstrated here, the tetrachoric correlation coefficient r t constitutes a timeefficient alternative to r as a measure of functional connectivity. ...
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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.
... Because of the large number of nodes, the construction and analysis of voxel-level graphs can involve considerable computational efforts. In response, the computational burden has often been reduced by sacrificing spatial resolution (using relatively large voxels to begin with or reslicing the data to a lower resolution) thus reducing the number of nodes in the graph [15,[25][26][27]. While reduction of spatial resolution is undesirable in general (given that the main advantage of fMRI as compared to other methods such as EEG/MEG is its superior spatial resolution), it can even render a study infeasible, e.g., when investigating very small brain structures or different regions that lie in close proximity to each other. ...
... In most previous studies investigating voxel-level functional connectivity graphs, internodal functional connectivity is measured using Pearson's sample correlation coefficient r [2,8,13,15,[21][22][23][24][25][26][27][29][30][31]. When using Pearson correlation as a measure of functional connectivity, it seems sensible to assume bivariate normality with respect to the distribution of pairwise observations arising from each pair of voxel time series. ...
... However, with high-resolution data sets, such analyses can become infeasible due to the computational demands involved. Most previous studies investigating voxel-level functional connectivity graphs relied on Pearson's r for estimating internodal functional connectivity [2,8,13,15,[21][22][23][24][25][26][27][29][30][31]. As demonstrated here, the tetrachoric correlation coefficient r t constitutes a timeefficient alternative to r as a measure of functional connectivity. ...
... Within the realm of cognitive neuroscience, modules are taken to represent differentiable function-specific processing systems that tend to be associated with specific neural structures (Barrett and Kurzban, 2006). Using graph theory measures in complex network analyses, modules are defined as subsets of nodes within networks that are more densely interconnected among themselves than the rest of the network (Newman and Girvan, 2004;Valencia et al., 2009). The modular nature of the brain allows the system to flexibly and efficiently adapt to multiple and changing goals in the environment (Kashtan and Alon, 2005;Bassett et al., 2011), while simultaneously increasing the robustness and stability of the brain network (Solé and Valverde, 2008;Valencia et al., 2009). ...
... Using graph theory measures in complex network analyses, modules are defined as subsets of nodes within networks that are more densely interconnected among themselves than the rest of the network (Newman and Girvan, 2004;Valencia et al., 2009). The modular nature of the brain allows the system to flexibly and efficiently adapt to multiple and changing goals in the environment (Kashtan and Alon, 2005;Bassett et al., 2011), while simultaneously increasing the robustness and stability of the brain network (Solé and Valverde, 2008;Valencia et al., 2009). Properly characterizing the modular structure of the brain is crucial for understanding brain network organization during different cognitive states (Valencia et al., 2009). ...
... The modular nature of the brain allows the system to flexibly and efficiently adapt to multiple and changing goals in the environment (Kashtan and Alon, 2005;Bassett et al., 2011), while simultaneously increasing the robustness and stability of the brain network (Solé and Valverde, 2008;Valencia et al., 2009). Properly characterizing the modular structure of the brain is crucial for understanding brain network organization during different cognitive states (Valencia et al., 2009). Effective cognitive performance on working memory tasks may necessitate the recruitment and optimal information processing of multiple modules serving different functions with weak connections between modules. ...
Article
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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.
... These probabilities are proportional to the density of axonal fibers between different areas, so each element of the matrix represents an approximation of the connection strength between the corresponding pair of brain regions. The functional brain connectivity was extracted from BOLD fMRI resting state recordings obtained as described in Valencia et al. (2009). All acquired brain volumes were corrected for motion and differences in slice acquisition times using the SPM5 1 software package. ...
... Regional time series were estimated for each individual by averaging the fMRI time series over all voxels in each of the 90 regions. To eliminate low frequency noise (e.g., slow scanner drifts) and higher frequency artifacts from cardiac and respiratory oscillations, time-series were digitally filtered with a finite impulse response (FIR) filter with zero-phase distortion (bandwidth 0.01—0.1 Hz) as in Valencia et al. (2009). A functional link between two time series x i (t) and x j (t) (normalized to zero mean and unit variance) was defined by means of the linear cross-correlation coefficient computed as r ij = x i (t)x j (t), where · denotes the temporal average. ...
... These probabilities are proportional to the density of axonal fibers between different areas, so each element of the matrix represents an approximation of the connection strength between the corresponding pair of brain regions. The functional brain connectivity was extracted from BOLD fMRI resting state recordings obtained as described in [13]. All acquired brain volumes were corrected for motion and differences in slice acquisition times using the SPM5 1 software package. ...
... To eliminate low frequency noise (e.g. slow scanner drifts) and higher frequency artifacts from cardiac and respiratory oscillations, time-series were digitally filtered with a finite impulse response (FIR) filter with zero-phase distortion (bandwidth 0.01 − 0.1 Hz) as in [13]. ...
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Understanding brain connectivity has become one of the most important issues in neuroscience. But connectivity data can reflect either the functional relationships of the brain activities or the anatomical properties between brain areas. Although one should expect a clear relationship between both representations it is not straightforward. Here we present a formalism that allows for the comparison of structural (DTI) and functional (fMRI) networks by embedding both in a common metric space. In this metric space one can then find for which regions the two networks are significantly different. Our methodology can be used not only to compare multimodal networks but also to extract statistically significant aggregated networks of a set of subjects. Actually, we use this procedure to aggregate a set of functional (fMRI) networks from different subjects in an aggregated network that is compared with the anatomical (DTI) connectivity. The comparison of the aggregated network reveals some features that are not observed when the comparison is done with the classical averaged network.
... Thus these complementary mechanisms come, conceptually, in analogy to the fundamental function of task-positive and task-negative networks that emerge during goal-directed behavior (Fox et al. 2005). Furthermore the studies that take into account the temporal evolution of these networks are, to our knowledge, very few (Valencia et al. 2009;Dimitriadis et al. 2010;Tang et al. 2010;Bassett et al. 2011). Therefore another challenge is the monitoring of the network evolution in time and the modeling of the underlying organizational properties. ...
... The modular organization seem to be a preferable property for every self-organized structure (He and Evans 2010), including brain networks,increasing the robustness of the network function and its capacity for adaptation and evolution (Bullmore and Sporns 2009;Meunier et al. 2010;Bassett et al. 2010). Furthermore several recent studies have identified systematically the modular organization as an inherent property of structural brain networks (Bassett et al. 2008;Chen et al. 2008) and fMRI resting state networks (He et al. 2009;Valencia et al. 2009;Ferrarini et al. 2009;Davis et al. 2013). ...
Article
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By performing sensor-level analysis on magnetoencephalography (MEG) data we identified the dynamic evolution of the functional connectivity networks during a simple visuomotor task. The functional connectivity networks were constructed using the concept of phase-locking value (PLV). We illustrate that the task-related activity is mediated by distinct complex networks related to the PLV desynchronization that configure their architecture dynamically during the task. These networks are prominent at β and α band, and are characterized by coherent modular organization. Moreover the time for the development of the desynchronization networks at α band predicts the intra-subject variability of reaction time. Thus, the spatio-temporal dynamics and the structural properties of the emerged functional networks share common characteristics with the mechanism of coactivation and resting state networks.
... In health, the brain displays a fractal-like "small world organization" enabling high global and local efficiency of information transfer (Achard and Bullmore, 2007;Bassett et al., 2006;Smit et al., 2008). Studies show that the healthy function of interconnected modules that make up the larger brain network modules is dependent on age (Fair et al., 2009;Ferreira et al., 2016;Meunier et al., 2009Meunier et al., , 2014Valencia et al., 2009) and physical fitness (Douw et al., 2014). The brain achieves a balance between segregation and integration (Valencia et al., 2009), in which an area's role in multiple functional modules is measured by its participation coefficient at rest and under cognitive demands (Cohen and D'Esposito, 2016). ...
... Studies show that the healthy function of interconnected modules that make up the larger brain network modules is dependent on age (Fair et al., 2009;Ferreira et al., 2016;Meunier et al., 2009Meunier et al., , 2014Valencia et al., 2009) and physical fitness (Douw et al., 2014). The brain achieves a balance between segregation and integration (Valencia et al., 2009), in which an area's role in multiple functional modules is measured by its participation coefficient at rest and under cognitive demands (Cohen and D'Esposito, 2016). Furthermore, centrality measures that quantify the functional influence of brain regions in global information transfer are higher in associative "hub" regions (Garcés et al., 2016;Lohmann et al., 2010). ...
Article
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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.
... These probabilities are proportional to the density of axonal fibers between different areas, so each element of the matrix represents an approximation of the connection strength between the corresponding pair of brain regions. The functional brain connectivity was extracted from BOLD fMRI resting state recordings obtained as described in Valencia et al. (2009). All acquired brain volumes were corrected for motion and differences in slice acquisition times using the SPM5 1 software package. ...
... Regional time series were estimated for each individual by averaging the fMRI time series over all voxels in each of the 90 regions. To eliminate low frequency noise (e.g., slow scanner drifts) and higher frequency artifacts from cardiac and respiratory oscillations, time-series were digitally filtered with a finite impulse response (FIR) filter with zero-phase distortion (bandwidth 0.01—0.1 Hz) as in Valencia et al. (2009). A functional link between two time series x i (t) and x j (t) (normalized to zero mean and unit variance) was defined by means of the linear cross-correlation coefficient computed as r ij = x i (t)x j (t), where · denotes the temporal average. ...
... Graph-based analysis of dense connectomes allows for spatially precise mapping of fMRI-based functional connectivity patterns but is associated with considerable computational demands (van den Heuvel et al., 2008;Hayasaka and Laurienti, 2010;de Reus and Van den Heuvel, 2013;Fornito et al., 2013). As a result, some previous studies have been conducted at reduced spatial resolution (Buckner et al., 2009;Valencia et al., 2009;Zuo et al., 2012). However, most previous studies have not used dense connectomes at all, neither at the full nor at a reduced resolution. ...
Article
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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.
... However, the FBN commonly has more "structures" than just sparsity (Sporns, 2011). In this paper, inspired by the fact that the FBN is organized with a modular structure (Valencia et al., 2009), we present a novel FBN estimation scheme by encoding a modularity prior in form of matrix regularizer. Note that, in a recent work (Varoquaux et al., 2012), Varoquaux et al. proposed to describe the FBN by identifying its clique structure (similar to the modular structure here) in a decomposable graphical model. ...
Article
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.
... Thus understood, modularity net safeguards a conception of specialized, segregated functioning, which is central to more traditional views of modularity. Indeed, it has been shown that a modular net architecture both exists in functional brain networks and is advantageous because it increases the robustness, flexibility, and stability of the system (Barabasi & Oltvai 2004;Valencia et al. 2009). ...
Article
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Neural reuse is a form of neuroplasticity whereby neural elements originally developed for one purpose are put to multiple uses. A diverse behavioral repertoire is achieved by means of the creation of multiple, nested, and overlapping neural coalitions, in which each neural element is a member of multiple different coalitions and cooperates with a different set of partners at different times. Neural reuse has profound implications for how we think about our continuity with other species, for how we understand the similarities and differences between psychological processes, and for how best to pursue a unified science of the mind. After Phrenology: Neural Reuse and the Interactive Brain (Anderson 2014; henceforth After Phrenology in this Précis) surveys the terrain and advocates for a series of reforms in psychology and cognitive neuroscience. The book argues that, among other things, we should capture brain function in a multidimensional manner, develop a new, action-oriented vocabulary for psychology, and recognize that higher-order cognitive processes are built from complex configurations of already evolved circuitry.
... Thus understood, modularity net safeguards a conception of specialized, segregated functioning, which is central to more traditional views of modularity. Indeed, it has been shown that a modular net architecture both exists in functional brain networks and is advantageous because it increases the robustness, flexibility, and stability of the system (Barabasi & Oltvai 2004;Valencia et al. 2009). ...
Article
Neural reuse is a form of neuroplasticity whereby neural elements originally developed for one purpose are put to multiple uses. A diverse behavioral repertoire is achieved by means of the creation of multiple, nested, and overlapping neural coalitions, in which each neural element is a member of multiple different coalitions and cooperates with a different set of partners at different times. Neural reuse has profound implications for how we think about our continuity with other species, for how we understand the similarities and differences between psychological processes, and for how best to pursue a unified science of the mind. After Phrenology: Neural Reuse and the Interactive Brain (Anderson 2014; henceforth After Phrenology in this Précis) surveys the terrain and advocates for a series of reforms in psychology and cognitive neuroscience. The book argues that, among other things, we should capture brain function in a multidimensional manner, develop a new, action-oriented vocabulary for psychology, and recognize that higher-order cognitive processes are built from complex configurations of already evolved circuitry.
... Este método da lugar a una matriz de interacciones que puede definirse como un grafo en el que los genes constituyen los nodos de la red y las interacciones los enlaces o arcos de la misma (ver Figura 3.1) [30]. ...
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La Enfermedad de Parkinson (EP) es un trastorno neurodegenerativo que se asocia con la pérdida progresiva de neuronas dopaminérgicas (DA) del mesencéfalo en la sustancia negra pars compacta. Aunque se desconoce cual es la causa principal, se acepta que la EP constituye un desorden complejo causado por la combinación de diferentes factores genéticos y ambientales que afectan las vías principales de señalización en las neuronas DA de la sustancia negra. A diferencia de como ocurre en otras zonas del cerebro, la muerte de algunas de esas células dopaminérgicas no produce síntomas perceptibles y sólo cuando se ha perdido un importante número de las mismas, la EP comienza a manifestarse. Las nuevas líneas de investigación orientadas a comprender el origen y evolución de la EP aúnan técnicas provenientes de muy diferentes disciplinas. En esta sinergia, recientes avances y desarrollos tecnológicos producidos dentro del campo de la genética han añadido una nueva dimensión en la percepción de la enfermedad. El análisis de los perfiles de expresión génica determinados a partir de estudios de microarrays de alta densidad han confirmado la existencia de cierta desregulación en varios grupos funcionales de genes así como la presencia de anomalías en varios factores de transcripción críticos para el desarrollo y funcionamiento celular. En particular, se produce desregulación en los miembros de la familia PARK y en múltiples genes asociados tanto con la muerte programada como con la supervivencia neuronal. Además, también se han identificado otros genes asociados a neurotransmisores y receptores de canales iónicos, apoyando la versión que apunta hacia que alteraciones en la actividad eléctrica puedan estar influyendo en la función de las neuronas DA. En el presente trabajo, emplearemos y extenderemos algunos de los métodos que actualmente son utilizados para identificar genes candidatos asociados a la EP. Además, propondremos un nueva herramienta que permite no solo la detección de genes involucrados en la EP, sino de las de anomalías que pudieran establecerse en las relaciones entre ellos. De esta forma, seremos capaces de estimar una red de interacciones en la que –por comparación entre la redes asociadas a muestras control de pacientes de EP–, se detectan grupos de genes que han modificado de forma conjunta su grado de interacción por efecto de la enfermedad. Así, identificamos diferentes procesos y funciones que se ven alterados en la EP, en un intento de comprender algunos de los mecanismos involucrados en el origen del parkinson, pretendiendo ofrecer nuevos elementos que en el futuro puedan servir para el desarrollo de posibles biomarcadores de la enfermedad.
... Subsequently, either functional or structural information is overlaid on top of the parcellation and p × p connectivity matrix C = (c ij ) that measures the strength of connectivity between brain regions i and j is obtained. Recently, we are beginning to see large-scale brain networks that are more effective in localizing regions and increasing prediction power [6,37]. However, increasing parcellation resolution also increases the computational burden exponentially. ...
Preprint
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Human brain activity is often measured using the blood-oxygen-level dependent (BOLD) signals obtained through functional magnetic resonance imaging (fMRI). The strength of connectivity between brain regions is then measured and represented as Pearson correlation matrices. As the number of brain regions increases, the dimension of matrix increases. It becomes extremely cumbersome to even visualize and quantify such weighted complete networks. To remedy the problem, we propose to embedded brain networks onto a hypersphere, which is a Riemannian manifold with constant positive curvature.
... The age-related change of modularity was not affected by the normalization by the volume of the network. The human brains have modular architecture [27][28][29] . Nodes within a module are densely connected, and the shortest path lengths between any nodes within a module are short. ...
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Entropy is a classical measure to quantify the amount of information or complexity of a system. Various entropy-based measures such as functional and spectral entropy have been proposed in brain network analysis. However, they are less widely used than traditional graph theoretic measures such as global and local efficiencies because they are not well-defined on a graph or difficult to interpret its biological meaning. In this paper, we propose a new entropy-based graph invariant, called volume entropy. It measures the exponential growth rate of the number of graph paths, based on the assumption that information flows through a graph forever. We model the information propagation on a brain graph by the generalized Markov system associated to a new edge transition matrix. The volume entropy is estimated by the stationary equation of the generalized Markov system. Moreover, its stationary distribution shows the information capacity of edge and the direction of information flow on a brain graph. The simulation results show that the volume entropy distinguishes the underlying graph topology and geometry better than the existing graph measures. In the clinical application, the volume entropy of brain graphs was significantly related to healthy normal aging from 20s to 60s. In addition, the stationary distribution of information propagation gives a new insight into the information flow of functional brain graph.
... At the local scale, the centrality or the degree of individual nodes can be computed and used to characterize the brain graph reorganization during different tasks and events. Although the global and local indices summarize the key aspects of the connectivity networks, they do not provide any information about the intermediate scale of network organization which is more accurately described by the community structure of the network [22], [23]. A community structure in a graph is defined as a densely connected set of nodes with sparse connections between communities in the network. ...
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A central question in cognitive neuroscience is how cognitive functions depend on the integration of specialized, widely distributed brain regions. In recent years, graph theoretical methods have been used to characterize the structure of the brain functional connectivity. In order to understand the organization of functional connectivity networks, it is important to determine the community structure underlying these complex networks. Moreover, the study of brain functional networks is confounded by the fact that most neurophysiological studies consist of data collected from multiple subjects, thus, it is important to identify communities representative of all subjects. Typically, this problem is addressed by averaging the data across subjects which omits the variability across subjects or using voting methods which requires a priori knowledge of cluster labels. In this paper, we propose a hierarchical consensus spectral clustering approach to address these problems. Furthermore, new information-theoretic criteria are introduced for selecting the optimal community structure. The proposed framework is applied to electroencephalogram (EEG) data collected during a study of error-related negativity (ERN) to better understand the community structure of functional networks involved in cognitive control.
... The partition that maximizes Q is considered as the partition that better captures the modular structure of the network. Further details can be found in [22,23]. ...
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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.
... As well discussed in Simpson et. al. (2012) there are many more examples exposing the importance of the underlying model network, ranging from their use as null networks as discussed above, to modularity analyses (Joyce et al., 2010;Meunier et al., 2009a,b;Valencia et al., 2009), to representing an individual's network based on several experimental runs (Zuo et al., 2011), to visualization tools (Song et al., 2009;Zuo et al., 2011), to their ability to assess a group of networks (Achard et al., 2006), to identifying hub/node types (Joyce et al., 2010), to constructing representative networks for brain dynamics studies (Jirsa et al., 2010). Additional examples for modularity include Expert et. ...
Article
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. 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 networks' 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.
... The use of data surrogates is also a good data-driven solution for the statistical assessment of FC measures in presence of short signals [57]. Other approaches allow to determine the probability that correlation-based FC measures are significantly higher than what expected from independent signals by using the Fisher's Z transformations [103,104]. Positive biases have been also reported for common FC nonlinear measures, such as phase synchrony [105,106] . Another important issue comes from the fact that statistical significance should be tested for each link. ...
Article
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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 a know-how of all the methodological steps of the processing pipeline that manipulates the input brain signals and extract the functional network properties. On the other hand, a knowledge of the neural phenomenon under study is required to perform physiological-relevant analysis. The aim of this review is to provide practical indications to make sense of brain network analysis and contrast counterproductive attitudes.
... Recent studies have reported a highly modular architecture of the human brain in its structural [12,13,65] as well as in its resting state functional connectivity (rsFC) [66][67][68]. Furthermore, studying the effect of ageing on the brain's modular structure, Meunier et al. [69] found marked differences in the composition and putative topological roles between the modules in the rsFC of younger and older human subjects. ...
Article
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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.
... An important utility of the simulation capability of this model is to generate representative group-level dynamic networks. The need for reliably generating representative group-level networks has been well documented (Jirsa, Sporns, Breakspear, Deco, & McIntosh, 2010;Meunier, Achard, Morcom, & Bullmore, 2009;Valencia et al., 2009;Zuo et al., 2012). Additionally, the simulation capability also provides a scientifically appropriate way to assess GOF (as shown in the Dynamic Network Simulation section) and simulate individual-level networks. ...
Article
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The emerging area of dynamic brain network analysis has gained considerable attraction 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 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.
... Community structures widely exist in all kinds of networks, such as social and biological systems [7], information networks [37], musical compositions [8], and brain networks [34], etc. There have to be some good reasons why community structures widely exist in so many real-life systems: intuitively, we may expect that the existence of community structures may in a certain way help make the systems function more efficiently. ...
Article
Community structures widely exist in various complex networks. Extensive studies have been carried out on defining and quantifying community structures as well as developing algorithms for detecting them in extra-large complex systems. Despite all these efforts, however, our understanding of why community structures widely exist in so many real-life systems, or in other words, the benefits/drawbacks for reallife systems to have community structures, remains to be rather limited. In this work, we discuss on the effects of community structures on infection propagation, detection and control in complex networks. Specifically, we investigate (i) the effects of community structures on transmission speed and infection size; (ii) when monitors can be deployed in the network to detect the infection spreading, the effects of community structures on early-stage infection detection and (iii) in adaptive networks with link rewiring for isolating the infected nodes, the effects of community structures on infection control. Our results show that the existence of community structures generally speaking helps slow down the infection spreading; whether it helps reduce the overall infection size when no control method is adopted however, depends on the network topology. When infection detection and controlling methods such as link rewiring are adopted, the existence of community structures steadily helps improve the efficiency of infection detection and control, though having too many communities may not necessarily bring along additional benefits.
... van Den Heuvel et al. (2009;van Straaten and Stam, 2013) explored a schematic amount of a graph symbol of the functional brain network in (Fig. 6). Hagmann et al. (2007;Valencia, et al., 2009;Meunier et al., 2009) studied about the resting-state fMRI for measuring of the functional brain network. They also told that the functional brain networks interactions between regions are abundant because it has an intrinsically cohesive modular (community) structure and functionally linked with brain regions. ...
... which is a result proposed much earlier by Bayley and Hammersley (1946) and which has found use in neuroimaging (Nicosia et al., 2013;Valencia et al., 2009). A closely related form (Dutilleul et al., 1993) that adjusts for mean centering has also been used in neuroimaging (Nevado et al., 2012;Pannunzi et al., 2018), though for typical time series lengths (i.e. ...
Article
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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.
... For example, Meunier et al. (2009a) studied the modular partitions of resting-state networks in the human brain, and investigated the influence of normal aging on the modular structure. Valencia et al. (2009) investigated modular organization in resting-state networks at the voxel level, and showed modules at a finer grain level. Although these studies on the partition of modules distinguished the different roles and status of nodes, they did not apply the modular structure to the analysis of FBNs (e.g., FBN construction, feature learning, and classification). ...
Article
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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.
... The main and most important networks for the modular control of the brain have been demonstrated before and include: the occipital, sensorimotor, and default mode networks 38,39 . These same networks were found at the hierarchical level of modulation 40 , whereas at the voxel level researchers found visual, auditory, and default mode networks and subcortical areas 41 . ...
Preprint
Studies based on a paradigm of free or natural viewing have revealed characteristics that allow us to know how the brain processes stimuli within a natural environment. This method has been little used to study brain function. With a connectivity approach, we examine the processing of emotions using an exploratory method to analyze functional magnetic resonance imaging (fMRI) data. This research describes our approach to modeling stress paradigms suitable for neuroimaging environments. We showed a short film (4.54 minutes) with high negative emotional valence and high arousal content to 24 healthy male subjects (36.42 years old; SD=12.14) during fMRI. Independent component analysis (ICA) was used to identify networks based on spatial statistical independence. Through this analysis we identified the sensorimotor system and its influence on the dorsal attention and default-mode networks, which in turn have reciprocal activity and modulate networks described as emotional.
... Baars (1988) described the brain as a conglomerate of highly specialized but unconscious, automatic processors, or modules, working together (also Fodor, 1983). Each of these modules may classify stimuli, control motor activity, and perform other computational tasks, but may also modulate other neural circuits (Valencia et al., 2009 and thus conform the intelligence of the system. The substrate is shaped by the neural circuits that support the representation of concepts. ...
Thesis
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Articial Intelligence and robotics are developing at a fast pace. However, implementation of general intelligence in computers remains elusive. Currently, there are no technologies able to solve unexpected challenges nor learning algorithms that outperform their initial requirements. This thesis takes an unconventional multidisciplinary perspective on cognitive systems to propose a universal theory of cognition that can be identied in systems exhibiting intelligent behaviour. I present a theory that is based on a formalization of trial and error that is composed of three cognitive components and has the capacity to produce intelligent behaviours. In absence of models, tentative trials to reach a specic goal are inevitable until one succeeds. Each attempt at fullling a goal is termed a variant. The cognitive components are: a substrate, a generator of variants and a selector. (1) The substrate holds the information that shapes each variant and it may be either physical or immaterial in nature. It is linked to environmental mechanisms that interpret the instructions conveyed by each variant. (2) A cog-nitive generator provides the heuristics to produce variants, and (3) the selector chooses amongst the generated variants which one is the most adequate for the pursued goal. Then, I argue that there are three families of intelligent-behaving systems that give evidence to the theory. Firstly, I propose a biologically-based cognition that relies on principles of evolutionary theory. Particularly, I give an alternative interpretation of Darwinism that diverts away from the traditional notion of evolution by chance and credits biological evolution with cognitive capabilities. Secondly, I identify a mapping between the theory and the latest advances in neuroscience and experimental psychology. Specically, attention drives selection and variants are represented in neural modules. Thirdly, I explore methods in articial intelligence and I justify their cognitive limitations. I discuss a comparison of these cognitive families where more analogies are drawn, including a description of a putative sequence of cognitive emergences. Finally, I deduce from the theory a novel cognitive architecture that does not rely on preconstructed models to interact with the environment.
... Since these approaches might be considered suboptimal, they can be alternatively replaced by theoretically-grounded nonparametric methods based on different criteria including statistical contrasts with data surrogates (92,93), topological optimization (94)(95)(96)89) and population-based consensus (97,98). ...
Preprint
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.
... Several methods of obtaining networks from correlation matrices have been previously explored. For instance, one could estimate the expected cross-correlation of two random spike trains and add an edge if the observed cross-correlation is significantly higher than this expected value [15]. Another possibility is to add edges in descending order of cross-correlation until the graph satisfies some property-e.g., until the graph is connected [16]. ...
Article
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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.
... where xx (τ ) is the autocorrelation of signal x at lag τ , see [20] for details. We can then invert the transformation, and assume that ρ can be reasonably described through a normal distribution N [r, tanh(σ Z )]. ...
Article
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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 here provide 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.
... It is associated with the community structure in networks, which means the appearance of modules which represent for densely connected groups of vertices, with only sparser connections between groups (Newman, 2006). Previous studies suggested that human brain existed a modular organization whatever in the structure and function network Ferrarini and Veer, 2010;Wu et al., 2012;Sporns and Betzel, 2016;Valencia et al., 2009;Wang et al., 2017b;Yong et al., 2009;Zhang et al., 2008). For UD patients, Peng et al., have reported a reorganized modular structure relative to healthy controls (HC) and suggested that this change might contribute to the feelings of helplessness in UD patients . ...
Article
Two popular debilitating illness, unipolar depression (UD) and bipolar disorder (BD), have the similar symptoms and tight association on the psychopathological level, leading to a clinical challenge to distinguish them. In order to figure out the underlying common and different mechanism of both mood disorders, resting-state functional magnetic resonance imaging (rs-fMRI) data derived from 36 UD patients, 42 BD patients (specially type I, BD-I) and 45 healthy controls (HC) were analyzed retrospectively in this study. Functional brain networks were firstly constructed on both group and individual levels with a density 0.2, which was determined by a network thresholding approach based on modular similarity. Then we investigated the alterations of modular structure and other topological properties of the functional brain network, including global network characteristics and nodal network measures. The results demonstrated that the functional brain networks of UD and BD-I groups preserved the modularity and small-worldness property. However, compared with HC, reduced number of modules was observed in both patients' groups with shared alterations occurring in hippocampus, para hippocampal gyrus, amygdala and superior parietal gyrus and distinct changes of modular composition mainly in the caudate regions of basal ganglia. Additionally, for the network characteristics, compared to HC, significantly decreased global efficiency and small-worldness were observed in BD-I. For the nodal metrics, significant decrease of local efficiency was found in several regions in both UD and BD-I, while a UD-specified increase of participant coefficient was found in the right paracentral lobule and the right thalamus. These findings may contribute to throw light on the neuropathological mechanisms underlying the two disorders and further help to explore objective biomarkers for the correct diagnosis of UD and BD.
... For instance, the temporal correlation in BOLD signals of two distinct brain regions is commonly employed to describe the functional connectivity (FC) between them [3]. A positive and strong temporal correlation corresponds to a strong FC, and some brain regions with strong FCs among them constitute a brain functional network [4][5][6]. Alterations of some FCs in a brain functional network are often associated with brain disorder, such as schizophrenia [7], major depression [8], autism [9], Alzheimer's Disease [10], and attention deficit hyperactivity disorder [11]. For example, Cheng et al. evaluated the FC between different brain regions in subjects with autism and found a key system in the middle temporal gyrus with reduced FC and a key system in the precuneus with reduced FC [12]. ...
Article
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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.
... Human brain neuroimaging studies have also provided the evidence of modular organization in both anatomical and functional brain networks Fig. 7The local brain network topology properties of the ADHD and normal control groups at the cost value of 0.42 (Ferrarini et al. 2009; Meunier et al. 2009). The underlying mechanisms of modularity of the brain have been widely discussed in various studies (Zhou et al. 2006; Bullmore and Sporns 2009; Valencia et al. 2009 ). For example, the modularity of brain organization might change as a function of age (Meunier et al. 2009). ...
Article
Brain is a complex network with an anatomical and functional organization. The differences in brain organization of those with attention-deficit/hyperactivity disorder (ADHD) are still not well understood. Here, we study brain organization in ADHD subjects using a complex network derived from resting-state functional magnetic resonance imaging (fMRI) data of ADHD and normal subjects. Our results reveal that the brain networks of ADHD subjects are reorganized compared to those without ADHD in global and local brain functional networks. We find that the ADHD subjects show decreasing brain network integration and increasing brain network segregation. More interestingly, we find similarities of brain topology properties between local and global brain networks. Our finding indicates that cognitive dysfunction in ADHD is probably associated with disrupted global and local brain network topological properties. Our results can help us understand the pathophysiological mechanism of ADHD and serve as a sensitive and specific biomarker of ADHD.
... As nodes and links are abstract concepts, they may refer to many different objects and types of interactions, respectively. Therefore, a rapid development of the so-called network science has found application in studies on a great variety of systems [1,2], like social networks [3][4][5][6][7][8], biological networks [9][10][11], networks representing financial dependencies [12][13][14][15][16][17], the structure of the Internet [18][19][20][21], or the organization of transportation systems [22][23][24][25][26]. ...
Preprint
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By representing a text by a set of words and their co-occurrences, one obtains a word-adjacency network - a network being in a way a reduced representation of the given language sample. In this paper, the possibility of using network representation in order to extract information about individual language styles of literary texts is studied. By determining selected quantitative characteristics of the networks and applying machine learning algorithms, it is made possible to distinguish between texts of different authors. It turns out that within the studied set of texts in English and Polish, the properly rescaled weighted clustering coefficients and weighted degrees of only a few nodes in the word-adjacency networks are sufficient to obtain the accuracy of authorship attribution over 90\%. A correspondence between the authorship of texts and the structure of word-adjacency networks can therefore clearly be found; it may be stated that the network representation allows to distinguish individual language styles by comparing the way the authors use particular words and punctuation marks. The presented approach can be viewed as a generalization of the authorship attribution methods based on simplest lexical features. Apart from the characteristics given above, other network parameters are studied, both local and global ones, for both the unweighted and weighted networks. Their potential to capture the diversity of writing styles is discussed; some differences between languages are also observed.
... As nodes and links are abstract concepts, they may refer to many different objects and types of interactions, respectively. Therefore, a rapid development of the so-called network science has found application in studies on a great variety of systems, like social networks, biological networks, networks representing financial dependencies, the structure of the Internet, or the organization of transportation systems [8,12,16,23,34,38,43] . ...
... a result proposed much earlier by Bayley and Hammersley (1946) which has found use in neuroimaging (Nicosia et al., 2013;Valencia et al., 2009). A closely related form (Dutilleul et al., 1993) that adjusts for mean centering has also been used in neuroimaging (Nevado et al., 2012;Pannunzi et al., 2018), though for typical time series lengths (i.e. ...
Preprint
Full-text available
The dependence between pairs of time series are 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 and the standard error is biased. This issue is vital in resting-state functional connectivity (rsFC) since the fMRI time series are notoriously autocorrelated and therefore rsFC inferences will be biased if not adjusted. We find 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. We propose a practical method that accounts not only for distinct autocorrelation in each time series, but instantaneous and lagged cross-correlation. 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.
... van Den Heuvel et al. (2009;van Straaten and Stam, 2013) explored a schematic amount of a graph symbol of the functional brain network in (Fig. 6). Hagmann et al. (2007;Valencia, et al., 2009;Meunier et al., 2009) studied about the resting-state fMRI for measuring of the functional brain network. They also told that the functional brain networks interactions between regions are abundant because it has an intrinsically cohesive modular (community) structure and functionally linked with brain regions. ...
Article
The brain network is the function of a structurally and functionally organized complex system. Its structure and activity analysis is one of the most significant challenges. The graph based techniques of brain complex networks have been successfully used in various types of image and medical data analysis. In this survey paper, we focus on a comprehensive study of the analytical methods for complex brain network based on graph theory. This review paper is intended to provide automated brain disease diagnosis based on functional and diffusional MRI modalities. Furthermore, we discuss subjective and objective quality evaluations of complex brain networks, important tools for automated brain disease diagnosis, challenging issues and future research directions in this increasingly evolving research field.
Conference Paper
When neural activity increases in a region of the brain, the local magnetic resonance signal produced in that part of the brain increases by a small amount owing to changes in blood oxygenation. This blood oxygenation level dependent (BOLD) effect is the basis for most functional magnetic resonance imaging (fMRI) studies done today to map patterns of activation in the working human brain. In this tutorial we will review the main techniques used to analyze fMRI data.
Article
The brain's connectome has a great impact on its function, as its structure 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 inter and intra hemispheric connections, that is - spices with highly connected hemispheres appear to have weaker inter-hemisphere 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 F). We explore the biological origins of this phenomenon, and heritability and 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 and inter hemispheric 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 a 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 between different brains.SIGNIFICANCE STATEMENTThe brain's network structure 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's 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 its origins, as well as observe its effect on cognitive abilities and behavior.
Article
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 work we provide, firstly, 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, secondly, 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 address: 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. IEEE
Article
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.
Article
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.
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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 (1st 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 2nd order interactome that includes proteins connected directly with proteins of 1st 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.
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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.
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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.
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Dense subgraphs of sparse graphs (communities), which appear in most real-world complex networks, play an important role in many contexts. Computing them however is generally expensive. We propose here a measure of similarities between vertices based on random walks which has several important advantages: it captures well the community structure in a network, it can be computed efficiently, and it can be used in an agglomerative algorithm to compute efficiently the community structure of a network. We propose such an algorithm, called Walktrap, which runs in time O(mn^2) and space O(n^2) in the worst case, and in time O(n^2log n) and space O(n^2) in most real-world cases (n and m are respectively the number of vertices and edges in the input graph). Extensive comparison tests show that our algorithm surpasses previously proposed ones concerning the quality of the obtained community structures and that it stands among the best ones concerning the running time.
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We investigated large-scale systems organization of the whole human brain using functional magnetic resonance imaging (fMRI) data acquired from healthy volunteers in a no-task or ‘resting’ state. Images were parcellated using a prior anatomical template, yielding regional mean time series for each of 90 regions (major cortical gyri and subcortical nuclei) in each subject. Significant pairwise functional connections, defined by the group mean inter-regional partial correlation matrix, were mostly either local and intrahemispheric or symmetrically interhemispheric. Low-frequency components in the time series subtended stronger inter-regional correlations than highfrequency components. Intrahemispheric connectivity was generally related to anatomical distance by an inverse square law; many symmetrical interhemispheric connections were stronger than predicted by the anatomical distance between bilaterally homologous regions. Strong interhemispheric connectivity was notably absent in data acquired from a single patient, minimally conscious following a brainstem lesion. Multivariate analysis by hierarchical clustering and multidimensional scaling consistently defined six major systems in healthy volunteers — corresponding approximately to four neocortical lobes, medial temporal lobe and subcortical nuclei — that could be further decomposed into anatomically and functionally plausible subsystems, e.g. dorsal and ventral divisions of occipital cortex. An undirected graph derived by thresholding the healthy group mean partial correlation matrix demonstrated local clustering or cliquishness of connectivity and short mean path length compatible with prior data on small world characteristics of non-human cortical anatomy. Functional MRI demonstrates a neurophysiological architecture of the normal human brain that is anatomically sensible, strongly symmetrical, disrupted by acute brain injury, subtended predominantly by low frequencies and consistent with a small world network topology.
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Networks of coupled dynamical systems have been used to model biological oscillators, Josephson junction arrays, excitable media, neural networks, spatial games, genetic control networks and many other self-organizing systems. Ordinarily, the connection topology is assumed to be either completely regular or completely random. But many biological, technological and social networks lie somewhere between these two extremes. Here we explore simple models of networks that can be tuned through this middle ground: regular networks 'rewired' to introduce increasing amounts of disorder. We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them 'small-world' networks, by analogy with the small-world phenomenon (popularly known as six degrees of separation. The neural network of the worm Caenorhabditis elegans, the power grid of the western United States, and the collaboration graph of film actors are shown to be small-world networks. Models of dynamical systems with small-world coupling display enhanced signal-propagation speed, computational power, and synchronizability. In particular, infectious diseases spread more easily in small-world networks than in regular lattices.
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The objective of this study was to separate multiple signal components present in functional MRI (fMRI) data sets. Blind source separation techniques were applied to the analysis of fMRI data to determine multiple physiologically relevant independent signal sources. Computer simulations were performed to test the reliability and robustness of the independent component analysis (ICA). Four subjects (3 males and 1 female between 14 and 29 years old) were scanned under various stimulus conditions: (1) rest while breathing room air, (2) bilateral finger tapping while breathing room air, and (3) hypercapnia during bilateral finger tapping. Simulations performed on synthetic data sets demonstrated that not only could the algorithm reliably detect the shapes of each of the source signals, but it also preserved their relative amplitudes. The algorithm also performed robustly in the presence of noise. With use of fMRI time series data sets from bilateral finger tapping during hypercapnia, distinct physiologically relevant independent sources were reliably estimated. One independent component corresponded to the hypercapnic cerebrovascular response, and another independent component corresponded to cortical activation from bilateral finger tapping. In three of the four subjects, the underlying fluctuations in signal related to baseline respiratory rate were identified in the third independent component. Principal component analysis (PCA) could not separate these two independent physiological components. With use of ICA, signals originating from independent sources could be separated from a linear mixture of observed data. Limitations of PCA were also demonstrated.
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In subjects performing no specific cognitive task ("resting state"), time courses of voxels within functionally connected regions of the brain have high cross-correlation coefficients ("functional connectivity"). The purpose of this study was to measure the contributions of low frequencies and physiological noise to cross-correlation maps. In four healthy volunteers, task-activation functional MR imaging and resting-state data were acquired. We obtained four contiguous slice locations in the "resting state" with a high sampling rate. Regions of interest consisting of four contiguous voxels were selected. The correlation coefficient for the averaged time course and every other voxel in the four slices was calculated and separated into its component frequency contributions. We calculated the relative amounts of the spectrum that were in the low-frequency (0 to 0.1 Hz), the respiratory-frequency (0.1 to 0.5 Hz), and cardiac-frequency range (0.6 to 1.2 Hz). For each volunteer, resting-state maps that resembled task-activation maps were obtained. For the auditory and visual cortices, the correlation coefficient depended almost exclusively on low frequencies (<0.1 Hz). For all cortical regions studied, low-frequency fluctuations contributed more than 90% of the correlation coefficient. Physiological (respiratory and cardiac) noise sources contributed less than 10% to any functional connectivity MR imaging map. In blood vessels and cerebrospinal fluid, physiological noise contributed more to the correlation coefficient. Functional connectivity in the auditory, visual, and sensorimotor cortices is characterized predominantly by frequencies slower than those in the cardiac and respiratory cycles. In functionally connected regions, these low frequencies are characterized by a high degree of temporal coherence.
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An anatomical parcellation of the spatially normalized single-subject high-resolution T1 volume provided by the Montreal Neurological Institute (MNI) (D. L. Collins et al., 1998, Trans. Med. Imag. 17, 463-468) was performed. The MNI single-subject main sulci were first delineated and further used as landmarks for the 3D definition of 45 anatomical volumes of interest (AVOI) in each hemisphere. This procedure was performed using a dedicated software which allowed a 3D following of the sulci course on the edited brain. Regions of interest were then drawn manually with the same software every 2 mm on the axial slices of the high-resolution MNI single subject. The 90 AVOI were reconstructed and assigned a label. Using this parcellation method, three procedures to perform the automated anatomical labeling of functional studies are proposed: (1) labeling of an extremum defined by a set of coordinates, (2) percentage of voxels belonging to each of the AVOI intersected by a sphere centered by a set of coordinates, and (3) percentage of voxels belonging to each of the AVOI intersected by an activated cluster. An interface with the Statistical Parametric Mapping package (SPM, J. Ashburner and K. J. Friston, 1999, Hum. Brain Mapp. 7, 254-266) is provided as a freeware to researchers of the neuroimaging community. We believe that this tool is an improvement for the macroscopical labeling of activated area compared to labeling assessed using the Talairach atlas brain in which deformations are well known. However, this tool does not alleviate the need for more sophisticated labeling strategies based on anatomical or cytoarchitectonic probabilistic maps.
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Many sources of fluctuation contribute to the functional magnetic resonance imaging (fMRI) signal, complicating attempts to infer those changes that are truly related to brain activation. Unlike methods of analysis of fMRI data that test the time course of each voxel against a hypothesized waveform, data-driven methods, such as independent component analysis and clustering, attempt to find common features within the data. This exploratory approach can be revealing when the brain activation is difficult to predict beforehand, such as with complex stimuli and internal shifts of activation that are not time-locked to an easily specified sensory or motor event. These methods can be further improved by incorporating prior knowledge regarding the tem